flexsurv/0000755000176200001440000000000014660035012012125 5ustar liggesusersflexsurv/tests/0000755000176200001440000000000014657665315013314 5ustar liggesusersflexsurv/tests/testthat/0000755000176200001440000000000014657665315015154 5ustar liggesusersflexsurv/tests/testthat/test_custom.R0000644000176200001440000002656614603725274017657 0ustar liggesuserscontext("Custom distributions in flexsurvreg") ## These previously didn't work when the d or h functions are ## defined in functions or testthat environments. To find the h or d ## function in form.dp, get() and exists() would need to look in ## parent.frame(2), i.e. the grandparent calling environment, but ## inherits=TRUE searches back through _enclosing_ (definition) ## environments. ## Even with d/h functions defined at top level, these still didn't ## work when called from R CMD check. ## Solve by adding dfns argument to flexsurvreg, passing functions through. if (is.element("eha", installed.packages()[,1])) { test_that("Custom distributions from another package",{ library(eha) dllogis2 <- eha::dllogis; pllogis2 <- eha::pllogis custom.llogis <- list(name="llogis2", pars=c("shape","scale"), location="scale", transforms=c(log, log), inv.transforms=c(exp, exp), inits=function(t){ c(1, median(t)) }) fitll <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.llogis, dfns=list(d=dllogis2, p=pllogis2)) custom.ev <- list(name="EV", pars=c("shape","scale"), location="scale", transforms=c(log, log), inv.transforms=c(exp, exp), inits=function(t){ c(1, median(t)) }) fitev <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.ev, dfns=list(d=dEV, p=pEV)) ### h(x) = (b/a)(x/a)^(b-1)exp((x / a)^b) ### H(x) = exp( (x / a)^b) ) - 1 detach("package:eha") fitll.builtin <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="llogis") expect_equal(fitll$loglik, fitll.builtin$loglik) }) } test_that("Custom distributions: hazard and cumulative hazard",{ hfoo <- function(x, rate=1){ rate } Hfoo <- function(x, rate=1){ rate*x } custom.foo <- list(name="foo", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=function(t)1/median(t)) fitf <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)) fite <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="exp") expect_equal(fitf$loglik, fite$loglik) }) test_that("Custom distributions: hazard only",{ hbar <- function(x, rate=1){ rate } hbar <- Vectorize(hbar) custom.bar <- list(name="bar", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=function(t)1/mean(t)) fitf <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.bar, dfns=list(h=hbar)) ### FIXME q is Inf. is it Surv object bug? time2 being used ### it's trying to get p from exp(-H(t)) with t = Inf, should get fite <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="exp") expect_equal(fitf$loglik, fite$loglik) ## with covariates. Approximation is less good. Many more integrations needed fitf <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist=custom.bar, dfns=list(h=hbar)) fite <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist="exp") expect_equal(fitf$loglik, fite$loglik, tolerance=1e-05) ## options to integrate() flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.bar, dfns=list(h=hbar), integ.opts=list(rel.tol=0.01)) flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.bar, dfns=list(h=hbar), integ.opts=list(subdivisions=200)) ## OK to omit inits from custom list if supply it to flexsurvreg custom.bar <- list(name="bar", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp)) flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.bar, dfns=list(h=hbar), inits=0.001) }) test_that("Custom distributions: density only",{ custom.baz <- list(name="baz", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=function(t)1/mean(t)) dbaz <- function(x, rate=1, log=FALSE){ if (log) {log(rate) - x*rate} else rate*exp(-rate*x) } dbaz <- Vectorize(dbaz) fitf <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.baz, dfns=list(d=dbaz)) fite <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="exp") expect_equal(fitf$loglik, fite$loglik) ## with covariates fitf <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist=custom.baz, dfns=list(d=dbaz), inits=c(9e-07, 0.12)) fite <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist="exp") expect_equal(fitf$loglik, fite$loglik, tolerance=1e-05) }) test_that("Custom distributions: summary", { custom.baz <- list(name="baz", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=function(t)1/mean(t)) dbaz <- function(x, rate=1, log=FALSE){ if (log) {log(rate) - x*rate} else rate*exp(-rate*x) } dbaz <- Vectorize(dbaz) fitd <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.baz, dfns=list(d=dbaz)) expect_no_error(summary(fitd, type='quantile')) hfoo <- function(x, rate=1){ rate } Hfoo <- function(x, rate=1){ rate*x } custom.foo <- list(name="foo", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=function(t)1/median(t)) fith <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)) expect_no_error(summary(fith, type='quantile')) }) ## Integration breaks for the Gompertz if (0) { hbar2 <- function(x, a=1, b=1){ b*exp(a*x) } hbar2 <- Vectorize(hbar2) custom.bar2 <- list(name="bar2", pars=c("a","b"), location="b", transforms=c(identity,log), inv.transforms=c(identity,exp), inits=function(t)c(0.001, 1/mean(t))) fitf <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.bar2, control=list(trace=1,REPORT=1,reltol=1e-16,maxit=10000)) fitgo <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gompertz", control=list(trace=1,REPORT=1,reltol=1e-16)) } ## test_that("Custom distributions: hazard only, unknown function, more than one arg",{ ## }) ## TODO a more complicated one test_that("Errors in custom distributions",{ hfoo <- function(x, rate=1){ rate } Hfoo <- function(x, rate=1){ rate*x } custom.foo <- list(pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp)) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "\"name\" element of custom distribution list not given") custom.foo <- list(name=0, pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp)) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "\"name\" element of custom distribution list should be a string") custom.foo <- list(name="foo", location="rate", transforms=c(log), inv.transforms=c(exp)) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "parameter names \"pars\" not given") custom.foo <- list(name="foo", pars=2, location="rate", transforms=c(log), inv.transforms=c(exp)) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "parameter names \"pars\" should be a character vector") custom.foo <- list(name="foo", pars="rate", transforms=c(log), inv.transforms=c(exp)) expect_warning(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo), fixedpars=TRUE, inits=1), "location parameter not given, assuming it is the first one") custom.foo <- list(name="foo", pars="rate", location="bar", transforms=c(log), inv.transforms=c(exp)) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo), fixedpars=TRUE, inits=1), "location parameter \"bar\" not in list of parameters") custom.foo <- list(name="foo", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp)) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "\"inits\" not supplied, and no function to estimate them found") custom.foo <- list(name="foo", pars=c("rate"), location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "transforms not given") custom.foo <- list(name="foo", pars=c("rate"), transforms=c(log), location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "transforms not given") custom.foo <- list(name="foo", pars=c("rate"), transforms=log, inv.transforms=exp, location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "\"transforms\" must be a list") custom.foo <- list(name="foo", pars=c("rate"), transforms=c(log), inv.transforms=exp, location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "\"inv.transforms\" must be a list") custom.foo <- list(name="foo", pars=c("rate"), transforms=list(2), inv.transforms=c(exp), location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "some of \"transforms\" are not functions") custom.foo <- list(name="foo", pars=c("rate"), transforms=c(log), inv.transforms=list(2), location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "some of \"inv.transforms\" are not functions") custom.foo <- list(name="foo", pars=c("rate"), transforms=c(log,log), inv.transforms=c(exp,exp), location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "transforms vector of length 2, parameter names of length 1") custom.foo <- list(name="foo", pars=c("rate"), transforms=c(log), inv.transforms=c(exp,exp), location="rate") expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "inverse transforms vector of length 2, parameter names of length 1") custom.foo <- list(name="foo", pars=c("rate"), transforms=c(log), inv.transforms=c(exp), location="rate", inits=1) expect_error(flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.foo, dfns=list(h=hfoo, H=Hfoo)), "\"inits\" element of custom distribution list must be a function") }) test_that("Errors in form.dp",{ expect_error(form.dp(dlist=list(), dfns=list()), "Neither density function .+ nor hazard function") }) flexsurv/tests/testthat/test_predict.R0000644000176200001440000003625314500662107017760 0ustar liggesuserstest_that('survival predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") # Single time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'survival', t = 500) p <- predict(fitw, ovarian, type = 'survival', times = 500) expect_equal(s$est, p$.pred_survival) # Multiple time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'survival', t = c(500, 1000)) p <- predict(fitw, ovarian, type = 'survival', times = c(500, 1000)) expect_equal(s$est, tidyr::unnest(p, .pred)$.pred_survival) }) test_that('hazard predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") # Single time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'hazard', t = 500) p <- predict(fitw, ovarian, type = 'hazard', times = 500) expect_equal(s$est, p$.pred_hazard) # Multiple time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'hazard', t = c(500, 1000)) p <- predict(fitw, ovarian, type = 'hazard', times = c(500, 1000)) expect_equal(s$est, tidyr::unnest(p, .pred)$.pred_hazard) }) test_that('cumhaz predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") # Single time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'cumhaz', t = 500) p <- predict(fitw, ovarian, type = 'cumhaz', times = 500) expect_equal(s$est, p$.pred_cumhaz) # Multiple time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'cumhaz', t = c(500, 1000)) p <- predict(fitw, ovarian, type = 'cumhaz', times = c(500, 1000)) expect_equal(s$est, tidyr::unnest(p, .pred)$.pred_cumhaz) }) test_that('rmst predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") # Single time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'rmst', t = 500) p <- predict(fitw, ovarian, type = 'rmst', times = 500) expect_equal(s$est, p$.pred_rmst) # Multiple time predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'rmst', t = c(500, 1000)) p <- predict(fitw, ovarian, type = 'rmst', times = c(500, 1000)) expect_equal(s$est, tidyr::unnest(p, .pred)$.pred_rmst) }) test_that('response/mean predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") s <- summary(fitw, ovarian, tidy = TRUE, type = 'mean') p <- predict(fitw, ovarian, type = 'response') expect_equal(s$est, p$.pred_time) p <- predict(fitw, ovarian, type = 'mean') expect_equal(s$est, p$.pred_time) }) test_that('quantile predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") # Single quantile predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'quantile', t = 500, quantiles = c(0.5)) p <- predict(fitw, ovarian, type = 'quantile', times = 500, p = c(0.5)) expect_equal(s$est, p$.pred_quantile) # Multiple quantiles predictions s <- summary(fitw, ovarian, tidy = TRUE, type = 'quantile', quantile = c(0.1, 0.9)) p <- predict(fitw, ovarian, type = 'quantile', p = c(0.1, 0.9)) expect_equal(s$est, tidyr::unnest(p, .pred)$.pred_quantile) }) test_that('link predictions', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") s <- summary(fitw, ovarian, tidy = TRUE, type = 'link') p <- predict(fitw, ovarian, type = 'link') expect_equal(s$est, p$.pred_link) p <- predict(fitw, ovarian, type = 'linear') expect_equal(s$est, p$.pred_link) p <- predict(fitw, ovarian, type = 'lp') expect_equal(s$est, p$.pred_link) }) test_that('test order (of age) stays the same', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") s <- summary(fitw, newdata = ovarian, type = 'survival', t = 500, tidy = TRUE) expect_equal(ovarian$age, s$age) }) test_that('predictions with missing data (gengamma)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (genf)', { # Use cancer data because genf is non-identifiable with ovarian data fitw <- flexsurvreg(Surv(time, status) ~ age, data = cancer, dist = "genf") cancer_miss <- cancer cancer_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = cancer_miss, type = 'mean') expect_equal(nrow(p), nrow(cancer_miss)) p <- predict(fitw, newdata = cancer_miss, type = 'link') expect_equal(nrow(p), nrow(cancer_miss)) p <- predict(fitw, newdata = cancer_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(cancer_miss)) p <- predict(fitw, newdata = cancer_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(cancer_miss)) p <- predict(fitw, newdata = cancer_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(cancer_miss)) p <- predict(fitw, newdata = cancer_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(cancer_miss)) p <- predict(fitw, newdata = cancer_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(cancer_miss)) # Multiple predictions p <- predict(fitw, newdata = cancer_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(cancer_miss)) }) test_that('predictions with missing data (weibull)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (gamma)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "gamma") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (exponential)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "exp") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (llogis)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "llogis") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (lnorm)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "lnorm") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (gompertz)', { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "gompertz") ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) test_that('predictions with missing data (spline)', { fitw <- flexsurvspline(Surv(futime, fustat) ~ age, data = ovarian, k = 3) ovarian_miss <- ovarian ovarian_miss$age[[5]] <- NA # Single predictions p <- predict(fitw, newdata = ovarian_miss, type = 'mean') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'link') expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'rmst', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'quantile', p = 0.5) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'hazard', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'cumhaz', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = 500) expect_equal(nrow(p), nrow(ovarian_miss)) # Multiple predictions p <- predict(fitw, newdata = ovarian_miss, type = 'survival', times = c(500, 1000)) expect_equal(nrow(p), nrow(ovarian_miss)) }) flexsurv/tests/testthat/test_flexsurvmix_opt.R0000644000176200001440000001025414471614302021576 0ustar liggesusersif (!identical(Sys.getenv("NOT_CRAN"), "true")) return() n <- 200 p <- 0.5 set.seed(1) death <- rbinom(n, 1, p) t <- numeric(n) x <- rnorm(n) y <- rbinom(n, 1, 0.5) t[death==0] <- rgamma(sum(death==0), 1*exp(0.3*x[death==0]), 3.2*exp(0.5*x[death==0])) t[death==1] <- rgamma(sum(death==1), 2.5, 1.2) cens <- as.numeric(t > 2) t[cens] <- 2 status <- 1 - cens event <- ifelse(cens, NA, death+1) # 1 is cure, 2 is death dat <- data.frame(t, status, event, x) dat$evname <- c("cure", "death")[dat$event] test_that("EM basic",{ x <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), method="em") xd <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), method="direct") expect_equivalent(x$loglik, xd$loglik, tol=1e-06) }) test_that("EM pformula",{ x <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), pformula = ~x+y, method="em") xd <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), pformula = ~x+y, method="direct") expect_equivalent(x$loglik, xd$loglik, tol=1e-04) }) test_that("EM with different covs on different components", { x <- flexsurvmix(list(cure=Surv(t, status) ~ 1, death=Surv(t, status) ~ x), data=dat, event=evname, dists=c("gamma","gamma"), method="em") xd <- flexsurvmix(list(cure=Surv(t, status) ~ 1, death=Surv(t, status) ~ x), data=dat, event=evname, dists=c("gamma","gamma"), method="direct") expect_equivalent(x$loglik, xd$loglik, tol=1e-04) }) test_that("EM with anc and different covs on different components", { x <- flexsurvmix(list(cure=Surv(t, status) ~ 1, death=Surv(t, status) ~ x), data=dat, event=evname, anc=list(cure=list(shape=~y), death=list(shape=~1)), dists=c("gamma","gamma"), method="em") xd <- flexsurvmix(list(cure=Surv(t, status) ~ 1, death=Surv(t, status) ~ x), data=dat, event=evname, anc=list(cure=list(shape=~y), death=list(shape=~1)), dists=c("gamma","gamma"), method="direct") expect_equivalent(x$loglik, xd$loglik, tol=1e-04) }) test_that("Variances in Aalen-Johansen",{ x <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), method="em") aj <- ajfit_flexsurvmix(x, B=3) expect_true(inherits(aj, "data.frame") & is.numeric(aj$lower)) }) n <- 100 set.seed(1) x <- rnorm(n) y <- rbinom(n, 1, 0.5) p <- plogis(qlogis(0.5) + 2*x - 3*y) death <- rbinom(n, 1, p) t <- numeric(n) t[death==0] <- rgamma(sum(death==0), 1, 3.2) t[death==1] <- rgamma(sum(death==1), 2.5, 1.2) cens <- as.numeric(t > 3) status <- 1 - cens t[cens] <- 3 event <- ifelse(cens, NA, death+1) # 1 is cure, 2 is death dat <- data.frame(t, status, event, x) dat$evname <- c("cure", "death")[dat$event] test_that("var.method",{ x <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), pformula = ~ x + y, method="em", fixedpars=c(3,4), em.control=list(var.method="louis")) x x2 <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), pformula = ~ x + y, method="em", fixedpars=c(3,4), em.control=list(var.method="direct")) x2 expect_equivalent(x$loglik, x2$loglik, tol=1e-04) expect_true(x$cov[1,1] != x2$cov[1,1]) }) test_that("Models with interactions",{ dat$x <- factor(rbinom(nrow(dat), size=1, prob=0.5)) dat$y <- factor(rbinom(nrow(dat), size=1, prob=0.4)) fsi <- flexsurvmix(formula = Surv(t, status) ~ x*y, data = dat, event = event, dists = c("gamma", "weibull"), fixedpars = FALSE, method="em", em.control=list(var.method="louis", reltol=1e-04)) aj <- ajfit_flexsurvmix(fsi) expect_equal(aj$val[1], 1) }) flexsurv/tests/testthat/test_splinedist.R0000644000176200001440000002251214531630662020502 0ustar liggesuserscontext("Spline distribution functions") test_that("Spline distribution functions",{ regscale <- 0.786; cf <- 1.82 a <- 1/regscale; b <- exp(cf) d1 <- dweibull(1, shape=a, scale=b) d2 <- dsurvspline(1, gamma=c(log(1 / b^a), a)) expect_equal(d1, d2) p1 <- pweibull(1, shape=a, scale=b) p2 <- psurvspline(1, gamma=c(log(1 / b^a), a)) expect_equal(p1, p2) meanlog <- 1.52; sdlog <- 1.11 d1 <- dlnorm(1, meanlog, sdlog) d2 <- dsurvspline(1, gamma = c(-meanlog/sdlog, 1/sdlog), scale="normal") expect_equal(d1, d2) p1 <- plnorm(1, meanlog, sdlog) p2 <- psurvspline(1, gamma = c(-meanlog/sdlog, 1/sdlog), scale="normal") expect_equal(p1, p2) p1 <- pweibull(1, shape=a, scale=b) p2 <- psurvspline(1, gamma=c(log(1 / b^a), a)) ## other way round gamma <- c(0.1, 0.2) d1 <- dweibull(1, shape=gamma[2], scale= exp(-gamma[1]/gamma[2])) d2 <- dsurvspline(1, gamma=gamma) expect_equal(d1, d2) scale <- exp(-gamma[1]/gamma[2]) d1 <- dweibullPH(1, shape=gamma[2], scale= scale^{-gamma[2]}) d1 <- dllogis(1, shape=gamma[2], scale= exp(-gamma[1]/gamma[2])) d2 <- dsurvspline(1, gamma=gamma, scale="odds") expect_equal(d1, d2) d1 <- dlnorm(1, meanlog=-gamma[1]/gamma[2], sdlog=1/gamma[2]) d2 <- dsurvspline(1, gamma=gamma, scale="normal") expect_equal(d1, d2) # TODO document #H1 <- Hlnorm(1, meanlog, sdlog) #H2 <- Hsurvspline(1, gamma = c(-meanlog/sdlog, 1/sdlog), scale="normal") #expect_equal(H1, H2) g <- c(0.1, 0.2, 0.3); k <- c(2,3,4) expect_equal(dsurvspline(1,g,knots=k)/(1 - psurvspline(1,g,knots=k)), hsurvspline(1,g,knots=k)) expect_equal(dsurvspline(1,g,knots=k,scale="odds")/(1 - psurvspline(1,g,knots=k,scale="odds")), hsurvspline(1,g,knots=k,scale="odds")) expect_equal(dsurvspline(1,g,knots=k,scale="normal")/(1 - psurvspline(1,g,knots=k,scale="normal")), hsurvspline(1,g,knots=k,scale="normal")) expect_equal(-log(1 - psurvspline(0.2,g,knots=k)), Hsurvspline(0.2,g,knots=k)) expect_equal(-log(1 - psurvspline(0.2,g,knots=k,scale="odds")), Hsurvspline(0.2,g,knots=k,scale="odds")) expect_equal(-log(1 - psurvspline(0.2,g,knots=k,scale="normal")), Hsurvspline(0.2,g,knots=k,scale="normal")) expect_equal(dsurvspline(c(-1,0,NA,NaN,Inf), g, knots=k), c(0,0,NA,NA,NaN)) expect_equal(psurvspline(qsurvspline(0.2,g,knots=k), g, knots=k), 0.2) expect_equal(qsurvspline(psurvspline(0.2,g,knots=k), g, knots=k), 0.2) ## Vectorised q and p functions, through qgeneric kvec <- rbind(k, k+1) gvec <- rbind(g, g*1.1) expect_equal(psurvspline(qsurvspline(0.2,gvec,knots=kvec), gvec, knots=kvec), c(0.2,0.2)) expect_equal(qsurvspline(psurvspline(0.2,gvec,knots=kvec), gvec, knots=kvec), c(0.2,0.2)) expect_equal(psurvspline(c(NA,NaN,-1,0), gamma=c(1,1), knots=c(-10, 10)), c(NA,NA,0,0)) expect_equal(qsurvspline(c(0,1), gamma=c(1,1), knots=c(-10, 10)), c(-Inf, Inf)) expect_equal(1 - psurvspline(1, g, knots=k), psurvspline(1, g, knots=k, lower.tail=FALSE)) expect_equal(log(psurvspline(c(-1,NA,1), g, knots=k)), psurvspline(c(-1,NA,1), g, knots=k, log.p=TRUE)) ## single x=0: fully defined in in dbase.survspline expect_equal(dsurvspline(0, g, knots=k), 0) ## value for x=0? currently zero, should it be limit as x reduces to 0? expect_equal(hsurvspline(0, g, knots=k), 0) if(0){ bc$foo <- factor(sample(1:3, nrow(bc), replace=TRUE)) spl <- flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, k=0) system.time(hist(rsurvspline(1000, gamma=c(log(1 / b^a), a)), prob=TRUE)) system.time(hist(rsurvspline(10000, gamma=c(log(1 / b^a), a)), prob=TRUE)) x <- 1:50 lines(x, dweibull(x, a, b)) } }) spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1) gamma <- spl$res[c("gamma0","gamma1","gamma2"), "est"] gamma_mat <- rbind(gamma, gamma*1.1) gamma0_vec <- gamma_mat[,"gamma0"] gamma1_vec <- gamma_mat[,"gamma1"] gamma2_vec <- gamma_mat[,"gamma2"] spl2 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=2) gamma2k <- spl2$res[c("gamma0","gamma1","gamma2","gamma3"), "est"] k2 <- spl2$knots spl3 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=3) gamma3k <- spl3$res[c("gamma0","gamma1","gamma2","gamma3","gamma4"), "est"] k3 <- spl3$knots test_that("fixed-knot convenience wrappers",{ gamma0 <- gamma["gamma0"]; gamma1 <- gamma["gamma1"]; gamma2 <- gamma["gamma2"] expect_equal(mean_survspline(gamma=gamma, knots=spl$knots, scale=spl$scale), mean_survspline1(gamma0, gamma1, gamma2, knots=spl$knots, scale=spl$scale)) expect_equal(mean_survspline(gamma, knots=spl$knots), mean_survspline1(gamma[1], gamma[2], gamma[3], knots=spl$knots)) expect_equal(mean_survspline(rbind(gamma,gamma), knots=spl$knots), mean_survspline1(c(gamma[1],gamma[1]), gamma[2], gamma[3], knots=spl$knots)) expect_equal(mean_survspline(gamma_mat, knots=spl$knots), mean_survspline1(c(gamma_mat[1,1], gamma_mat[2,1]), c(gamma_mat[1,2], gamma_mat[2,2]), c(gamma_mat[1,3], gamma_mat[2,3]), knots=spl$knots)) expect_equal(c( mean_survspline(gamma=gamma_mat[1,], knots=spl$knots, scale=spl$scale), mean_survspline(gamma=gamma_mat[2,], knots=spl$knots, scale=spl$scale)), mean_survspline(gamma=gamma_mat, knots=spl$knots, scale=spl$scale)) expect_equal(mean_survspline(gamma=gamma_mat, knots=spl$knots, scale=spl$scale), rmst_generic(psurvspline, t=c(Inf,Inf), gamma = gamma_mat, knots=spl$knots, matargs = c("gamma","knots"))) expect_is(summary(spl, fn=mean_survspline1, t=1, ci=FALSE), "list") expect_is(summary(spl, fn=mean_survspline1, t=1, ci=FALSE), "list") expect_equal(psurvspline(1, gamma, knots=spl$knots, scale=spl$scale), psurvspline1(1, gamma0, gamma1, gamma2, knots=spl$knots, scale=spl$scale)) expect_equal( psurvspline(1, gamma_mat, knots=spl$knots, scale=spl$scale), psurvspline1(1, gamma0_vec, gamma1_vec, gamma2_vec, knots=spl$knots, scale=spl$scale)) expect_equal(hsurvspline(1, gamma, knots=spl$knots, scale=spl$scale), hsurvspline1(1, gamma0, gamma1, gamma2, knots=spl$knots, scale=spl$scale)) expect_equal(Hsurvspline(1, gamma, knots=spl$knots, scale=spl$scale), Hsurvspline1(1, gamma0, gamma1, gamma2, knots=spl$knots, scale=spl$scale)) expect_equal(hsurvspline(1, gamma_mat, knots=spl$knots, scale=spl$scale), hsurvspline1(1, gamma0_vec, gamma1_vec, gamma2_vec, knots=spl$knots, scale=spl$scale)) expect_equal(Hsurvspline(1, gamma_mat, knots=spl$knots, scale=spl$scale), Hsurvspline1(1, gamma0_vec, gamma1_vec, gamma2_vec, knots=spl$knots, scale=spl$scale)) gamma0 <- gamma2k["gamma0"]; gamma1 <- gamma2k["gamma1"]; gamma2 <- gamma2k["gamma2"]; gamma3 <- gamma2k["gamma3"] expect_equal(psurvspline(1, gamma2k, knots=k2), psurvspline2(1, gamma0, gamma1, gamma2, gamma3, knots=k2)) expect_equal(dsurvspline(1, gamma2k, knots=k2, scale=spl$scale), dsurvspline2(1, gamma0, gamma1, gamma2, gamma3, knots=k2)) expect_equal(qsurvspline(0.4, gamma2k, knots=k2, scale=spl$scale), qsurvspline2(0.4, gamma0, gamma1, gamma2, gamma3, knots=k2)) expect_equal(qsurvspline(0.4, gamma2k, knots=k2, lower.tail=FALSE), qsurvspline2(0.4, gamma0, gamma1, gamma2, gamma3, knots=k2, lower.tail=FALSE)) set.seed(1); r1 <- rsurvspline(10, gamma2k, knots=k2) set.seed(1); r2 <- rsurvspline2(10, gamma0, gamma1, gamma2, gamma3, knots=k2) expect_equal(r1, r2) gamma4 <- 0.01; gamma3k <- c(gamma2k, gamma4) expect_equal(psurvspline(1, gamma3k, knots=k3, scale=spl$scale), psurvspline3(1, gamma0, gamma1, gamma2, gamma3, gamma4, knots=k3)) expect_equal(dsurvspline(1, gamma3k, knots=k3, scale=spl$scale), dsurvspline3(1, gamma0, gamma1, gamma2, gamma3, gamma4, knots=k3)) expect_equal(qsurvspline(0.4, gamma3k, knots=k3, scale=spl$scale), qsurvspline3(0.4, gamma0, gamma1, gamma2, gamma3, gamma4, knots=k3)) expect_equal(qsurvspline(0.4, gamma3k, knots=k3, lower.tail=FALSE), qsurvspline3(0.4, gamma0, gamma1, gamma2, gamma3, gamma4, knots=k3, lower.tail=FALSE)) set.seed(1); r1 <- rsurvspline(10, gamma3k, knots=k3) set.seed(1); r2 <- rsurvspline3(10, gamma0, gamma1, gamma2, gamma3, gamma4, knots=k3) expect_equal(r1, r2) }) test_that("removing support for beta, X and offset",{ gamma <- c(0.1, 0.2) d2 <- dsurvspline(1, gamma=gamma) expect_warning(d2 <- dsurvspline(1, gamma=gamma, beta = 0.1)) expect_warning(d2 <- dsurvspline(1, gamma=gamma, X = 0.1)) expect_warning(d2 <- dsurvspline(1, gamma=gamma, offset = 0.1)) suppressWarnings({ d3 <- dsurvspline(1, gamma=gamma, X = 0.1) expect_equal(d2, d3) }) }) flexsurv/tests/testthat/test_aic.R0000644000176200001440000000137514470676366017101 0ustar liggesuserstest_that("Information criteria",{ p <- 3 n <- nrow(ovarian) fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma") expect_equal(nobs(fitg), n) AIC(fitg) expect_equal(BIC(fitg), AIC(fitg, k=log(n))) nevent <- sum(ovarian$fustat) expect_equal(BIC(fitg, cens=FALSE), AIC(fitg, k=log(nevent))) expect_equal(BIC(fitg), BIC.flexsurvreg(fitg)) expect_equal(BIC(fitg,cens=FALSE), BIC.flexsurvreg(fitg,cens=FALSE)) expect_equal(AICc(fitg), AIC(fitg, k=(2*n) / (n - p - 1))) expect_equal(AICc(fitg,cens=FALSE), AIC(fitg, k=(2*nevent) / (nevent - p - 1))) expect_equal(AICC(fitg), AICc(fitg)) expect_equal(AICc.flexsurvreg(fitg), AICc(fitg)) expect_equal(AICC.flexsurvreg(fitg), AICc(fitg)) }) flexsurv/tests/testthat/simulate.R0000644000176200001440000000160214020431707017075 0ustar liggesusers test_that("Simulation with no covariates",{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gengamma") sim <- simulate(fitg) expect_true(is.data.frame(sim)) }) test_that("Simulation with covariates",{ ovarian$rx2 <- as.numeric(ovarian$rx == 2) fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ rx2, data = ovarian, dist="gamma") sim <- simulate(fitg, nsim=1) expect_true(is.data.frame(sim)) sim <- simulate(fitg, nsim=2) expect_true(is.data.frame(sim)) sim <- simulate(fitg, nsim=2, censtime=5) expect_true(is.data.frame(sim)) sim <- simulate(fitg, nsim=2, censtime=seq(5, 10, length.out = nrow(ovarian))) expect_true(is.data.frame(sim)) }) test_that("Setting seed makes simulations reproducible",{ sim1 <- simulate(fitg, nsim=2, censtime=5, seed=2) sim2 <- simulate(fitg, nsim=2, censtime=5, seed=2) expect_equal(sim1, sim2) }) flexsurv/tests/testthat/test_residuals.R0000644000176200001440000000106114564157676020332 0ustar liggesuserstest_that("residuals",{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") expect_true(is.numeric(residuals(fitg, type="response"))) expect_true(is.numeric(residuals(fitg, type="coxsnell"))) cs <- coxsnell_flexsurvreg(fitg) surv <- survfit(Surv(cs$est, ovarian$fustat) ~ 1) if (interactive()){ plot(surv, fun="cumhaz", xlim=c(0,1), ylim=c(0,1)) abline(0, 1, col="red") } expect_lt(max(surv$cumhaz[-1] / surv$time[-1]), 1.5) expect_gt(min(surv$cumhaz[-1] / surv$time[-1]), 0.5) }) flexsurv/tests/testthat/test_genf.R0000644000176200001440000001257414472141270017246 0ustar liggesuserscontext("Generalized F distribution") tol <- 1e-06 test_that("Generalized F", { expect_equal(dgenf(c(-1,1,2,3,4), mu=0, sigma=1, Q=0, P=1), # FIXME add limiting value for x=0 c(0, 0.353553390593274, 0.140288989252053, 0.067923038519582, 0.038247711235678), tolerance=tol) expect_error(Hgenf(c(-1,1,2,3,4), mu=0, sigma=1, P=1), "argument \"Q\" is missing") expect_error(Hgenf(c(-1,1,2,3,4), mu=0, sigma=1, Q=1), "argument \"P\" is missing") expect_error(dgenf(1, mu=numeric(), sigma=numeric(), Q=numeric(), P=numeric()), "zero length") }) test_that("Generalized F reduces to generalized gamma: d",{ expect_equal(dgenf(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0, P=0), dgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0)) x <- c(-1,0,1,2,3,4); mu <- 2.2; sigma <- 1.6; Q <- 0.2; P <- 1.2 delta <- (Q^2 + 2*P)^{1/2} s1 <- 2 / (Q^2 + 2*P + Q*delta); s2 <- 2 / (Q^2 + 2*P - Q*delta) expect_equal(dgenf(x, mu=mu, sigma=sigma, Q=Q, P=P), dgenf.orig(x, mu=mu, sigma=sigma/delta, s1=s1, s2=s2)) expect_equal(dgenf(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=c(0,1,2), P=0), dgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=c(0,1,2))) }) x <- c(-1,1,2,3,4); mu <- 2.2; sigma <- 1.6; Q <- 0; P <- 1 delta <- (Q^2 + 2*P)^{1/2} s1 <- 2 / (Q^2 + 2*P + Q*delta); s2 <- 2 / (Q^2 + 2*P - Q*delta) test_that("Generalized F reduces to log logistic", { expect_equal(dgenf(x, mu=mu, sigma=sigma, Q=Q, P=P), dllogis(x, shape=sqrt(2)/sigma, scale=exp(mu)), tolerance=tol) }) test_that("Generalized F reduces to gamma",{ expect_equal(dgengamma(x, mu=mu, sigma=sigma, Q=sigma), dgamma(x, shape=1/sigma^2, scale=exp(mu)*sigma^2)) }) test_that("Generalized F reduces to generalized gamma: p",{ expect_equal(pgenf(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0, P=1), c(0, 0, 0.5, 0.727159434644773, 0.825443507527843, 0.876588815661789)) expect_equal(pgenf(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0, P=0), pgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0)) expect_equal(pgenf(x, mu=mu, sigma=sigma, Q=Q, P=P), pgenf.orig(x, mu=mu, sigma=sigma/delta, s1=s1, s2=s2)) }) test_that("Generalized F reduces to generalized gamma: q",{ expect_equal(qgenf(p=0.25, mu=0, sigma=1, Q=0, P=1), 0.459858613264917) expect_equal(qgenf(p=0.25, mu=0, sigma=1, Q=0, P=1), qgeneric(pgenf, p=0.25, mu=0, sigma=1, Q=0, P=1)) expect_equal(qgenf(p=0, mu=0, sigma=1, Q=0, P=1), 0) expect_equal(qgenf(p=0.25, mu=0, sigma=1, Q=0, P=0), qgengamma(p=0.25, mu=0, sigma=1, Q=0)) expect_equal(qgenf(pgenf(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, Q=0, P=1), mu=0, sigma=1, Q=0, P=1), c(0,0,0,1,2,3,4)) expect_equal(qgenf(pgenf(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, Q=-1, P=1), mu=0, sigma=1, Q=-1, P=1), c(0,0,0,1,2,3,4)) expect_equal(qgengamma(pgenf(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, Q=0, P=0), mu=0, sigma=1, Q=0), c(0,0,0,1,2,3,4)) x <- c(0.1,0.4,0.6) expect_equal(qgenf(x, mu=mu, sigma=sigma, Q=Q, P=P), qgenf.orig(x, mu=mu, sigma=sigma/delta, s1=s1, s2=s2)) }) test_that("Generalized F reduces to generalized gamma: r",{ rgenf(n=10, mu=0, sigma=1, Q=0, P=1) set.seed(22061976) x <- rgenf(n=10, mu=0, sigma=1, Q=0, P=0) set.seed(22061976) y <- rgengamma(n=10, mu=0, sigma=1, Q=0) expect_equal(x, y) if (interactive()) { x <- c(-1,0,1,2,3,4); mu <- 2.2; sigma <- 0.6; Q <- 0.2; P=0.1 delta <- (Q^2 + 2*P)^{1/2} s1 <- 2 / (Q^2 + 2*P + Q*delta); s2 <- 2 / (Q^2 + 2*P - Q*delta) plot(density(rgenf(10000, mu=mu, sigma=sigma, Q=Q, P=P))) lines(density(rgenf.orig(10000, mu=mu, sigma=sigma/delta, s1=s1, s2=s2)), lty=2) } }) test_that("Gives errors",{ expect_warning(dgenf(c(1,1), 1, -2, 1, -1), "Negative scale") expect_warning(dgenf(c(1,1), 1, -2, 1, -1), "Negative shape") expect_warning(pgenf(1, 1, -2, 1, 1), "Negative") expect_warning(qgenf(0.1, 1, -2, 1, 0), "Negative") expect_warning(rgenf(4, 1, -2, 1, 1), "Negative") }) test_that("Avoid underflow in pgenf",{ mu <- 7.495875 sigma <- 0.35362 Q <- 0.4572124 P <- 16.68415 tmp <- Q * Q + 2*P delta <- sqrt(tmp) s1 <- 2 / (tmp + Q*delta) s2 <- 2 / (tmp - Q*delta) xlow <- 80 expw <- xlow^(delta/sigma) * exp(-mu*delta/sigma) pbeta(s2/(s2 + s1*expw), s2, s1, lower.tail=FALSE) # underflows pbeta(s1*expw/(s2 + s1*expw), s1, s2, lower.tail=TRUE) # works expect_equal(pgenf(xlow, mu, sigma, Q, P), 0.03214437, tolerance=1e-05) xmid <- 3000 expw <- xmid^(delta/sigma) * exp(-mu*delta/sigma) pbeta(s2/(s2 + s1*expw), s2, s1, lower.tail=FALSE) pbeta(s1*expw/(s2 + s1*expw), s1, s2, lower.tail=TRUE) # both work expect_equal(pgenf(xmid, mu, sigma, Q, P), 0.7276473, tolerance=1e-05) xhi <- 1e+5 expw <- xhi^(delta/sigma) * exp(-mu*delta/sigma) pbeta(s2/(s2 + s1*expw), s2, s1, lower.tail=FALSE) # works pbeta(s1*expw/(s2 + s1*expw), s1, s2, lower.tail=TRUE) # underflows expect_equal(pgenf(xhi, mu, sigma, Q, P), 0.9933716, tolerance=1e-05) }) ## When x is small, thus s2/(s2 + s1*expw) is close to 1, use second pbeta construction ## When x is high, thus s2/(s2 + s1*expw) is close to 0, use first pbeta construction flexsurv/tests/testthat/test_gengamma_orig.R0000644000176200001440000000522713231112051021103 0ustar liggesuserscontext("Generalized gamma (original)") test_that("Generalized gamma (original)",{ expect_equal(dgengamma.orig(c(-1,0,1,2,3,4), shape=1.2, scale=1.3, k=1.4), c(0, 0, 0.419477559803262, 0.260699967439176, 0.120081193404263, 0.0474236822588797)) expect_equal(dgengamma.orig(c(1,2,3,4), shape=1.2, scale=1.3, k=1), dweibull(c(1,2,3,4), shape=1.2, scale=1.3)) expect_equal(dgengamma.orig(c(1,2,3,4), shape=1, scale=1.3, k=1), dexp(c(1,2,3,4), rate=1/1.3)) expect_equal(dgengamma.orig(c(1,2,3,4), shape=1, scale=1.3, k=1.4), dgamma(c(1,2,3,4), shape=1.4, scale=1.3)) shape <- 1.2; scale <- 1.3; k <- 10000 pgengamma.orig(2800 + 1:4, shape=shape, scale=scale, k=k) plnorm(2800 + 1:4, log(scale) + log(k)/shape, 1/(shape*sqrt(k))) expect_equal(pgengamma.orig(c(1,2,3,4), shape=1.2, scale=1.3, k=1), pweibull(c(1,2,3,4), shape=1.2, scale=1.3)) expect_equal(pgengamma.orig(c(1,2,3,4), shape=1, scale=1.3, k=1), pexp(c(1,2,3,4), rate=1/1.3)) expect_equal(pgengamma.orig(c(1,2,3,4), shape=1, scale=1.3, k=1.4), pgamma(c(1,2,3,4), shape=1.4, scale=1.3)) expect_equal(qgengamma.orig(p=0.25, shape=1.2, scale=1.3, k=1), qgeneric(pgengamma.orig, p=0.25, shape=1.2, scale=1.3, k=1)) expect_equal(qgengamma.orig(c(0.1, 0.4, 0.7), shape=1.2, scale=1.3, k=1), qweibull(c(0.1, 0.4, 0.7), shape=1.2, scale=1.3)) expect_equal(qgengamma.orig(c(0.1, 0.4, 0.7), shape=1, scale=1.3, k=1), qexp(c(0.1, 0.4, 0.7), rate=1/1.3)) expect_equal(qgengamma.orig(c(0.1, 0.4, 0.7), shape=1, scale=1.3, k=1.4), qgamma(c(0.1, 0.4, 0.7), shape=1.4, scale=1.3)) if (interactive()){ plot(density(rgengamma.orig(100000, shape=1.2, scale=1.3, k=1))) lines(density(rweibull(100000, shape=1.2, scale=1.3)), lty=2) plot(density(rgengamma.orig(100000, shape=1, scale=1.5, k=1))) lines(density(rexp(100000, rate=1/1.5)), lty=2) plot(density(rgengamma.orig(100000, shape=1, scale=3.3, k=1.2))) lines(density(rgamma(100000, shape=1.2, scale=3.3)), lty=2) } }) test_that("Gives errors", { expect_warning(dgengamma.orig(c(1,2,3,4), shape=-1.2, scale=-1.3, k=-1), "Negative shape") expect_warning(dgengamma.orig(c(1,2,3,4), shape=-1.2, scale=-1.3, k=-1), "Negative scale") expect_warning(dgengamma.orig(c(1,2,3,4), shape=c(-1.2, 1), scale=1.3, k=1), "Negative shape") expect_warning(pgengamma.orig(c(1,2,3,4), shape=-1.2, scale=-1.3, k=-1), "Negative") expect_warning(qgengamma.orig(c(1,2,3,4), shape=-1.2, scale=-1.3, k=-1), "Negative") expect_warning(rgengamma.orig(3, shape=-1.2, scale=-1.3, k=-1), "Negative") }) flexsurv/tests/testthat/test_gompertz.R0000644000176200001440000000634314472142437020201 0ustar liggesuserscontext("Testing Gompertz") test_that("dgompertz",{ x <- c(-1,0,1,2,3,4) expect_equal(dgompertz(x, shape=0.1, rate=0.2), c(0, 0.2, 0.179105591827508, 0.156884811322895, 0.134101872197705, 0.111571759992743)) dgompertz(x, shape=0.0001, rate=0.2) dgompertz(x, shape=-0.0001, rate=0.2) dexp(x, rate=0.2) expect_equal(dgompertz(x, shape=0, rate=0.2), dexp(x, rate=0.2)) d <- numeric(6); for (i in 1:6) d[i] <- dgompertz(x[i], shape=-0.0001, rate=i/5) expect_equal(d, dgompertz(x, shape=-0.0001, rate=1:6/5)) expect_warning(dgompertz(x, shape=-0.0001, rate=-1), "Negative rate") expect_error(dgompertz(x, shape=numeric(), rate=numeric()), "zero length vector") expect_error(dgompertz(numeric, shape=1), "Non-numeric") expect_error(dgompertz(1, shape="wibble"), "Non-numeric") }) test_that("pgompertz",{ x <- c(-1,0,1,2,3,4) pgompertz(x, shape=0, rate=0.2) pgompertz(x, shape=0.001, rate=0.2) pgompertz(x, shape=-0.001, rate=0.2) expect_equal(pgompertz(x, shape=0, rate=0.2), pexp(x, rate=0.2)) p <- numeric(6); for (i in 1:6) p[i] <- pgompertz(x[i], shape=-0.0001, rate=i/5) expect_equal(p, pgompertz(x, shape=-0.0001, rate=1:6/5)) expect_equal(p, 1 - exp(-Hgompertz(x, shape=-0.0001, rate=1:6/5))) expect_warning(pgompertz(x, shape=-0.0001, rate=-1), "Negative rate") }) test_that("qgompertz",{ x <- c(0.1, 0.2, 0.7) expect_equal(qgompertz(x, shape=0.1, rate=0.2), qgeneric(pgompertz, p=x, shape=0.1, rate=0.2)) expect_equal(qgompertz(x, shape=0, rate=0.2), qexp(x, rate=0.2)) expect_equal(x, pgompertz(qgompertz(x, shape=0.1, rate=0.2), shape=0.1, rate=0.2)) q <- numeric(3); for (i in 1:3) q[i] <- qgompertz(x[i], shape=-0.0001, rate=i/5) expect_equal(q, qgompertz(x, shape=-0.0001, rate=1:3/5)) x <- c(0.5, 1.06, 4.7) expect_equal(x, qgompertz(pgompertz(x, shape=0.1, rate=0.2), shape=0.1, rate=0.2)) q <- numeric(3); for (i in 1:3) q[i] <- qgompertz(x[i], shape=-0.0001, rate=i/5) expect_equal(q, qgompertz(x, shape=-0.0001, rate=1:3/5)) qgompertz(p=c(-1, 0, 1, 2), 1, 1) }) test_that("Gompertz with chance of living forever",{ shape <- -0.6; rate <- 1.8 x <- c(0.8, 0.9, 0.97, 0.99) expect_equal(qgompertz(x, shape=shape, rate=rate), c(1.28150707286845, 2.4316450975351, Inf, Inf)) # qgeneric(pgompertz, p=x, shape=shape, rate=rate) # won't work - needs smoothness expect_equal(pgompertz(Inf, shape=shape, rate=rate, lower.tail = F), exp(rate/shape)) expect_equal( pgompertz(Inf, shape=shape, rate=rate, lower.tail = F), pgompertz(9999999, shape=shape, rate=rate, lower.tail = F) ) }) test_that("Gompertz hazards",{ expect_equal(hgompertz(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)), dgompertz(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)) / (1 - pgompertz(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)))) expect_equal(Hgompertz(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)), -pgompertz(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3), lower.tail=FALSE, log.p=TRUE)) ## reduction to exponential expect_equal(hgompertz(c(2,4), c(0,0), c(2,2)), hexp(c(2,4), c(2,2))) expect_equal(Hgompertz(c(2,4), c(0,0), c(2,2)), Hexp(c(2,4), c(2,2))) }) flexsurv/tests/testthat/test_spline.R0000644000176200001440000003675314645517220017632 0ustar liggesuserscontext("flexsurvspline model fits") suppressWarnings(RNGversion("3.5.0")) set.seed(11082012) bc$foo <- factor(sample(1:3, nrow(bc), replace=TRUE)) spl <- flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, k=0) test_that("Basic flexsurvspline, Weibull",{ expect_equal(spl$loglik, -810.926859076725, tol=1e-06) }) test_that("flexsurvspline summary method",{ summ <- summary(spl, B=3)$"group=Good,foo=1" expect_equal(summ$est[1],0.999838214156694, tol=1e-05) expect_true(all(summ$est > summ$lcl)) expect_true(all(summ$est < summ$ucl)) expect_true(all(summ$ucl < 1)) expect_true(all(summ$lcl > 0)) summ <- summary(spl, type="survival", B=3, t=0:5)$`group=Good,foo=1` expect_equal(summ$est[2], 0.9684014494284117, tol=1e-05) summ <- summary(spl, type="cumhaz", B=3, t=0:5)$`group=Good,foo=1` expect_equal(summ$est[2], 0.03210855719443461, tol=1e-05) summ <- summary(spl, type="hazard", B=3, t=0:5)$`group=Good,foo=1` expect_equal(summ$est[2], 0.04446356223043756, tol=1e-05) }) if (covr::in_covr() || interactive()){ test_that("flexsurvspline plot method",{ expect_no_error({ plot(spl, col=c("red","blue","green")) plot(spl, ci=TRUE, B=40) plot(spl, type="cumhaz") plot(spl, type="hazard") plot(spl, type="hazard", ci=TRUE, B=40) ## multicoloured plots plot(spl, col=c("red","purple","blue","green","brown","black","orange","yellow","pink")) plot(spl, lwd=1) lines(spl, X=rbind(c(0,0,0,0)), col="red") lines(spl, X=rbind(c(1,0,0,0)), col="purple") lines(spl, X=rbind(c(0,1,0,0)), col="blue") legend("bottomleft", levels(bc$group), col=c("red","purple","blue"), lwd=2) }) }) } test_that("Basic flexsurvspline, Weibull, no covs",{ spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=0) expect_equal(-873.207054864145, spl$loglik, tol=1e-06) }) test_that("Basic flexsurvspline, one knot, best fitting in paper",{ skip_if(covr::in_covr()) # optimisation for scale="odds" doesn't converge under covr for some reason spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1, scale="odds") expect_equal(spl$loglik, -788.981901798638, tol=1e-05) expect_equal(spl$loglik + sum(log(bc$recyrs[bc$censrec==1])), -615.49431514184, tol=1e-05) expect_equal(spl$AIC + sum(log(bc$recyrs[bc$censrec==1])), 1761.45139087546, tol=1e-05) # #results from the paper expect_equal(as.numeric(coef(spl))[1:3], c(-3.451, 2.915, 0.191), tol=1e-03) expect_equal(as.numeric(spl$res[1:3,"se"]), c(0.203, 0.298, 0.044), tol=1e-03) if (interactive()) { plot(spl) plot(spl, type="cumhaz") plot(spl, type="haz") } }) test_that("Spline models with hazard and normal scales",{ splh <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1, scale="hazard") expect_equal(splh$loglik, -792.863797823674, tol=1e-05) spln <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1, scale="normal") expect_equal(spln$loglik, -785.623256840396, tol=1e-05) if (interactive()){ plot(spl, ci=TRUE, lwd.ci=1, B=30) lines(splh, col="blue", ci=TRUE, B=30) lines(spln, col="green", ci=TRUE, B=30) } }) ### log(H(t)) = g0 + g1 log(t) + Bz ### H(t) = exp(g0) t^g1 exp(Bz) ### S(t) = exp(-H(t)) = exp( - exp(g0) t^g1 exp(Bz) ) ### pweibull has par exp( - (x/b) ^ a) ### a = g1, 1/b^a = exp(g0 + Bz) = b ^ -a = exp(-a log b) ### g0 + Bz = - a (log b + Bz) test_that("Spline proportional hazards models reduce to Weibull",{ wei <- survreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") wei.base <- survreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull") a <- 1/wei$scale b1 <- exp(coef(wei)[1]); b2 <- exp(coef(wei)[1]+coef(wei)[2]); b3 <- exp(coef(wei)[1]+coef(wei)[3]) a.base <- 1/wei.base$scale b.base <- exp(coef(wei.base[1])) ## Compare three implementations of the Weibull, with and without covs fit <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull", fixedpars=FALSE, inits=c(a,b1,coef(wei)[2:3])) spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=0, inits=c(-a*log(b1), a, -a*coef(wei)[2:3]), fixedpars=FALSE) expect_equal(fit$loglik, spl$loglik) expect_equal(fit$loglik, wei$loglik[2]) fit <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull", fixedpars=FALSE, inits=c(a,b1)) # NaNs here dues to zeroes for dweibull being visited by optimiser spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=0, inits=c(log(1 / b.base^a.base), a.base), fixedpars=FALSE) expect_equal(fit$loglik, spl$loglik) expect_equal(fit$loglik, wei.base$loglik[1]) }) test_that("Spline proportional odds models reduce to log-logistic",{ skip_if(covr::in_covr()) # optimisation for fitsp doesn't converge under covr for some reason fitll <- flexsurvreg(formula = Surv(recyrs, censrec) ~ 1, data = bc, dist="llogis") fitsp <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=0, scale="odds", control=list(reltol=1e-16), fixedpars=FALSE) expect_equal(fitsp$loglik, fitll$loglik) expect_equal(1/fitll$res["scale",1]^fitll$res["shape",1], exp(fitsp$res["gamma0",1]), tol=1e-02) expect_equal(fitsp$res["gamma1",1], fitll$res["shape",1], tol=1e-02) }) test_that("Spline normal models reduce to log-normal",{ fitln <- flexsurvreg(formula = Surv(recyrs, censrec) ~ 1, data = bc, dist="lnorm") fitsp <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=0, scale="normal") expect_equal(fitsp$res["gamma0",1], -fitln$res["meanlog",1]/fitln$res["sdlog",1], tol=1e-02) expect_equal(fitsp$res["gamma1",1], 1 /fitln$res["sdlog",1], tol=1e-02) }) test_that("Spline models with time-varying covariate effects",{ spl <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group), data=bc, knots=1) expect_equal(spl$loglik, -789.002098222827, tol=1e-04) expect_equal(spl$res["gamma1(groupMedium)","est"], -0.410859123437426, tol=1e-04) summ.g <- summary(spl, ci=FALSE, t=c(1,5,10))$`group=Good` expect_equal(summ.g$est[1], 0.9853637097617495, tol=1e-04) summ.m <- summary(spl, ci=FALSE, t=c(1,5,10))$`group=Medium` expect_equal(summ.m$est[1], 0.9391492993851021, tol=1e-04) summ2 <- summary(spl, ci=FALSE, t=c(1,5,10), newdata=data.frame(group=c("Good","Medium"))) expect_equal(summ2[[1]]$est[1], summ.g$est[[1]]) expect_equal(summ2[[2]]$est[1], summ.m$est[[1]]) spl2 <- flexsurvspline(Surv(recyrs, censrec) ~ group, anc=list(gamma1=~group), data=bc, knots=1) expect_equal(spl$loglik, spl2$loglik) if (interactive()) plot(spl) spl3 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group), data=bc, k=2) if (interactive()) lines(spl3, col="blue") }) test_that("Spline models with left-truncation",{ bc2 <- bc[bc$recyrs>2,] (spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc2, k=0, fixedpars=TRUE)) expect_equal(spl$loglik, -951.4567686517325, tol=1e-06) expect_equal(spl$loglik, sum(spl$logliki), tol=1e-06) (spl <- flexsurvspline(Surv(rep(0, nrow(bc2)), recyrs, censrec) ~ 1, data=bc2, k=0)) expect_equal(spl$loglik, -432.9048860461514, tol=1e-06) spl <- flexsurvspline(Surv(rep(1.9, nrow(bc2)), recyrs, censrec) ~ 1, data=bc2, k=0) expect_equal(spl$loglik, -400.3556493114977, tol=1e-06) # if(interactive()) lines(spl, col="blue") # truncated model fits much better }) test_that("Spline models with weighting",{ wt <- rep(1, nrow(bc)); wt[1:30] <- 2 spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=0, weights=wt) wei <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull", weights=wt) expect_equal(spl$loglik, wei$loglik, tol=1e-06) }) test_that("Spline models with relative survival",{ expect_error({ bc$bh <- rep(0.01, nrow(bc)) a <- 0.1; b <- 0.2 iniw <- c(a, b^(-a)) inis <- c(-a*log(b), a) spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=0, bhazard=bh, inits=inis, fixedpars=TRUE) wei <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibullPH", bhazard=bh, inits=iniw, fixedpars=TRUE) expect_equal(spl$loglik, wei$loglik, tol=1e-05) }, NA) }) test_that("flexsurvspline results match stpm in Stata",{ skip_if(covr::in_covr()) # optimisation for scale="odds" doesn't converge under covr for some reason ## Numbers copied from Stata output for equivalent stpm commands ## see ~/flexsurv/stpm/do1.do spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=0) expect_equal(spl$loglik + sum(log(bc$recyrs[bc$censrec==1])), -638.45432, tol=1e-05) expect_equal(as.numeric(spl$res[,"est"]), c(-3.360303, 1.379652, .8465394, 1.672433), tol=1e-02) spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=2) expect_equal(spl$loglik + sum(log(bc$recyrs[bc$censrec==1])), -674.75128, tol=1e-04) expect_equal(as.numeric(spl$res[,"est"]), c(-1.728339, 3.476179, .567432, -.3420749), tol=1e-02) spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=2, scale="odds") expect_equal(spl$loglik + sum(log(bc$recyrs[bc$censrec==1])), -675.271, tol=1e-04) spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=2, scale="normal") expect_equal(spl$loglik + sum(log(bc$recyrs[bc$censrec==1])), -675.73591 , tol=1e-04) ## stpm needs all or no ancillary pars to depend on covs ## not tested under stpm2 spl <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + gamma2(group) + gamma3(group), data=bc, k=2, scale="hazard") expect_equal(spl$loglik + sum(log(bc$recyrs[bc$censrec==1])), -607.47942, tol=1e-04) ## coefficients are the same to about 2sf }) test_that("Expected survival",{ spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1) gamma <- coef(spl)[1:3] surv <- function(x,...)psurvspline(q=x, gamma=gamma, knots=spl$knots, scale=spl$scale, lower.tail=FALSE, ...) expect_equal(integrate(surv, 0, 5)$value, 4.341222955052117, tol=1e-04) # For group="good" }) test_that("gamma in d/psurvspline can be matrix or vector",{ require(mvtnorm) boot <- rmvnorm(10, spl$opt$par, spl$cov) psurvspline(5, gamma=coef(spl)[1:2], knots=spl$knots, scale=spl$scale, lower.tail=FALSE) expect_equal(psurvspline(5, gamma=boot[3,1:2], knots=spl$knots, scale=spl$scale, lower.tail=FALSE), psurvspline(5, gamma=boot[,1:2], knots=spl$knots, scale=spl$scale, lower.tail=FALSE)[3]) dsurvspline(5, gamma=coef(spl)[1:2], knots=spl$knots, scale=spl$scale) expect_equal(dsurvspline(5, gamma=boot[3,1:2], knots=spl$knots, scale=spl$scale), dsurvspline(5, gamma=boot[,1:2], knots=spl$knots, scale=spl$scale)[3]) }) test_that("Errors in spline",{ expect_error(flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, knots="foo"), "\"knots\" must be a numeric vector") expect_error(flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, knots=c(-5, 2)), "knot -5 less than or equal to minimum log time") expect_error(flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, knots=c(2)), "knot 2 greater than or equal to maximum log time") expect_error(flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, k=0, bknots=c("foo")), "boundary knots should be") expect_error(flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, k=0, bknots=c(0,1,2)), "boundary knots should be") expect_warning( flexsurvspline(Surv(recyrs, censrec) ~ foo, data=bc, subset=1:10, k=0, inits=c(1,1,0,0,0,0), fixedpars=TRUE) , "minimum and maximum log death times are the same") }) test_that("supplying knots",{ ldtimes <- log(bc$recyrs[bc$censrec==1]) expect_equal(flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1)$loglik, flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, knots=median(ldtimes), bknots=range(ldtimes))$loglik, tol=1e-08) expect_true(flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, k=1)$loglik != flexsurvspline(Surv(recyrs, censrec) ~ group + foo, data=bc, k=1, bknots=c(-5, 2))$loglik) }) test_that("subset",{ subflex <- flexsurvspline(Surv(time = time, event = status) ~ sex + cut(age, 4), data = survival::lung, subset = !is.na(wt.loss)) subflex2 <- flexsurvspline(Surv(time = time, event = status) ~ sex + cut(age, 4), data = survival::lung[!is.na(survival::lung$wt.loss),]) expect_equal(subflex$loglik, subflex2$loglik, tol=1e-08) subflex <- flexsurvspline(Surv(time = time, event = status) ~ sex + cut(age, 4), data = survival::lung, subset = survival::lung$age > 60) # empty factor level in subset, should be dropped since 0.7 }) test_that("spline basis function with vector or matrix knots",{ expect_not_equal <- function(x,y)expect_true(!isTRUE(identical(x,y))) x <- c(1.5, 1.6) b1 <- basis(knots=0:3, x=x) knots_same <- matrix(rep(0:3,2),byrow=TRUE,nrow=2) knots_diff <- matrix(c(0:3, 0:3+0.1), byrow=TRUE, nrow=2) b2 <- basis(knots=knots_same, x=x) expect_equal(b1, b2) b3 <- basis(knots=knots_diff, x=x) expect_not_equal(b1, b3) b1 <- basis(knots=0:3, x=x, spline="splines2ns") b2 <- basis(knots=knots_same, x=x, spline="splines2ns") expect_equal(b1, b2) b3 <- basis(knots=knots_diff, x=x, spline="splines2ns") expect_equal(b1[1,], b3[1,]) expect_not_equal(b1, b3) }) test_that("splines2 orthogonal basis",{ spl_rp <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=2, spline="rp") spl_ns <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bc, k=2, spline="splines2ns") # fits better expect_equal(spl_ns$loglik, spl_rp$loglik, tol=1) p1 <- predict(spl_ns, type = "rmst", times = 500, newdata = tibble(age = 50)) p2 <- predict(spl_rp, type = "rmst", times = 500, newdata = tibble(age = 50)) expect_equal(p1$.pred_rmst, p2$.pred_rmst, tol=1e-01) spl_rp <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=2, spline="rp") spl_ns <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=2, spline="splines2ns") # fits better expect_equal(spl_rp$res["groupMedium","est"], spl_ns$res["groupMedium","est"], tol=1e-03) expect_equal(spl_rp$res["groupPoor","est"], spl_ns$res["groupPoor","est"], tol=1e-03) }) test_that("interval censored data",{ bc$recyrs1 <- bc$recyrs + 0.001 bci <- bc[bc$censrec==1,] ## knots chosen from interval midpoints spl1 <- flexsurvspline(Surv(recyrs, recyrs1, type="interval2") ~ 1, data=bci, k=1) spl <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bci, knots=spl1$knots[2], bknots=spl1$knots[c(1,3)]) expect_equal(spl1$res["gamma0","est"], spl$res["gamma0","est"], tol=1e-02) spl0 <- flexsurvspline(Surv(recyrs, censrec) ~ 1, data=bci, k=1) expect_equal(spl0$res["gamma0","est"], spl$res["gamma0","est"], tol=1e-02) }) test_that("spline with weights",{ set.seed(1) bc$w <- bc$recyrs # weight later obs splw <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, weights=w, k=1) spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1) expect_true(!isTRUE(identical(splw$knots, spl$knots))) ## knots chosen to account for weights, so should be higher in weighted model expect_lt(mean(spl$knots), mean(splw$knots)) }) flexsurv/tests/testthat/test_gengamma.R0000644000176200001440000001061414361010245020066 0ustar liggesuserscontext("Generalized gamma distribution") tol <- 1e-06 x <- c(-1,1,2,3,4); mu <- 2.2; sigma <- 1.6; Q <- 0; P <- 1 delta <- (Q^2 + 2*P)^{1/2} s1 <- 2 / (Q^2 + 2*P + Q*delta); s2 <- 2 / (Q^2 + 2*P - Q*delta) x <- c(-1,1,2,3,4); shape <- 2.2; scale <- 1.6; k <- 1.9 test_that("Generalized gamma reductions: d",{ expect_equal(dgengamma(c(-1,1,2,3,4), mu=0, sigma=1, Q=1), # FIXME value for x=0 and add here c(0, 0.367879441171442, 0.135335283236613, 0.0497870683678639, 0.0183156388887342)) expect_equal(dgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0), dlnorm(c(-1,0,1,2,3,4), meanlog=0, sdlog=1)) expect_equal(dgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1:3, Q=0), dlnorm(c(-1,0,1,2,3,4), meanlog=0, sdlog=1:3)) expect_equal(dgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1:3, Q=0, log=TRUE), dlnorm(c(-1,0,1,2,3,4), meanlog=0, sdlog=1:3, log=TRUE)) expect_equal(dgengamma(c(1,2,3,4), mu=0.1, sigma=1.2, Q=1), dweibull(c(1,2,3,4), shape=1/1.2, scale=exp(0.1))) # only defined for x>0 anyway x <- c(1,2,3,4); mu <- 0.4; sigma <- 1.2 expect_equal(dgengamma(x, mu=mu, sigma=sigma, Q=sigma), dgamma(x, shape=1/sigma^2, scale=exp(mu)*sigma^2)) # FIXME add limiting value for x=0 expect_equal(dgengamma.orig(x, shape=shape, scale=scale, k=k), dgengamma(x, mu=log(scale) + log(k)/shape, sigma=1/(shape*sqrt(k)), Q=1/sqrt(k))) }) test_that("Generalized gamma reductions: p",{ expect_equal(pgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=1), c(0, 0, 0.632120558828558, 0.864664716763387, 0.950212931632136, 0.981684361111266)) expect_equal(pgengamma(c(-1,0,1,2,3,4), mu=0, sigma=1, Q=0), plnorm(c(-1,0,1,2,3,4), meanlog=0, sdlog=1)) expect_equal(pgengamma(c(-1,0,1,2,3,4), mu=0.1, sigma=1.2, Q=1), pweibull(c(-1,0,1,2,3,4), shape=1/1.2, scale=exp(0.1))) x <- c(1,2,3,4); mu <- 0.4; sigma <- 1.2 expect_equal(pgengamma(x, mu=mu, sigma=sigma, Q=sigma), pgamma(x, shape=1/sigma^2, scale=exp(mu)*sigma^2)) }) test_that("Generalized gamma reductions: q",{ expect_equal(qgengamma(p=0.25, mu=0, sigma=1, Q=1), 0.287682072451781) expect_equal(qgengamma(p=0.25, mu=0, sigma=1, Q=1), qgeneric(pgengamma, p=0.25, mu=0, sigma=1, Q=1)) expect_equal(qgengamma(p=0, mu=0, sigma=1, Q=1), 0) expect_equal(qgengamma(p=0.25, mu=0, sigma=1, Q=0), qlnorm(p=0.25, meanlog=0, sdlog=1)) expect_equal(qgengamma(p=0.25, mu=0, sigma=1.2, Q=0), qlnorm(p=0.25, meanlog=0, sdlog=1.2)) expect_equal(qgengamma(p=0.25, mu=0.1, sigma=1.2, Q=1), qweibull(p=0.25, scale=exp(0.1), shape=1/1.2)) expect_equal(qgengamma(pgengamma(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, Q=1), mu=0, sigma=1, Q=1), c(0,0,0,1,2,3,4)) expect_equal(qgengamma(pgengamma(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, Q=-1), mu=0, sigma=1, Q=-1), c(0,0,0,1,2,3,4)) expect_equal(qlnorm(pgengamma(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1.2, Q=0), meanlog=0, sdlog=1.2), c(0,0,0,1,2,3,4)) expect_equal(qlnorm(pgengamma(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, Q=0, log.p=TRUE), meanlog=0, sdlog=1, log.p=TRUE), c(0,0,0,1,2,3,4)) expect_equal(qgengamma(p=0.25, mu=0, sigma=1, Q=1, lower.tail=TRUE), qgeneric(pgengamma, p=0.25, mu=0, sigma=1, Q=1, lower.tail=TRUE)) }) test_that("Generalized gamma reductions: r",{ rgengamma(n=10, mu=0, sigma=1, Q=0) set.seed(22061976) x <- rgengamma(n=10, mu=0, sigma=1.1, Q=0) set.seed(22061976) y <- rlnorm(n=10, meanlog=0, sdlog=1.1) expect_equal(x, y) }) test_that("Gives errors", { expect_warning(dgengamma(1, 1, -2, 1), "Negative") expect_warning(pgengamma(1, 1, -2, 1), "Negative") expect_warning(qgengamma(0.1, 1, -2, 1), "Negative") expect_warning(rgengamma(1, 1, -2, 1), "Negative") }) test_that("Generalized gamma definition in Stata manual",{ Sgg <- function(t, mu, sigma, kappa){ IGF <- function(a, x){ pgamma(x, a) } # incomplete gamma function gamma <- 1 / kappa^2 z <- (log(t) - mu)/sigma z[kappa<0] <- -z[kappa<0] # Stata manual uses sign(0) = 1 u <- gamma*exp(abs(kappa)*z) ifelse(kappa > 0, 1 - IGF(gamma, u), ifelse(kappa==0, 1 - pnorm(z), IGF(gamma, u))) } expect_equal( Sgg(c(1,2,3),c(-1,2,0.2),c(1,2,1),c(-1, 0, 1)), pgengamma(c(1,2,3),c(-1,2,0.2),c(1,2,1),c(-1, 0, 1), lower.tail=FALSE) ) }) flexsurv/tests/testthat/test_fmsm.R0000644000176200001440000000637314472153104017270 0ustar liggesusers#### Functions that summarise outputs from fmsm multi-state model objects ## Three state competing risks model for testing functions that only work on ## Markov models tmat <- rbind(c(NA,1,2),c(NA,NA,NA),c(NA,NA,NA)) set.seed(1) bosms3$x <- rnorm(nrow(bosms3)) bweic <- bweim <- vector(2, mode="list") for (i in 1:2) { bweic[[i]] <- flexsurvreg(Surv(years, status) ~ x, subset=(trans==i), data = bosms3, dist = "weibull") bweim[[i]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==i), data = bosms3, dist = "weibull") } weic <- fmsm("Well-BOS"=bweic[[1]], "Well-Death"=bweic[[2]], trans=tmat) weim <- fmsm("Well-BOS"=bweim[[1]], "Well-Death"=bweim[[2]], trans=tmat) nd <- data.frame(x=c(0,0.01,-10,10)) test_that("pfinal_fmsm", { expect_equal(pfinal_fmsm(weim, fromstate="State 1")$val, c(0.717737627151196, 0.282262372848804)) expect_error(pfinal_fmsm(weim, fromstate="State 2"), "No destination states") expect_equal(pfinal_fmsm(weic, newdata=nd, fromstate="State 1")$val[1:2], c(0.715828147070156, 0.715333178039627)) expect_true(is.numeric(pfinal_fmsm(weim, fromstate="State 1", B=3)$lower)) expect_equal(pfinal_fmsm(weim, fromstate="State 1", maxt=100000)$val, pfinal_fmsm(weim, fromstate="State 1", maxt=10000000)$val, tolerance=1e-06) expect_error(pfinal_fmsm(weim, fromstate="1"), "not found") }) test_that("simfinal_fmsm",{ set.seed(1) sm <- simfinal_fmsm(weim) expect_equal(sm$val[sm$quantity=="prob"], c(0.71758, 0.28242)) expect_equal(sm$val[sm$quantity=="50%"], c(2.25618202292384, 4.67377970752349)) sm2 <- simfinal_fmsm(weim, probs=c(0.25, 0.75)) sm3 <- simfinal_fmsm(weim, probs=c(0.25, 0.75), t=10000) expect_equal(sm2$val[sm$quantity=="prob"], sm3$val[sm$quantity=="prob"], tolerance=0.1) sm2 <- simfinal_fmsm(weim, probs=c(0.25, 0.75), M=1000, B=10) expect_error(simfinal_fmsm(weic), "`newdata` should be supplied") nd <- data.frame(x=c(0, 0.01)) simfinal_fmsm(weic, newdata=nd) simfinal_fmsm(weic, newdata=nd, M=1000, B=10) }) bosms3$hix <- factor(bosms3$x > 0, labels = c("lo","hi")) test_that("ajfit_fmsm", { expect_equal(ajfit_fmsm(weim, maxt=5)$val[1], 1) expect_error(ajfit_fmsm(weic, maxt=5, newdata=list(x=1)), "Nonparametric estimation not supported with non-factor") weicf <- fmsm( "Well-BOS"=flexsurvreg(Surv(years, status) ~ hix, subset=(trans==1), data = bosms3, dist = "weibull"), "Well-Death"=flexsurvreg(Surv(years, status) ~ hix, subset=(trans==2), data = bosms3, dist = "weibull"), trans=tmat ) expect_equal(ajfit_fmsm(weicf, maxt=5)$val[1], 1) expect_equal(ajfit_fmsm(weicf, maxt=5, newdata=data.frame(hix="lo"))$val[1], 1) weicfd <- fmsm( "Well-BOS"=flexsurvreg(Surv(years, status) ~ hix, subset=(trans==1), data = bosms3, dist = "weibull"), "Well-Death"=flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "weibull"), trans=tmat ) expect_error(ajfit_fmsm(weicfd, maxt=5), "Not currently supported with different covariates on different transitions") }) flexsurv/tests/testthat/test_hess.R0000644000176200001440000001723314633575437017305 0ustar liggesusersif (!identical(Sys.getenv("NOT_CRAN"), "true")) return() if (!require("numDeriv")) return() library(numDeriv) library(testthat) test_that("Weibull AFT Hessian",{ pars <- log(c(shape=1.2,scale=1.1)) lds <- function(pars){dweibull(2,exp(pars[1]),exp(pars[2]),log=TRUE)} expect_equivalent(grad(lds, pars), flexsurv:::DLdweibull(2, exp(pars[1]), exp(pars[2]))) expect_equivalent(hessian(lds, pars), D2Ldweibull(2, exp(pars[1]), exp(pars[2]))[1,,]) lss <- function(pars){pweibull(2,exp(pars[1]),exp(pars[2]),log=TRUE, lower.tail = FALSE)} expect_equivalent(grad(lss, pars), flexsurv:::DLSweibull(2, exp(pars[1]), exp(pars[2]))) expect_equivalent(hessian(lss, pars), D2LSweibull(2, exp(pars[1]), exp(pars[2]))[1,,]) }) test_that("Weibull PH Hessian",{ pars <- log(c(shape=1.2,scale=1.1)) lds <- function(pars){dweibullPH(2,exp(pars[1]),exp(pars[2]),log=TRUE)} expect_equivalent(grad(lds, pars), flexsurv:::DLdweibullPH(2, exp(pars[1]), exp(pars[2]))) lss <- function(pars){pweibullPH(2,exp(pars[1]),exp(pars[2]),log=TRUE, lower.tail = FALSE)} expect_equivalent(grad(lss, pars), flexsurv:::DLSweibullPH(2, exp(pars[1]), exp(pars[2]))) expect_equivalent(hessian(lds, pars), D2LdweibullPH(2, exp(pars[1]), exp(pars[2]))[1,,]) hess <- hessian(lss, pars) expect_equivalent(hessian(lss, pars), D2LSweibullPH(2, exp(pars[1]), exp(pars[2]))[1,,]) }) test_that("Gompertz Hessian",{ pars <- c(shape=1.2,scale=log(1.1)) ## nonzero shape lds <- function(pars){dgompertz(2,pars[1],exp(pars[2]),log=TRUE)} lss <- function(pars){pgompertz(2,pars[1],exp(pars[2]),log=TRUE, lower.tail = FALSE)} expect_equivalent(grad(lds, pars), flexsurv:::DLdgompertz(2, pars[1], exp(pars[2]))) expect_equivalent(grad(lss, pars), flexsurv:::DLSgompertz(2, pars[1], exp(pars[2]))) expect_equivalent(hessian(lss, pars), D2LSgompertz(2, pars[1], exp(pars[2]))[1,,]) expect_equivalent(hessian(lss, pars), D2Ldgompertz(2, pars[1], exp(pars[2]))[1,,]) ## zero shape pars <- c(shape=0,scale=log(1.1)) lds <- function(pars){dgompertz(2,0,exp(pars[2]),log=TRUE)} lss <- function(pars){pgompertz(2,0,exp(pars[2]),log=TRUE, lower.tail = FALSE)} expect_equivalent(grad(lds, pars), flexsurv:::DLdgompertz(2, pars[1], exp(pars[2]))) expect_equivalent(grad(lss, pars), flexsurv:::DLSgompertz(2, pars[1], exp(pars[2]))) expect_equivalent(hessian(lss, pars), D2LSgompertz(2, pars[1], exp(pars[2]))[1,,]) expect_equivalent(hessian(lds, pars), D2Ldgompertz(2, pars[1], exp(pars[2]))[1,,]) }) hess_error <- function(object){ if (!isTRUE(getOption("flexsurv.test.analytic.derivatives"))) stop("flexsurv.test.analytic.derivatives option not set") object$hess.test$error } options(flexsurv.test.analytic.derivatives=TRUE) test_that("flexsurvreg fit hessian",{ err <- 1e-03 fl <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="exp") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, data=bc, dist="exp") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="weibull") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, anc=list(shape=~group), data=bc, dist="weibull") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="weibullPH") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, data=bc, dist="weibullPH") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, anc=list(shape=~group), data=bc, dist="weibullPH") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gompertz") expect_lt(hess_error(fl), err) err <- 1e-02 fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, data=bc, dist="gompertz") expect_lt(hess_error(fl), err) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, anc=list(shape=~group), data=bc, dist="gompertz") expect_lt(hess_error(fl), err) set.seed(1) simt <- rweibull(1000, 2, 0.5) status <- ifelse(simt>0.6, 0, 1) simt[status==0] <- 0.6 tmin <- simt tmax <- ifelse(status==1, simt, Inf) tmax.sr <- ifelse(status==1, simt, NA) fl <- flexsurvreg(Surv(tmin, tmax.sr, type="interval2") ~ 1, dist="weibull") expect_lt(hess_error(fl), err) set.seed(1) sim <- rgenf(3000, 1.5, 1, -0.4, 0.6) dead <- as.numeric(sim<=30) simt <- ifelse(sim<=30, sim, 30) obs <- simt>3; simt <- simt[obs]; dead <- dead[obs] fl <- flexsurvreg(Surv(simt, dead) ~ 1, dist="weibull") expect_lt(hess_error(fl), err) wts <- rep(1, length(simt)); wts[1:200] <- 1.2 fl <- flexsurvreg(Surv(simt, dead) ~ 1, weights=wts, dist="weibull") expect_lt(hess_error(fl), err) bc$bhaz <- rep(0.1, nrow(bc)) fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, anc=list(shape=~group), data=bc, bhazard=bhaz, dist="weibull") expect_lt(hess_error(fl), err) bc$wts <- 1; bc$wts[1:300] <- 1.1 fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, anc=list(shape=~group), data=bc, weights=wts, dist="weibull") expect_lt(hess_error(fl), err) bc$bhaz <- rep(0.1, nrow(bc)) bc$wts <- 1; bc$wts[1:300] <- 1.1 fl <- flexsurvreg(formula = Surv(recyrs, censrec) ~ group, anc=list(shape=~group), data=bc, bhazard=bhaz, weights=wts, dist="weibull") expect_lt(hess_error(fl), err) }) ## TODO documentation test_that("flexsurvspline fit hessian",{ err <- 1e-03 fl <- flexsurvspline(formula = Surv(recyrs, censrec) ~ group, k = 1, data=bc, scale = "hazard") expect_lt(hess_error(fl), err) # fails on codecov system for some reason # fl <- flexsurvspline(formula = Surv(recyrs, censrec) ~ group, # k = 1, data=bc, scale="odds") # expect_lt(hess_error(fl), err) }) options(flexsurv.test.analytic.derivatives=FALSE) test_that("nearest positive-definite control",{ # sub-optimal solution near to optimal solution of: # flexsurvreg(formula=Surv(futime, fustat) ~ 1, dist="gengamma", data=ovarian) perturbed <- c(mu=6.4049977, sigma=1.2217696, Q=-0.6432642) short_optim <- list(maxit=0) expect_warning( flexsurvreg(formula=Surv(futime, fustat) ~ 1, data=ovarian, dist="gengamma", inits=perturbed, control=short_optim, hess.control=list(tol.evalues=0)), "Hessian not positive definite" ) expect_silent( flexsurvreg(formula=Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", inits=perturbed, control=short_optim, hess.control=list(tol.evalues=1.1E1)) ) fl_nearPD <- flexsurvreg(formula=Surv(futime, fustat) ~ 1, data=ovarian, dist="gengamma", inits=perturbed, control=short_optim, hess.control=list(tol.evalues=1.1E1)) expect_gt(min(eigen(vcov(fl_nearPD))$values), 0) }) flexsurv/tests/testthat/test_flexsurvreg.R0000644000176200001440000007264614621151032020702 0ustar liggesuserscontext("flexsurvreg model fits") test_that("Generalized F (p parameter) not identifiable from ovarian data",{ expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf"), "non-finite finite-difference") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf.orig"), "non-finite finite-difference") }) test_that("Generalized gamma fit",{ fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma") # print(fitg) # print(fitg, digits=4) fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gengamma") ovarian2 <- ovarian fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian2, dist="gengamma") ## GF with "p" fixed at 0 fitffix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", fixedpars=4, inits=c(NA,NA,NA,1e-05)) expect_equal(fitffix$loglik, sum(fitffix$logliki)) expect_equal(fitffix$res[1:3,"est"], fitg$res[1:3,"est"], tolerance=1e-03) expect_equal(fitffix$res[1:3,2:3], fitg$res[1:3,2:3], tolerance=1e-02) }) test_that("Same answers as survreg for Weibull regression",{ fitw <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull") fitws <- survreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull") expect_equal(fitw$loglik, fitws$loglik[1], tolerance=1e-04) expect_equal(fitws$scale, 1 / fitw$res["shape","est"], tolerance=1e-03) expect_equal(as.numeric(coef(fitws)[1]), log(fitw$res["scale","est"]), tolerance=1e-03) }) test_that("Exponential",{ sr <- survreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="exponential") fite <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="exp") expect_equal(sr$loglik[2], fite$loglik) expect_warning(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="exp", sr.control=list(maxiter=2)), "Ran out of iterations") }) test_that("Log-normal",{ sr <- survreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="lognormal") fitl <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="lognormal") expect_equal(sr$loglik[2], fitl$loglik) expect_warning(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="exp", sr.control=list(maxiter=2)), "Ran out of iterations") }) test_that("Weighted fits",{ wt <- rep(1, nrow(ovarian)) wt[c(1,3,5,7,9)] <- 10 fitw <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull", weights=wt) fitws <- survreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull", weights=wt) expect_equal(fitws$loglik[2],fitw$loglik,tolerance=1e-06) }) test_that("subset",{ fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, subset=-(1:2), dist="gengamma") fitg2 <- flexsurvreg(formula = Surv(ovarian$futime[-(1:2)], ovarian$fustat[-(1:2)]) ~ 1, dist="gengamma") expect_equal(fitg$loglik,fitg2$loglik) }) test_that("na.action",{ ovarian2 <- ovarian ovarian2$futime[1] <- NA fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data=ovarian2, na.action=na.omit, dist="gengamma") ovarian3 <- ovarian[-1,] fitg2 <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data=ovarian3, na.action=na.omit, dist="gengamma") expect_equal(fitg$loglik,fitg2$loglik) expect_error(flexsurvreg(formula = Surv(futime, fustat) ~ 1, data=ovarian2, na.action=na.fail, dist="gengamma"), "missing values") }) test_that("Log-normal",{ fitln <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="lnorm") expect_equal(fitln$loglik, -97.12174204265681, tolerance=1e-06) }) test_that("Gompertz",{ fitgo <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gompertz", fixedpars=TRUE) # model fit is unstable expect_equal(fitgo$loglik, -112.8294446076947, tolerance=1e-06) }) test_that("Log-logistic",{ fitlls <- survreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ age, data = ovarian, dist="loglogistic") fitll <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist="llogis") expect_equal(fitll$loglik, fitlls$loglik[2], tolerance=1e-06) }) test_that("Gamma",{ fitga <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gamma") expect_equal(fitga$loglik, -97.86379723453011, tolerance=1e-06) }) test_that("Loglikelihoods of flexible distributions reduce to less flexible ones for certain parameters",{ ## Test distributions reducing to others with fixed pars fitffix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", fixedpars=TRUE, inits=c(0,1,0,1)) ## GG = GF with p -> 0 fitffix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", fixedpars=TRUE, inits=c(0,1,0,1e-08)) fitgfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gengamma", fixedpars=TRUE, inits=c(0,1,0)) expect_equal(fitgfix$loglik, fitffix$loglik, tolerance=1e-02) ## Weib = GG with q=1 fitgfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gengamma", fixedpars=TRUE, inits=c(6,0.8,1)) fitwfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull", fixedpars=TRUE, inits=c(1/0.8,exp(6))) expect_equal(fitwfix$loglik, fitgfix$loglik) ## Gamma = GG with sig=q fitgfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gengamma", fixedpars=TRUE, inits=c(6,0.5,0.5)) fitgafix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gamma", fixedpars=TRUE, inits=c(1/0.5^2,exp(-6)/0.5^2)) expect_equal(fitgafix$loglik,fitgfix$loglik) ## Log-normal = GG with q=0 fitgfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gengamma", fixedpars=TRUE, inits=c(6,0.8,0)) fitlfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="lnorm", fixedpars=TRUE, inits=c(6,0.8)) expect_equal(fitlfix$loglik,fitgfix$loglik) ## Compare with weib/lnorm fit from survreg fitw <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull", inits=c(1/0.8,exp(6))) fitw2 <- survreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull") expect_equal(1 / fitw2$scale, fitw$res["shape","est"], tolerance=1e-03) expect_equal(as.numeric(coef(fitw2)[1]), log(fitw$res["scale","est"]), tolerance=1e-03) }) test_that("Fits of flexible distributions reduce to less flexible ones with fixed parameters",{ fitgfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gengamma.orig", fixedpars=3, inits=c(NA,NA,1)) fitw <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull") expect_equal(logLik(fitgfix), logLik(fitw), tolerance=1e-06) fitgfix <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gengamma.orig", fixedpars=1, inits=c(1,NA,NA)) fitga <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="gamma") expect_equal(logLik(fitgfix), logLik(fitga), tolerance=1e-06) fite <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="exp") fitw <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull", inits=c(1, mean(ovarian$futime)), fixedpars=1) expect_equal(logLik(fite), logLik(fitw), tolerance=1e-06) expect_equal(fitw$res["scale",1], 1 / fite$res["rate",1], tolerance=1e-06) }) fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ factor(rx), data = ovarian, dist="weibull") test_that("Model fit with covariates",{ expect_equal(fitg$loglik, -97.3641506645869, tolerance=1e-06) if (covr::in_covr() || interactive()) { plot(fitg, ci=TRUE) plot(fitg, X=rbind(c(0), c(1)), ci=TRUE, col="red") lines(fitg, X=rbind(c(1.1), c(1.2)), ci=TRUE, col="blue") plot(fitg, type="hazard") plot(fitg, type="cumhaz") fitg1 <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="weibull") plot(fitg1, type="hazard") } }) test_that("Summary function: alternative ways to supply covariates",{ expect_equal(summary(fitg, X=c(0), ci=FALSE)[[1]]$est, summary(fitg, newdata=data.frame(rx=1), ci=FALSE)[[1]]$est) expect_equal(summary(fitg, X=c(1), ci=FALSE)[[1]]$est, summary(fitg, newdata=data.frame(rx=2), ci=FALSE)[[1]]$est) expect_equivalent(summary(fitg, X=matrix(c(0,1),ncol=1), ci=FALSE)[1:2], summary(fitg, newdata=data.frame(rx=c(1,2)), ci=FALSE)[1:2]) fitg2 <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ factor(rx) + factor(ecog.ps), data = ovarian, dist="weibull") expect_equivalent(summary(fitg2, newdata=data.frame(rx=1,ecog.ps=2), ci=FALSE)[[1]][1:2], summary(fitg2, X=matrix(c(0,1), nrow=1))[[1]][1:2]) }) test_that("summary with CIs",{ summ <- summary(fitg, newdata=data.frame(rx=1), B=2, type="survival") expect_true(all(unlist(summ[[1]][,2:4]) <= 1)) expect_true(all(unlist(summ[[1]][,2:4]) >= 0)) }) test_that("Errors in summary function",{ expect_error(summary(fitg, newdata=list(foo=1)), "Value of covariate \"rx\" not supplied") expect_error(summary(fitg, X=matrix(c(0,1),ncol=2), ci=FALSE), "expected X to be a matrix with 1 column or a vector with 1 element") expect_error(summary(fitg, X=matrix(c(0,1),ncol=1), start=1:2, ci=FALSE), "length of \"start\"") expect_error(summary(fitg, start=1:2, ci=FALSE), "length of \"start\"") }) test_that("Model fit with covariates and simulated data",{ x <- rnorm(500,0,1) sim <- rgenf(500, 1.5 - 0.2*x, 1, -0.4, 0.6) dead <- as.numeric(sim<=30) simt <- ifelse(sim<=30, sim, 30) fit <- flexsurvreg(Surv(simt, dead) ~ x, dist="genf", control=list(maxit=10000)) if (covr::in_covr() || interactive()) { fit # estimate should be -0.2 summary(fit) plot(fit) lines(fit, X=matrix(c(1,2),nrow=2)) plot(fit, type="hazard", min.time=0, max.time=25) lines(fit, type="hazard", X=matrix(c(1,2),nrow=2)) x2 <- factor(rbinom(500, 1, 0.5)) fit <- flexsurvreg(Surv(simt, dead) ~ x + x2, dist="genf", control=list(maxit=10000)) plot(fit) plot(fit, type="cumhaz") plot(fit, type="hazard", min.time=0, max.time=25) x3 <- factor(rbinom(500, 1, 0.5)) fit <- flexsurvreg(Surv(simt, dead) ~ x2 + x3, dist="genf", control=list(maxit=10000)) fit <- flexsurvreg(Surv(simt, dead) ~ x2, dist="genf", control=list(maxit=10000)) plot(fit) summary(fit, type="hazard", ci=FALSE) plot(fit, type="hazard", ci=FALSE) } x2 <- factor(rbinom(500, 1, 0.5)) x3 <- rnorm(500,0,1) sim <- rgengamma(500, 1.5 + 2*x3, 1, -0.4) dead <- as.numeric(sim<=30) simt <- ifelse(sim<=30, sim, 30) expect_error({ fit <- flexsurvreg(Surv(simt, dead) ~ x3, dist="gengamma", control=list(maxit=10000)) fit <- flexsurvreg(Surv(simt, dead) ~ x + x2 + x3, dist="gengamma", control=list(maxit=10000)) fit <- flexsurvreg(Surv(simt, dead)[1:100] ~ x[1:100] + x2[1:100], dist="gengamma", control=list(maxit=10000), method="BFGS") fit <- flexsurvreg(Surv(simt, dead)[1:100] ~ x[1:100], dist="gengamma", control=list(maxit=10000)) }, NA) }) test_that("Covariates on ancillary parameters",{ set.seed(11082012) x3 <- rnorm(1500,0,1) x4 <- rnorm(1500,0,1) x5 <- rnorm(1500,0,1) sim <- rgengamma(1500, 1, exp(0.5 + 0.1*x3 + -0.3*x4), -0.4 + 1.2*x5) dead <- as.numeric(sim<=30) simt <- ifelse(sim<=30, sim, 30) expect_error({ ## Cov on ancillary, not on location flexsurvreg(Surv(simt, dead) ~ sigma(x3), dist="gengamma", fixedpars=TRUE) flexsurvreg(Surv(simt, dead) ~ 1, anc=list(sigma=~x3), dist="gengamma", fixedpars=TRUE) ## Cov on both location and ancillary flexsurvreg(Surv(simt, dead) ~ x3 + sigma(x3), dist="gengamma", fixedpars=TRUE) flexsurvreg(Surv(simt, dead) ~ x3, anc=list(sigma=~x3), dist="gengamma", fixedpars=TRUE) ## More than one covariate on an ancillary parameter flexsurvreg(Surv(simt, dead) ~ x3 + sigma(x3) + sigma(x4), dist="gengamma", fixedpars=TRUE) flexsurvreg(Surv(simt, dead) ~ x3, anc=list(sigma=~x3+x4), dist="gengamma", fixedpars=TRUE) ## More than one ancillary parameter with covariates flexsurvreg(Surv(simt, dead) ~ x3 + sigma(x3) + sigma(x4) + Q(x5), dist="gengamma", fixedpars=TRUE) x <- flexsurvreg(Surv(simt, dead) ~ x3, anc=list(sigma=~x3+x4, Q=~x5), dist="gengamma", fixedpars=TRUE) }, NA) ## Warning if location parameter supplied as ancillary expect_warning( expect_error(flexsurvreg(Surv(simt, dead) ~ mu(x3), dist="gengamma", fixedpars=TRUE), "could not find function"), "Ignoring location parameter") expect_warning(flexsurvreg(Surv(simt, dead) ~ scale(x3), dist="weibull", fixedpars=TRUE), "Ignoring location parameter") ## base::scale exists expect_warning(flexsurvreg(Surv(simt, dead) ~ 1, anc=list(mu= ~x3), dist="gengamma", fixedpars=TRUE), "Ignoring location parameter") expect_warning(flexsurvreg(Surv(simt, dead) ~ 1, anc=list(scale=~x3), dist="weibull", fixedpars=TRUE), "Ignoring location parameter") }) test_that("formula can contain dot", { fit_dot <- flexsurvreg( formula = Surv(ovarian$futime, ovarian$fustat) ~ ., data = ovarian, dist = "weibull" ) exp_fit <- flexsurvreg( formula = Surv(ovarian$futime, ovarian$fustat) ~ age + resid.ds + rx + ecog.ps, data = ovarian, dist = "weibull" ) call_index <- 1 expect_equal(fit_dot[-call_index], exp_fit[-call_index]) fit_dot <- flexsurvreg( formula = Surv(ovarian$futime, ovarian$fustat) ~ ., data = ovarian, anc = list(sigma = ~ age), dist = "gengamma", fixedpars=TRUE ) exp_fit <- flexsurvreg( formula = Surv(ovarian$futime, ovarian$fustat) ~ age + resid.ds + rx + ecog.ps, data = ovarian, anc = list(sigma = ~ age), dist = "gengamma", fixedpars=TRUE ) call_index <- 1 expect_equal(fit_dot[-call_index], exp_fit[-call_index]) }) test_that("Various errors",{ expect_error(flexsurvreg(data = ovarian, dist="genf", inits = c(1,2,3)),"\"formula\" is missing") expect_error(flexsurvreg(formula="foo", data = ovarian, dist="genf", inits = c(1,2,3)),"\"formula\" must be a formula") expect_error(flexsurvreg(formula= futime ~ fustat, data = ovarian, dist="genf", inits = c(1,2,3)),"Response must be a survival object") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, inits = c(1,2,3)),"Distribution \"dist\" not specified") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist=1, data = ovarian, inits = c(1,2,3)),"\"dist\" should be a") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", data = ovarian, anc=1, inits = c(1,2,3)),"\"anc\" must be a") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", inits = c(1,2,3)),"Initial values .+ length") expect_warning(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", inits = c(1,2,3,4,5), fixedpars=TRUE),"Initial values are a vector length .+ using only the first") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", inits = "foo"),"init.+ must be a numeric vector") suppressWarnings({ expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", inits = c(1,2,3,-1)),"Initial value for parameter 4 out of range") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", inits = c(1,-2,3,-1)),"Initial values for parameters 2,4 out of range") }) expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", fixedpars = c(3,4,5,6,7)), "fixedpars must be TRUE/FALSE") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="genf", fixedpars = "foo"), "fixedpars must be TRUE/FALSE") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="lnorm",cl=-1), "cl must be a number in") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="lnorm",cl=1.1), "cl must be a number in") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="lnorm",cl=c(1,2)), "cl must be a number in") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="lnorm",cl="foo"), "cl must be a number in") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian, dist="foo"), "\'arg\' should be one of") expect_error(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, data = ovarian), "Distribution \"dist\" not specified") }) test_that("Calling flexsurvreg from within a function",{ expect_error({ f <- function(){ ovarian2 <- ovarian fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian2, dist="gengamma") fitg <- flexsurvreg(formula = Surv(ovarian2$futime, ovarian2$fustat) ~ factor(ovarian2$rx), dist="gengamma",method="Nelder-Mead") } f() }, NA) }) test_that("Calling flexsurvreg from a function within a function",{ expect_error({ f <- function(){ ovarian2 <- ovarian g <- function(){ fitw <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian2, dist="weibull") fitw <- flexsurvreg(formula = Surv(ovarian2$futime, ovarian2$fustat) ~ factor(ovarian2$rx), dist="weibull") } g() } f() }, NA) }) ## Left-truncation. ## Time passed as arg to initial values is stop - start, ## since, e.g. mean of trunc exponential dist is 1/lam + b, mean par plus trunc point ## time at risk in returned object is currently sum of (stop - start) ## default knot choice for spline - start + quantiles of log dt test_that("Left-truncation",{ set.seed(12082012) sim <- rgenf(3000, 1.5, 1, -0.4, 0.6) dead <- as.numeric(sim<=30) simt <- ifelse(sim<=30, sim, 30) obs <- simt>3; simt <- simt[obs]; dead <- dead[obs] fit <- flexsurvreg(Surv(simt, dead) ~ 1, dist="gengamma") summ <- summary(fit, ci=FALSE) expect_true(all(summ$time>3)) if (interactive()) plot(fit, ci=FALSE, xlim=c(0,10)) fit <- flexsurvreg(Surv(rep(3, length(simt)), simt, dead) ~ 1, dist="gengamma") if (interactive()) lines(fit, ci=FALSE, col="blue") # truncated model fits truncated data better. }) test_that("Interval censoring",{ set.seed(1) simt <- rweibull(1000, 2, 0.5) tmin <- simt status <- ifelse(simt>0.6, 0, 1) simt[status==0] <- 0.6 tmin <- simt tmax <- ifelse(status==1, simt, Inf) tmax.sr <- ifelse(status==1, simt, NA) sr1 <- survreg(Surv(tmin, tmax.sr, type="interval2") ~ 1, dist="weibull") sr2 <- survreg(Surv(tmin, status) ~ 1, dist="weibull") expect_equal(sr1$loglik[2], sr2$loglik[2]) fs1_inf <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="weibull") fs1_na <- flexsurvreg(Surv(tmin, tmax.sr, type="interval2") ~ 1, dist="weibull") fs2 <- flexsurvreg(Surv(simt, status) ~ 1, dist="weibull") expect_equal(fs1_inf$loglik, fs2$loglik) expect_equal(fs1_na$loglik, fs2$loglik) expect_equal(fs1_inf$loglik, sr1$loglik[2]) ## put an upper bound on censored times tmax <- ifelse(status==1, simt, 0.7) fs1 <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="weibull") fs2 <- flexsurvreg(Surv(simt, status) ~ 1, dist="weibull") expect_true(fs1$loglik != fs2$loglik) ## using type="interval" status[status==0] <- 3 fs3 <- flexsurvreg(Surv(tmin, tmax, status, type="interval") ~ 1, dist="weibull") expect_equal(fs1$loglik, fs3$loglik) ## interval censoring with zero width interval set.seed(1) tmin <- tmax <- rweibull(100, 1.1, 1.5) fs1 <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="weibull") fs2 <- flexsurvreg(Surv(tmin) ~ 1, dist="weibull") expect_equal(fs1$loglik, fs2$loglik) ## interval censoring close around the event set.seed(1) tev <- rweibull(100, 1.1, 1.5) tmin <- tev - 0.001 tmax <- tev + 0.001 fs1 <- flexsurvreg(Surv(tev) ~ 1, dist="weibull") fs2 <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="weibull") expect_equal(fs2$res["shape","est"], fs1$res["shape","est"], tol=1e-03) ## relative survival with left and interval censoring ## at left cens times, bhazard contains the background cond prob of surviving interval bh <- rep(0.01, length(tmax)) back_cdeath <- 1 - rep(exp(-0.002*0.01), length(tmax)) fs1 <- flexsurvreg(Surv(tev) ~ 1, dist="weibull", bhazard=bh) fs2 <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="weibull", bhazard=back_cdeath) fs1 <- flexsurvreg(Surv(tev) ~ 1, dist="weibull", bhazard=bh) fs2 <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="weibull", bhazard=back_cdeath, inits=c(1.24, 1.4)) expect_equal(fs2$res["shape","est"], fs1$res["shape","est"], tol=1e-03) }) test_that("inits",{ fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", inits=c(6,1,-1)) fitg2 <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma") expect_equal(fitg$loglik, fitg2$loglik, tolerance=1e-05) }) test_that("fixedpars",{ fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", fixedpars=1:2, inits=c(6,1,-1)) expect_equivalent(fitg$res[1:2,"est"], c(6,1)) expect_equivalent(fitg$res[1:2,"L95%"], c(NA_real_,NA_real_)) }) test_that("aux is ignored if it contains parameters",{ fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma") fitg2 <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", aux=list(sigma=1)) expect_equal(fitg$loglik, fitg2$loglik) }) test_that("cl",{ fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", cl=0.99) fitg2 <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", cl=0.999) expect_true(fitg2$res[1,2] < fitg$res[1,2]) expect_true(fitg2$res[1,3] > fitg$res[1,2]) }) test_that("Relative survival", { bc$bh <- rep(0.01, nrow(bc)) ## Compare with stata stgenreg, using Weibull PH model fs6b <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibullPH", bhazard=bh) expect_equal(log(fs6b$res[1,"est"]), 0.3268327417773233, tolerance=1e-05) expect_equal(log(fs6b$res[2,"est"]), -3.5308925743338038, tolerance=1e-05) expect_equal(fs6b$res["groupMedium","est"], 0.9343799681269026, tolerance=1e-04) expect_equal(fs6b$res["groupPoor","est"], 1.799204192587765, tolerance=1e-04) ## Check fit from 3 par model reduces to 1 par ## Deriv calculation bug causing false convergence fixed in 2.1 fshgg <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="gengamma", inits=c(1,1,1), fixedpars=2:3, bhazard=bh) fshe <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="exponential", bhazard=bh) fshw <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull", inits = c(1,10), fixedpars=1, bhazard=bh) expect_equal(fshgg$loglik, fshe$loglik, tolerance=1e-06) expect_equal(fshgg$loglik, fshw$loglik, tolerance=1e-06) ## same results as ## cd /home/chris/flexsurv/stata ## use stpm/bc ## gen rec = 1 - censrec ## gen recyrs = rectime / 365 ## gen bh = 0.01 ## stset recyrs, failure(censrec) ## stgenreg, loghazard([ln_lambda] :+ [ln_gamma] :+ (exp([ln_gamma]) :- 1) :* log(#t)) nodes(100) ln_lambda(group2 group3) bhazard(bh) ## Check we can convert from partial to full likelihood by adding the ## sum of the cumulative hazards mdl_0 <- flexsurvreg(Surv(time/365, status == 2) ~ 1, data = lung, dist = "exp") bhaz <- 0.1 mdl_1 <- flexsurvreg(Surv(time/365, status == 2) ~ 1, dist = "exp", data = lung, inits = mdl_0$res[, "est"] - bhaz, fixedpars = TRUE, bhazard = rep(bhaz, nrow(lung))) expect_equal(mdl_0$loglik, mdl_1$loglik - sum(bhaz * lung$time/365)) }) test_that("warning with strata", { ## need double backslash to escape $ expect_warning(flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ strata(ovarian$resid.ds), dist="gengamma", inits=c(6,1,-1,0)), "Ignoring \"strata\" function: interpreting \"ovarian\\$resid.ds\" as a covariate on \"mu\"") }) test_that("error with frailty() and offset()", { expect_error(flexsurvreg(formula = Surv(futime, fustat) ~ frailty(resid.ds), data="ovarian", dist="weibull"), "frailty models are not supported") expect_error(flexsurvreg(formula = Surv(futime, fustat) ~ offset(resid.ds), data="ovarian", dist="weibull"), "offset\\(\\) terms are not supported") }) test_that("Distribution names are case insensitive",{ fs1 = flexsurvreg(Surv(rectime, censrec)~group,dist="weibull",data=bc) fs2 = flexsurvreg(Surv(rectime, censrec)~group,dist="Weibull",data=bc) expect_equal(fs1$loglik, fs2$loglik, tolerance=1e-06) }) test_that("Weibull hazards from summary are reliable",{ fs1 = flexsurvreg(Surv(rectime, censrec)~group ,dist="weibull",data=bc) output = summary(fs1, t=seq(from=0,to=30000,length.out=100), ci=F, tidy=T) expect_true(all(is.finite(output$est))) }) test_that("No events in the data",{ set.seed(1) tmin <- rexp(100, 1) tmax <- tmin + 0.1 bhazard <- rep(0.0001, 100) mod <- flexsurvreg(Surv(tmin, tmax, type="interval2") ~ 1, dist="exponential") expect_equal(mod$loglik, -337.9815, tolerance=1e-03) modb <- flexsurvreg(Surv(tmin,tmax,type='interval2')~1, bhazard = 1 - exp(-bhazard*(tmax-tmin)), dist="exponential") expect_equal(mod$res["rate","est"], modb$res["rate","est"], tolerance=1e-02) }) test_that("No censoring in the data",{ bcev <- bc[bc$censrec==1,] mod <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bcev, dist="weibull") expect_equal(mod$loglik, -477.2455, tolerance=1e-03) }) test_that("summary type=quantile is consistent",{ expect_equal(summary(fitg, type='quantile', quantiles=.5)[[1]][1,2] ,summary(fitg, type='median')[[1]][1,1]) expect_equal(summary(fitg, type='quantile', quantiles=.5, start = 50)[[1]][1,2] ,summary(fitg, type='median', start = 50)[[1]][1,1]) }) test_that("Errors in summary type=quantile",{ expect_error(summary(fitg, type='quantile', quantiles=1.5), "Quantiles should not be less than 0 or greater than 1") expect_error(summary(fitg, type='quantile', quantiles=-.5), "Quantiles should not be less than 0 or greater than 1") }) test_that("SEs in summary function",{ expect_true(is.numeric(summary(fitg, se=TRUE)[[1]]$se)) }) test_that("summary type `link`",{ expect_equal(summary(fitg, type="link")[["factor(rx)=1"]]$est, fitg$res["scale","est"]) expect_equal(summary(fitg, type="link")[["factor(rx)=2"]]$est, exp(fitg$res.t["scale","est"] + fitg$res.t["factor(rx)2","est"])) }) test_that("With and without analytic Hessian", { fla <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="weibull") fln <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="weibull", hess.control = list(numeric=TRUE)) expect_true(all(fla$cov != fln$cov)) # analytic derivatives available fla <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma") fln <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma", hess.control = list(numeric=TRUE)) expect_equivalent(fla$cov, fln$cov) # analytic derivatives not available }) flexsurv/tests/testthat/test_survsplinek.R0000644000176200001440000003427614471605166020727 0ustar liggesusersgamma <- seq(1, 1.2, length.out=9) names(gamma) <- 0:8 test_that("mean_survsplinek",{ expect_equal(mean_survspline0(gamma["0"], gamma["1"]), mean_survspline(gamma[1:2])) expect_equal(mean_survspline1(gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,0)), mean_survspline(gamma[1:3], knots = c(-10,0,0))) expect_equal(mean_survspline2(gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,0,0)), mean_survspline(gamma[1:4], knots=c(-10,0,0,0))) expect_equal(mean_survspline3(gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,0,0,0)), mean_survspline(gamma[1:5], knots=c(-10,0,0,0,0))) expect_equal(mean_survspline4(gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,0,0,0,0)), mean_survspline(gamma[1:6], knots=c(-10,0,0,0,0,0))) expect_equal(mean_survspline5(gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,0,0,0,0,0)), mean_survspline(gamma[1:7], knots=c(-10,0,0,0,0,0,0))) expect_equal(mean_survspline6(gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,0,0,0,0,0,0)), mean_survspline(gamma[1:8], knots=c(-10,0,0,0,0,0,0,0))) expect_equal(mean_survspline7(gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,0,0,0,0,0,0,0)), mean_survspline(gamma[1:9], knots=c(-10,0,0,0,0,0,0,0,0))) }) test_that("rmst_survsplinek",{ t <- 1 expect_equal(rmst_survspline0(t=t, gamma["0"], gamma["1"]), rmst_survspline(t=t, gamma[1:2])) expect_equal(rmst_survspline1(t=t, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10)), rmst_survspline(t=t, gamma[1:3], knots = c(-10,0,10))) expect_equal(rmst_survspline2(t=t, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10)), rmst_survspline(t=t, gamma[1:4], knots=c(-10,0,1,10))) expect_equal(rmst_survspline3(t=t, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10)), rmst_survspline(t=t, gamma[1:5], knots=c(-10,0,1,2,10))) expect_equal(rmst_survspline4(t=t, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10)), rmst_survspline(t=t, gamma[1:6], knots=c(-10,0,1,2,3,10))) expect_equal(rmst_survspline5(t=t, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10)), rmst_survspline(t=t, gamma[1:7], knots=c(-10,0,1,2,3,4,10))) expect_equal(rmst_survspline6(t=t, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10)), rmst_survspline(t=t, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))) expect_equal(rmst_survspline7(t=t, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10)), rmst_survspline(t=t, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))) }) test_that("dsurvsplinek",{ x <- 1 expect_equal(dsurvspline0(x=x, gamma["0"], gamma["1"], knots=c(-10,10)), dsurvspline(x=x, gamma[1:2], knots=c(-10,10))) expect_equal(dsurvspline1(x=x, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10)), dsurvspline(x=x, gamma[1:3], knots = c(-10,0,10))) expect_equal(dsurvspline2(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10)), dsurvspline(x=x, gamma[1:4], knots=c(-10,0,1,10))) expect_equal(dsurvspline3(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10)), dsurvspline(x=x, gamma[1:5], knots=c(-10,0,1,2,10))) expect_equal(dsurvspline4(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10)), dsurvspline(x=x, gamma[1:6], knots=c(-10,0,1,2,3,10))) expect_equal(dsurvspline5(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10)), dsurvspline(x=x, gamma[1:7], knots=c(-10,0,1,2,3,4,10))) expect_equal(dsurvspline6(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10)), dsurvspline(x=x, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))) expect_equal(dsurvspline7(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10)), dsurvspline(x=x, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))) }) test_that("psurvsplinek",{ x <- 1 expect_equal(psurvspline0(q=x, gamma["0"], gamma["1"], knots=c(-10,10)), psurvspline(q=x, gamma[1:2], knots=c(-10,10))) expect_equal(psurvspline1(q=x, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10)), psurvspline(q=x, gamma[1:3], knots = c(-10,0,10))) expect_equal(psurvspline2(q=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10)), psurvspline(q=x, gamma[1:4], knots=c(-10,0,1,10))) expect_equal(psurvspline3(q=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10)), psurvspline(q=x, gamma[1:5], knots=c(-10,0,1,2,10))) expect_equal(psurvspline4(q=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10)), psurvspline(q=x, gamma[1:6], knots=c(-10,0,1,2,3,10))) expect_equal(psurvspline5(q=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10)), psurvspline(q=x, gamma[1:7], knots=c(-10,0,1,2,3,4,10))) expect_equal(psurvspline6(q=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10)), psurvspline(q=x, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))) expect_equal(psurvspline7(q=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10)), psurvspline(q=x, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))) }) if (covr::in_covr()){ # these are slow test_that("qsurvsplinek",{ p <- 0.4 expect_equal(qsurvspline0(p=p, gamma["0"], gamma["1"], knots=c(-10,10)), qsurvspline(p=p, gamma[1:2], knots=c(-10,10))) expect_equal(qsurvspline1(p=p, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10)), qsurvspline(p=p, gamma[1:3], knots = c(-10,0,10))) expect_equal(qsurvspline2(p=p, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10)), qsurvspline(p=p, gamma[1:4], knots=c(-10,0,1,10))) expect_equal(qsurvspline3(p=p, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10)), qsurvspline(p=p, gamma[1:5], knots=c(-10,0,1,2,10))) expect_equal(qsurvspline4(p=p, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10)), qsurvspline(p=p, gamma[1:6], knots=c(-10,0,1,2,3,10))) expect_equal(qsurvspline5(p=p, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10)), qsurvspline(p=p, gamma[1:7], knots=c(-10,0,1,2,3,4,10))) expect_equal(qsurvspline6(p=p, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10)), qsurvspline(p=p, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))) expect_equal(qsurvspline7(p=p, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10)), qsurvspline(p=p, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))) }) test_that("rsurvsplinek",{ expect_equal({set.seed(1); rsurvspline0(n=1, gamma["0"], gamma["1"], knots=c(-10,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:2], knots=c(-10,10))}) expect_equal({set.seed(1); rsurvspline1(n=1, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:3], knots = c(-10,0,10))}) expect_equal({set.seed(1); rsurvspline2(n=1, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:4], knots=c(-10,0,1,10))}) expect_equal({set.seed(1); rsurvspline3(n=1, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:5], knots=c(-10,0,1,2,10))}) expect_equal({set.seed(1); rsurvspline4(n=1, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:6], knots=c(-10,0,1,2,3,10))}) expect_equal({set.seed(1); rsurvspline5(n=1, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:7], knots=c(-10,0,1,2,3,4,10))}) expect_equal({set.seed(1); rsurvspline6(n=1, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))}) expect_equal({set.seed(1); rsurvspline7(n=1, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10))}, {set.seed(1); rsurvspline(n=1, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))}) }) } test_that("hsurvsplinek",{ x <- 1 expect_equal(hsurvspline0(x=x, gamma["0"], gamma["1"], knots=c(-10,10)), hsurvspline(x=x, gamma[1:2], knots=c(-10,10))) expect_equal(hsurvspline1(x=x, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10)), hsurvspline(x=x, gamma[1:3], knots = c(-10,0,10))) expect_equal(hsurvspline2(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10)), hsurvspline(x=x, gamma[1:4], knots=c(-10,0,1,10))) expect_equal(hsurvspline3(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10)), hsurvspline(x=x, gamma[1:5], knots=c(-10,0,1,2,10))) expect_equal(hsurvspline4(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10)), hsurvspline(x=x, gamma[1:6], knots=c(-10,0,1,2,3,10))) expect_equal(hsurvspline5(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10)), hsurvspline(x=x, gamma[1:7], knots=c(-10,0,1,2,3,4,10))) expect_equal(hsurvspline6(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10)), hsurvspline(x=x, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))) expect_equal(hsurvspline7(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10)), hsurvspline(x=x, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))) }) test_that("Hsurvsplinek",{ x <- 1 expect_equal(Hsurvspline0(x=x, gamma["0"], gamma["1"], knots=c(-10,10)), Hsurvspline(x=x, gamma[1:2], knots=c(-10,10))) expect_equal(Hsurvspline1(x=x, gamma["0"], gamma["1"], gamma["2"], knots = c(-10,0,10)), Hsurvspline(x=x, gamma[1:3], knots = c(-10,0,10))) expect_equal(Hsurvspline2(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], knots=c(-10,0,1,10)), Hsurvspline(x=x, gamma[1:4], knots=c(-10,0,1,10))) expect_equal(Hsurvspline3(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], knots=c(-10,0,1,2,10)), Hsurvspline(x=x, gamma[1:5], knots=c(-10,0,1,2,10))) expect_equal(Hsurvspline4(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], knots=c(-10,0,1,2,3,10)), Hsurvspline(x=x, gamma[1:6], knots=c(-10,0,1,2,3,10))) expect_equal(Hsurvspline5(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], knots=c(-10,0,1,2,3,4,10)), Hsurvspline(x=x, gamma[1:7], knots=c(-10,0,1,2,3,4,10))) expect_equal(Hsurvspline6(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], knots=c(-10,0,1,2,3,4,5,10)), Hsurvspline(x=x, gamma[1:8], knots=c(-10,0,1,2,3,4,5,10))) expect_equal(Hsurvspline7(x=x, gamma["0"], gamma["1"], gamma["2"], gamma["3"], gamma["4"], gamma["5"], gamma["6"], gamma["7"], gamma["8"], knots=c(-10,0,1,2,3,4,5,6,10)), Hsurvspline(x=x, gamma[1:9], knots=c(-10,0,1,2,3,4,5,6,10))) }) flexsurv/tests/testthat/test_genf_orig.R0000644000176200001440000000353113231112051020242 0ustar liggesuserscontext("Testing generalized F (original)") tol <- 1e-06 test_that("Generalized F (original)",{ expect_equal(dgenf.orig(c(-1,1,2,3,4), mu=0, sigma=1, s1=1, s2=1), c(0, 0.25, 0.111111111111111, 0.0625, 0.04)) x <- c(-1,0,1,2,3,4); mu <- 0.1; sigma <- 1.2; s1 <- 1.7; s2 <- 10000000 dgenf.orig(x, mu=mu, sigma=sigma, s1=s1, s2=s2) dgengamma.orig(x, shape=1/sigma, scale=exp(mu) / s1^sigma, k=s1) # equal for large s2 expect_equal(pgenf.orig(c(-1,0,1,2,3,4), mu=0, sigma=1, s1=1, s2=1), c(0, 0, 0.5, 0.666666666666667, 0.75, 0.8)) x <- c(-1,0,1,2,3,4); mu <- 0.1; sigma <- 1.2; s1 <- 1.7; s2 <- 10000000 pgenf.orig(x, mu=mu, sigma=sigma, s1=s1, s2=s2) pgengamma.orig(x, shape=1/sigma, scale=exp(mu) / s1^sigma, k=s1) # equal for large s2 expect_equal(qgenf.orig(p=0.25, mu=0, sigma=1, s1=1, s2=1), 0.333333333333333) expect_equal(qgenf.orig(p=0.25, mu=0, sigma=1, s1=1, s2=1), qgeneric(pgenf.orig, p=0.25, mu=0, sigma=1, s1=1, s2=1)) expect_equal(qgenf.orig(p=0, mu=0, sigma=1, s1=1, s2=1), 0) expect_equal(qgenf.orig(pgenf.orig(q=c(-2,-1,0,1,2,3,4), mu=0, sigma=1, s1=1, s2=1), mu=0, sigma=1, s1=1, s2=1), c(0,0,0,1,2,3,4)) x <- c(0.1, 0.4, 0.7); mu <- 0.1; sigma <- 1.2; s1 <- 1.7; s2 <- 10000000 qgenf.orig(x, mu=mu, sigma=sigma, s1=s1, s2=s2) hgenf.orig(x, mu=mu, sigma=sigma, s1=s1, s2=s2) qgengamma.orig(x, shape=1/sigma, scale=exp(mu) / s1^sigma, k=s1) # equal for large s2 expect_error(Hgenf.orig(x, mu=mu, sigma=sigma, s1=s1), "argument \"s2\" is missing") rgenf.orig(n=10, mu=0, sigma=1, s1=1, s2=1) if (interactive()) { mu <- 0.1; sigma <- 1.2; s1 <- 1.7; s2 <- 100000000 plot(density(rgenf.orig(10000, mu=mu, sigma=sigma, s1=s1, s2=s2))) lines(density(rgengamma.orig(10000, shape=1/sigma, scale=exp(mu) / s1^sigma, k=s1)), lty=2) } }) flexsurv/tests/testthat/test_mstate.R0000644000176200001440000002235714623351645017633 0ustar liggesuserscontext("Multi-state modelling and prediction") bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) tgrid <- seq(0,14,by=0.1) bwei <- flexsurvreg(Surv(years, status) ~ trans + shape(trans), data=bosms3, dist="weibull") bspl <- flexsurvspline(Surv(years, status) ~ trans + gamma1(trans), data=bosms3, k=3) bexp.markov <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, data=bosms3, dist="exp") bln.markov <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, data=bosms3, dist="lnorm") test_that("msfit.flexsurvreg",{ mexp <- msfit.flexsurvreg(bexp, t=0.01, trans=tmat, tvar="trans") summ <- summary(bexp, t=0.01, type="cumhaz", ci=FALSE, newdata=list(trans=factor(1:3, levels=1:3))) summ <- as.numeric(unlist(lapply(summ, function(x)x$est[x$time==0.01]))) expect_equal(mexp$Haz$Haz[mexp$Haz$time==0.01], summ) mwei <- msfit.flexsurvreg(bwei, t=c(0.01, 0.02), trans=tmat, tvar="trans", B=10) mspl <- msfit.flexsurvreg(bspl, t=c(0.01, 0.02), trans=tmat, tvar="trans", B=10) }) ## With covariates suppressWarnings(RNGversion("3.5.0")) set.seed(1) bosms3$x <- rnorm(nrow(bosms3)) bexp.cov <- flexsurvreg(Surv(years, status) ~ trans + x, data=bosms3, dist="exp") bexp.markov.cov <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans + x, data=bosms3, dist="exp") test_that("newdata in msfit.flexsurvreg",{ expect_error({ msfit.flexsurvreg(bexp.cov, newdata=list(x=1), t=c(0,5,10), trans=tmat, variance=FALSE) msfit.flexsurvreg(bexp.cov, newdata=list(x=2), t=c(0,5,10), trans=tmat, variance=FALSE) msfit.flexsurvreg(bexp.cov, newdata=list(x=c(1,2,3)), t=c(0,5,10), trans=tmat, variance=FALSE) }, NA) }) test_that("Errors in msfit.flexsurvreg",{ expect_error(msfit.flexsurvreg(bexp.cov, t=seq(0,150,10), trans=tmat), "Value.* of covariate.* .+ not supplied") expect_error(msfit.flexsurvreg(bexp.cov, t=seq(0,150,10), trans=tmat, tvar="foo"), "variable .* not in model") expect_error(msfit.flexsurvreg(bexp.cov, newdata=list(x=c(1,2)), t=c(0,5,10), trans=tmat, variance=FALSE), "length of variables .+ must be") }) test_that("pmatrix.fs",{ pmat <- pmatrix.fs(bexp.markov, t=c(5,10), trans=tmat) expect_equal(pmat$"5"[1,2], 0.267218506920585, tolerance=1e-04) pmat <- pmatrix.fs(bexp.markov.cov, t=c(5,10), trans=tmat, newdata=list(x=1)) expect_equal(pmat$"5"[1,2], 0.259065437633427, tolerance=1e-04) }) test_that("totlos.fs for flexsurvreg objects",{ tl <- totlos.fs(bexp.markov, t=c(5), trans=tmat) expect_equal(as.numeric(tl), c(2.89231556324412, 0, 0, 1.06822543404334, 2.77639174263866, 0, 1.03945900271255, 2.22360825736133, 5), tolerance=1e-06) tl <- totlos.fs(bexp.markov.cov, t=c(5), trans=tmat, newdata=list(x=1)) expect_equal(as.numeric(tl), c(2.76115934740386, 0, 0, 1.08844199049896, 2.64568022609759, 0, 1.15039866209718, 2.35431977390241, 5)) tl <- totlos.fs(bexp.markov, t=c(5,10), trans=tmat) expect_equal(as.numeric(tl[[1]]), c(2.89231557124359, 0, 0, 1.06822540869797, 2.77639177178247, 0, 1.03945902005845, 2.22360822821753, 5)) tl <- totlos.fs(bexp.markov.cov, t=c(5,10), trans=tmat, newdata=list(x=1)) expect_equal(as.numeric(tl[[1]]),c(2.76115934740386, 0, 0, 1.08844199049896, 2.64568022609759, 0, 1.15039866209718, 2.35431977390241, 5)) attr(tl, "P") }) test_that("pmatrix.simfs for flexsurvreg objects",{ expect_error({ pmatrix.simfs(bwei, t=5, trans=tmat, M=100) pmatrix.simfs(bexp.cov, t=5, trans=tmat, newdata=list(x=1), M=100) }, NA) dimnames(tmat) <- rep(list(paste("State",1:3)),2) set.seed(1) p5 <- pmatrix.simfs(bexp, t=5, trans=tmat, M=1000) p10 <- pmatrix.simfs(bexp, t=10, trans=tmat, M=1000) pboth <- pmatrix.simfs(bexp, t=c(0, 5,10), trans=tmat) expect_equivalent(p5, pboth[,,"5"], tol=0.1) (p5 <- pmatrix.simfs(bexp, t=5, trans=tmat, ci=TRUE, M=100, B=3)) expect_gt(p5[1,1], attr(p5,"lower")[1,1]) set.seed(1) (pboth <- pmatrix.simfs(bexp, t=c(0, 5,10), trans=tmat, ci=TRUE, M=1000, B=3)) expect_gt(pboth[1,1,"5"], attr(pboth,"lower")[1,1,"5"]) set.seed(1) (pt <- pmatrix.simfs(bexp, t=c(0, 5,10), trans=tmat, ci=TRUE, M=1000, B=3, tidy=TRUE)) expect_equal(pboth[1,2,"5"], pt[pt$from=="State 1" & pt$to=="State 2" & pt$t==5, "p"]) expect_equal(attr(pboth,"lower")[1,2,"5"], pt[pt$from=="State 1" & pt$to=="State 2" & pt$t==5, "lower"]) expect_equal(attr(pboth,"upper")[1,2,"5"], pt[pt$from=="State 1" & pt$to=="State 2" & pt$t==5, "upper"]) }) test_that("totlos.simfs for flexsurvreg objects",{ expect_error({ totlos.simfs(bexp, t=5, trans=tmat, M=100) totlos.simfs(bwei, t=5, trans=tmat, M=100) totlos.simfs(bexp.cov, t=5, trans=tmat, newdata=list(x=1), M=100) totlos.simfs(bexp, t=5, trans=tmat, M=100) totlos.simfs(bwei, t=5, trans=tmat, M=100) totlos.simfs(bexp.cov, t=5, trans=tmat, newdata=list(x=1), M=100) }, NA) }) ### List format for independent transition-specific models bwei.list <- bweic.list <- bweim.list <- bexpc.list <- vector(3, mode="list") for (i in 1:3) { bwei.list[[i]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==i), data = bosms3, dist = "weibull") bweic.list[[i]] <- flexsurvreg(Surv(years, status) ~ x, subset=(trans==i), data = bosms3, dist = "weibull") bweim.list[[i]] <- flexsurvreg(Surv(Tstart, Tstop, status) ~ 1, subset=(trans==i), data=bosms3, dist="weibull") bexpc.list[[i]] <- flexsurvreg(Surv(years, status) ~ x, subset=(trans==i), data=bosms3, dist="exp") } test_that("multistate output functions for list of models objects", { set.seed(1) totlos.simfs(bwei.list, t=5, trans=tmat, M=10) totlos.simfs(bweic.list, t=5, trans=tmat, M=100, newdata=list(x=0)) totlos.simfs(bweic.list, t=5, trans=tmat, M=100, newdata=list(x=0), tcovs="x") pmatrix.simfs(bwei.list, t=5, trans=tmat, M=100) pmatrix.simfs(bweic.list, t=10, trans=tmat, M=10000, newdata=list(x=0), tcovs="x") set.seed(1) pnt <- pmatrix.simfs(bweic.list, t=5, trans=tmat, M=100, newdata=list(x=0)) set.seed(1) pt <- pmatrix.simfs(bweic.list, t=c(5), trans=tmat, M=100, newdata=list(x=0), tidy=TRUE) expect_equal(pnt[1,2], pt$p[pt$from=="1" & pt$to=="2" & pt$t==5]) pmatrix.fs(bweim.list, t=5, trans=tmat) pmatrix.fs(bweim.list, t=c(5,10), trans=tmat) pmat1 <- pmatrix.fs(bweic.list, t=c(5,10), trans=tmat, newdata=list(x=-1)) pmat3 <- pmatrix.fs(bweic.list, t=c(5,10), trans=tmat, newdata=list(x=c(-1,-1,-1))) expect_equal(pmat1[[1]], pmat3[[1]]) expect_error(pmatrix.fs(bweic.list, t=c(5,10), trans=tmat, newdata=list(x=c(-1,-1))), "must either have one row, or one row for each of the 3 allowed transitions") pmatrix.fs(bln.markov, t=5, trans=tmat) totlos.fs(bweim.list, t=5, trans=tmat) totlos.fs(bln.markov, t=5, trans=tmat) }) test_that("list and non-list format give same estimates", { expect_equal( as.numeric(pars.fmsm(bwei, trans=tmat)[[1]]), as.numeric(pars.fmsm(bwei.list, trans=tmat)[[1]]), tolerance=1e-04) bexpci <- flexsurvreg(Surv(years, status) ~ trans*x, data=bosms3, dist="exp") expect_equal( as.numeric(pars.fmsm(bexpci, newdata=list(x=1), trans=tmat)[[2]]), as.numeric(pars.fmsm(bexpc.list, newdata=list(x=1), trans=tmat)[[2]]), tolerance=1e-05) expect_equal(pmatrix.fs(bwei, trans=tmat), pmatrix.fs(bwei.list, trans=tmat), tolerance=1e-04) expect_equal(totlos.fs(bwei, trans=tmat), totlos.fs(bwei.list, trans=tmat), tolerance=1e-04) expect_equal(msfit.flexsurvreg(bwei, trans=tmat, t=1:10, variance=FALSE), msfit.flexsurvreg(bwei.list, trans=tmat, t=1:10, variance=FALSE), tolerance=1e-04) expect_equal(msfit.flexsurvreg(bexpci, newdata=list(x=1), trans=tmat, t=1:10, variance=FALSE), msfit.flexsurvreg(bexpc.list, newdata=list(x=1), trans=tmat, t=1:10, variance=FALSE), tolerance=1e-05) }) test_that("different model families for different transitions", { blist <- vector(3, mode="list") blist[[1]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data=bosms3, dist="exp") blist[[2]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data=bosms3, dist="gamma") blist[[3]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==3), data=bosms3, dist="weibull") expect_equal(pmatrix.fs(blist, t=c(5,10), trans=tmat)$`5`[1,2], 0.2423839, tolerance=1e-04) expect_equal(totlos.fs(blist, trans=tmat)[1,2], 0.08277735, tolerance=1e-04) blistx <- vector(3, mode="list") blistx[[1]] <- flexsurvreg(Surv(years, status) ~ x, subset=(trans==1), data=bosms3, dist="exp") blistx[[2]] <- flexsurvreg(Surv(years, status) ~ x, subset=(trans==2), data=bosms3, dist="gamma") blistx[[3]] <- flexsurvreg(Surv(years, status) ~ x, subset=(trans==3), data=bosms3, dist="weibull") expect_equal(pmatrix.fs(blistx, t=c(5,10), trans=tmat, newdata=list(x=1))$`5`[1,2], 0.2291726, tolerance=1e-04) expect_equal(totlos.fs(blistx, trans=tmat, newdata=list(x=1))[1,2],0.08698692 , tolerance=1e-04) }) flexsurv/tests/testthat/test_fmixmsm.R0000644000176200001440000000555314272447617020022 0ustar liggesuserstest_that("fmixmsm state pathways: basic competing risks",{ tbl_data <- data.frame( to = factor(1:3, levels = 1:3, labels = c("response", "progression", "death")), dt = rep(1, 3), status = rep(1, 3)) fit1 <- flexsurvmix(Surv(dt, status) ~ 1, event = tbl_data$to, data = tbl_data, dists = c("response" = "exponential", "progression" = "exponential", "death" = "exponential")) fit <- fmixmsm("stable" = fit1) expect_equivalent(attr(fit, "pathways"), list(c("stable", "response"), c("stable", "progression"), c("stable", "death"))) }) test_that("fmixmsm state pathways: multiple routes to same absorbing state",{ tbl_data <- data.frame( to = factor(1:3, levels = 1:3, labels = c("response", "progression", "death")), dt = rep(1, 3), status = rep(1, 3)) fit1 <- flexsurvmix(Surv(dt, status) ~ 1, event = tbl_data$to, data = tbl_data, dists = c("response" = "exponential", "progression" = "exponential", "death" = "exponential")) tbl_data <- data.frame( to = factor(1:2, levels = 1:2, labels = c("progression", "death")), dt = rep(1, 2), status = rep(1, 2)) fit2 <- flexsurvmix(Surv(dt, status) ~ 1, event = tbl_data$to, data = tbl_data, dists = c("progression" = "exponential", "death" = "exponential")) tbl_data <- data.frame( to = factor(1:1, levels = 1:1, labels = c("death")), dt = rep(1, 1), status = rep(1, 1)) fit3 <- flexsurvmix( Surv(dt, status) ~ 1, event = tbl_data$to, data = tbl_data, dists = c("death" = "exponential")) fit <- fmixmsm("stable" = fit1, "response" = fit2, "progression" = fit3) expect_equivalent(attr(fit, "pathways"), list(c("stable", "response", "progression", "death"), c("stable", "response", "death"), c("stable", "progression", "death"), c("stable", "death"))) expect_false(attr(fit, "cycle")) }) test_that("fmixmsm state pathways: cycles",{ tbl_data <- data.frame( to = factor(1:3, levels = 1:3, labels = c("response", "progression", "death")), dt = rep(1, 3), status = rep(1, 3)) fit1 <- flexsurvmix(Surv(dt, status) ~ 1, event = tbl_data$to, data = tbl_data, dists = c("response" = "exponential", "progression" = "exponential", "death" = "exponential")) tbl_data <- data.frame( to = factor(1:2, levels = 1:2, labels = c("progression", "stable")), dt = rep(1, 2), status = rep(1, 2)) fit2 <- flexsurvmix(Surv(dt, status) ~ 1, event = tbl_data$to, data = tbl_data, dists = c("progression" = "exponential", "stable" = "exponential")) fit <- fmixmsm("stable" = fit1, "response" = fit2) expect_true(attr(fit, "cycle")) }) flexsurv/tests/testthat/test_utils.R0000644000176200001440000000770514472137051017471 0ustar liggesuserscontext("Distribution functions and utilities") ## note - standard q fns in R return zero for p=0 for positive dists, but -Inf for real dists. tol <- 1e-06 test_that("Exponential hazards",{ expect_equal(hexp(c(-Inf, NaN, Inf, NA, -1, 0, 1), c(1,2,3)), c(0,NaN,3,NA,0,3,1)) expect_equal(hexp(c(-Inf, NaN, Inf, NA, -1, 0, 1), c(1,2,3), log=TRUE), log(c(0,NaN,3,NA,0,3,1))) expect_equal(Hexp(c(-Inf, NaN, Inf, NA, -1, 0, 1, 2, 4), c(1,2,3)), c(0,NaN,Inf, NA,0,0, 1, 4, 12)) expect_equal(Hexp(c(-Inf, NaN, Inf, NA, -1, 0, 1, 2, 4), c(1,2,3), log=TRUE), log(c(0,NaN,Inf, NA,0,0, 1, 4, 12))) expect_equal(dexp(c(1,2,3), c(2,3,4)) / (1 - pexp(c(1,2,3), c(2,3,4))), hexp(c(1,2,3), c(2,3,4))) expect_equal(-log(1 - pexp(c(1,2,3), c(2,3,4))), Hexp(c(1,2,3), c(2,3,4))) expect_equal(log(-log(1 - pexp(c(1,2,3), c(2,3,4)))), Hexp(c(1,2,3), c(2,3,4), log=TRUE)) expect_warning(hexp(c(1,1,1), c(-1, 0, 2)), "Negative rate") expect_warning(dexp(c(1,1,1), c(-1, 0, 2)), "NaNs produced") }) test_that("Weibull hazards",{ expect_equal(hweibull(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)), dweibull(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)) / (1 - pweibull(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)))) expect_equal(Hweibull(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3)), -pweibull(c(1,1,1,1), c(1,1,2,2), c(1,3,1,3), lower.tail=FALSE, log.p=TRUE)) ## exponential reduction expect_equal(hweibull(c(-Inf, NaN, Inf, NA, -1, 0, 1), c(1,1,1), c(1,2,3)), c(0,NaN,1/3,NA,0,1/3,1)) ### positive shape, increasing hweibull(c(-Inf, -1, 0, 1, 2, Inf), 2, 2.5) ### neg shape, decreasing hweibull(c(-Inf, -1, 0, 1, 2, Inf), 0.5, 1) expect_equal(Hexp(c(-Inf, NaN, Inf, NA, -1, 0, 1, 2, 4), c(1,2,3)), c(0,NaN,Inf, NA,0,0, 1, 4, 12)) }) test_that("Log-normal hazards",{ expect_equal(hlnorm(1, 2, 3, log=TRUE), log(hlnorm(1,2,3,log=FALSE))) expect_equal(Hlnorm(1, 2, 3, log=TRUE), log(-log(1 - plnorm(1,2,3,log=FALSE)))) }) test_that("Gamma hazards",{ expect_equal(hgamma(1, 2, 3, log=TRUE), log(hgamma(1,2,3,log=FALSE))) expect_equal(Hgamma(1, 2, 3, log=TRUE), log(-log(1 - pgamma(1,2,3,log=FALSE)))) }) test_that("WeibullPH",{ a <- 0.1; m <- 2 b <- m^(-1/a) x <- c(-Inf, NaN, NA, -1, 0, 1, 2, Inf) expect_equal(dweibullPH(x, a, m), dweibull(x, a, b)) expect_equal(dweibullPH(x, a, m), dweibull(x, a, b), log=TRUE) expect_equal(pweibullPH(x, a, m), pweibull(x, a, b)) expect_equal(pweibullPH(x, a, m), pweibull(x, a, b), log.p=TRUE) expect_equal(pweibullPH(x, a, m), pweibull(x, a, b), lower.tail=FALSE) qq <- c(0, 0.5, 0.7, 1) expect_equal(qweibullPH(qq, a, m), qweibull(qq, a, b)) expect_equal(hweibullPH(x, a, m), hweibull(x, a, b)) expect_equal(hweibullPH(x, a, m), hweibull(x, a, b), log=TRUE) expect_equal(HweibullPH(x, a, m), Hweibull(x, a, b)) expect_equal(HweibullPH(x, a, m), Hweibull(x, a, b), log=TRUE) set.seed(1); x1 <- rweibull(10, a, b) set.seed(1); x2 <- rweibullPH(10, a, m) expect_equal(x1, x2) fitw <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ rx, data = ovarian, dist="weibull") fitwp <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ rx, data = ovarian, dist="weibullPH") expect_equal(fitw$res["shape","est"], fitwp$res["shape","est"], tolerance=1e-06) expect_equal(fitw$res["scale","est"], fitwp$res["scale","est"]^(-1/fitwp$res["shape","est"]), tolerance=1e-05) expect_equal(coef(fitw)["rx"], -coef(fitwp)["rx"] / fitwp$res["shape","est"]) }) test_that("rmst_generic",{ expect_equal(rmst_lnorm(500, start=250, meanlog=7.4225, sdlog = 1.1138), rmst_generic(plnorm, t=500, start=250, meanlog=7.4225, sdlog = 1.1138)) }) #implemented in C++ test_that("exph",{ exph_r <- function(y)(y + sqrt(y^2 + 1)) dexph_r <- function(y)(1 + y / sqrt(y^2 + 1)) expect_equal(exph(1.1), exph_r(1.1)) expect_equal(dexph(1.1), dexph_r(1.1)) }) flexsurv/tests/testthat/test_fmixmsm_outputs.R0000644000176200001440000000705714471606611021616 0ustar liggesusersif (!identical(Sys.getenv("NOT_CRAN"), "true")) return() ## simulate events following hospital n <- 1000 set.seed(1) x <- rnorm(n) y <- rbinom(n, 1, 0.5) events <- c("icu","death","discharge") pbase <- c(0.2, 0.3, 0.5) event <- numeric(n) for (i in 1:n){ p <- pmnlogit(qmnlogit(pbase) + 2*x[i] + 3*y[i]) event[i] <- sample(events, size=1, prob=p, replace=TRUE) } t <- numeric(n) t[event=="death"] <- rgamma(sum(event=="death"), 2.5, 1.2) t[event=="discharge"] <- rgamma(sum(event=="discharge"), 3.5, 0.6) t[event=="icu"] <- rgamma(sum(event=="icu"), 1, 3.2) cens <- as.numeric(t > 3) t[cens] <- 3 status <- 1 - cens dat <- data.frame(t, status, x, y, event) ## model for event following hospital fhosp <- flexsurvmix(Surv(t, status) ~ x, pformula = ~x + y, data=dat, event=event, dists=c("gamma","gamma","gamma")) ## simulate events following ICU nicu <- sum(dat$event=="icu") picu <- c(0.4, 0.6) set.seed(1) evicu <- sample(c("death","discharge"), size=nicu, prob=picu, replace=TRUE) ti <- numeric(nicu) ti[evicu=="death"] <- rgamma(sum(evicu=="death"), 1.5, 1) ti[evicu=="discharge"] <- rgamma(sum(evicu=="discharge"), 0.5, 3) censi <- as.numeric(ti > 1) ti[censi] <- 1 statusi <- 1 - censi dati <- data.frame(ti, statusi, evicu) ## model for event following ICU ficu <- flexsurvmix(Surv(ti, statusi) ~ 1, data=dati, event=evicu, dists=c("gamma","gamma")) ## Construct multi-state model object fm <- fmixmsm("hospital"=fhosp, "icu"=ficu) nd <- data.frame(x=c(0,0.02), y=c(0,0.01)) test_that("ppath_fmixmsm",{ probh <- probs_flexsurvmix(fhosp) probi <- probs_flexsurvmix(ficu) pp <- ppath_fmixmsm(fm) expect_equal( probh$val[probh$event=="icu"] * probi$val[probi$event=="death"], pp$val[pp$pathway=="hospital-icu-death"] ) ppath_fmixmsm(fm, final=TRUE) probh <- probs_flexsurvmix(fhosp,newdata=nd) probi <- probs_flexsurvmix(ficu,newdata=nd) pp <- ppath_fmixmsm(fm, newdata=nd) expect_equal( probh$val[probh$event=="icu" & probh$x==0.02 & probh$y==0.01] * probi$val[probi$event=="death" & probi$x==0.02 & probi$y==0.01], pp$val[pp$pathway=="hospital-icu-death" & pp$x==0.02 & pp$y==0.01] ) ppath_fmixmsm(fm, newdata=nd, final=TRUE) expect_true(is.numeric(ppath_fmixmsm(fm, B=3)$lower)) expect_true(is.numeric(ppath_fmixmsm(fm, final=TRUE, B=3)$lower)) expect_true(is.numeric(ppath_fmixmsm(fm, newdata=nd, B=3)$lower)) expect_true(is.numeric(ppath_fmixmsm(fm, newdata=nd, final=TRUE, B=3)$lower)) }) test_that("meanfinal_fmixmsm",{ meanfinal_fmixmsm(fm) meanfinal_fmixmsm(fm, final=TRUE) meanfinal_fmixmsm(fm, newdata=nd) meanfinal_fmixmsm(fm, newdata=nd, final=TRUE) expect_true(is.numeric(meanfinal_fmixmsm(fm, B=3)$lower)) expect_true(is.numeric(meanfinal_fmixmsm(fm, final=TRUE, B=3)$lower)) expect_true(is.numeric(meanfinal_fmixmsm(fm, newdata=nd, B=3)$lower)) expect_true(is.numeric(meanfinal_fmixmsm(fm, newdata=nd, final=TRUE, B=3)$lower)) }) if (covr::in_covr()){ test_that("qfinal_fmixmsm",{ expect_error({ qfinal_fmixmsm(fm, newdata=nd) qfinal_fmixmsm(fm, newdata=nd, final=TRUE) qfinal_fmixmsm(fm, newdata=nd, probs=c(0.25, 0.75)) qfinal_fmixmsm(fm, newdata=nd, probs=c(0.25, 0.75), final=TRUE) qfinal_fmixmsm(fm, newdata=nd, B=10) qfinal_fmixmsm(fm, newdata=nd, B=10, final=TRUE) qfinal_fmixmsm(fm, newdata=nd, n=100, B=10) qfinal_fmixmsm(fm, newdata=nd, n=100, B=10, final=TRUE) }, NA) }) } flexsurv/tests/testthat/test_simulate.R0000644000176200001440000000237414632520504020146 0ustar liggesusersfit <- flexsurvreg(formula = Surv(futime, fustat) ~ rx, data = ovarian, dist="weibull") nd <- data.frame(rx=1:2) test_that("simulate.flexsurvreg",{ sim <- simulate(fit) expect_true(nrow(sim)==nrow(ovarian)) sim <- simulate(fit, newdata=nd) expect_true(all(sim$time_1 > 0)) sim <- simulate(fit, seed=1002, newdata=nd) expect_equal(sim$time_1, c(575, 2392), tolerance=1) sim <- simulate(fit, seed=1002, newdata=nd, nsim=5) expect_true(all(sim$time_2 > 0)) sim <- simulate(fit, seed=1002, newdata=nd, nsim=5, censtime = 1000, tidy=TRUE) expect_equal(sim$event[sim$time==1000], rep(0, 5)) sim <- simulate(fit, seed=1002, newdata=nd, nsim=5, censtime = c(500,1000), tidy=TRUE) expect_equal(sim$event, c(0,0,0,1,1,0,0,0,1,0)) sim <- simulate(fit, seed=1002, newdata=nd, start=500, tidy=TRUE) expect_true(all(sim$time > 500)) sim <- simulate(fit, seed=1002, newdata=nd, start=c(500,700), tidy=TRUE) expect_true(all(sim$time > 500)) }) test_that("simulate.flexsurvreg with left truncation",{ fit <- flexsurvreg(formula = Surv(futime, fustat) ~ rx, data = ovarian, dist="weibull") nd <- ovarian sim <- simulate(fit, seed=1003, newdata=nd, nsim = 20, start = nd$futime) expect_true(all(sim[,1:20] > nd$futime)) }) flexsurv/tests/testthat/test-broom.R0000644000176200001440000000247014434176644017370 0ustar liggesuserstest_that("check tidy", { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") expect_equal( tidy(fitw, transform = 'baseline.real')$estimate, coef(fitw) ) }) test_that("check tidy against survreg", { fit_fs <- flexsurvreg(Surv(futime, fustat) ~ ecog.ps, data = ovarian, dist = "weibull") fit_sr <- survreg(Surv(futime, fustat) ~ ecog.ps, data = ovarian, dist = "weibull") expect_equal( object = as.data.frame(tidy(fit_fs)[3, ]), expected = as.data.frame(broom::tidy(fit_sr)[2, ]), tolerance = 1e-6 ) }) test_that("check glance", { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") gl <- glance(fitw) expect_equal(gl$N, fitw$N) expect_equal(gl$events, fitw$events) expect_equal(gl$trisk, fitw$trisk) expect_equal(gl$df, fitw$npars) expect_equal(gl$logLik, fitw$loglik) expect_equal(gl$AIC, fitw$AIC) expect_equal(gl$BIC, BIC(fitw)) }) test_that("check augment", { fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") expect_equal(augment(fitw)$.pred_time, predict(fitw)$.pred_time) expect_equal(augment(fitw)$.resid, residuals(fitw)) }) flexsurv/tests/testthat/test_standsurv.R0000644000176200001440000004227014554246735020371 0ustar liggesuserstest_that('survival predictions', { fitw <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") # Single time predictions ss <- standsurv(fitw, at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4) s <- summary(fitw, tidy = TRUE, type = 'survival', t = 4, ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est) # Multiple time predictions ss <- standsurv(fitw, at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = c(4,5)) s <- summary(fitw, tidy = TRUE, type = 'survival', t = c(4,5), ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est) }) test_that('hazard predictions', { fitw <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") # Single time predictions ss <- standsurv(fitw, type="hazard", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4) s <- summary(fitw, tidy = TRUE, type = 'hazard', t = 4, ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est) # Multiple time predictions ss <- standsurv(fitw, type="hazard", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = c(4,5)) s <- summary(fitw, tidy = TRUE, type = 'hazard', t = c(4,5), ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est) }) test_that('quantile predictions', { fitw <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") # Multiple quantile predictions (q=0.1 and 0.5) ss <- standsurv(fitw, type="quantile", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), quantiles = seq(0.1,0.9, by=0.1)) s <- summary(fitw, tidy = TRUE, type = 'quantile', quantiles = seq(0.1,0.9, by=0.1), ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est, tolerance = .Machine$double.eps^0.25) # use same tolerance as uniroot # Test marginal predictions of quantiles correspond to inverse marginal survival set.seed(136) bc$age <- rnorm(dim(bc)[1], mean = 65 - bc$recyrs, sd = 5) fitw2 <- flexsurvreg(Surv(recyrs, censrec) ~ group + age, data=bc, dist="weibull") ss <- standsurv(fitw2, type="quantile", at=list(list(group="Good")), quantiles = seq(0.1, 0.9, by=0.1)) ss # Feed back in the quantiles and calculate marginal survival probabilities ss2 <- standsurv(fitw2, type="survival", at=list(list(group="Good")), t=ss$at1) expect_equal(1-seq(0.1, 0.9, by=0.1), ss2$at1, tolerance = .Machine$double.eps^0.25) # use same tolerance as uniroot }) test_that('rmst predictions', { fitw <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") # Single time predictions ss <- standsurv(fitw, type="rmst", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4) s <- summary(fitw, tidy = TRUE, type = 'rmst', t = 4, ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est) # Multiple time predictions ss <- standsurv(fitw, type="rmst", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = c(4,5)) s <- summary(fitw, tidy = TRUE, type = 'rmst', t = c(4,5), ci = FALSE) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s$est) }) test_that('marginal_predictions', { set.seed(136) bc$age <- rnorm(dim(bc)[1], mean = 65 - bc$recyrs, sd = 5) # Single time marginal predictions for survival fitw2 <- flexsurvreg(Surv(recyrs, censrec) ~ group + age, data=bc, dist="weibull") ss <- standsurv(fitw2, at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4) s.good <- summary(fitw2, bc %>% mutate(group="Good"), tidy = TRUE, type = 'survival', t = 4, ci = FALSE) s.medium <- summary(fitw2, bc %>% mutate(group="Medium"), tidy = TRUE, type = 'survival', t = 4, ci = FALSE) s.poor <- summary(fitw2, bc %>% mutate(group="Poor"), tidy = TRUE, type = 'survival', t = 4, ci = FALSE) s.marginal <- c(mean(s.good$est), mean(s.medium$est), mean(s.poor$est)) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s.marginal) # Single time marginal predictions for hazard ss <- standsurv(fitw2, type="hazard", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4) h.good <- summary(fitw2, bc %>% mutate(group="Good"), tidy = TRUE, type = 'hazard', t = 4, ci = FALSE) h.medium <- summary(fitw2, bc %>% mutate(group="Medium"), tidy = TRUE, type = 'hazard', t = 4, ci = FALSE) h.poor <- summary(fitw2, bc %>% mutate(group="Poor"), tidy = TRUE, type = 'hazard', t = 4, ci = FALSE) s.marginal <- c(weighted.mean(h.good$est, s.good$est), weighted.mean(h.medium$est, s.medium$est), weighted.mean(h.poor$est, s.poor$est)) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s.marginal) # Single time marginal predictions for rmst ss <- standsurv(fitw2, type="rmst", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4) rmst.good <- summary(fitw2, bc %>% mutate(group="Good"), tidy = TRUE, type = 'rmst', t = 4, ci = FALSE) rmst.medium <- summary(fitw2, bc %>% mutate(group="Medium"), tidy = TRUE, type = 'rmst', t = 4, ci = FALSE) rmst.poor <- summary(fitw2, bc %>% mutate(group="Poor"), tidy = TRUE, type = 'rmst', t = 4, ci = FALSE) s.marginal <- c(mean(rmst.good$est), mean(rmst.medium$est), mean(rmst.poor$est)) expect_equal(c(ss$at1, ss$at2, ss$at3) ,s.marginal) }) test_that('predictions with missing data', { set.seed(136) bc$age <- rnorm(dim(bc)[1], mean = 65 - bc$recyrs, sd = 5) bc_miss <- bc bc_miss$age[[5]] <- NA fitw2 <- flexsurvreg(Surv(recyrs, censrec) ~ group + age, data=bc_miss, dist="weibull") # Single time predictions expect_warning(standsurv(fitw2, type="rmst", at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4, newdata = bc_miss)) }) test_that('model with no covariates', { fitw <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull") # Single time prediction - checking survival with predict.flexsurvreg expect_equal(as.numeric(standsurv(fitw, t = 4, newdata = bc)[1,2]), as.numeric(predict(fitw, type = "survival", times = 4, newdata = bc)[1,2])) }) test_that('all-cause predictions from RS model', { # Single time prediction - checking all-cause survival from an RS model # with predict.flexsurvreg, where background rates are zero fitw <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull") set.seed(136) bc$age <- rnorm(dim(bc)[1], mean = 65 - bc$recyrs, sd = 5) bc$agedays <- floor(bc$age * 365.25) ## Create some random diagnosis dates centred on 01/01/2010 with SD=1 year bc$diag <- as.Date(floor(rnorm(dim(bc)[1], mean = as.Date("01/01/2010", "%d/%m/%Y"), sd=365)), origin="1970-01-01") ## Create sex (assume all are female) bc$sex <- factor("female") ## Assume background hazard of zero bc$bhazard <- 0 ## ratetable (used by standsurv) new.ratetable <- survexp.us new.ratetable[!is.na(new.ratetable)] <- 0 fitw2 <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull", bhazard=bhazard) pred1 <- as.numeric(predict(fitw, type = "survival", times = 4, newdata = bc)[1,2]) pred2 <- as.numeric(standsurv(fitw2, t=4, newdata=bc, type="survival", rmap=list(sex = sex, year = diag, age = agedays ), ratetable = new.ratetable, scale.ratetable = 365.25)[1,2]) expect_equal(pred1, pred2) # all-cause survival quantile # just use one row of data pred1 <- summary(fitw, type = "quantile", quantiles = seq(0.1, 0.9, 0.1), newdata = bc[1,], ci=F, tidy=T) pred2 <- standsurv(fitw2, quantiles = seq(0.1, 0.9, 0.1), newdata=bc[1,], type="quantile", rmap=list(sex = sex, year = diag, age = agedays ), ratetable = new.ratetable, scale.ratetable = 365.25) expect_equal(pred1$est, pred2$at1, tolerance = .Machine$double.eps^0.25) # use same tolerance as uniroot) }) test_that("standsurv deltamethod and bootstrap SEs",{ fitw <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") ss <- standsurv(fitw, at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4, se=TRUE, boot=FALSE) expect_true(is.numeric(ss$at1_se)) ssb <- standsurv(fitw, at=list(list(group="Good"), list(group="Medium"), list(group="Poor")), t = 4, se=TRUE, boot=TRUE, B=5) expect_true(ssb$at1_se != ss$at1_se) }) if (interactive() || covr::in_covr()){ test_that("standsurv plot",{ expect_error({ ## Use bc dataset, with an age variable appended ## mean age is higher in those with smaller observed survival times newbc <- bc newbc$age <- rnorm(dim(bc)[1], mean = 65-scale(newbc$recyrs, scale=FALSE), sd = 5) ## Fit a Weibull flexsurv model with group and age as covariates weib_age <- flexsurvreg(Surv(recyrs, censrec) ~ group+age, data=newbc, dist="weibull") ## Calculate standardized survival and the difference in standardized survival ## for the three levels of group across a grid of survival times standsurv_weib_age <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length=100), contrast = "difference", ci=TRUE, boot = TRUE, B=10, seed=123) plot(standsurv_weib_age) plot(standsurv_weib_age) + ggplot2::theme_bw() + ggplot2::ylab("Survival") + ggplot2::xlab("Time (years)") + ggplot2::guides(color=ggplot2::guide_legend(title="Prognosis"), fill=ggplot2::guide_legend(title="Prognosis")) plot(standsurv_weib_age, contrast=TRUE, ci=TRUE) + ggplot2::ylab("Difference in survival") }, NA) }) } test_that("examples from help(standsurv) run",{ skip_on_cran() expect_error({ ## mean age is higher in those with smaller observed survival times newbc <- bc set.seed(1) newbc$age <- rnorm(dim(bc)[1], mean = 65-scale(newbc$recyrs, scale=FALSE), sd = 5) ## Fit a Weibull flexsurv model with group and age as covariates weib_age <- flexsurvreg(Surv(recyrs, censrec) ~ group+age, data=newbc, dist="weibull") ## Calculate standardized survival and the difference in standardized survival ## for the three levels of group across a grid of survival times standsurv_weib_age <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length.out=100), contrast = "difference", ci=FALSE) standsurv_weib_age ## Calculate hazard of standardized survival and the marginal hazard ratio ## for the three levels of group across a grid of survival times ## 10 bootstraps for confidence intervals (this should be larger) haz_standsurv_weib_age <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length.out=100), type="hazard", contrast = "ratio", boot = TRUE, B=10, ci=TRUE) haz_standsurv_weib_age if (interactive()){ plot(haz_standsurv_weib_age, ci=TRUE) ## Hazard ratio plot shows a decreasing marginal HR ## Whereas the conditional HR is constant (model is a PH model) plot(haz_standsurv_weib_age, contrast=TRUE, ci=TRUE) } ## Calculate standardized survival from a Weibull model together with expected ## survival matching to US lifetables ## age at diagnosis in days. This is required to match to US ratetable, whose ## timescale is measured in days newbc$agedays <- floor(newbc$age * 365.25) ## Create some random diagnosis dates centred on 01/01/2010 with SD=1 year ## These will be used to match to expected rates in the lifetable newbc$diag <- as.Date(floor(rnorm(dim(newbc)[1], mean = as.Date("01/01/2010", "%d/%m/%Y"), sd=365)), origin="1970-01-01") ## Create sex (assume all are female) newbc$sex <- factor("female") standsurv_weib_expected <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length.out=100), rmap=list(sex = sex, year = diag, age = agedays), ratetable = survival::survexp.us, scale.ratetable = 365.25, newdata = newbc) ## Plot marginal survival with expected survival superimposed plot(standsurv_weib_expected, expected=TRUE) }, NA) }) test_that('t ordering', { test_mod <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist="weibull") # surv tvec <- c(3,1,4,2,3) ss1 <- standsurv(test_mod, t=tvec, type = "surv") ## summary.flexsurvreg output sum1 <- summary(test_mod, t=tvec, type = "surv") expect_equal(ss1$time, tvec) expect_equal(ss1$at1[1], ss1$at1[5]) expect_equal(ss1$at1, sum1[[1]]$est) # haz ss2 <- standsurv(test_mod, t=tvec, type = "haz") sum2 <- summary(test_mod, t=tvec, type = "haz") expect_equal(ss2$time, tvec) expect_equal(ss2$at1[1], ss2$at1[5]) expect_equal(ss2$at1, sum2[[1]]$est) # rmst ss3 <- standsurv(test_mod, t=tvec, type = "rmst") sum3 <- summary(test_mod, t=tvec, type = "rmst") expect_equal(ss3$time, tvec) expect_equal(ss3$at1[1], ss3$at1[5]) expect_equal(ss3$at1, sum3[[1]]$est) # bootstrap CIs set.seed(1) ss4 <- standsurv(test_mod, t=tvec, type = "surv", se = TRUE, ci = TRUE, boot = T, B = 5, seed = 1) expect_true(all(ss4$at1 >= ss4$at1_lci)) expect_true(all(ss4$at1 <= ss4$at1_uci)) # delta method CIs ss5 <- standsurv(test_mod, t=tvec, type = "surv", se = TRUE, ci = TRUE, boot = F) expect_true(all(ss5$at1 >= ss5$at1_lci)) expect_true(all(ss5$at1 <= ss5$at1_uci)) }) flexsurv/tests/testthat/test_rtrunc.R0000644000176200001440000000503614471622332017641 0ustar liggesusers set.seed(1) ## simulate time to initial event X <- rexp(1000, 0.2) ## simulate time between initial and final event tdelay <- rgamma(1000, 2, 10) tmax <- 40 obs <- X + tdelay < tmax rtrunc <- tmax - X dat <- data.frame(X, tdelay, rtrunc)[obs,] fs <- flexsurvrtrunc(t=tdelay, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gamma", theta=0.2) test_that("flexsurvrtrunc works", { expect_equal(fs$loglik, -7846.25011895056) }) test_that("summary.flexsurvtrunc works", { summmean <- summary(fs, type="mean") expect_equal(summmean$est, 0.2095068) summmed <- summary(fs, type="median") expect_equal(summmed$est, 0.1746857) summary(fs, type="rmst", t=0.3) summq <- summary(fs, type="quantile") summq2 <- summary(fs, type="quantile", quantiles=c(0.025, 0.5, 0.975)) expect_equal(summmed$est, summq$est) expect_equal(summmed$est, summq2$est[summq2$quantile==0.5]) summ <- summary(fs, type="survival", t=c(0.01, 0.02, 0.03)) expect_equal(summ$est[summ$time==0.02], pgamma(0.02, fs$res["shape","est"], fs$res["rate","est"], lower.tail=FALSE)) summary(fs, type="cumhaz", t=seq(0.01, 0.05, by=0.01)) summary(fs, type="hazard", t=seq(0.01, 0.05, by=0.01)) fntest <- function(shape, rate){2 * mean_gamma(shape,rate)} summfn <- summary(fs, fn=fntest, t=1) expect_equal(summfn$est, 2*summmean$est) set.seed(1) summse <- summary(fs, type="median", se=TRUE) expect_equal(summse$se, 0.004329825) }) test_that("survrtrunc works", { ## simulate some event time data set.seed(1) X <- rweibull(100, 2, 10) T <- rweibull(100, 2, 10) ## truncate above tmax <- 20 obs <- X + T < tmax rtrunc <- tmax - X dat <- data.frame(X, T, rtrunc)[obs,] sf <- survrtrunc(T, rtrunc, data=dat, tmax=tmax) sfnaive <- survfit(Surv(T) ~ 1, data=dat) ## Kaplan-Meier estimate ignoring truncation is biased expect_true(all(sf$surv[10:20] > sfnaive$surv[10:20])) if (interactive() || covr::in_covr()){ plot(sf, conf.int=TRUE) lines(sfnaive, conf.int=TRUE, lty=2, col="red") plot(sfnaive, conf.int=TRUE) lines(sf, conf.int=TRUE, lty=2, col="red") } ## truncate above the maximum observed time tmax <- max(X + T) + 10 obs <- X + T < tmax rtrunc <- tmax - X dat <- data.frame(X, T, rtrunc)[obs,] sf <- survrtrunc(T, rtrunc, data=dat, tmax=tmax) ## estimates identical to the standard Kaplan-Meier sfnaive <- survfit(Surv(T) ~ 1, data=dat) expect_equal(sf$surv[1:10], sfnaive$surv[1:10]) }) flexsurv/tests/testthat/test_outputs.R0000644000176200001440000002254414417262424020054 0ustar liggesuserstest_that("normboot.flexsurvreg",{ fite <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist="exp") set.seed(1); b1 <- normboot.flexsurvreg(fite, B=10, newdata=list(age=0)) set.seed(1); b1 <- normboot.flexsurvreg(fite, B=10, newdata=list(age=50)) set.seed(1); b2 <- normboot.flexsurvreg(fite, B=10, X=matrix(50,nrow=1)) expect_equivalent(b1, b2) set.seed(1); b1 <- normboot.flexsurvreg(fite, B=10, newdata=list(age=c(0,50))) set.seed(1); b2 <- normboot.flexsurvreg(fite, B=10, X=matrix(c(0,50),nrow=2)) expect_equivalent(b1, b2) ## return cov effs, not adjusted set.seed(1) normboot.flexsurvreg(fite, B=5, raw=TRUE) set.seed(1) normboot.flexsurvreg(fite, B=5, raw=TRUE, transform=TRUE) ## no covs fite <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="exp") normboot.flexsurvreg(fite, B=5) normboot.flexsurvreg(fite, B=5, transform=TRUE) }) test_that("custom function in summary.flexsurvreg",{ fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist="weibull") median.weibull <- function(t, start, shape, scale) { qweibull(0.5, shape=shape, scale=scale) } summ <- summary(fitw, newdata=list(age=50), fn=median.weibull, t=1, B=10) expect_equal(summ[[1]][1,"est"], 1575.803185910278, tol=1e-04) summ <- summary(fitw, newdata=list(age=50), fn=median.weibull, t=c(1,2,3), B=10) expect_equal(summ[[1]][1,"est"], summ[[1]][2,"est"]) mean.weibull <- function(shape, scale=1) { scale * gamma(1 + 1/shape) } median.weibull <- function(t, start, shape, scale) { scale * log(2)^(1/shape) } }) test_that("newdata in summary.flexsurvreg: dynamic cut, unknown factor level",{ fl2a <- flexsurvspline(Surv(time, event = status) ~ factor(sex) + cut(age,c(0,56,69,100)), data = lung, k = 2) su <- summary(fl2a, newdata = lung, B = 0) su1 <- su[[2]][1:5,] su <- summary(fl2a, newdata = lung[2,], B = 0) su2 <- su[[1]][1:5,] expect_equal(su1, su2) fl2b <- flexsurvspline(Surv(time, event = status) ~ factor(sex) + cut(age,4), data = lung, k = 2) # should break second summary expect_error(summary(fl2b, newdata = lung[2,], B = 0), "factor .+ has new level") }) lung$sex <- factor(lung$sex) fl3 <- flexsurvspline(Surv(time, event = status) ~ sex + age, data = lung, k = 2) test_that("newdata in summary.flexsurvreg: extra covariates in the list",{ su1 <- summary(fl3, newdata = lung, B = 0)[[1]][1:5,] su2 <- summary(fl3, newdata = lung[1,], B = 0)[[1]][1:5,] expect_equal(su1, su2) }) test_that("newdata in summary.flexsurvreg: are missing values passed through or dropped",{ luna <- lung[1:5,] luna$age[1] <- NA summ <- summary(fl3, newdata = luna, B = 0, t=100, tidy=TRUE) expect_true(is.na(summ$est[1])) summ <- summary(fl3, newdata = luna, B = 0, t=100, tidy=TRUE, na.action=na.omit) expect_true(!is.na(summ$est[1])) fitw <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist = "weibull") ovarian_miss <- ovarian[1:2,] ovarian_miss$age[[1]] <- NA summ <- summary(fitw, ovarian_miss, type = 'rmst', t = 500, tidy=TRUE) expect_true(is.na(summ$est[1])) expect_true(!is.na(summ$est[2])) }) test_that("newdata in summary.flexsurvreg: missing covariates, factor not supplied as factor",{ expect_error(summary(fl3, newdata = list(age=10), B = 0), "Value of covariate .+ not supplied") }) test_that("newdata in summary.flexsurvreg: factor not supplied as factor",{ lung2 <- lung[1,]; lung2$sex <- as.numeric(1) expect_warning(expect_error(summary(fl3, newdata = lung2, B=0), "variable .+ fitted with type"), "not a factor") ## numeric doesn't work expect_warning(expect_error(summary(fl3, newdata = list(age=60, sex=1), B=0), "variable .+ fitted with type"), "not a factor") ## character works if matches one of the factor levels su <- summary(fl3, newdata = list(age=60, sex="1"), B=0) expect_error(summary(fl3, newdata = list(age=60, sex="foo"), B=0), "factor .+ has new level") }) test_that("summary.flexsurvreg tidy output",{ lung$sex2 <- as.factor(lung$sex) lung$agecat <- ifelse(lung$age<65,"<65",">=65") head(lung,20) Model.1 <- flexsurvreg(Surv(time, status) ~sex2+agecat ,data=lung, dist="weibull") Extrapolation.Data <- model.frame(Model.1)[,c(-1,-dim(model.frame(Model.1))[2])] Unique.counts <- as.data.frame(table(Extrapolation.Data)) ## bug reported by Owain Saunders st <- summary.flexsurvreg(Model.1, newdata=Unique.counts[,-3],t= c(4,5),tidy=TRUE, ci=FALSE) snt <- summary.flexsurvreg(Model.1, newdata=Unique.counts[,-3],t= c(4,5), ci=FALSE) expect_equal(st[st$time==5 & st$sex2==2 & st$agecat=="<65", "est"], snt[["sex2=2,agecat=<65"]][2,2]) res <- Model.1$res[,"est"] res.t <- Model.1$res.t[,"est"] expect_equal(pweibull(5, shape=res["shape"], scale=exp(res.t["scale"]+res.t["sex22"]), lower.tail=FALSE), snt[["sex2=2,agecat=<65"]][2,2]) ## no covariates Model.nc <- flexsurvreg(Surv(time, status) ~1 ,data=lung, dist="weibull") expect_equivalent(summary.flexsurvreg(Model.nc, t= c(4,5),tidy=TRUE, ci=FALSE), summary.flexsurvreg(Model.nc, t= c(4,5),tidy=FALSE, ci=FALSE)[[1]]) ## covariates but no newdata - covariate column should be included st <- summary.flexsurvreg(Model.1, tidy=TRUE, ci=FALSE) expect_equal(st[1,"est"], 0.99604726078272, tol=1e-06) expect_equivalent(st[1,"agecat"], ">=65") }) test_that("summary.flexsurvreg untidy output back compatibility",{ nd <- lung[c(1,1,2),] s1 <- summary(fl3, newdata = nd, B=0, tidy=TRUE, t=c(5,10)) s2 <- summary(fl3, newdata = nd, B=0, tidy=FALSE, t=c(5,10)) expect_equal(s1[3,"est"], s2[[2]][1,"est"]) }) test_that("hazard ratio",{ t <- c(100,200,300) haz2 <- summary(fl3, type="hazard", t=t, newdata=list(age=60, sex="2"), ci=FALSE, tidy=TRUE) haz1 <- summary(fl3, type="hazard", t=t, newdata=list(age=60, sex="1"), ci=FALSE, tidy=TRUE) hr <- haz2$est / haz1$est hr2 <- hr_flexsurvreg(fl3, newdata=as.data.frame(list(age=60, sex=c("1","2"))), t=t, ci=FALSE) expect_equal(hr, hr2$est) hr2 <- hr_flexsurvreg(fl3, newdata=as.data.frame(list(age=60, sex=c("1","2"))), t=t, ci=TRUE, B=10) expect_is(hr2$lcl, "numeric") ## default t hr2 <- hr_flexsurvreg(fl3, newdata=as.data.frame(list(age=60, sex=c("1","2"))), ci=FALSE) expect_equal(nrow(hr2), length(unique(lung$time))) ## a non-proportional hazards model fl4 <- flexsurvspline(Surv(time, event = status) ~ sex + age, anc=list(gamma1=~sex), data = lung, k = 2) hr4 <- hr_flexsurvreg(fl4, newdata=as.data.frame(list(age=60, sex=c("1","2"))), t=t, ci=TRUE, B=10) expect_false(hr4$est[1] == hr4$est[2]) expect_error(hr_flexsurvreg(fl4, t=t), "`newdata` must be specified") ## default newdata: factor fitw <- flexsurvreg(Surv(futime, fustat) ~ factor(rx), data = ovarian, dist="weibull") expect_equal(hr_flexsurvreg(fitw, t=t)$est, hr_flexsurvreg(fitw, t=t, newdata=list(rx=c("1","2")))$est) ## default newdata: numeric ovarian$rxbin <- ovarian$rx - 1 fitw <- flexsurvreg(Surv(futime, fustat) ~ rxbin, data = ovarian, dist="weibull") expect_equal(hr_flexsurvreg(fitw, t=t)$est, hr_flexsurvreg(fitw, t=t, newdata=list(rxbin=c(0,1)))$est) }) test_that("summary.flexsurvreg quantiles",{ fitw <- flexsurvreg(Surv(futime, fustat) ~ factor(rx), data = ovarian, dist="weibull") nd <- list(rx=c("1","2")) cf <- fitw$res[,"est"]; sh <- cf["shape"]; sc <- cf["scale"] qu <- summary(fitw, newdata=nd, type="quantile", q=0.4, tidy=TRUE) q1 <- qweibull(0.4, shape=sh, scale=sc) q2 <- qweibull(0.4, shape=sh, scale=sc*exp(cf["factor(rx)2"])) expect_equal(qu$est[1], q1) expect_equal(qu$est[2], q2) ## Quantiles of truncated distribution qu <- summary(fitw, newdata=nd, type="quantile", q=0.4, tidy=TRUE, start=100) pstart1 <- pweibull(100, shape=sh, scale=sc) pstart2 <- pweibull(100, shape=sh, scale=sc*exp(cf["factor(rx)2"])) q1 <- qweibull(pstart1+(1-pstart1)*0.4, shape=sh, scale=sc) q2 <- qweibull(pstart2+(1-pstart2)*0.4, shape=sh, scale=sc*exp(cf["factor(rx)2"])) expect_equal(qu$est[1], q1) expect_equal(qu$est[2], q2) expect_equal((pweibull(q1, shape=sh, scale=sc) - pweibull(100, shape=sh, scale=sc))/ (1 - pweibull(100, shape=sh, scale=sc)), 0.4) }) test_that("newdata in summary and predict with no covariates",{ fitw <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="weibull") nd <- model.frame(fitw) expect_equal(nrow(summary(fitw, newdata=nd, type="quantile", tidy=TRUE, ci=FALSE)), nrow(nd)) fitw <- flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="weibull") summ <- summary(fitw, newdata=nd, type="mean", tidy=TRUE, ci=FALSE) expect_equal(nrow(summ), nrow(nd)) summ <- summary(fitw, newdata=nd, type="quantile", quantiles=c(0.1, 0.9), tidy=TRUE, ci=FALSE) expect_equal(nrow(summ), nrow(nd)*2) pred <- predict(fitw, newdata=nd, type="quantile", p=0.5) expect_equal(nrow(pred), nrow(nd)) pred <- predict(fitw, newdata=nd, type="quantile", p=c(0.1, 0.9)) expect_equal(nrow(pred), nrow(nd)) }) flexsurv/tests/testthat/test_contrasts.R0000644000176200001440000000201714554246713020347 0ustar liggesusers## Thanks to Andrea Discacciati @https://github.com/anddis ## Fixed https://github.com/chjackson/flexsurv/issues/178 test_that("Non-default factor contrasts", { veteran$celltype <- factor(veteran$celltype) fit.noc <- flexsurvreg(Surv(time, status) ~ celltype, data = veteran, dist = "exp") veteran$celltype2 <- veteran$celltype contrasts(veteran$celltype2) <- stats::contr.helmert(4) fit.c <- flexsurvreg(Surv(time, status) ~ celltype2, data = veteran, dist = "exp") fit.poi <- glm(status ~ celltype2 + offset(log(time)), data = veteran, family = "poisson") expect_equivalent(coef(fit.c), coef(fit.poi)) expect_true(coef(fit.c)[1] != coef(fit.noc)[1]) summ.noc <- summary(fit.noc, type="survival", t=10, tidy=TRUE, ci=FALSE) summ.c <- summary(fit.c, type="survival", t=10, tidy=TRUE, ci=FALSE) expect_equivalent(summ.noc$estimates, summ.c$estimates) }) flexsurv/tests/testthat/test_flexsurvmix.R0000644000176200001440000001757214471612577020742 0ustar liggesusers n <- 1000 p <- 0.5 set.seed(1) death <- rbinom(n, 1, p) t <- numeric(n) t[death==0] <- rgamma(sum(death==0), 1, 3.2) t[death==1] <- rgamma(sum(death==1), 2.5, 1.2) cens <- as.numeric(t > 4) status <- 1 - cens event <- ifelse(cens, NA, death+1) # 1 is cure, 2 is death t[cens] <- 4 dat <- data.frame(t, status, event) dat$evname <- c("cure", "death")[dat$event] dat$evnamef <- factor(dat$evname) test_that("flexsurvmix basic",{ fs <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","gamma"), fixedpars=TRUE) expect_equivalent(fs$loglik, -1550.65934372248) fs2 <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","gamma"), fixedpars=1:2, em.control = list(var.method="louis")) fs2$cov expect_no_error({ ## event as character fs <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), fixedpars=TRUE) ## event as factor fs <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evnamef, dists=c("gamma","gamma"), fixedpars=TRUE) ## user supplied inits fs <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), inits = list(cure=c(2, 1), death=c(1, 3)), fixedpars=TRUE) x <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","weibull"), fixedpars=TRUE) }) }) n <- 1000 p <- 0.5 set.seed(1) death <- rbinom(n, 1, p) t <- numeric(n) x <- rnorm(n) y <- rbinom(n, 1, 0.5) t[death==0] <- rgamma(sum(death==0), 1*exp(0.3*x[death==0]), 3.2*exp(0.5*x[death==0])) t[death==1] <- rgamma(sum(death==1), 2.5, 1.2) cens <- as.numeric(t > 2) t[cens] <- 2 status <- 1 - cens event <- ifelse(cens, NA, death+1) # 1 is cure, 2 is death dat <- data.frame(t, status, event, x) dat$evname <- c("cure", "death")[dat$event] test_that("flexsurvmix with covariates on time to event distributions",{ ## covariates on all location pars fs <- flexsurvmix(Surv(t, status) ~ x, data=dat, event=event, dists=c("gamma","weibull"), fixedpars=TRUE) ## covariates on all location pars, and some shape pars ## this is the right model here fs <- flexsurvmix(Surv(t, status) ~ x, data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(shape=~x), list(shape=~1)), fixedpars=TRUE) ## covariates supplied manually for location pars fs <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(rate=~x, shape=~x), list(rate=~x)), fixedpars=TRUE) ## covariates on location for one component but not another. two ways to do ini <- list(c(1,3,0.6,0.2), c(1,0.3)) fs1 <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(rate=~x, shape=~x), list(rate=~1)), inits=ini, fixedpars=TRUE) fs2 <- flexsurvmix(list(`1`=Surv(t, status) ~ x, `2`=Surv(t, status) ~ 1), data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(shape=~x), list(rate=~1)), inits=ini, fixedpars=TRUE) expect_equal(fs1$loglik, fs2$loglik) ## We can either put location formula in first arg (adding ~1 in anc if necessary)... ini <- list(c(1,3, 0.6, 0.2, 0.01), c(1, 0.3, 0.01)) fs3 <- flexsurvmix(list(`1`=Surv(t, status) ~ x, `2`=Surv(t, status) ~ x), data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(shape=~x), list(rate=~1)), inits=ini, fixedpars=TRUE) ## ...or include the location formula in anc. fs4 <- flexsurvmix(Surv(t, status) ~ 1 , data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(shape = ~x, rate = ~x), list(rate = ~x)), inits=ini, fixedpars=TRUE) expect_equal(fs3$loglik, fs4$loglik) expect_error( {fs <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","gamma"), anc=list(list(rate=~x, shape=~x)), fixedpars=TRUE)}, "`anc` of length 1, should equal the number of") ## user-supplied inits fs <- flexsurvmix(Surv(t, status) ~ x, data=dat, event=evname, dists=c("gamma","gamma"), anc=list(list(shape=~x), list(shape=~1)), inits=list(cure=c(2, 1, 0, 0), death=c(1, 3, 0)), fixedpars=TRUE) }) n <- 10000 set.seed(1) x <- rnorm(n) y <- rbinom(n, 1, 0.5) p <- plogis(qlogis(0.5) + 2*x - 3*y) death <- rbinom(n, 1, p) t <- numeric(n) t[death==0] <- rgamma(sum(death==0), 1, 3.2) t[death==1] <- rgamma(sum(death==1), 2.5, 1.2) cens <- as.numeric(t > 3) status <- 1 - cens t[cens] <- 3 event <- ifelse(cens, NA, death+1) # 1 is cure, 2 is death dat <- data.frame(t, status, event, x) dat$evname <- c("cure", "death")[dat$event] test_that("flexsurvmix with covariates on mixing probabilities",{ x <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), pformula = ~ x + y, fixedpars=TRUE) expect_equal(x$res$est[x$res$terms=="prob2(x)"], 0) }) test_that("dot in formulae in flexsurvmix",{ expect_error(flexsurvmix(Surv(t, status) ~ ., data=dat, event=evname, dists=c("gamma","gamma"), fixedpars=TRUE), "`.` in formulae is not supported") expect_error(flexsurvmix(Surv(t, status) ~ 1, data=dat, event=evname, dists=c("gamma","gamma"), pformula=~., fixedpars=TRUE), "`.` in formulae is not supported") }) ## Partially-observed outcomes n <- 1000 set.seed(1) x <- rnorm(n) y <- rbinom(n, 1, 0.5) events <- c("icu","death","discharge") p <- c(0.2, 0.3, 0.5) event <- sample(events, size=n, prob=p, replace=TRUE) t <- numeric(n) t[event=="death"] <- rgamma(sum(event=="death"), 2.5, 1.2) t[event=="discharge"] <- rgamma(sum(event=="discharge"), 3.5, 0.6) t[event=="icu"] <- rgamma(sum(event=="icu"), 1, 3.2) cens <- as.numeric(t > 3) t[cens] <- 3 status <- 1 - cens ## Out of those still alive at cens time, or those discharged, label some as as partially observed, ## so we don't know if they've been discharged yet or they are still in hosp at the cens time pobs_eligible <- (event == "discharge") | (t > 3) pobs <- rbinom(n=sum(pobs_eligible), size=1, prob=0.2) == 1 ## Construct data # Partially-obs people: know alive at cens time, else don't know anything # Time of death and ICU are right cens # Time of discharge interval cens on 0 to Inf ie no info # Note we don't need a "partial_events" indicator in the event data # partially obs people still at risk of all events in the future # we just know they are still alive at cens time, so could die in future or go to ICU t1disc <- t2disc <- t t2disc[cens] <- Inf t1disc[pobs] <- 0 dat <- data.frame(t, status, t1disc, t2disc, event) # No censoring, all events known, likelihood factorises nicely # Use "EM algorithm" code with one iteration, since no latent data n <- 1000 p <- 0.5 set.seed(1) death <- rbinom(n, 1, p) t <- numeric(n) t[death==0] <- rgamma(sum(death==0), 1, 3.2) t[death==1] <- rgamma(sum(death==1), 2.5, 1.2) status <- 1 event <- death+1 # 1 is cure, 2 is death dat <- data.frame(t, status, event) dat$evname <- c("cure", "death")[dat$event] dat$evnamef <- factor(dat$evname) test_that("With no censored data, we get the obvious estimates of the event probabilities",{ ## Observed proportions 0.52, 0.48 should be MLEs of the probs. EM looks to work better here. fse <- flexsurvmix(Surv(t, status) ~ 1, data=dat, event=event, dists=c("gamma","gamma")) expect_equal(fse$res$est[fse$res$terms=="prob1"], sum(event==1)/length(event), tolerance=1e-04) expect_equal(fse$loglik, -1344.29387018376, tolerance=1e-05) }) flexsurv/tests/testthat/test_llogis.R0000644000176200001440000000372314472143261017616 0ustar liggesuserscontext("Log-logistic distribution") test_that("llogis",{ x <- c(0.1, 0.2, 0.7) suppressWarnings({ if (require("eha")) expect_equal(dllogis(x, shape=0.1, scale=0.2), eha::dllogis(x, shape=0.1, scale=0.2)) }) expect_equal(qllogis(x, shape=0.1, scale=0.2), qgeneric(pllogis, p=x, shape=0.1, scale=0.2)) expect_equal(x, pllogis(qllogis(x, shape=0.1, scale=0.2), shape=0.1, scale=0.2)) expect_equal(x, 1 - exp(-Hllogis(qllogis(x, shape=0.1, scale=0.2), shape=0.1, scale=0.2))) expect_equal(hllogis(x, shape=0.1, scale=0.2), dllogis(x, shape=0.1, scale=0.2) / (1 - pllogis(x, shape=0.1, scale=0.2))) q <- numeric(3); for (i in 1:3) q[i] <- qllogis(x[i], shape=0.0001, scale=i/5) expect_equal(q, qllogis(x, shape=0.0001, scale=1:3/5)) x <- c(0.5, 1.06, 4.7) expect_equal(x, qllogis(pllogis(x, shape=0.1, scale=0.2), shape=0.1, scale=0.2)) if (interactive()) { rl <- rllogis(10000, shape=1.5, scale=1.2) plot(density(rl[rl<100]), xlim=c(0,10)) x <- seq(0, 10, by=0.001) lines(x, dllogis(x, shape=1.5, scale=1.2), lty=2) } expect_equal(mean_llogis(shape=0.1, scale=0.2), NaN) expect_equal(var.llogis(shape=1.1, scale=0.2), NaN) mean_llogis(shape=1.1, scale=0.2) var.llogis(shape=2.1, scale=0.2) x <- c(0.1,0.4,0.6,0.9) expect_equal(pllogis(qllogis(p=x, lower.tail=FALSE), lower.tail=FALSE), x) expect_equal(qlogis(p=x, lower.tail=TRUE), rev(qlogis(p=x, lower.tail=FALSE))) expect_warning(dllogis(1.2, shape=1, scale=-1), "Non-positive scale") expect_warning(dllogis(1.2, shape=-1, scale=1), "Non-positive shape") expect_warning(pllogis(1.2, shape=1, scale=-1), "Non-positive scale") expect_warning(pllogis(1.2, shape=-1, 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from right-truncated, uncensored data by ##' reversing time, interpreting the data as left-truncated, applying the ##' Kaplan-Meier / Lynden-Bell estimator and transforming back. ##' ##' Note that this does not estimate the untruncated survivor function - instead ##' it estimates the survivor function truncated above at a time defined by the ##' maximum possible time that might have been observed in the data. ##' ##' @param t Vector of observed times from an initial event to a final event. ##' ##' @param rtrunc Individual-specific right truncation points, so that each ##' individual's survival time \code{t} would not have been observed if it was ##' greater than the corresponding element of \code{rtrunc}. If any of these ##' are greater than \code{tmax}, then the actual individual-level truncation ##' point for these individuals is taken to be \code{tmax}. ##' ##' @param tmax Maximum possible time to event that could have been observed. ##' ##' @param data Data frame to find \code{t} and \code{rtrunc} in. If not ##' supplied, these should be in the working environment. ##' ##' @param eps Small number that is added to \code{t} before implementing the ##' time-reversed estimator, to ensure the risk set is consistent between ##' forward and reverse time scales. It should be just large enough that ##' \code{t+eps} is not \code{==t}. This should not need changing from the ##' default of 0.001, unless \code{t} are extremely large or small and the ##' data are rounded to integer. ##' ##' @param conf.int Confidence level, defaulting to 0.95. ##' ##' @return A list with components: ##' ##' \code{time} Time points where the estimated survival changes. ##' ##' \code{surv} Estimated survival at \code{time}, truncated above at ##' \code{tmax}. ##' ##' \code{se.surv} Standard error of survival. ##' ##' \code{std.err} Standard error of -log(survival). Named this way for consistency with \code{survfit}. ##' ##' \code{lower} Lower confidence limits for survival. ##' ##' \code{upper} Upper confidence limits for survival. ##' ##' @details ##' ##' Define \eqn{X} as the time of the initial event, \eqn{Y} as the time of the ##' final event, then we wish to determine the distribution of \eqn{T = Y- X}. ##' ##' Observations are only recorded if \eqn{Y \leq t_{max}}. Then the ##' distribution of \eqn{T} in the resulting sample is right-truncated by ##' \code{rtrunc} \eqn{ = t_{max} - X}. ##' ##' Equivalently, the distribution of \eqn{t_{max} - T} is left-truncated, since ##' it is only observed if \eqn{t_{max} - T \geq X}. Then the standard ##' Kaplan-Meier type estimator as implemented in ##' \code{\link[survival]{survfit}} is used (as described by Lynden-Bell, 1971) ##' and the results transformed back. ##' ##' This situation might happen in a disease epidemic, where \eqn{X} is the date ##' of disease onset for an individual, \eqn{Y} is the date of death, and we ##' wish to estimate the distribution of the time \eqn{T} from onset to death, ##' given we have only observed people who have died by the date \eqn{t_{max}}. ##' ##' If the estimated survival is unstable at the highest times, then consider ##' replacing \code{tmax} by a slightly lower value, then if necessary, removing ##' individuals with \code{t > tmax}, so that the estimand is changed to the ##' survivor function truncated over a slightly narrower interval. ##' ##' @examples ##' ##' ## simulate some event time data ##' set.seed(1) ##' X <- rweibull(100, 2, 10) ##' T <- rweibull(100, 2, 10) ##' ##' ## truncate above ##' tmax <- 20 ##' obs <- X + T < tmax ##' rtrunc <- tmax - X ##' dat <- data.frame(X, T, rtrunc)[obs,] ##' sf <- survrtrunc(T, rtrunc, data=dat, tmax=tmax) ##' plot(sf, conf.int=TRUE) ##' ## Kaplan-Meier estimate ignoring truncation is biased ##' sfnaive <- survfit(Surv(T) ~ 1, data=dat) ##' lines(sfnaive, conf.int=TRUE, lty=2, col="red") ##' ##' ## truncate above the maximum observed time ##' tmax <- max(X + T) + 10 ##' obs <- X + T < tmax ##' rtrunc <- tmax - X ##' dat <- data.frame(X, T, rtrunc)[obs,] ##' sf <- survrtrunc(T, rtrunc, data=dat, tmax=tmax) ##' plot(sf, conf.int=TRUE) ##' ## estimates identical to the standard Kaplan-Meier ##' sfnaive <- survfit(Surv(T) ~ 1, data=dat) ##' lines(sfnaive, conf.int=TRUE, lty=2, col="red") ##' ##' ##' @references ##' ##' D. Lynden-Bell (1971) A method of allowing for known observational ##' selection in small samples applied to 3CR quasars. Monthly Notices of the ##' Royal Astronomical Society, 155:95–118. ##' ##' Seaman, S., Presanis, A. and Jackson, C. (2020) Review of methods for ##' estimating distribution of time to event from right-truncated data. ##' ##' @export survrtrunc <- function(t, rtrunc, tmax, data=NULL, eps=0.001, conf.int=0.95){ t <- eval(substitute(t), data, parent.frame()) rtrunc <- eval(substitute(rtrunc), data, parent.frame()) check_survrtrunc(t, rtrunc, tmax) rtrunc[rtrunc > tmax] <- tmax X <- tmax - rtrunc - eps trev <- tmax - t event <- rep(1, length(X)) sfleft <- survival::survfit(Surv(time=X, time2=trev, event=event, type="counting") ~ 1) sf <- list(time = rev(tmax - sfleft$time), surv = c(rev(1 - sfleft$surv)[-1], 0)) d <- sfleft$n.event N <- sfleft$n.risk cdf <- 1 - sf$surv[-length(sf$surv)] h <- d / (N*(N - d)) se <- sqrt(cdf^2 * rev(cumsum(h[-length(h)]))) selog <- sqrt((1/log(cdf)^2) * rev(cumsum(h[-length(h)]))) L <- log(-log(cdf)) alpha <- (1 - conf.int)/2 lower <- exp(-exp(L + qnorm(alpha)*selog)) upper <- exp(-exp(L - qnorm(alpha)*selog)) se <- c(se, 0); selog <- c(selog, 0); lower <- c(lower, 1); upper <- c(upper, 1) sf <- list(surv=sf$surv, time=sf$time, se.surv=se, std.err=selog, lower=1-lower, upper=1-upper) class(sf) <- "survrtrunc" sf } check_survrtrunc <- function(t, rtrunc, tmax) { if (!all(t <= rtrunc)) stop("Not all `t` are <= `rtrunc`") if (!all(t <= tmax)) stop("Not all `t` are <= `tmax`") } ##' Plot nonparametric estimates of survival from right-truncated data. ##' ##' \code{plot.survrtrunc} creates a new plot, while \code{lines.survrtrunc} adds lines to an exising plot. ##' ##' @param x Object of class \code{"survrtrunc"} as returned by \code{\link{survrtrunc}}. ##' ##' @param ... Other arguments to be passed to \code{\link[survival]{plot.survfit}} or \code{\link[survival]{lines.survfit}}. ##' ##' @rdname plot_survtrunc ##' @export plot.survrtrunc <- function(x, ...){ class(x) <- "survfit" plot(x, ...) } ##' ##' @rdname plot_survtrunc ##' @export lines.survrtrunc <- function(x, ...){ class(x) <- "survfit" lines(x, ...) } flexsurv/R/flexsurvmix_louis.R0000644000176200001440000000735513752454647016316 0ustar liggesusers## Calculate the covariance matrix for a flexsurvmix model fitted by the EM algorithm ## using the method of Louis (JRSSB, 1982) flexsurvmix_louis <- function(K, nthetal, dlists, ncoveffsl, locform, data, dists, anc, aux, fixedpars_em, optpars_em, inits, optim.control, ttepars.t, nobs, ntparsl, nppars, w, alpha, covp, ncovsp, Xp, hess_full_p, hess_full_t, hess.control) { ESST_t <- vector(K, mode="list") ctrl <- optim.control for (k in 1:K){ ## unweighted indiv loglik (not minus loglik) if (is.null(optim.control$ndeps)) ctrl$ndeps = rep(1e-06, length(optpars_em$t[[as.character(k)]])) logliki_flexsurvreg <- function(parsopt){ pars <- inits[[k]] pars[optpars_em$t[[k]]] <- parsopt theta <- inv.transform(pars[seq_len(nthetal[k])], dlists[[k]]) coveffs <- pars[nthetal[k] + seq_len(ncoveffsl[k])] initsk <- c(theta, coveffs) fs <- do.call("flexsurvreg", list(formula=locform[[k]], data=data, dist=dists[[k]], anc=anc[[k]], inits=initsk, aux=aux[[k]], fixedpars = fixedpars_em$t[[as.character(k)]], hessian=FALSE, control=ctrl) ) fs$logliki } parsopt <- ttepars.t[[k]][optpars_em$t[[k]]] nopt <- length(parsopt) J <- numDeriv::jacobian(logliki_flexsurvreg, parsopt) # nindiv x npars. ## Quick with nindiv=1000 SST <- array(dim=c(nobs, nopt, nopt)) for (i in 1:nopt) { for (j in 1:nopt) { SST[,i,j] <- J[,i] * J[,j] } } # w[,k] # nindiv vector ESST_t[[k]] <- apply(SST * w[,k], c(2,3), sum) } # Analytic derivatives of imputed-data log-likelihood for the component # membership probs (and covariates on these) alphamat <- matrix(c(0,alpha), nrow=nobs, ncol=K, byrow=TRUE) # by individual if (ncovsp > 0) { for (k in 2:K){ cpinds <- (k-2)*ncovsp + 1:ncovsp alphamat[,k] <- alpha[k-1] + Xp %*% covp[cpinds] } } dmat <- array(dim=c(nobs, nppars, K)) sumexp <- rowSums(exp(alphamat)) for (j in 2:K) { esum <- exp(alphamat[,j]) / sumexp for (k in 1:K) { dmat[,j-1,k] <- if (k==1) - esum else if (k==j) 1 - esum else (-exp(alphamat[,j]) / sumexp) if (ncovsp > 0) { for (i in 1:ncovsp){ ind <- K-1 + (j-2)*ncovsp + i dmat[,ind,k] <- if (k==1) - Xp[,i] * esum else if (k==j) Xp[,i] * (1 - esum) else Xp[,i] * (-exp(alphamat[,j]) / sumexp) } } } } dmat <- -dmat Dw <- array(dim=c(nobs, nppars, K)) DDw <- array(dim=c(nobs, nppars, nppars, K)) for (k in 1:K){ for (i in 1:nppars){ Dw[,i,k] <- dmat[,i,k] * w[,k] for (j in 1:nppars){ DDw[,i,j,k] <- dmat[,i,k] * dmat[,j,k] * w[,k] } } } SDw <- array(dim=c(nobs, nppars)) for (i in 1:nppars){ SDw[,i] <- rowSums(Dw[,i,]) } SDw <- SDw[,optpars_em$p,drop=FALSE] DDw <- DDw[,optpars_em$p,optpars_em$p,,drop=FALSE] noptp <- length(optpars_em$p) ESST_p <- array(dim=c(noptp, noptp)) for (i in 1:noptp){ for (j in 1:noptp){ ESST_p[i,j] <- sum(DDw[,i,j,]) + sum(SDw[,i])*sum(SDw[,j]) - sum(SDw[,i]*SDw[,j]) } } ESST <- Matrix::bdiag(ESST_p, Matrix::bdiag(ESST_t)) hess_full <- - Matrix::bdiag(hess_full_p, Matrix::bdiag(hess_full_t)) hess <- hess_full - ESST cov <- .hess_to_cov(-hess, hess.control$tol.solve, hess.control$tol.evalues) cov # of loglik } flexsurv/R/RcppExports.R0000644000176200001440000000404014501417340014742 0ustar liggesusers# Generated by using Rcpp::compileAttributes() -> do not edit by hand # Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393 dgenf_work <- function(x, mu, sigma, Q, P, log) { .Call(`_flexsurv_dgenf_work`, x, mu, sigma, Q, P, log) } pgenf_work <- function(q, mu, sigma, Q, P, lower_tail, give_log) { .Call(`_flexsurv_pgenf_work`, q, mu, sigma, Q, P, lower_tail, give_log) } check.genf <- function(mu, sigma, Q, P) { .Call(`_flexsurv_check_genf`, mu, sigma, Q, P) } dgengamma_work <- function(x, mu, sigma, Q, log) { .Call(`_flexsurv_dgengamma_work`, x, mu, sigma, Q, log) } pgengamma_work <- function(q, mu, sigma, Q, lower_tail, give_log) { .Call(`_flexsurv_pgengamma_work`, q, mu, sigma, Q, lower_tail, give_log) } check.gengamma <- function(mu, sigma, Q) { .Call(`_flexsurv_check_gengamma`, mu, sigma, Q) } dgompertz_work <- function(x, shape, rate, log) { .Call(`_flexsurv_dgompertz_work`, x, shape, rate, log) } pgompertz_work <- function(q, shape, rate, lower_tail, give_log) { .Call(`_flexsurv_pgompertz_work`, q, shape, rate, lower_tail, give_log) } check.gompertz <- function(shape, rate) { .Call(`_flexsurv_check_gompertz`, shape, rate) } dllogis_work <- function(x, shape, scale, log) { .Call(`_flexsurv_dllogis_work`, x, shape, scale, log) } pllogis_work <- function(q, shape, scale, lower_tail, give_log) { .Call(`_flexsurv_pllogis_work`, q, shape, scale, lower_tail, give_log) } check.llogis <- function(shape, scale) { .Call(`_flexsurv_check_llogis`, shape, scale) } exph <- function(y) { .Call(`_flexsurv_exph`, y) } dexph <- function(y) { .Call(`_flexsurv_dexph`, y) } basis_vector <- function(knots, x) { .Call(`_flexsurv_basis_vector`, knots, x) } basis_matrix <- function(knots, x) { .Call(`_flexsurv_basis_matrix`, knots, x) } dbasis_vector <- function(knots, x) { .Call(`_flexsurv_dbasis_vector`, knots, x) } dbasis_matrix <- function(knots, x) { .Call(`_flexsurv_dbasis_matrix`, knots, x) } flexsurv/R/Lnorm.R0000644000176200001440000000301614203411131013531 0ustar liggesusers### Hazard and cumulative hazard functions for R built in ### distributions. Where possible, use more numerically stable ### formulae than d/(1-p) and -log(1-p) ##' @export ##' @rdname hazard hlnorm <- function(x, meanlog=0, sdlog=1, log=FALSE){ h <- dbase("lnorm", log=log, x=x, meanlog=meanlog, sdlog=sdlog) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) logdens <- dlnorm(x = x, meanlog = meanlog, sdlog = sdlog, log=TRUE) logsurv <- plnorm(q = x, meanlog = meanlog, sdlog = sdlog, lower.tail = FALSE, log.p=TRUE) loghaz <- logdens - logsurv ret[ind] <- if (log) loghaz else exp(loghaz) ret } ##' @export ##' @rdname hazard Hlnorm <- function(x, meanlog=0, sdlog=1, log=FALSE){ h <- dbase("lnorm", log=log, x=x, meanlog=meanlog, sdlog=sdlog) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) ret[ind] <- - plnorm(x, meanlog, sdlog, lower.tail=FALSE, log.p=TRUE) if (log) ret[ind] <- log(ret[ind]) ret } check.lnorm <- function(meanlog=0, sdlog=1){ ret <- rep(TRUE, length(meanlog)) if (any(!is.na(sdlog) & sdlog<0)) { warning("Negative SD parameter") ret[!is.na(sdlog) & sdlog<0] <- FALSE } ret } ##' @export ##' @rdname means mean_lnorm <- function(meanlog=0, sdlog=1){ exp(meanlog + 0.5*sdlog^2) } ##' @export ##' @rdname means rmst_lnorm = function(t, meanlog=0, sdlog=1, start=0){ rmst_generic(plnorm, t, start=start, meanlog=meanlog, sdlog=sdlog) } var.lnorm <- function(meanlog=0, sdlog=1){ exp(2*meanlog + sdlog^2)*(exp(sdlog^2) - 1) } flexsurv/R/plot.flexsurvreg.R0000644000176200001440000003015414644755415016027 0ustar liggesusers##' Plots of fitted flexible survival models ##' ##' Plot fitted survival, cumulative hazard or hazard from a parametric model ##' against nonparametric estimates to diagnose goodness-of-fit. Alternatively ##' plot a user-defined function of the model parameters against time. ##' ##' ##' @param x Output from \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}}, representing a fitted survival model object. ##' @param newdata Data frame containing covariate values to produce fitted ##' values for. See \code{\link{summary.flexsurvreg}}. ##' ##' If there are only factor covariates in the model, then Kaplan-Meier (or ##' nonparametric hazard...) curves are plotted for all distinct groups, and ##' by default, fitted curves are also plotted for these groups. To plot ##' Kaplan-Meier and fitted curves for only a subset of groups, use ##' \code{plot(survfit())} followed by \code{lines.flexsurvreg()}. ##' ##' If there are any continuous covariates, then a single population ##' Kaplan-Meier curve is drawn. By default, a single fitted curve is drawn ##' with the covariates set to their mean values in the data - for categorical ##' covariates, the means of the 0/1 indicator variables are taken. ##' @param X Alternative way to supply covariate values, as a model matrix. ##' See \code{\link{summary.flexsurvreg}}. \code{newdata} is an easier way. ##' @param type \code{"survival"} for survival, to be plotted against ##' Kaplan-Meier estimates from \code{\link[survival]{plot.survfit}}. ##' ##' \code{"cumhaz"} for cumulative hazard, plotted against transformed ##' Kaplan-Meier estimates from \code{\link[survival]{plot.survfit}}. ##' ##' \code{"hazard"} for hazard, to be plotted against smooth nonparametric ##' estimates from \code{\link[muhaz]{muhaz}}. The nonparametric estimates ##' tend to be unstable, and these plots are intended just to roughly indicate ##' the shape of the hazards through time. The \code{min.time} and ##' \code{max.time} options to \code{\link[muhaz]{muhaz}} may sometimes need to ##' be passed as arguments to \code{\link{plot.flexsurvreg}} to avoid an error ##' here. ##' ##' Ignored if \code{"fn"} is specified. ##' @param fn Custom function of the parameters to summarise against time. The ##' first two arguments of the function must be \code{t} representing time, and ##' \code{start} representing left-truncation points, and any remaining ##' arguments must be parameters of the distribution. It should return a ##' vector of the same length as \code{t}. ##' @param t Vector of times to plot fitted values for, see ##' \code{\link{summary.flexsurvreg}}. ##' @param start Left-truncation points, see \code{\link{summary.flexsurvreg}}. ##' @param est Plot fitted curves (\code{TRUE} or \code{FALSE}.) ##' @param ci Plot confidence intervals for fitted curves. By default, this is ##' \code{TRUE} if one observed/fitted curve is plotted, and \code{FALSE} if ##' multiple curves are plotted. ##' @param B Number of simulations controlling accuracy of confidence ##' intervals, as used in \code{\link[=summary.flexsurvreg]{summary}}. ##' Decrease for greater speed at the expense of accuracy, or set \code{B=0} to ##' turn off calculation of CIs. ##' @param cl Width of confidence intervals, by default 0.95 for 95\% ##' intervals. ##' @param col.obs Colour of the nonparametric curve. ##' @param lty.obs Line type of the nonparametric curve. ##' @param lwd.obs Line width of the nonparametric curve. ##' @param col Colour of the fitted parametric curve(s). ##' @param lty Line type of the fitted parametric curve(s). ##' @param lwd Line width of the fitted parametric curve(s). ##' @param col.ci Colour of the fitted confidence limits, defaulting to the ##' same as for the fitted curve. ##' @param lty.ci Line type of the fitted confidence limits. ##' @param lwd.ci Line width of the fitted confidence limits. ##' @param ylim y-axis limits: vector of two elements. ##' @param add If \code{TRUE}, add lines to an existing plot, otherwise new ##' axes are drawn. ##' @param ... Other options to be passed to \code{\link[survival]{plot.survfit}} or ##' \code{\link[muhaz]{muhaz}}, for example, to control the smoothness of the ##' nonparametric hazard estimates. The \code{min.time} and \code{max.time} ##' options to \code{\link[muhaz]{muhaz}} may sometimes need to be changed from ##' the defaults. ##' ##' @note Some standard plot arguments such as \code{"xlim","xlab"} may not ##' work. This function was designed as a quick check of model fit. Users ##' wanting publication-quality graphs are advised to set up an empty plot with ##' the desired axes first (e.g. with \code{plot(...,type="n",...)}), then use ##' suitable \code{\link{lines}} functions to add lines. ##' ##' If case weights were used to fit the model, these are used when producing ##' nonparametric estimates of survival and cumulative hazard, but not for ##' the hazard estimates. ##' ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @seealso \code{\link{flexsurvreg}} ##' @keywords models hplot ##' @export plot.flexsurvreg <- function(x, newdata=NULL, X=NULL, type="survival", fn=NULL, t=NULL, start=0, est=TRUE, ci=NULL, B=1000, cl=0.95, col.obs="black", lty.obs=1, lwd.obs=1, col="red",lty=1,lwd=2, col.ci=NULL,lty.ci=2,lwd.ci=1,ylim=NULL, add=FALSE,...) { ## don't calculate or plot CIs by default if all covs are categorical -> multiple curves if (!add && is.null(x[["data"]])) stop("Goodness-of-fit plots are not available if the data have been removed from the model object") if (is.null(ci)) ci <- ((x$ncovs == 0) || (!all(x$covdata$isfac))) if (!ci) B <- 0 summ <- summary(x, newdata=newdata, X=X, type=type, fn=fn, t=t, start=start, ci=ci, B=B, cl=cl) t <- summ[[1]]$time X <- if (is.null(attr(summ,"X"))) as.matrix(0, nrow=1, ncol=max(x$ncoveffs,1)) else attr(summ,"X") if (is.null(col.ci)) col.ci <- col if (is.null(lwd.ci)) lwd.ci <- lwd dat <- x$data if (!is.null(fn)) type <- "" if (!add) { mf <- model.frame(x) Xraw <- mf[,attr(mf, "covnames.orig"), drop=FALSE] mm <- as.data.frame(model.matrix(x)) if (isTRUE(attr(dat$Y, "type")=="interval")){ # guard against NULL from older versions form <- "Surv(dat$Y[,\"time1\"],dat$Y[,\"time2\"],type=\"interval2\") ~ " } else form <- "Surv(dat$Y[,\"start\"],dat$Y[,\"stop\"],dat$Y[,\"status\"]) ~ " form <- paste(form, if (x$ncovs > 0 && all(x$covdata$isfac)) paste("mm[,",1:x$ncoveffs,"]", collapse=" + ") else 1) form <- as.formula(form) ## If any continuous covariates, it is hard to define subgroups ## so just plot the population survival if (type=="survival") { plot(survfit(form, data=mm, weights=dat$m$`(weights)`), col=col.obs, lty=lty.obs, lwd=lwd.obs, ylim=ylim, ...) } else if (type=="cumhaz") { plot(survfit(form, data=mm, weights=dat$m$`(weights)`), fun="cumhaz", col=col.obs, lty=lty.obs, lwd=lwd.obs, ylim=ylim, ...) } else if (type=="hazard") { muhaz.args <- list(...)[names(list(...)) %in% names(formals(muhaz))] if (is.null(muhaz.args$min.time)) muhaz.args$min.time <- 0 plot.args <- list(...)[!names(list(...)) %in% names(formals(muhaz))] if (!all(dat$Y[,"start"]==0)) warning("Left-truncated data not supported by muhaz: ignoring truncation point when plotting observed hazard") if (any(dat$Y[,"status"] > 1)) stop("Interval-censored data not supported by muhaz") if (!all(x$covdata$isfac)){ if (is.null(muhaz.args$max.time)) muhaz.args$max.time <- with(as.data.frame(dat$Y), max(time[status==1])) haz <- do.call("muhaz", c(list(times=dat$Y[,"stop"], delta=dat$Y[,"status"]), muhaz.args)) do.call("plot", c(list(haz), list(col=col.obs, lty=lty.obs, lwd=lwd.obs), plot.args)) } else { ## plot hazard for all groups defined by unique combinations of covariates group <- if(x$ncovs>0) do.call("interaction", mm) else factor(rep(0,nrow(dat$Y))) Xgroup <- factor(do.call("interaction", as.data.frame(X)), levels=levels(group)) haz <- list() for (i in 1:nrow(X)) { mha <- muhaz.args if (is.null(mha$max.time)) mha$max.time <- with(as.data.frame(dat$Y[group==Xgroup[i],,drop=FALSE]), max(time[status==1])) haz[[i]] <- do.call("muhaz", c(list(times=dat$Y[,"time"], delta=dat$Y[,"status"], subset=(group==Xgroup[i])), mha)) } if (missing(ylim)) ylim <- range(sapply(haz, function(x)range(x$haz.est))) do.call("plot", c(list(haz[[1]]), list(col=col.obs, lty=lty.obs, lwd=lwd.obs, ylim=ylim), plot.args)) if (nrow(X)>1) { for (i in 1:nrow(X)) { lines(haz[[i]], col=col.obs, lty=lty.obs, lwd=lwd.obs) } } } } } col <- rep(col, length=nrow(X)); lty=rep(lty, length=nrow(X)); lwd=rep(lwd, length=nrow(X)) col.ci <- rep(col.ci, length=nrow(X)); lty.ci=rep(lty.ci, length=nrow(X)); lwd.ci=rep(lwd.ci, length=nrow(X)) for (i in 1:length(summ)) { if (est) lines(summ[[i]]$time, summ[[i]]$est, col=col[i], lty=lty[i], lwd=lwd[i]) if (ci) { lines(summ[[i]]$time, summ[[i]]$lcl, col=col.ci[i], lty=lty.ci[i], lwd=lwd.ci[i]) lines(summ[[i]]$time, summ[[i]]$ucl, col=col.ci[i], lty=lty.ci[i], lwd=lwd.ci[i]) } } } ##' Add fitted flexible survival curves to a plot ##' ##' Add fitted survival (or hazard or cumulative hazard) curves from a ##' \code{\link{flexsurvreg}} model fit to an existing plot. ##' ##' Equivalent to \code{\link{plot.flexsurvreg}(...,add=TRUE)}. ##' ##' ##' @param x Output from \code{\link{flexsurvreg}}, representing a fitted ##' survival model object. ##' @param newdata Covariate values to produce fitted curves for, as a data ##' frame, as described in \code{\link{plot.flexsurvreg}}. ##' @param X Covariate values to produce fitted curves for, as a matrix, as ##' described in \code{\link{plot.flexsurvreg}}. ##' @param type \code{"survival"} for survival, \code{"cumhaz"} for cumulative ##' hazard, or \code{"hazard"} for hazard, as in ##' \code{\link{plot.flexsurvreg}}. ##' @param t Vector of times to plot fitted values for. ##' @param est Plot fitted curves (\code{TRUE} or \code{FALSE}.) ##' @param ci Plot confidence intervals for fitted curves. ##' @param B Number of simulations controlling accuracy of confidence ##' intervals, as used in \code{\link[=summary.flexsurvreg]{summary}}. ##' @param cl Width of confidence intervals, by default 0.95 for 95\% ##' intervals. ##' @param col Colour of the fitted curve(s). ##' @param lty Line type of the fitted curve(s). ##' @param lwd Line width of the fitted curve(s). ##' @param col.ci Colour of the confidence limits, defaulting to the same as ##' for the fitted curve. ##' @param lty.ci Line type of the confidence limits. ##' @param lwd.ci Line width of the confidence limits, defaulting to the same ##' as for the fitted curve. ##' @param ... Other arguments to be passed to the generic \code{\link{plot}} ##' and \code{\link{lines}} functions. ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @seealso \code{\link{flexsurvreg}} ##' @keywords models aplot ##' @export lines.flexsurvreg <- function(x, newdata=NULL, X=NULL, type="survival", t=NULL, est=TRUE, ci=NULL, B=1000, cl=0.95, col="red",lty=1,lwd=2, col.ci=NULL,lty.ci=2,lwd.ci=1, ...) { plot.flexsurvreg(x, newdata=newdata, X=X, type=type, t=t, est=est, ci=ci, B=B, cl=cl, col=col, lty=lty, lwd=lwd, col.ci=col.ci,lty.ci=lty.ci,lwd.ci=lwd.ci, add=TRUE, ...) } flexsurv/R/predict.flexsurvreg.R0000644000176200001440000002272314644755623016507 0ustar liggesusers#' Predictions from flexible survival models #' #' Predict outcomes from flexible survival models at the covariate values #' specified in \code{newdata}. #' #' @param object Output from \code{\link{flexsurvreg}} or #' \code{\link{flexsurvspline}}, representing a fitted survival model object. #' #' @param newdata Data frame containing covariate values at which to produce #' fitted values. There must be a column for every covariate in the model #' formula used to fit \code{object}, and one row for every combination of #' covariate values at which to obtain the fitted predictions. #' #' If \code{newdata} is omitted, then the original data used to fit the model #' are used, as extracted by \code{model.frame(object)}. However this will #' currently not work if the model formula contains functions, e.g. #' \code{~ factor(x)}. The names of the model frame must correspond to #' variables in the original data. #' #' @param type Character vector for the type of predictions desired. #' #' * \code{"response"} for mean survival time (the default). \code{"mean"} is #' an acceptable synonym #' #' * \code{"quantile"} for quantiles of the survival distribution as specified #' by \code{p} #' #' * \code{"rmst"} for restricted mean survival time #' #' * \code{"survival"} for survival probabilities #' #' * \code{"cumhaz"} for cumulative hazards #' #' * \code{"hazard"} for hazards #' #' * \code{"link"} for fitted values of the location parameter, analogous to #' the linear predictor in generalized linear models (\code{type = "lp"} and #' \code{type = "linear"} are acceptable synonyms). This is on the natural #' scale of the parameter, not the log scale. #' #' @param times Vector of time horizons at which to compute fitted values. #' Only applies when \code{type} is \code{"survival"}, \code{"cumhaz"}, #' \code{"hazard"}, or \code{"rmst"}. Will be silently ignored for all other #' types. #' #' If not specified, predictions for \code{"survival"}, \code{"cumhaz"}, and #' \code{"hazard"} will be made at each observed event time in #' \code{model.frame(object)}. #' #' For \code{"rmst"}, when \code{times} is not specified predictions will be #' made at the maximum observed event time from the data used to fit #' \code{object}. Specifying \code{times = Inf} is valid, and will return #' mean survival (equal to \code{type = "response"}). #' #' @param start Optional left-truncation time or times. The returned #' survival, hazard, or cumulative hazard will be conditioned on survival up #' to this time. `start` must be length 1 or the same length as `times`. #' Predicted times returned with \code{type} \code{"rmst"} or \code{"quantile"} ##' will be times since time zero, not times since the \code{start} time. #' #' @param conf.int Logical. Should confidence intervals be returned? #' Default is \code{FALSE}. #' #' @param conf.level Width of symmetric confidence intervals, relative to 1. #' #' @param se.fit Logical. Should standard errors of fitted values be returned? #' Default is \code{FALSE}. #' #' @param p Vector of quantiles at which to return fitted values when #' \code{type = "quantile"}. Default is \code{c(0.1, 0.9)}. #' #' @param ... Not currently used. #' #' @return A \code{\link[tibble]{tibble}} with same number of rows as #' \code{newdata} and in the same order. If multiple predictions are #' requested, a \code{\link[tibble]{tibble}} containing a single list-column #' of data frames. #' #' For the list-column of data frames - the dimensions of each data frame #' will be identical. Rows are added for each value of \code{times} or #' \code{p} requested. #' #' This function is a wrapper around \code{\link{summary.flexsurvreg}}, #' designed to help \pkg{flexsurv} to integrate with the "tidymodels" #' ecosystem, in particular the \pkg{censored} package. #' \code{\link{summary.flexsurvreg}} returns the same results but in a more #' conventional format. #' #' @seealso \code{\link{summary.flexsurvreg}}, #' \code{\link{residuals.flexsurvreg}} #' #' @author Matthew T. Warkentin (\url{https://github.com/mattwarkentin}) #' #' @importFrom tibble tibble #' @importFrom stats predict #' #' @md #' #' @export #' #' @examples #' #' fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") #' #' ## Simplest prediction: mean or median, for covariates defined by original dataset #' predict(fitg) #' predict(fitg, type = "quantile", p = 0.5) #' #' ## Simple prediction for user-defined covariate values #' predict(fitg, newdata = data.frame(age = c(40, 50, 60))) #' predict(fitg, type = "quantile", p = 0.5, newdata = data.frame(age = c(40,50,60))) #' #' ## Predict multiple quantiles and unnest #' require(tidyr) #' pr <- predict(fitg, type = "survival", times = c(600, 800)) #' tidyr::unnest(pr, .pred) #' predict.flexsurvreg <- function(object, newdata, type = "response", times, start = 0, conf.int = FALSE, conf.level = 0.95, se.fit = FALSE, p = c(0.1, 0.9), ... ) { if (missing(newdata)) newdata <- model.frame(object) assertthat::assert_that( inherits(newdata, "data.frame"), msg = "`newdata` must inherit the class `data.frame`" ) assertthat::assert_that( is.logical(se.fit), msg = '`se.fit` must be a logical (TRUE/FALSE).' ) assertthat::assert_that( is.logical(conf.int), msg = '`conf.int` must be a logical (TRUE/FALSE).' ) assertthat::assert_that( all(is.numeric(p), p <= 1, p >= 0), msg = "`p` should be a vector of quantiles in the range [0, 1]" ) assertthat::assert_that( is.numeric(start), msg = "`start` must be a numeric vector of left-truncation times" ) if (conf.int) assertthat::assert_that( is.numeric(conf.level), conf.level > 0, conf.level < 1, length(conf.level) == 1, msg = "`conf.level` must be length one and between 0 and 1" ) type <- match.arg(type, c("mean", "response", "quantile", "link", "lp", "linear", "survival", "cumhaz", "hazard", "rmst")) stype <- switch( type, response = "mean", lp = "link", linear = "link", type # all others keep their type ) if (stype %in% c("survival", "cumhaz", "hazard")) { if (missing(times)) times <- object$data$Y[,1][order(object$data$Y[,1])] assertthat::assert_that( all(is.numeric(times), times >= 0), msg = "`times` must be a vector of non-negative real-valued numbers." ) } else if (stype == "rmst" && !missing(times)) { assertthat::assert_that( all(is.numeric(times), times >= 0), msg = "`times` must be a vector of non-negative real-valued numbers." ) } else { times <- NULL } assertthat::assert_that( length(start) == 1 | length(start) == length(times), msg = paste0( "Length of `start` is ", length(start), ". Length should be 1, or the same length as `times`, which is ", length(times) ) ) nest_output <- ((stype == "quantile" && length(p) > 1) | (stype %in% c("survival", "cumhaz", "hazard", "rmst") && length(times) > 1)) res <- if (stype %in% c("survival", "hazard", "cumhaz", "rmst")) { summary( object = object, newdata = newdata, type = stype, quantiles = p, t = times, start = start, ci = conf.int, cl = conf.level, se = se.fit, tidy = TRUE, na.action = na.pass, cross = TRUE ) } else { # Avoid passing `t = times` for non-time based predictions # to avoid noisy warnings summary( object = object, newdata = newdata, type = stype, quantiles = p, start = start, ci = conf.int, cl = conf.level, se = se.fit, tidy = TRUE, na.action = na.pass, cross = TRUE ) } res <- tidy_rename(res, stype) if (nest_output) { if (stype == 'quantile') { num_reps <- length(p) } else { num_reps <- length(times) } orig_nrow <- nrow(newdata) res <- dplyr::mutate(res, .id = rep(1:orig_nrow, each = num_reps)) res <- tidyr::nest(res, .pred = -.id) res <- dplyr::select(res, .pred) } res } utils::globalVariables('.id') tidy_names <- function() { tibble::tibble( old = c("time", "quantile", "est", "se", "lcl", "ucl"), new = c(".eval_time", ".quantile", ".pred", ".std_error", ".pred_lower", ".pred_upper") ) } tidy_rename <- function(x, type) { names_tbl <- tidy_names() names_to_change <- names_tbl[names_tbl$old %in% names(x), ] out <- dplyr::select(x, names_to_change$old) colnames(out) <- names_to_change$new out <- tibble::as_tibble(out) if (type == "mean") type <- "time" name_with_type <- rlang::sym(paste0('.pred_', type)) dplyr::rename(out, !!name_with_type := .pred) } flexsurv/R/Gompertz.R0000644000176200001440000001270214472142471014273 0ustar liggesusers##' The Gompertz distribution ##' ##' Density, distribution function, hazards, quantile function and random ##' generation for the Gompertz distribution with unrestricted shape. ##' ##' The Gompertz distribution with \code{shape} parameter \eqn{a} and ##' \code{rate} parameter \eqn{b}{b} has probability density function ##' ##' \deqn{f(x | a, b) = be^{ax}\exp(-b/a (e^{ax} - 1))}{f(x | a, b) = b exp(ax) ##' exp(-b/a (exp(ax) - 1))} ##' ##' and hazard ##' ##' \deqn{h(x | a, b) = b e^{ax}}{h(x | a, b) = b exp(ax)} ##' ##' The hazard is increasing for shape \eqn{a>0} and decreasing for \eqn{a<0}. ##' For \eqn{a=0} the Gompertz is equivalent to the exponential distribution ##' with constant hazard and rate \eqn{b}. ##' ##' The probability distribution function is \deqn{F(x | a, b) = 1 - \exp(-b/a ##' (e^{ax} - 1))}{F(x | a, b) = 1 - exp(-b/a (exp(ax) - 1))} ##' ##' Thus if \eqn{a} is negative, letting \eqn{x} tend to infinity shows that ##' there is a non-zero probability \eqn{\exp(b/a)}{exp(b/a)} of living ##' forever. On these occasions \code{qgompertz} and \code{rgompertz} will ##' return \code{Inf}. ##' ##' @aliases Gompertz dgompertz pgompertz qgompertz hgompertz Hgompertz ##' rgompertz ##' @param x,q vector of quantiles. ##' @param p vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the length is ##' taken to be the number required. ##' @param shape,rate vector of shape and rate parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dgompertz} gives the density, \code{pgompertz} gives the ##' distribution function, \code{qgompertz} gives the quantile function, ##' \code{hgompertz} gives the hazard function, \code{Hgompertz} gives the ##' cumulative hazard function, and \code{rgompertz} generates random deviates. ##' @note Some implementations of the Gompertz restrict \eqn{a} to be strictly ##' positive, which ensures that the probability of survival decreases to zero ##' as \eqn{x} increases to infinity. The more flexible implementation given ##' here is consistent with \code{streg} in Stata. ##' ##' The functions \code{\link[eha:Gompertz]{eha::dgompertz}} and similar available in the ##' package \pkg{eha} label the parameters the other way round, so that what is ##' called the \code{shape} there is called the \code{rate} here, and what is ##' called \code{1 / scale} there is called the \code{shape} here. The ##' terminology here is consistent with the exponential \code{\link{dexp}} and ##' Weibull \code{\link{dweibull}} distributions in R. ##' @author Christopher Jackson ##' @seealso \code{\link{dexp}} ##' @references Stata Press (2007) Stata release 10 manual: Survival analysis ##' and epidemiological tables. ##' @keywords distribution ##' @name Gompertz NULL ## consistent with paper and Stata ## shape pos: inc haz, shape neg: dec haz just like weibull, shape zero=exponential ## ## in eha: shape=lam, gamma=1/scale ## log(shape) + x/scale - shape * scale * (exp(x/scale) - 1)) ## shape/scale labelled wrong way round. ##' @export ##' @rdname Gompertz dgompertz <- function(x, shape, rate=1, log=FALSE) { check_numeric(x=x, shape=shape, rate=rate) dgompertz_work(x, shape, rate, log) } ##' @export ##' @rdname Gompertz pgompertz <- function(q, shape, rate=1, lower.tail = TRUE, log.p = FALSE) { check_numeric(q=q, shape=shape, rate=rate) pgompertz_work(q, shape, rate, lower.tail, log.p) } ##' @export ##' @rdname Gompertz qgompertz <- function(p, shape, rate=1, lower.tail = TRUE, log.p = FALSE) { d <- dbase("gompertz", lower.tail=lower.tail, log=log.p, p=p, shape=shape, rate=rate) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) ret[ind][shape==0] <- qexp(p[shape==0], rate=rate[shape==0]) sn0 <- shape!=0 if (any(sn0)) { p <- p[sn0]; shape <- shape[sn0]; rate <- rate[sn0] asymp <- 1 - exp(rate/shape) immortal <- shape < 0 & p > asymp ret[ind][sn0][immortal] <- Inf ret[ind][sn0][!immortal] <- 1 / shape[!immortal] * log1p(-log1p(-p[!immortal]) * shape[!immortal] / rate[!immortal]) } ret } ##' @export ##' @rdname Gompertz rgompertz <- function(n, shape = 1, rate = 1){ r <- rbase("gompertz", n=n, shape=shape, rate=rate) for (i in seq_along(r)) assign(names(r)[i], r[[i]]) ret[ind] <- qgompertz(p=runif(sum(ind)), shape=shape, rate=rate) ret } ##' @export ##' @rdname Gompertz hgompertz <- function(x, shape, rate = 1, log = FALSE) { h <- dbase("gompertz", log=log, x=x, shape=shape, rate=rate) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) if (log) ret[ind] <- log(rate) + (shape * x) else ret[ind] <- rate * exp(shape * x) ret } ##' @export ##' @rdname Gompertz Hgompertz <- function(x, shape, rate = 1, log = FALSE) { h <- dbase("gompertz", log=log, x=x, shape=shape, rate=rate) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) ret[ind] <- ifelse(shape==0, rate*x, rate/shape * expm1(shape*x)) if (log) ret[ind] <- log(ret[ind]) ret } ##' @export ##' @rdname means rmst_gompertz = function(t, shape, rate=1, start=0){ rmst_generic(pgompertz, t, start=start, shape=shape, rate=rate) } ##' @export ##' @rdname means mean_gompertz = function(shape, rate = 1){ rmst_generic(pgompertz, Inf, start=0, shape=shape, rate=rate) } flexsurv/R/mstate.R0000644000176200001440000021531614644767543014005 0ustar liggesusers### FUNCTIONS FOR MULTI-STATE MODELLING is.flexsurvlist <- function(x){ is.list(x) && (length(x) > 0) && inherits(x[[1]], "flexsurvreg") && all(sapply(x, inherits, "flexsurvreg")) } form.msm.newdata <- function(x, newdata=NULL, tvar="trans", trans){ tr <- sort(unique(na.omit(as.vector(trans)))) ntr <- length(tr) if (!(tvar %in% x$covdata$covnames)){ if (missing(tvar)) stop("\"tvar\" not supplied and variable \"", tvar, "\" not in model") else stop("\"variable \"", tvar, "\" not in model") } if (!x$covdata$isfac[[tvar]]) stop("`tvar` should have been fitted as a factor covariate in the model") if(is.null(newdata)){ newdata <- data.frame(trans=factor(tr, levels=x$covdata$xlev[[tvar]])) names(newdata) <- tvar } else { newdata <- as.data.frame(newdata) if (nrow(newdata)==1) newdata <- newdata[rep(1,ntr),,drop=FALSE] else if (nrow(newdata) != ntr) stop(sprintf("length of variables in \"newdata\" must be either 1 or number of transitions, %d", ntr)) newdata[,tvar] <- factor(tr, levels=x$covdata$xlev[[tvar]]) } newdata } ##' Cumulative intensity function for parametric multi-state models ##' ##' Cumulative transition-specific intensity/hazard functions for ##' fully-parametric multi-state or competing risks models, using a ##' piecewise-constant approximation that will allow prediction using the ##' functions in the \pkg{mstate} package. ##' ##' ##' @param object Output from \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}}, representing a fitted survival model object. ##' ##' The model should have been fitted to data consisting of one row for each ##' observed transition and additional rows corresponding to censored times to ##' competing transitions. This is the "long" format, or counting process ##' format, as explained in the \pkg{flexsurv} vignette. ##' ##' The model should contain a categorical covariate indicating the transition. ##' In \code{flexsurv} this variable can have any name, indicated here by the ##' \code{tvar} argument. In the Cox models demonstrated by \pkg{mstate} it is ##' usually included in model formulae as \code{strata(trans)}, but note that ##' the \code{strata} function does not do anything in \pkg{flexsurv}. The ##' formula supplied to \code{\link{flexsurvreg}} should be precise about which ##' parameters are assumed to vary with the transition type. ##' ##' Alternatively, if the parameters (including covariate effects) are assumed ##' to be different between different transitions, then a list of ##' transition-specific models can be formed. This list has one component for ##' each permitted transition in the multi-state model. This is more ##' computationally efficient, particularly for larger models and datasets. ##' See the example below, and the vignette. ##' @param t Vector of times. These do not need to be the same as the observed ##' event times, and since the model is parametric, they can be outside the ##' range of the data. A grid of more frequent times will provide a better ##' approximation to the cumulative hazard trajectory for prediction with ##' \code{\link[mstate]{probtrans}} or \code{\link[mstate]{mssample}}, at the ##' cost of greater computational expense. ##' @param newdata A data frame specifying the values of covariates in the ##' fitted model, other than the transition number. This must be specified if ##' there are other covariates. The variable names should be the same as those ##' in the fitted model formula. There must be either one value per covariate ##' (the typical situation) or \eqn{n} values per covariate, a different one ##' for each of the \eqn{n} allowed transitions. ##' @param variance Calculate the variances and covariances of the transition ##' cumulative hazards (\code{TRUE} or \code{FALSE}). This is based on ##' simulation from the normal asymptotic distribution of the estimates, which ##' is computationally-expensive. ##' @param tvar Name of the categorical variable in the model formula that ##' represents the transition number. This should have been defined as a factor, ##' with factor levels that ##' correspond to elements of \code{trans}, conventionally a sequence of ##' integers starting from 1. Not required if \code{x} is a list of ##' transition-specific models. ##' @param trans Matrix indicating allowed transitions in the multi-state ##' model, in the format understood by \pkg{mstate}: a matrix of integers whose ##' \eqn{r,s} entry is \eqn{i} if the \eqn{i}th transition type (reading across ##' rows) is \eqn{r,s}, and has \code{NA}s on the diagonal and where the ##' \eqn{r,s} transition is disallowed. ##' @param B Number of simulations from the normal asymptotic distribution used ##' to calculate variances. Decrease for greater speed at the expense of ##' accuracy. ##' @return An object of class \code{"msfit"}, in the same form as the objects ##' used in the \pkg{mstate} package. The \code{\link[mstate]{msfit}} method ##' from \pkg{mstate} returns the equivalent cumulative intensities for Cox ##' regression models fitted with \code{\link[survival]{coxph}}. ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @seealso \pkg{flexsurv} provides alternative functions designed ##' specifically for predicting from parametric multi-state models without ##' calling \pkg{mstate}. These include \code{\link{pmatrix.fs}} and ##' \code{\link{pmatrix.simfs}} for the transition probability matrix, and ##' \code{\link{totlos.fs}} and \code{\link{totlos.simfs}} for expected total ##' lengths of stay in states. These are generally more efficient than going ##' via \pkg{mstate}. ##' @references Liesbeth C. de Wreede, Marta Fiocco, Hein Putter (2011). ##' \pkg{mstate}: An R Package for the Analysis of Competing Risks and ##' Multi-State Models. \emph{Journal of Statistical Software}, 38(7), 1-30. ##' \doi{10.18637/jss.v038.i07} ##' ##' Mandel, M. (2013). "Simulation based confidence intervals for functions ##' with complicated derivatives." The American Statistician 67(2):76-81 ##' @keywords models ##' @examples ##' ##' ## 3 state illness-death model for bronchiolitis obliterans ##' ## Compare clock-reset / semi-Markov multi-state models ##' ##' ## Simple exponential model (reduces to Markov) ##' ##' bexp <- flexsurvreg(Surv(years, status) ~ trans, ##' data=bosms3, dist="exp") ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' mexp <- msfit.flexsurvreg(bexp, t=seq(0,12,by=0.1), ##' trans=tmat, tvar="trans", variance=FALSE) ##' ##' ## Cox semi-parametric model within each transition ##' ##' bcox <- coxph(Surv(years, status) ~ strata(trans), data=bosms3) ##' ##' if (require("mstate")){ ##' ##' mcox <- mstate::msfit(bcox, trans=tmat) ##' ##' ## Flexible parametric spline-based model ##' ##' bspl <- flexsurvspline(Surv(years, status) ~ trans + gamma1(trans), ##' data=bosms3, k=3) ##' mspl <- msfit.flexsurvreg(bspl, t=seq(0,12,by=0.1), ##' trans=tmat, tvar="trans", variance=FALSE) ##' ##' ## Compare fit: exponential model is OK but the spline is better ##' ##' plot(mcox, lwd=1, xlim=c(0, 12), ylim=c(0,4)) ##' cols <- c("black","red","green") ##' for (i in 1:3){ ##' lines(mexp$Haz$time[mexp$Haz$trans==i], mexp$Haz$Haz[mexp$Haz$trans==i], ##' col=cols[i], lwd=2, lty=2) ##' lines(mspl$Haz$time[mspl$Haz$trans==i], mspl$Haz$Haz[mspl$Haz$trans==i], ##' col=cols[i], lwd=3) ##' } ##' legend("topright", lwd=c(1,2,3), lty=c(1,2,1), ##' c("Cox", "Exponential", "Flexible parametric"), bty="n") ##' ##' } ##' ##' ## Fit a list of models, one for each transition ##' ## More computationally efficient, but only valid if parameters ##' ## are different between transitions. ##' ##' \dontrun{ ##' bexp.list <- vector(3, mode="list") ##' for (i in 1:3) { ##' bexp.list[[i]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==i), ##' data=bosms3, dist="exp") ##' } ##' ##' ## The list of models can be passed to this and other functions, ##' ## as if it were a single multi-state model. ##' ##' msfit.flexsurvreg(bexp.list, t=seq(0,12,by=0.1), trans=tmat) ##' } ##' ##' @export msfit.flexsurvreg <- function(object, t, newdata=NULL, variance=TRUE, tvar="trans", trans, B=1000){ tr <- sort(unique(na.omit(as.vector(trans)))) ntr <- length(tr) if (is.flexsurvlist(object)) { Haz <- vector(ntr, mode="list") for (i in seq_len(ntr)) Haz[[i]] <- summary(object[[i]], type="cumhaz", t=t, newdata=newdata, ci=FALSE)[[1]] } else { newdata <- form.msm.newdata(object, newdata=newdata, tvar=tvar, trans=trans) X <- form.model.matrix(object, newdata) Haz <- summary(object, type="cumhaz", t=t, X=X, ci=FALSE) } Haz <- do.call("rbind",Haz[seq_along(tr)]) rownames(Haz) <- NULL Haz$trans <- rep(seq_along(tr), each=length(t)) names(Haz)[names(Haz)=="est"] <- "Haz" res <- list(Haz=Haz, trans=trans) foundse <- if (is.flexsurvlist(object)) !anyNA(sapply(object, function(x)x$cov[[1]])) else !is.na(object$cov[1]) if (variance && foundse){ boot <- array(dim=c(B, length(t), ntr)) for (i in seq_along(tr)) boot[,,i] <- if (is.flexsurvlist(object)) normbootfn.flexsurvreg(object[[i]], t=t, start=0, newdata=newdata, B=B, fn=summary_fns(object[[i]],"cumhaz")) else normbootfn.flexsurvreg(object, t=t, start=0, X=X[i,,drop=FALSE], B=B, fn=summary_fns(object,"cumhaz")) ntr2 <- 0.5*ntr*(ntr+1) nt <- length(t) mat <- matrix(nrow=ntr, ncol=ntr) trans1 <- rep(t(row(mat))[!t(lower.tri(mat))], each=nt) trans2 <- rep(t(col(mat))[!t(lower.tri(mat))], each=nt) res$varHaz <- data.frame(time=rep(t, ntr2), varHaz=numeric(ntr2*nt), trans1=trans1, trans2=trans2) for (i in 1:ntr){ for (j in i:ntr){ res$varHaz$varHaz[trans1==i & trans2==j] <- mapply(cov, split(t(boot[,,i]),seq_along(t)), split(t(boot[,,j]),seq_along(t))) } } } class(res) <- "msfit" res } ##' Transition-specific parameters in a flexible parametric multi-state model ##' ##' List of maximum likelihood estimates of transition-specific parameters in ##' a flexible parametric multi-state model, at given covariate values. ##' ##' ##' @param x A multi-state model fitted with \code{\link{flexsurvreg}}. See ##' \code{\link{msfit.flexsurvreg}} for the required form of the model and the ##' data. ##' ##' \code{x} can also be a list of \code{\link{flexsurvreg}} models, with one ##' component for each permitted transition in the multi-state model, as ##' illustrated in \code{\link{msfit.flexsurvreg}}. ##' ##' @param trans Matrix indicating allowed transitions. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param newdata A data frame specifying the values of covariates in the ##' fitted model, other than the transition number. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param tvar Variable in the data representing the transition type. Not ##' required if \code{x} is a list of models. ##' ##' @return A list with one component for each permitted transition. Each component ##' has one element for each parameter of the parametric distribution that generates ##' the corresponding event in the multi-state model. ##' ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk}. ##' ##' @keywords models survival ##' ##' @export pars.fmsm <- function(x, trans, newdata=NULL, tvar="trans") { if (is.flexsurvlist(x)){ ntr <- length(x) # number of allowed transitions if (ntr != length(na.omit(as.vector(trans)))) stop(sprintf("x is a list of %s flexsurvreg objects, but trans indicates %s transitions", ntr, length(na.omit(as.vector(trans))))) basepar <- vector(ntr, mode="list") newdata <- as.data.frame(newdata) for (i in 1:ntr){ if (x[[i]]$ncovs==0) X <- matrix(0) else { if(nrow(newdata) == 1L) { X <- form.model.matrix(x[[i]], as.data.frame(newdata), na.action=na.omit) } else if(nrow(newdata) == ntr){ X <- form.model.matrix(x[[i]], as.data.frame(newdata[i, ,drop = FALSE]), na.action=na.omit) } else stop(sprintf("`newdata` has %s rows. It must either have one row, or one row for each of the %s allowed transitions",nrow(newdata),ntr)) ## } else stop(sprintf("`newdata` must only have one row")) # use case for ntr rows is unclear } beta <- if (x[[i]]$ncovs==0) 0 else x[[i]]$res.t[x[[i]]$covpars,"est"] basepar[[i]] <- add.covs(x[[i]], x[[i]]$res.t[x[[i]]$dlist$pars,"est"], beta, X, transform=FALSE) } } else if (inherits(x, "flexsurvreg")) { newdata <- form.msm.newdata(x, newdata=newdata, tvar=tvar, trans=trans) X <- form.model.matrix(x, newdata, na.action=na.omit) basepar <- add.covs(x, pars=x$res.t[x$dlist$pars,"est"], beta=x$res.t[x$covpars,"est"], X=X) ntrans <- length(na.omit(as.vector(trans))) basepar <- split(basepar, seq_len(ntrans)) basepar <- lapply(basepar, function(y){y <- matrix(y,nrow=1); colnames(y) <- x$dlist$pars; y}) } else stop("expected x to be a flexsurvreg object or list of flexsurvreg objects") basepar } state_nums <- function(state, object){ if (is.character(state)){ badstates <- state[! (state %in% attr(object, "statenames"))] if (length(badstates) > 0) stop(paste(badstates,collapse=","), " not found in state names") state <- match(state, attr(object, "statenames")) } state } state_names <- function(state, object){ if (is.character(attr(object, "statenames"))) state <- attr(object, "statenames")[state] state } ##' Transition probability matrix from a fully-parametric, time-inhomogeneous ##' Markov multi-state model ##' ##' The transition probability matrix for time-inhomogeneous Markov multi-state ##' models fitted to time-to-event data with \code{\link{flexsurvreg}}. This ##' has \eqn{r,s} entry giving the probability that an individual is in state ##' \eqn{s} at time \eqn{t}, given they are in state \eqn{r} at time \eqn{0}. ##' ##' This is computed by solving the Kolmogorov forward differential equation ##' numerically, using the methods in the \pkg{deSolve} package. The ##' equation is ##' ##' \deqn{\frac{dP(t)}{dt} = P(t) Q(t)} ##' ##' where \eqn{P(t)} is the transition probability matrix for time \eqn{t}, and ##' \eqn{Q(t)} is the transition hazard or intensity as a function of \eqn{t}. ##' The initial condition is \eqn{P(0) = I}. ##' ##' Note that the package \pkg{msm} has a similar method \code{pmatrix.msm}. ##' \code{pmatrix.fs} should give the same results as \code{pmatrix.msm} when ##' both of these conditions hold: ##' ##' \itemize{ \item the time-to-event distribution is exponential for all ##' transitions, thus the \code{flexsurvreg} model was fitted with ##' \code{dist="exp"} and the model is time-homogeneous. \item the \pkg{msm} ##' model was fitted with \code{exacttimes=TRUE}, thus all the event times are ##' known, and there are no time-dependent covariates. } ##' ##' \pkg{msm} only allows exponential or piecewise-exponential time-to-event ##' distributions, while \pkg{flexsurvreg} allows more flexible models. ##' \pkg{msm} however was designed in particular for panel data, where the ##' process is observed only at arbitrary times, thus the times of transition ##' are unknown, which makes flexible models difficult. ##' ##' This function is only valid for Markov ("clock-forward") multi-state ##' models, though no warning or error is currently given if the model is not ##' Markov. See \code{\link{pmatrix.simfs}} for the equivalent for semi-Markov ##' ("clock-reset") models. ##' ##' @param x A model fitted with \code{\link{flexsurvreg}}. See ##' \code{\link{msfit.flexsurvreg}} for the required form of the model and the ##' data. Additionally, this must be a Markov / clock-forward model, but can ##' be time-inhomogeneous. See the package vignette for further explanation. ##' ##' \code{x} can also be a list of models, with one component for each ##' permitted transition, as illustrated in \code{\link{msfit.flexsurvreg}}. ##' @param trans Matrix indicating allowed transitions. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param t Time or vector of times to predict state occupancy probabilities ##' for. ##' ##' @param newdata A data frame specifying the values of covariates in the ##' fitted model, other than the transition number. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param condstates xInstead of the unconditional probability of being in state \eqn{s} at time \eqn{t} given state \eqn{r} at time 0, return the probability conditional on being in a particular subset of states at time \eqn{t}. This subset is specified in the \code{condstates} argument, as a vector of character labels or integers. ##' ##' This is used, for example, in competing risks situations, e.g. if the competing states are death or recovery from a disease, and we want to compute the probability a patient has died, given they have died or recovered. If these are absorbing states, then as \eqn{t} increases, this converges to the case fatality ratio. To compute this, set \eqn{t} to a very large number, \code{Inf} will not work. ##' ##' @param ci Return a confidence interval calculated by simulating from the ##' asymptotic normal distribution of the maximum likelihood estimates. Turned ##' off by default, since this is computationally intensive. If turned on, ##' users should increase \code{B} until the results reach the desired ##' precision. ##' ##' @param tvar Variable in the data representing the transition type. Not ##' required if \code{x} is a list of models. ##' ##' @param sing.inf If there is a singularity in the observed hazard, for ##' example a Weibull distribution with \code{shape < 1} has infinite hazard at ##' \code{t=0}, then as a workaround, the hazard is assumed to be a large ##' finite number, \code{sing.inf}, at this time. The results should not be ##' sensitive to the exact value assumed, but users should make sure by ##' adjusting this parameter in these cases. ##' ##' @param B Number of simulations from the normal asymptotic distribution used ##' to calculate variances. Decrease for greater speed at the expense of ##' accuracy. ##' ##' @param cl Width of symmetric confidence intervals, relative to 1. ##' ##' @param tidy If TRUE then return the results as a tidy data frame ##' ##' @param ... Arguments passed to \code{\link[deSolve]{ode}} in \pkg{deSolve}. ##' ##' @return The transition probability matrix, if \code{t} is of length 1. If \code{t} is longer, return a list of matrices, or a data frame if \code{tidy} is TRUE. ##' ##' If \code{ci=TRUE}, each element has attributes \code{"lower"} and ##' \code{"upper"} giving matrices of the corresponding confidence limits. ##' These are formatted for printing but may be extracted using \code{attr()}. ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk}. ##' @seealso \code{\link{pmatrix.simfs}}, \code{\link{totlos.fs}}, ##' \code{\link{msfit.flexsurvreg}}. ##' @keywords models survival ##' @examples ##' ##' # BOS example in vignette, and in msfit.flexsurvreg ##' bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, ##' data=bosms3, dist="exp") ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' # more likely to be dead (state 3) as time moves on, or if start with ##' # BOS (state 2) ##' pmatrix.fs(bexp, t=c(5,10), trans=tmat) ##' @export pmatrix.fs <- function(x, trans=NULL, t=1, newdata=NULL, condstates = NULL, ci=FALSE, tvar="trans", sing.inf=1e+10, B=1000, cl=0.95, tidy=FALSE, ...){ if (is.null(trans)) { if (!is.null(attr(x, "trans"))) trans <- attr(x, "trans") else stop("`trans` not supplied and not found in `x`") } ntr <- sum(!is.na(trans)) nst <- nrow(trans) dp <- function(t, y, parms, ...){ P <- matrix(y, nrow=nst, ncol=nst) haz <- numeric(nst) for (i in 1:ntr){ xi <- if (is.flexsurvlist(x)) x[[i]] else x hcall <- list(x=t) for (j in seq_along(xi$dlist$pars)) hcall[[xi$dlist$pars[j]]] <- parms$par[[i]][j] for (j in seq_along(xi$aux)) hcall[[names(xi$aux)[j]]] <- xi$aux[[j]] haz[i] <- do.call(xi$dfns$h, hcall) } Q <- haz[trans] Q[is.na(Q)] <- 0 Q[is.infinite(Q) & Q>0] <- sing.inf Q <- matrix(Q, nrow=nst, ncol=nst) diag(Q) <- -rowSums(Q) list(P %*% Q) } nt <- length(t) if (nt<1) stop("number of times should be at least one") basepar <- pars.fmsm(x=x, trans=trans, newdata=newdata, tvar=tvar) auxpar <- if (!is.flexsurvlist(x)) x$aux else lapply(x, function(x)x$aux) res <- ode(y=diag(nst), times=c(0,t), func=dp, parms=list(par=basepar, aux=auxpar), ...)[-1,-1] if (is.null(condstates)) condstates <- 1:nst condstates <- state_nums(condstates, x) if (any(condstates > nst)) stop(sprintf("all `condstates` should be in 1 to %s",nst)) to_pmatrix <- function(x){ res <- matrix(x,nrow=nst,dimnames=dimnames(trans)) anyevent <- rowSums(res[,condstates,drop=FALSE]) res <- res[,condstates] / anyevent } res <- lapply(split(res,1:nt), to_pmatrix) names(res) <- t if (ci){ resci <- bootci.fmsm(x, B, fn=pmatrix.fs, cl=cl, ci=FALSE, cores=NULL, trans=trans, t=t, newdata=newdata, condstates=condstates, tvar=tvar, sing.inf=sing.inf, tidy=tidy, ...) if (tidy) resci <- resci[,1:(nt*nst*nst),drop=FALSE] resl <- lapply(split(resci[1,],rep(1:nt, each=nst*nst)), function(x)matrix(x,nrow=nst,dimnames=dimnames(trans))) resu <- lapply(split(resci[2,],rep(1:nt, each=nst*nst)), function(x)matrix(x,nrow=nst,dimnames=dimnames(trans))) names(resl) <- names(resu) <- t for (i in 1:nt){ attr(res[[i]], "lower") <- resl[[i]] attr(res[[i]], "upper") <- resu[[i]] class(res[[i]]) <- "fs.msm.est" } } if (nt==1) res <- res[[1]] if (tidy) { if (is.list(res)) res <- do.call("rbind", res) res <- as.data.frame(res) rownames(res) <- NULL res$start <- rep(1:nst, nt) res$time <- rep(t, each=nst) res } attr(res, "statenames") <- rownames(trans) attr(res, "nst") <- nst res } ## Obtains matrix T(t) of expected times spent in state (col) starting ## from state (row) up to time t. ## Solves the second order linear ODE system T''(t) = P(t) Q(t) ## Express as dT/dt = P(t), dP/dt = P(t)Q(t), solve for both P and T at once ##' Total length of stay in particular states for a fully-parametric, ##' time-inhomogeneous Markov multi-state model ##' ##' The matrix whose \eqn{r,s} entry is the expected amount of time spent in ##' state \eqn{s} for a time-inhomogeneous, continuous-time Markov multi-state ##' process that starts in state \eqn{r}, up to a maximum time \eqn{t}. This is ##' defined as the integral of the corresponding transition probability up to ##' that time. ##' ##' This is computed by solving a second order extension of the Kolmogorov ##' forward differential equation numerically, using the methods in the ##' \pkg{deSolve} package. The equation is expressed as a linear ##' system ##' ##' \deqn{\frac{dT(t)}{dt} = P(t)} \deqn{\frac{dP(t)}{dt} = P(t) Q(t)} ##' ##' and solved for \eqn{T(t)} and \eqn{P(t)} simultaneously, where \eqn{T(t)} ##' is the matrix of total lengths of stay, \eqn{P(t)} is the transition ##' probability matrix for time \eqn{t}, and \eqn{Q(t)} is the transition ##' hazard or intensity as a function of \eqn{t}. The initial conditions are ##' \eqn{T(0) = 0} and \eqn{P(0) = I}. ##' ##' Note that the package \pkg{msm} has a similar method \code{totlos.msm}. ##' \code{totlos.fs} should give the same results as \code{totlos.msm} when ##' both of these conditions hold: ##' ##' \itemize{ \item the time-to-event distribution is exponential for all ##' transitions, thus the \code{flexsurvreg} model was fitted with ##' \code{dist="exp"}, and is time-homogeneous. \item the \pkg{msm} model was ##' fitted with \code{exacttimes=TRUE}, thus all the event times are known, and ##' there are no time-dependent covariates. } ##' ##' \pkg{msm} only allows exponential or piecewise-exponential time-to-event ##' distributions, while \pkg{flexsurvreg} allows more flexible models. ##' \pkg{msm} however was designed in particular for panel data, where the ##' process is observed only at arbitrary times, thus the times of transition ##' are unknown, which makes flexible models difficult. ##' ##' This function is only valid for Markov ("clock-forward") multi-state ##' models, though no warning or error is currently given if the model is not ##' Markov. See \code{\link{totlos.simfs}} for the equivalent for semi-Markov ##' ("clock-reset") models. ##' ##' @param x A model fitted with \code{\link{flexsurvreg}}. See ##' \code{\link{msfit.flexsurvreg}} for the required form of the model and the ##' data. Additionally, this must be a Markov / clock-forward model, but can ##' be time-inhomogeneous. See the package vignette for further explanation. ##' ##' \code{x} can also be a list of models, with one component for each ##' permitted transition, as illustrated in \code{\link{msfit.flexsurvreg}}. ##' @param trans Matrix indicating allowed transitions. See ##' \code{\link{msfit.flexsurvreg}}. ##' @param t Time or vector of times to predict up to. Must be finite. ##' @param newdata A data frame specifying the values of covariates in the ##' fitted model, other than the transition number. See ##' \code{\link{msfit.flexsurvreg}}. ##' @param ci Return a confidence interval calculated by simulating from the ##' asymptotic normal distribution of the maximum likelihood estimates. Turned ##' off by default, since this is computationally intensive. If turned on, ##' users should increase \code{B} until the results reach the desired ##' precision. ##' @param tvar Variable in the data representing the transition type. Not ##' required if \code{x} is a list of models. ##' @param sing.inf If there is a singularity in the observed hazard, for ##' example a Weibull distribution with \code{shape < 1} has infinite hazard at ##' \code{t=0}, then as a workaround, the hazard is assumed to be a large ##' finite number, \code{sing.inf}, at this time. The results should not be ##' sensitive to the exact value assumed, but users should make sure by ##' adjusting this parameter in these cases. ##' ##' @param B Number of simulations from the normal asymptotic distribution used ##' to calculate variances. Decrease for greater speed at the expense of ##' accuracy. ##' ##' @param cl Width of symmetric confidence intervals, relative to 1. ##' ##' @param ... Arguments passed to \code{\link[deSolve]{ode}} in \pkg{deSolve}. ##' ##' @return The matrix of lengths of stay \eqn{T(t)}, if \code{t} is of length ##' 1, or a list of matrices if \code{t} is longer. ##' ##' If \code{ci=TRUE}, each element has attributes \code{"lower"} and ##' \code{"upper"} giving matrices of the corresponding confidence limits. ##' These are formatted for printing but may be extracted using \code{attr()}. ##' ##' The result also has an attribute \code{P} giving the transition probability ##' matrices, since these are unavoidably computed as a side effect. These are ##' suppressed for printing, but can be extracted with \code{attr(...,"P")}. ##' ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk}. ##' @seealso \code{\link{totlos.simfs}}, \code{\link{pmatrix.fs}}, ##' \code{\link{msfit.flexsurvreg}}. ##' @keywords models survival ##' @examples ##' ##' # BOS example in vignette, and in msfit.flexsurvreg ##' bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, ##' data=bosms3, dist="exp") ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' ##' # predict 4 years spent without BOS, 3 years with BOS, before death ##' # As t increases, this should converge ##' ##' totlos.fs(bexp, t=10, trans=tmat) ##' totlos.fs(bexp, t=1000, trans=tmat) ##' totlos.fs(bexp, t=c(5,10), trans=tmat) ##' ##' # Answers should match results in help(totlos.simfs) up to Monte Carlo ##' # error there / ODE solving precision here, since with an exponential ##' # distribution, the "semi-Markov" model there is the same as the Markov ##' # model here ##' @export totlos.fs <- function(x, trans=NULL, t=1, newdata=NULL, ci=FALSE, tvar="trans", sing.inf=1e+10, B=1000, cl=0.95, ...){ if (is.null(trans)) { if (!is.null(attr(x, "trans"))) trans <- attr(x, "trans") else stop("`trans` not supplied and not found in `x`") } ntr <- sum(!is.na(trans)) n <- nrow(trans) nsq <- n*n dp <- function(t, y, parms, ...){ P <- matrix(y[nsq + 1:nsq], nrow=n, ncol=n) haz <- numeric(n) for (i in 1:ntr){ xi <- if (is.flexsurvlist(x)) x[[i]] else x hcall <- list(x=t) for (j in seq_along(xi$dlist$pars)) hcall[[xi$dlist$pars[j]]] <- parms$par[[i]][j] hcall <- c(hcall, parms$aux[[i]]) haz[i] <- do.call(xi$dfns$h, hcall) } Q <- haz[trans] Q[is.na(Q)] <- 0 Q[is.infinite(Q) & Q>0] <- sing.inf Q <- matrix(Q, nrow=n, ncol=n) diag(Q) <- -rowSums(Q) list(cbind(P, P %*% Q)) } nt <- length(t) if (nt<1) stop("number of times should be at least one") basepar <- pars.fmsm(x=x, trans=trans, newdata=newdata, tvar=tvar) auxpar <- if (!is.flexsurvlist(x)) x$aux else lapply(x, function(x)x$aux) init <- cbind(matrix(0, nrow=n, ncol=n), diag(n)) res <- ode(y=init, times=c(0,t), func=dp, parms=list(par=basepar,aux=auxpar), ...)[-1,-1] res.t <- lapply(split(res,1:nt), function(x)matrix(x[1:nsq],nrow=n)) res.p <- lapply(split(res,1:nt), function(x)matrix(x[nsq + 1:nsq],nrow=n)) names(res.t) <- names(res.p) <- t if (ci){ resci <- bootci.fmsm(x, B, fn=totlos.fs, attrs="P", cl=cl, ci=FALSE, trans=trans, t=t, newdata=newdata, tvar=tvar, sing.inf=sing.inf, ...) tind <- rep(rep(1:nt,each=n*n), 2) res.tl <- lapply(split(resci[1,],tind), function(x)matrix(x[1:nsq],nrow=n)) res.tu <- lapply(split(resci[2,],tind), function(x)matrix(x[1:nsq],nrow=n)) res.pl <- lapply(split(resci[1,],tind), function(x)matrix(x[nsq + 1:nsq],nrow=n)) res.pu <- lapply(split(resci[2,],tind), function(x)matrix(x[nsq + 1:nsq],nrow=n)) names(res.tl) <- names(res.tu) <- names(res.pl) <- names(res.pu) <- t for (i in 1:nt){ attr(res.t[[i]], "lower") <- res.tl[[i]] attr(res.t[[i]], "upper") <- res.tu[[i]] class(res.t[[i]]) <- "fs.msm.est" attr(res.p[[i]], "lower") <- res.pl[[i]] attr(res.p[[i]], "upper") <- res.pu[[i]] class(res.p[[i]]) <- "fs.msm.est" } } if(nt==1) {res.t <- res.t[[1]]; res.p <- res.p[[1]]} attr(res.t, "P") <- res.p class(res.t) <- "totlos.fs" res.t } ##' @export print.totlos.fs <- function(x, ...){attr(x, "P") <- NULL; print(unclass(x),...)} # TODO make pmatrix generic # pmatrix.flexsurvreg <- pmatrix.fs #' @noRd format.ci <- function(x, l, u, digits=NULL, ...) { if (is.null(digits)) digits <- 4 ## note format() aligns nicely on point, unlike formatC est <- format(x, digits=digits, ...) if (!is.null(l)) { low <- format(l, digits=digits, ...) upp <- format(u, digits=digits, ...) res <- paste(est, " (", low, ",", upp, ")", sep="") res[x==0] <- 0 } else res <- est dim(res) <- dim(x) dimnames(res) <- dimnames(x) names(res) <- names(x) res } #' @noRd print.ci <- function(x, l, u, digits=NULL,...){ res <- format.ci(x, l, u, digits) print(res, quote=FALSE) } #' @noRd print.fs.msm.est <- function(x, digits=NULL, ...) { if (!is.null(attr(x, "lower"))) print.ci(x, attr(x, "lower"), attr(x, "upper"), digits=digits) else print(unclass(x)) } absorbing <- function(trans){ which(apply(trans, 1, function(x) all(is.na(x)))) } transient <- function(trans){ which(apply(trans, 1, function(x) !all(is.na(x)))) } ## Handle predictable time-dependent covariates in simulating from ## semi-Markov models. Assume the covariate changes at same rate as ## time (e.g. age), but the covariate values used in simulation only ## change when the clock resets, at each change of state. form.basepars.tcovs <- function(x, transi, # index of allowed transition newdata, tcovs, t # time increment ){ if (is.flexsurvlist(x)){ x <- x[[transi]] dat <- as.list(newdata) } else if (inherits(x, "flexsurvreg")) { dat <- as.list(newdata[transi,,drop=FALSE]) } for (i in tcovs) { dat[[i]] <- dat[[i]] + t} dat <- as.data.frame(dat) X <- form.model.matrix(x, dat, na.action=na.omit) beta <- if (x$ncovs==0) 0 else x$res.t[x$covpars,"est"] basepars.mat <- add.covs(x, x$res.t[x$dlist$pars,"est"], beta, X, transform=FALSE) as.list(as.data.frame(basepars.mat)) ## for distribution with npars parameters, whose values are required at nt different times ## returns (as list) data frame with nt rows, npars cols } ## TODO Unclear how to check for semi Markov vs nonhomogenous Markov ## model. attr(model.response(model.frame(x)), "type") will be ## "counting" for a nonhomogeneous model, but also if there are ## time-dependent covariates ##' Simulate paths through a fully parametric semi-Markov multi-state model ##' ##' Simulate changes of state and transition times from a semi-Markov ##' multi-state model fitted using \code{\link{flexsurvreg}}. ##' ##' \code{sim.fmsm} relies on the presence of a function to sample random ##' numbers from the parametric survival distribution used in the fitted model ##' \code{x}, for example \code{\link{rweibull}} for Weibull models. If ##' \code{x} was fitted using a custom distribution, called \code{dist} say, ##' then there must be a function called (something like) \code{rdist} either ##' in the working environment, or supplied through the \code{dfns} argument to ##' \code{\link{flexsurvreg}}. This must be in the same format as standard R ##' functions such as \code{\link{rweibull}}, with first argument \code{n}, and ##' remaining arguments giving the parameters of the distribution. It must be ##' vectorised with respect to the parameter arguments. ##' ##' This function is only valid for semi-Markov ("clock-reset") models, though ##' no warning or error is currently given if the model is not of this type. An ##' equivalent for time-inhomogeneous Markov ("clock-forward") models has ##' currently not been implemented. ##' ##' @param x A model fitted with \code{\link{flexsurvreg}}. See ##' \code{\link{msfit.flexsurvreg}} for the required form of the model and the ##' data. ##' ##' Alternatively \code{x} can be a list of fitted \code{\link{flexsurvreg}} ##' model objects. The \code{i}th element of this list is the model ##' corresponding to the \code{i}th transition in \code{trans}. This is a more ##' efficient way to fit a multi-state model, but only valid if the parameters ##' are different between different transitions. ##' ##' @param trans Matrix indicating allowed transitions. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param t Time, or vector of times for each of the \code{M} individuals, to ##' simulate trajectories until. ##' ##' @param newdata A data frame specifying the values of covariates in the ##' fitted model, other than the transition number. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param start Starting state, or vector of starting states for each of the ##' \code{M} individuals. ##' ##' @param M Number of individual trajectories to simulate. ##' ##' @param tvar Variable in the data representing the transition type. Not ##' required if \code{x} is a list of models. ##' ##' @param tcovs Names of "predictable" time-dependent covariates in ##' \code{newdata}, i.e. those whose values change at the same rate as time. ##' Age is a typical example. During simulation, their values will be updated ##' after each transition time, by adding the current time to the value ##' supplied in \code{newdata}. This assumes the covariate is measured in the ##' same unit as time. \code{tcovs} is supplied as a character vector. ##' ##' @param tidy If \code{TRUE} then the simulated data are returned as a tidy data frame with one row per simulated transition. See \code{\link{simfs_bytrans}} for a function to rearrange the data into this format if it was simulated in non-tidy format. Currently this includes only event times, and excludes any times of censoring that are reported when \code{tidy=FALSE}. ##' ##' @return If \code{tidy=TRUE}, a data frame with one row for each simulated transition, giving the individual ID \code{id}, start state \code{start}, end state \code{end}, transition label \code{trans}, time of the transition since the start of the process (\code{time}), and time since the previous transition (\code{delay}). ##' ##' If \code{tidy=FALSE}, a list of two matrices named \code{st} and \code{t}. The rows of ##' each matrix represent simulated individuals. The columns of \code{t} ##' contain the times when the individual changes state, to the corresponding ##' states in \code{st}. ##' ##' The first columns will always contain the starting states and the starting ##' times. The last column of \code{t} represents either the time when the ##' individual moves to an absorbing state, or right-censoring in a transient ##' state at the time given in the \code{t} argument to \code{sim.fmsm}. ##' ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk}. ##' ##' @seealso \code{\link{pmatrix.simfs}},\code{\link{totlos.simfs}} ##' ##' @keywords models survival ##' ##' @examples ##' ##' bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' sim.fmsm(bexp, M=10, t=5, trans=tmat) ##' @export sim.fmsm <- function(x, trans=NULL, t, newdata=NULL, start=1, M=10, tvar="trans", tcovs=NULL, tidy=FALSE){ if (is.null(trans)) { if (!is.null(attr(x, "trans"))) trans <- attr(x, "trans") else stop("`trans` not supplied and not found in `x`") } if (length(t)==1) t <- rep(t, M) else if (length(t)!=M) stop("length of t should be 1 or M=",M) if (length(start)==1) start <- rep(start, M) else if (length(start)!=M) stop("length of start should be 1 or M=",M) basepars.all <- pars.fmsm(x=x, trans=trans, newdata=newdata, tvar=tvar) nst <- nrow(trans) ## TODO only need a max time if model is transient, else if absorbing, can allocate these up front res.st <- cur.st <- start res.t <- cur.t <- rep(0, M) todo <- seq_len(M) while (any(todo)){ cur.st.out <- cur.st[todo] cur.t.out <- cur.t[todo] done <- numeric() for (i in unique(cur.st[todo])){ if (i %in% transient(trans)) { ## simulate next time and states for people whose current state is i transi <- na.omit(trans[i,]) ni <- sum(cur.st[todo]==i) t.trans1 <- matrix(0, nrow=ni, ncol=length(transi)) ## simulate times to all potential destination states for (j in seq_along(transi)) { xbase <- if (is.flexsurvlist(x)) x[[transi[j]]] else x if (length(tcovs)>0){ basepars <- form.basepars.tcovs(x, transi[j], newdata, tcovs, cur.t[todo][cur.st[todo]==i]) } else basepars <- as.list(as.data.frame(basepars.all[[transi[j]]])) fncall <- c(list(n=ni), basepars, xbase$aux) if (is.null(xbase$dfns$r)) stop("No random sampling function found for this model") t.trans1[,j] <- do.call(xbase$dfns$r, fncall) } ## simulated next state is the one with minimum simulated time mc <- max.col(-t.trans1) next.state <- match(transi[mc], trans[i,]) next.time <- t.trans1[cbind(seq_along(next.state), mc)] inds <- which(cur.st[todo]==i) cur.t.out[inds] <- cur.t.out[inds] + next.time ## if final simulated state is greater than target time, censor at target time cens <- cur.t.out[inds] > t[inds] cur.t.out[inds][cens] <- t[inds][cens] cur.st.out[inds][!cens] <- next.state[!cens] done <- todo[inds][cens] } } cur.st[todo] <- cur.st.out cur.t[todo] <- cur.t.out res.st <- cbind(res.st, cur.st) res.t <- cbind(res.t, cur.t) done <- union(done, which(cur.st %in% absorbing(trans))) todo <- setdiff(todo, done) } res <- list(st=unname(res.st), t=unname(res.t)) attr(res, "trans") <- trans attr(res, "statenames") <- attr(x, "statenames") if (tidy) res <- simfs_bytrans(res) res # TODO set S3 class and adapt methods } ##' Reformat simulated multi-state data with one row per simulated transition ##' ##' @param simfs Output from \code{\link{sim.fmsm}} representing simulated histories from a multi-state model. ##' ##' @return Data frame with four columns giving transition start state, transition end state, transition name and the time taken by the transition. ##' ##' @export ##' simfs_bytrans <- function(simfs){ ## TODO check for simfs having proper attributes trans <- attr(simfs, "trans") ## all possible starting states start <- which(apply(trans, 1, function(x) !all(is.na(x)))) suball <- NULL for (i in seq_along(start)){ subi <- NULL ## all possible end states for each start state endi <- which(!is.na(trans[start[i],])) for (j in 1:(ncol(simfs$st)-1)){ sub <- (simfs$st[,j] == start[i] & simfs$st[,j+1] %in% endi) if (length(sub) > 0){ subj <- data.frame(end = simfs$st[sub,j+1], time = simfs$t[sub,j+1], delay = simfs$t[sub,j+1] - simfs$t[sub,j], id = which(sub)) subi <- rbind(subi, subj) } } if (nrow(subi) > 0){ subi$start <- start[i] suball <- rbind(suball, subi) } } suball$start <- state_names(suball$start, simfs) suball$end <- state_names(suball$end, simfs) suball$trans <- paste(suball$start, suball$end, sep=" - ") rownames(suball) <- NULL res <- suball[,c("id","start","end","trans","time","delay")] attr(res, "trans") <- trans attr(res, "statenames") <- attr(simfs, "statenames") res[order(res$id),] } ##' Bootstrap confidence intervals for flexsurv output functions ##' ##' Calculate a confidence interval for a model output by repeatedly replacing the parameters in a fitted model object with a draw from the multivariate normal distribution of the maximum likelihood estimates, then recalculating the output function. ##' ##' @param x Output from \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}}, representing a fitted survival model object. Or a list of such objects, defining a multi-state model. ##' ##' @param B Number of parameter draws to use ##' ##' @param fn Function to bootstrap the results of. It must have an argument named \code{x} giving a fitted flexsurv model object. This may return a value with any format, e.g. list, matrix or vector, as long as it can be converted to a numeric vector with \code{unlist}. See the example below. ##' ##' @param attrs Any attributes of the value returned from \code{fn} which we want confidence intervals for. These will be unlisted, if possible, and appended to the result vector. ##' ##' @param sample If \code{TRUE} then the bootstrap sample itself is returned. If \code{FALSE} then the quantiles of the sample are returned giving a confidence interval. ##' ##' @param cl Width of symmetric confidence interval, by default 0.95 ##' ##' @param cores Number of cores to use for parallel processing. ##' ##' @param ... Additional arguments to pass to \code{fn}. ##' ##' @return A matrix with two rows, giving the upper and lower confidence limits respectively. Each row is a vector of the same length as the unlisted result of the function corresponding to \code{fncall}. ##' ##' @examples ##' ##' ## How to use bootci.fmsm ##' ##' ## Write a function with one argument called x giving a fitted model, ##' ## and returning some results of the model. The results may be in any form. ##' ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, data=bosms3, dist="exp") ##' ##' summfn <- function(x, t){ ##' resp <- flexsurv::pmatrix.fs(x, trans=tmat, t=t) ##' rest <- flexsurv::totlos.fs(x, trans=tmat, t=t) ##' list(resp, rest) ##' } ##' ##' ## Use bootci.fmsm to obtain the confidence interval ##' ## The matrix columns are in the order of the unlisted results of the original ##' ## summfn. You will have to rearrange them into the format that you want. ##' ## If summfn has any extra arguments, in this case \code{t}, make sure they are ##' ## passed through via the ... argument to bootci.fmsm ##' ##' bootci.fmsm(bexp, B=3, fn=summfn, t=10) ##' bootci.fmsm(bexp, B=3, fn=summfn, t=5) ##' ##' @export bootci.fmsm <- function(x, B, fn, cl=0.95, attrs=NULL, cores=NULL, sample=FALSE, ...){ if (is.null(cores) || cores==1) parallel <- FALSE else parallel <- TRUE if (is.flexsurvlist(x)){ sim <- vector("list", length(x)) for (j in seq_along(x)){ sim[[j]] <- normboot.flexsurvreg(x=x[[j]], B=B, raw=TRUE, transform=TRUE) } } else { sim <- normboot.flexsurvreg(x=x, B=B, raw=TRUE, transform=TRUE) } boot_fn <- function(i, fn, ...){ x.rep <- x if (is.flexsurvlist(x)){ for (j in seq_along(x)) x.rep[[j]]$res.t[,"est"] <- sim[[j]][i,] } else x.rep$res.t[,"est"] <- sim[i,] args <- list(...) args$x <- x.rep resi <- do.call(fn, args) resivec <- unlist(resi) if (!is.numeric(resivec)) stop("boot_fn returns a non-numeric result") c(resivec, unlist(attributes(resi)[attrs])) } if (parallel) { cid <- parallel::makeCluster(cores) parallel::clusterExport(cl=cid, varlist=ls(.GlobalEnv)) res.rep.list <- parallel::parLapply(cid, seq_len(B), boot_fn, fn=fn, ...) parallel::stopCluster(cid) res.rep <- do.call("rbind", res.rep.list) } else { res.rep <- vector(B, mode="list") for (i in 1:B){ res.rep[[i]] <- boot_fn(i,fn,...) } res.rep <- do.call(rbind, lapply(res.rep, as.numeric)) } if (!sample) res <- apply(res.rep, 2, quantile, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE) else res <- res.rep res } ##' Transition probability matrix from a fully-parametric, semi-Markov ##' multi-state model ##' ##' The transition probability matrix for semi-Markov multi-state models fitted ##' to time-to-event data with \code{\link{flexsurvreg}}. This has \eqn{r,s} ##' entry giving the probability that an individual is in state \eqn{s} at time ##' \eqn{t}, given they are in state \eqn{r} at time \eqn{0}. ##' ##' This is computed by simulating a large number of individuals \code{M} using ##' the maximum likelihood estimates of the fitted model and the function ##' \code{\link{sim.fmsm}}. Therefore this requires a random sampling function ##' for the parametric survival model to be available: see the "Details" ##' section of \code{\link{sim.fmsm}}. This will be available for all built-in ##' distributions, though users may need to write this for custom models. ##' ##' Note the random sampling method for \code{flexsurvspline} models is ##' currently very inefficient, so that looping over the \code{M} individuals ##' will be very slow. ##' ##' \code{\link{pmatrix.fs}} is a more efficient method based on solving the ##' Kolmogorov forward equation numerically, which requires the multi-state ##' model to be Markov. No error or warning is given if running ##' \code{\link{pmatrix.simfs}} with a Markov model, but this is still invalid. ##' ##' @param x A model fitted with \code{\link{flexsurvreg}}. See ##' \code{\link{msfit.flexsurvreg}} for the required form of the model and the ##' data. Additionally this should be semi-Markov, so that the time variable ##' represents the time since the last transition. In other words the response ##' should be of the form \code{Surv(time,status)}. See the package vignette ##' for further explanation. ##' ##' \code{x} can also be a list of \code{\link{flexsurvreg}} models, ##' with one component for each permitted transition, as illustrated ##' in \code{\link{msfit.flexsurvreg}}. This can be constructed by ##' \code{\link{fmsm}}. ##' ##' @param trans Matrix indicating allowed transitions. See ##' \code{\link{msfit.flexsurvreg}}. This is not required if \code{x} ##' is a list constructed by \code{\link{fmsm}}. ##' ##' @param t Time to predict state occupancy probabilities for. This can ##' be a single number or a vector of different numbers. ##' ##' @param newdata A data frame specifying the values of covariates in the ##' fitted model, other than the transition number. See ##' \code{\link{msfit.flexsurvreg}}. ##' ##' @param ci Return a confidence interval calculated by simulating from the ##' asymptotic normal distribution of the maximum likelihood estimates. This ##' is turned off by default, since two levels of simulation are required. If ##' turned on, users should adjust \code{B} and/or \code{M} until the results ##' reach the desired precision. The simulation over \code{M} is generally ##' vectorised, therefore increasing \code{B} is usually more expensive than ##' increasing \code{M}. ##' ##' @param tvar Variable in the data representing the transition type. Not ##' required if \code{x} is a list of models. ##' ##' @param tcovs Predictable time-dependent covariates such as age, see ##' \code{\link{sim.fmsm}}. ##' ##' @param M Number of individuals to simulate in order to approximate the ##' transition probabilities. Users should adjust this to obtain the required ##' precision. ##' ##' @param B Number of simulations from the normal asymptotic distribution used ##' to calculate confidence limits. Decrease for greater speed at the expense of ##' accuracy. ##' ##' @param cl Width of symmetric confidence intervals, relative to 1. ##' ##' @param cores Number of processor cores used when calculating confidence ##' limits by repeated simulation. The default uses single-core processing. ##' ##' @param tidy If \code{TRUE} then the results are returned as a tidy data frame with ##' columns for the estimate and confidence limits, and rows per state transition and ##' time interval. ##' ##' @return The transition probability matrix. If \code{ci=TRUE}, there are ##' attributes \code{"lower"} and \code{"upper"} giving matrices of the ##' corresponding confidence limits. These are formatted for printing but may ##' be extracted using \code{attr()}. ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk}. ##' @seealso ##' \code{\link{pmatrix.fs}},\code{\link{sim.fmsm}},\code{\link{totlos.simfs}}, ##' \code{\link{msfit.flexsurvreg}}. ##' @keywords models survival ##' @examples ##' ##' # BOS example in vignette, and in msfit.flexsurvreg ##' ##' bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' ##' # more likely to be dead (state 3) as time moves on, or if start with ##' # BOS (state 2) ##' ##' pmatrix.simfs(bexp, t=5, trans=tmat) ##' pmatrix.simfs(bexp, t=10, trans=tmat) ##' ##' # these results should converge to those in help(pmatrix.fs), as M ##' # increases here and ODE solving precision increases there, since with ##' # an exponential distribution, the semi-Markov model is the same as the ##' # Markov model. ##' @export pmatrix.simfs <- function(x, trans, t=1, newdata=NULL, ci=FALSE, tvar="trans", tcovs=NULL, M=100000, B=1000, cl=0.95, cores=NULL, tidy=FALSE) { n <- nrow(trans) T <- length(t) check_nonnegative_numeric(t) res <- array(0, dim=c(n,n,T)) statenames <- rownames(trans) if (is.null(statenames)) statenames <- 1:n dimnames(res) <- list(statenames, statenames, t) for (i in seq_len(n)){ sim <- sim.fmsm(x=x, trans=trans, t=max(t), newdata=newdata, start=i, M=M, tvar=tvar, tcovs=tcovs) for (j in seq_len(T)){ st <- find_state_at(sim,t[j]) res[i,,j] <- prop.table(table(factor(st, levels=seq_len(n)))) } } if (T==1) res <- res[,,1] ### if t is a scalar, drop dimension, for backward compatibility if (tidy){ rest <- data.frame(from = rep(rep(statenames, n), T), to = rep(rep(statenames, each=n), T), t = rep(t, each=n*n), p = as.vector(res)) } else rest <- res if (ci){ resci <- bootci.fmsm(x, B, fn=pmatrix.simfs, ci=FALSE, cl=cl, cores=cores, trans=trans, t=t, newdata=newdata, tvar=tvar, tcovs=tcovs, M=M, tidy=FALSE) resl <- array(resci[1,], dim=c(n,n,T)) resu <- array(resci[2,], dim=c(n,n,T)) dimnames(resl) <- dimnames(resu) <- dimnames(res) if (T==1) resl <- resl[,,1] if (T==1) resu <- resu[,,1] if (tidy) { rest$lower <- as.vector(resl) rest$upper <- as.vector(resu) } else { attr(rest, "lower") <- resl attr(rest, "upper") <- resu class(rest) <- "fs.msm.est" } } rest } ## sim should be a object returned by sim.fmsm in non-tidy format ## ## t should be a scalar (a single number) ## ## Returns the state at time t for each individual find_state_at <- function(sim, t){ check_numeric_scalar(t) tind <- rowSums(sim$t <= t) sim$st[cbind(seq_len(nrow(sim$st)), tind)] } check_numeric <- function(x){ if (!is.numeric(x)) stop(sprintf("%s must be numeric",deparse(substitute(x)))) } check_nonnegative_numeric <- function(x) { check_numeric(x) if (!all(x>=0)) stop(sprintf("%s must all be non-negative",deparse(substitute(x)))) } check_numeric_scalar <- function(x) { check_numeric(x) if (length(x) > 1) stop(sprintf("%s must have length 1",deparse(substitute(x)))) } ## TODO test the multi time thing ##' Expected total length of stay in specific states, from a fully-parametric, ##' semi-Markov multi-state model ##' ##' The expected total time spent in each state for semi-Markov multi-state ##' models fitted to time-to-event data with \code{\link{flexsurvreg}}. This ##' is defined by the integral of the transition probability matrix, though ##' this is not analytically possible and is computed by simulation. ##' ##' This is computed by simulating a large number of individuals \code{M} using ##' the maximum likelihood estimates of the fitted model and the function ##' \code{\link{sim.fmsm}}. Therefore this requires a random sampling function ##' for the parametric survival model to be available: see the "Details" ##' section of \code{\link{sim.fmsm}}. This will be available for all built-in ##' distributions, though users may need to write this for custom models. ##' ##' Note the random sampling method for \code{flexsurvspline} models is ##' currently very inefficient, so that looping over \code{M} will be very ##' slow. ##' ##' The equivalent function for time-inhomogeneous Markov models is ##' \code{\link{totlos.fs}}. Note neither of these functions give errors or ##' warnings if used with the wrong type of model, but the results will be ##' invalid. ##' ##' @inheritParams pmatrix.simfs ##' ##' @param t Maximum time to predict to. ##' ##' @param start Starting state. ##' ##' @param group Optional grouping for the states. For example, if there are ##' four states, and \code{group=c(1,1,2,2)}, then \code{\link{totlos.simfs}} ##' returns the expected total time in states 1 and 2 combined, and states 3 ##' and 4 combined. ##' ##' @return The expected total time spent in each state (or group of states ##' given by \code{group}) up to time \code{t}, and corresponding confidence ##' intervals if requested. ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk}. ##' @seealso ##' \code{\link{pmatrix.simfs}},\code{\link{sim.fmsm}},\code{\link{msfit.flexsurvreg}}. ##' @keywords models survival ##' @examples ##' ##' # BOS example in vignette, and in msfit.flexsurvreg ##' bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") ##' tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) ##' ##' # predict 4 years spent without BOS, 3 years with BOS, before death ##' # As t increases, this should converge ##' totlos.simfs(bexp, t=10, trans=tmat) ##' totlos.simfs(bexp, t=1000, trans=tmat) ##' @export totlos.simfs <- function(x, trans, t=1, start=1, newdata=NULL, ci=FALSE, tvar="trans", tcovs=NULL, group=NULL, M=100000, B=1000, cl=0.95, cores=NULL) { if (length(t)>1) stop("\"t\" must be a single number") sim <- sim.fmsm(x=x, trans=trans, t=t, newdata=newdata, start=start, M=M, tvar=tvar, tcovs=tcovs) dt <- diff(t(cbind(sim$t, t))) st <- factor(t(sim$st), levels=1:nrow(trans)) res <- tapply(dt, st, sum) / M res[is.na(res)] <- 0 if (!is.null(group)) { if(length(group) != nrow(trans)) stop("\"group\" must be a vector of length ",nrow(trans), " = number of states") res <- tapply(res, group, sum) } if (ci){ resci <- bootci.fmsm(x, B, fn=totlos.simfs, ci=FALSE, cl=cl, cores=cores, trans=trans, t=t, start=start, newdata=newdata, tvar=tvar, tcovs=tcovs, group=group, M=M) resl <- resci[1,] resu <- resci[2,] names(resl) <- names(resu) <- t attr(res, "lower") <- resl attr(res, "upper") <- resu class(res) <- "fs.msm.est" res <- cbind(est=res, L=resl, U=resu) } res } check_trans <- function(trans, flist){ if (!is.matrix(trans)) stop("`trans` should be a matrix") if (!is.numeric(trans)) stop("`trans` should be numeric") if (nrow(trans) != ncol(trans)) stop("`trans should be a square matrix") ntrans <- length(na.omit(as.vector(trans))) if (ntrans != length(flist)) stop(sprintf( "`trans` has %s numeric entries, but `flist` is of length %s. These should match and equal the number of transitions", ntrans, length(flist) )) } default_statenames <- function(trans){ statenames <- rownames(trans) if (is.null(statenames)) statenames <- colnames(trans) nstates <- nrow(trans) if (is.null(statenames)) statenames <- paste("State", 1:nstates) statenames } default_transnames <- function(flist, trans){ statenames <- default_statenames(trans) res <- names(flist) if (is.null(res)){ tid <- trans[!is.na(trans)] from <- statenames[row(trans)[!is.na(trans)]] to <- statenames[col(trans)[!is.na(trans)]] res <- sprintf("%s - %s",from,to)[order(tid)] } res } ##' Construct a multi-state model from a set of parametric survival models ##' ##' @param ... Objects returned by \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}} representing fitted survival models. ##' ##' @param trans A matrix of integers specifying which models correspond to ##' which transitions. The \eqn{r,s} entry is \code{i} if the \eqn{i}th ##' argument specified in \code{...} is the model for the state \eqn{r} to ##' state \eqn{s} transition. The entry should be \code{NA} if the ##' transition is disallowed. ##' ##' @return A list containing the objects given in \code{...}, and with ##' attributes \code{"trans"} and \code{"statenames"} defining the transition ##' structure matrix and state names, and with list components named to ##' describe the transitions they correspond to. If any of the arguments in ##' \code{...} are named, then these are used to define the transition names, ##' otherwise default names are chosen based on the state names. ##' ##' @export fmsm <- function(..., trans){ flist <- list(...) if (!is.flexsurvlist(flist)) stop("extra arguments should all be `flexsurvreg` objects") res <- flist statenames <- default_statenames(trans) rownames(trans) <- colnames(trans) <- statenames check_trans(trans, res) names(res) <- default_transnames(res, trans) attr(res, "trans") <- trans attr(res, "statenames") <- statenames class(res) <- "fmsm" # note sim.fmsm is named inappropriately as it's not a S3 ethod res } ##' @export print.fmsm <- function(x, ...){ for (i in seq_along(x)){ cat(names(x)[i], "\n") print(x[[i]]$call) if (i < length(x)) cat("\n") } } ##' Akaike's information criterion from a flexible parametric multistate model ##' ##' Defined as the sum of the AICs of the transition-specific models. ##' ##' @param object Object returned by \code{\link{fmsm}} representing a multistate model. ##' ##' @param k Penalty applied to number of parameters (defaults to the standard 2). ##' ##' @param ... Further arguments (currently unused). ##' ##' @return The sum of the AICs of the transition-specific models. ##' ##' @export AIC.fmsm <- function(object,...,k=2){ nmods <- length(object) aics <- numeric(nmods) for (i in 1:nmods){ aics[i] <- AIC(object[[i]],...,k=k) } sum(aics) } nextstates <- function(x, fromstate){ trans <- attr(x,"trans") colnames(trans)[!is.na(trans[fromstate,])] } simfinal_fmsm_noci <- function(x, newdata=NULL, t=1000, M=100000, probs=c(0.025, 0.5, 0.975)){ ncovvals <- if (is.null(newdata)) 1 else nrow(newdata) simfs <- vector(ncovvals, mode="list") for (i in 1:ncovvals){ nd <- if (is.null(newdata)) NULL else newdata[i,,drop=FALSE] simfs[[i]] <- sim.fmsm(x, newdata=nd, t=t, M=M, tidy=TRUE) } rest <- vector(ncovvals, mode="list") statenames <- names(absorbing(attr(x,"trans"))) for (i in 1:ncovvals){ sf <- simfs[[i]] abs <- sf$end %in% statenames finaldat <- sf[abs,,drop=FALSE] means <- data.frame(state=statenames, val=tapply(finaldat$time, finaldat$end, mean)[statenames], quantity="mean") probsu <- data.frame(state=statenames, val=as.numeric(prop.table(table(finaldat$end))[statenames]), quantity="prob") quants <- tapply(finaldat$time, finaldat$end, quantile, probs) quants <- quants[statenames] quants <- as.data.frame(do.call("rbind",quants)) qnames <- colnames(quants) quants$state <- statenames quants <- tidyr::pivot_longer(quants, cols=c(all_of(qnames)), names_to="quantity", values_to="val") rest[[i]] <- quants %>% dplyr::full_join(means,by=c("state","quantity","val")) %>% dplyr::full_join(probsu,by=c("state","quantity","val")) rest[[i]] <- newdata[i,,drop=FALSE] %>% tidyr::crossing(rest[[i]]) } do.call("rbind",rest) } ##' Simulate and summarise final outcomes from a flexible parametric multi-state ##' model ##' ##' Estimates the probability of each final outcome ("absorbing" state), and the ##' mean and quantiles of the time to that outcome for people who experience it, ##' by simulating a large sample of individuals from the model. This can be used ##' for both Markov and semi-Markov models. ##' ##' For a competing risks model, i.e. a model defined by just one starting state ##' and multiple destination states representing competing events, this returns ##' the probability governing the next event that happens, and the distribution ##' of the time to each event conditionally on that event happening. ##' ##' ##' @param x Object returned by \code{\link{fmsm}}, representing a multi-state ##' model formed from transition-specific time-to-event models fitted by ##' \code{\link{flexsurvreg}}. ##' ##' @param newdata Data frame of covariate values, with one column per ##' covariate, and one row per alternative value. ##' ##' @param probs Quantiles to calculate, by default, \code{c(0.025, 0.5, 0.975)} ##' for a median and 95\% interval. ##' ##' @param t Maximum time to simulate to, passed to \code{\link{sim.fmsm}}, so ##' that the summaries are taken from the subset of individuals in the ##' simulated data who are in the absorbing state at this time. ##' ##' @param M Number of individuals to simulate. ##' ##' @param B Number of simulations to use to calculate 95\% confidence intervals ##' based on the asymptotic normal distribution of the basic parameter ##' estimates. If \code{B=0} then no intervals are calculated. ##' ##' @param cores Number of processor cores to use. If \code{NULL} (the default) ##' then a single core is used. ##' ##' @return A tidy data frame with rows for each combination of covariate values ##' and quantity of interest. The quantity of interest is identified in the ##' column \code{quantity}, and the value of the quantity is in \code{val}, ##' with additional columns \code{lower} and \code{upper} giving 95\% ##' confidence intervals for the quantity, if \code{B>0}. ##' ##' @export simfinal_fmsm <- function(x, newdata=NULL, probs=c(0.025, 0.5, 0.975), t=1000, M=100000, B=0, cores=NULL){ if (x[[1]]$ncoveffs > 0 & is.null(newdata)) stop("`newdata` should be supplied if there are covariates in the model") ests <- simfinal_fmsm_noci(x=x, newdata=newdata, probs=probs, t=t, M=M) valfn <- function(x, newdata=NULL, t, M, probs){ simfinal_fmsm_noci(x=x, newdata=newdata, t=t, M=M, probs=probs)$val } if (B>0){ bci <- bootci.fmsm(x, fn=valfn, newdata=newdata, t=t, M=M, B=B, cores=cores, probs=probs) ests$lower <- bci[1,] ests$upper <- bci[2,] } ests } pfinal_fmsm_noci <- function(x, newdata=NULL, fromstate, maxt=100000){ tmat <- attr(x, "trans") if (!(fromstate %in% rownames(tmat))) stop(sprintf("State `%s` not found in rownames(attr(x,\"trans\"))",fromstate)) tostates <- colnames(tmat)[!is.na(tmat[fromstate,])] ncovvals <- if (is.null(newdata)) 1 else nrow(newdata) pres <- as.data.frame(matrix(nrow=ncovvals, ncol=length(tostates))) colnames(pres) <- tostates if (length(tostates)==0) stop(sprintf("No destination states possible from state %s",fromstate)) for (i in 1:ncovvals){ nd <- if (is.null(newdata)) NULL else newdata[i,,drop=FALSE] pm <- pmatrix.fs(x, newdata=nd, condstates=tostates, t=maxt, tidy=TRUE)[1,tostates] pres[i,tostates] <- unlist(pm) } if (!is.null(newdata)) pres <- cbind(newdata, pres) pres } ##' Probabilities of final states in a flexible parametric competing risks model ##' ##' This requires the model to be Markov, and is not valid for semi-Markov ##' models, as it works by wrapping \code{\link{pmatrix.fs}} to calculate the ##' transition probability over a very large time. As it also works on a ##' \code{fmsm} object formed from transition-specific time-to-event models, ##' it therefore only works on competing risks models, defined by just one starting ##' state with multiple destination states representing competing events. ##' For these models, this function returns the probability governing which ##' competing event happens next. However this function simply wraps \code{pmatrix.fs}, ##' so for other models, \code{pmatrix.fs} or \code{pmatrix.simfs} can be used with a ##' large forecast time \code{t}. ##' ##' @inheritParams simfinal_fmsm ##' ##' @param fromstate State from which to calculate the transition probability ##' state. This should refer to the name of a row of the transition matrix ##' \code{attr(x,trans)}. ##' ##' @param maxt Large time to use for forecasting final state probabilities. ##' The transition probability from zero to this time is used. Note ##' \code{Inf} will not work. The default is \code{100000}. ##' ##' @return A data frame with one row per covariate value and destination state, ##' giving the state in column \code{state}, and probability in column ##' \code{val}. Additional columns \code{lower} and \code{upper} for the ##' confidence limits are returned if \code{B=0}. ##' ##' @export pfinal_fmsm <- function(x, newdata=NULL, fromstate, maxt=100000, B=0, cores=NULL){ ests <- pfinal_fmsm_noci(x, newdata, fromstate=fromstate, maxt=maxt) tostates <- nextstates(x, fromstate) ests <- pivot_longer(ests, all_of(tostates), names_to="state", values_to="val") ests$state <- factor(ests$state, levels=tostates) ests <- ests[order(ests$state),] if (B>0){ bci <- bootci.fmsm(x, fn=pfinal_fmsm_noci, newdata=newdata, fromstate=fromstate, maxt=maxt, B=B, cores=cores) if (!is.null(newdata)) bci <- bci[,-seq_along(unlist(newdata)),drop=FALSE] ests$lower <- bci[1,] ests$upper <- bci[2,] } ests } flexsurv/R/flexsurv-package.R0000644000176200001440000003074514554254207015744 0ustar liggesusers##' flexsurv: Flexible parametric survival and multi-state models ##' ##' flexsurv: Flexible parametric models for time-to-event data, including the ##' generalized gamma, the generalized F and the Royston-Parmar spline model, ##' and extensible to user-defined distributions. ##' ##' \code{\link{flexsurvreg}} fits parametric models for time-to-event ##' (survival) data. Data may be right-censored, and/or left-censored, and/or ##' left-truncated. Several built-in parametric distributions are available. ##' Any user-defined parametric model can also be employed by supplying a list ##' with basic information about the distribution, including the density or ##' hazard and ideally also the cumulative distribution or hazard. ##' ##' Covariates can be included using a linear model on any parameter of the ##' distribution, log-transformed to the real line if necessary. This ##' typically defines an accelerated failure time or proportional hazards ##' model, depending on the distribution and parameter. ##' ##' \code{\link{flexsurvspline}} fits the flexible survival model of Royston ##' and Parmar (2002) in which the log cumulative hazard is modelled as a ##' natural cubic spline function of log time. Covariates can be included on ##' any of the spline parameters, giving either a proportional hazards model or ##' an arbitrarily-flexible time-dependent effect. Alternative proportional ##' odds or probit parameterisations are available. ##' ##' Output from the models can be presented as survivor, cumulative hazard and ##' hazard functions (\code{\link{summary.flexsurvreg}}). These can be plotted ##' against nonparametric estimates (\code{\link{plot.flexsurvreg}}) to assess ##' goodness-of-fit. Any other user-defined function of the parameters may be ##' summarised in the same way. ##' ##' Multi-state models for time-to-event data can also be fitted with the same ##' functions. Predictions from those models can then be made using the ##' functions \code{\link{pmatrix.fs}}, \code{\link{pmatrix.simfs}}, ##' \code{\link{totlos.fs}}, \code{\link{totlos.simfs}}, or ##' \code{\link{sim.fmsm}}, or alternatively by \code{\link{msfit.flexsurvreg}} ##' followed by \code{mssample} or \code{probtrans} from the package ##' \pkg{mstate}. ##' ##' Distribution (``dpqr'') functions for the generalized gamma and F ##' distributions are given in \code{\link{GenGamma}}, \code{\link{GenF}} ##' (preferred parameterisations) and \code{\link{GenGamma.orig}}, ##' \code{\link{GenF.orig}} (original parameterisations). ##' \code{\link{flexsurv}} also includes the standard Gompertz distribution ##' with unrestricted shape parameter, see \code{\link{Gompertz}}. ##' ##' @name flexsurv-package ##' @aliases flexsurv-package flexsurv ##' @docType package ##' @section User guide: The \bold{flexsurv user guide} vignette explains the ##' methods in detail, and gives several worked examples. A further vignette ##' \bold{flexsurv-examples} gives a few more complicated examples, and users ##' are encouraged to submit their own. ##' @author Christopher Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @references Jackson, C. (2016). flexsurv: A Platform for Parametric ##' Survival Modeling in R. Journal of Statistical Software, 70(8), 1-33. ##' doi:10.18637/jss.v070.i08 ##' ##' Royston, P. and Parmar, M. (2002). Flexible parametric ##' proportional-hazards and proportional-odds models for censored survival ##' data, with application to prognostic modelling and estimation of treatment ##' effects. Statistics in Medicine 21(1):2175-2197. ##' ##' Cox, C. (2008). The generalized \eqn{F} distribution: An umbrella for ##' parametric survival analysis. Statistics in Medicine 27:4301-4312. ##' ##' Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007). Parametric ##' survival analysis and taxonomy of hazard functions for the generalized ##' gamma distribution. Statistics in Medicine 26:4252-4374 ##' @keywords package ##' @importFrom Rcpp sourceCpp ##' @useDynLib flexsurv, .registration = TRUE ##' @import stats ##' @importFrom magrittr %>% ##' @importFrom dplyr mutate rename full_join bind_rows distinct ##' @importFrom tidyr pivot_longer pivot_wider ##' @importFrom tidyselect all_of num_range ##' @importFrom rlang .data ##' @importFrom mstate msfit probtrans ##' @importFrom graphics plot lines ##' @importFrom survival Surv survfit coxph survreg survreg.control ##' @importFrom muhaz muhaz ##' @importFrom mvtnorm rmvnorm ##' @importFrom deSolve ode ##' @importFrom quadprog solve.QP ##' @importFrom utils globalVariables "_PACKAGE" .onUnload <- function(libpath) { library.dynam.unload("flexsurv", libpath) } ##' Hazard and cumulative hazard functions ##' ##' Hazard and cumulative hazard functions for distributions which are built ##' into flexsurv, and whose distribution functions are in base R. ##' ##' For the exponential and the Weibull these are available analytically, and ##' so are programmed here in numerically stable and efficient forms. ##' ##' For the gamma and log-normal, these are simply computed as minus the log of ##' the survivor function (cumulative hazard) or the ratio of the density and ##' survivor function (hazard), so are not expected to be robust to extreme ##' values or quick to compute. ##' ##' @aliases hexp Hexp hweibull Hweibull hgamma Hgamma hlnorm Hlnorm ##' @param x Vector of quantiles ##' @param rate Rate parameter (exponential and gamma) ##' @param shape Shape parameter (Weibull and gamma) ##' @param scale Scale parameter (Weibull) ##' @param meanlog Mean on the log scale (log normal) ##' @param sdlog Standard deviation on the log scale (log normal) ##' @param log Compute log hazard or log cumulative hazard ##' @return Hazard (functions beginning 'h') or cumulative hazard (functions ##' beginning 'H'). ##' @author Christopher Jackson ##' @seealso ##' \code{\link{dexp}},\code{\link{dweibull}},\code{\link{dgamma}},\code{\link{dlnorm}},\code{\link{dgompertz}},\code{\link{dgengamma}},\code{\link{dgenf}} ##' @keywords distribution ##' @name hazard NULL ##' Mean and restricted mean survival functions ##' ##' Mean and restricted mean survival time functions for distributions which are built ##' into flexsurv. ##' ##' For the exponential, Weibull, log-logistic, lognormal, and gamma, mean survival is ##' provided analytically. Restricted mean survival for the exponential distribution ##' is also provided analytically. Mean and restricted means for other distributions ##' are calculated via numeric integration. ##' ##' @aliases mean_exp rmst_exp mean_weibull rmst_weibull mean_weibullPH rmst_weibullPH ##' mean_llogis rmst_llogis mean_lnorm rmst_lnorm mean_gamma rmst_gamma mean_gompertz ##' rmst_gompertz mean_gengamma rmst_gengamma mean_gengamma.orig rmst_gengamma.orig ##' mean_genf rmst_genf mean_genf.orig rmst_genf.orig ##' @param t Vector of times to which restricted mean survival time is evaluated ##' @param start Optional left-truncation time or times. The returned ##' restricted mean survival will be conditioned on survival up to ##' this time. ##' @param rate Rate parameter (exponential and gamma) ##' @param shape Shape parameter (Weibull, gamma, log-logistic, generalized gamma [orig], ##' generalized F [orig]) ##' @param scale Scale parameter (Weibull, log-logistic, generalized gamma [orig], ##' generalized F [orig]) ##' @param meanlog Mean on the log scale (log normal) ##' @param sdlog Standard deviation on the log scale (log normal) ##' @param mu Mean on the log scale (generalized gamma, generalized F) ##' @param sigma Standard deviation on the log scale (generalized gamma, generalized F) ##' @param Q Vector of first shape parameters (generalized gamma, generalized F) ##' @param P Vector of second shape parameters (generalized F) ##' @param k vector of shape parameters (generalized gamma [orig]). ##' @param s1 Vector of first F shape parameters (generalized F [orig]) ##' @param s2 vector of second F shape parameters (generalized F [orig]) ##' @return mean survival (functions beginning 'mean') or restricted mean survival ##' (functions beginning 'rmst_'). ##' @author Christopher Jackson ##' @seealso ##' \code{\link{dexp}},\code{\link{dweibull}},\code{\link{dgamma}},\code{\link{dlnorm}},\code{\link{dgompertz}},\code{\link{dgengamma}},\code{\link{dgenf}} ##' @keywords distribution ##' @name means NULL ##' Breast cancer survival data ##' ##' Survival times of 686 patients with primary node positive breast cancer. ##' ##' ##' @format A data frame with 686 rows. \tabular{rll}{ \code{censrec} \tab ##' (numeric) \tab 1=dead, 0=censored \cr \code{rectime} \tab (numeric) \tab ##' Time of death or censoring in days\cr \code{group} \tab (numeric) \tab ##' Prognostic group: \code{"Good"},\code{"Medium"} or \code{"Poor"}, \cr \tab ##' \tab from a regression model developed by Sauerbrei and Royston (1999).\cr ##' } ##' @seealso \code{\link{flexsurvspline}} ##' @references Royston, P. and Parmar, M. (2002). Flexible parametric ##' proportional-hazards and proportional-odds models for censored survival ##' data, with application to prognostic modelling and estimation of treatment ##' effects. Statistics in Medicine 21(1):2175-2197. ##' ##' Sauerbrei, W. and Royston, P. (1999). Building multivariable prognostic and ##' diagnostic models: transformation of the predictors using fractional ##' polynomials. Journal of the Royal Statistical Society, Series A 162:71-94. ##' @source German Breast Cancer Study Group, 1984-1989. Used as a reference ##' dataset for the spline-based survival model of Royston and Parmar (2002), ##' implemented here in \code{\link{flexsurvspline}}. Originally provided with ##' the \code{stpm} (Royston 2001, 2004) and \code{stpm2} (Lambert 2009, 2010) ##' Stata modules. ##' @keywords datasets "bc" ##' Bronchiolitis obliterans syndrome after lung transplants ##' ##' A dataset containing histories of bronchiolitis obliterans syndrome (BOS) ##' from lung transplant recipients. BOS is a chronic decline in lung function, ##' often observed after lung transplantation. ##' ##' The entry time of each patient into each stage of BOS was estimated by ##' clinicians, based on their history of lung function measurements and acute ##' rejection and infection episodes. BOS is only assumed to occur beyond six ##' months after transplant. In the first six months the function of each ##' patient's new lung stabilises. Subsequently BOS is diagnosed by comparing ##' the lung function against the "baseline" value. ##' ##' The same data are provided in the \pkg{msm} package, but in the ##' native format of \pkg{msm} to allow Markov models to be fitted. ##' In \pkg{flexsurv}, much more flexible models can be fitted. ##' @name bos ##' @aliases bosms3 bosms4 ##' @docType data ##' @format A data frame containing a sequence of observed or censored ##' transitions to the next stage of severity or death. It is grouped ##' by patient and includes histories of 204 patients. All patients ##' start in state 1 (no BOS) at six months after transplant, and may ##' subsequently develop BOS or die. ##' ##' \code{bosms3} contains the data for a three-state model: no BOS, BOS or ##' death. \code{bosms4} uses a four-state representation: no BOS, mild BOS, ##' moderate/severe BOS or death. \tabular{rll}{ \code{id} \tab (numeric) \tab ##' Patient identification number \cr \code{from} \tab (numeric) \tab Observed ##' starting state of the transition \cr \code{to} \tab (numeric) \tab Observed ##' or potential ending state of the transition \cr \code{Tstart} \tab ##' (numeric) \tab Time at the start of the interval \cr \code{Tstop} \tab ##' (numeric) \tab Time at the end of the interval \cr \code{time} \tab ##' (numeric) \tab Time difference \code{Tstart}-\code{Tstop} \cr \code{status} ##' \tab (numeric) \tab 1 if the transition to state \code{to} was observed, or ##' 0 if the transition to state \code{to} was censored (for example, if the ##' patient was observed to move to a competing state) \cr \code{trans} \tab ##' (factor) \tab Number of the transition \code{from}-\code{to} in the set of ##' all \code{ntrans} allowed transitions, numbered from 1 to \code{ntrans}. } ##' @references Heng. D. et al. (1998). Bronchiolitis Obliterans Syndrome: ##' Incidence, Natural History, Prognosis, and Risk Factors. Journal of Heart ##' and Lung Transplantation 17(12)1255--1263. ##' @source Papworth Hospital, U.K. ##' @keywords datasets NULL flexsurv/R/Gamma.R0000644000176200001440000000265214203407517013506 0ustar liggesusers### Hazard and cumulative hazard functions for R built in ### distributions. Where possible, use more numerically stable ### formulae than d/(1-p) and -log(1-p) ##' @export ##' @rdname hazard hgamma <- function(x, shape, rate=1, log=FALSE){ h <- dbase("gamma", log=log, x=x, shape=shape, rate=rate) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) ret[ind] <- dgamma(x, shape, rate) / pgamma(x, shape, rate, lower.tail=FALSE) if (log) ret[ind] <- log(ret[ind]) ret } ##' @export ##' @rdname hazard Hgamma <- function(x, shape, rate=1, log=FALSE){ h <- dbase("gamma", log=log, x=x, shape=shape, rate=rate) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) ret[ind] <- - pgamma(x, shape, rate, lower.tail=FALSE, log.p=TRUE) if (log) ret[ind] <- log(ret[ind]) ret } check.gamma <- function(shape, rate=1){ ret <- rep(TRUE, length(shape)) if (any(!is.na(shape) & shape<0)) { warning("Negative shape parameter") ret[!is.na(shape) & shape<0] <- FALSE } if (any(!is.na(rate) & rate<0)) { warning("Negative rate parameter") ret[!is.na(rate) & rate<0] <- FALSE } ret } ##' @export ##' @rdname means mean_gamma <- function(shape, rate=1) {shape / rate} var.gamma <- function(shape, rate=1) {shape / rate^2} ##' @export ##' @rdname means rmst_gamma = function(t, shape, rate=1, start=0){ rmst_generic(pgamma, t, start=start, shape=shape, rate=rate) } flexsurv/R/flexsurvmix.R0000644000176200001440000012422514644755116015073 0ustar liggesusers##' Flexible parametric mixture models for times to competing events ##' ##' In a mixture model for competing events, an individual can experience one of ##' a set of different events. We specify a model for the probability that they ##' will experience each event before the others, and a model for the time to ##' the event conditionally on that event occurring first. ##' ##' This differs from the more usual "competing risks" models, where we specify ##' "cause-specific hazards" describing the time to each competing event. This ##' time will not be observed for an individual if one of the competing events ##' happens first. The event that happens first is defined by the minimum of ##' the times to the alternative events. ##' ##' The \code{flexsurvmix} function fits a mixture model to data consisting of a ##' single time to an event for each individual, and an indicator for what type ##' of event occurs for that individual. The time to event may be observed or ##' censored, just as in \code{\link{flexsurvreg}}, and the type of event may be ##' known or unknown. In a typical application, where we follow up a set of ##' individuals until they experience an event or a maximum follow-up time is ##' reached, the event type is known if the time is observed, and the event type ##' is unknown when follow-up ends and the time is right-censored. ##' ##' The model is fitted by maximum likelihood, either directly or by using an ##' expectation-maximisation (EM) algorithm, by wrapping ##' \code{\link{flexsurvreg}} to compute the likelihood or to implement the E ##' and M steps. ##' ##' Some worked examples are given in the package vignette about multi-state ##' modelling, which can be viewed by running \code{vignette("multistate", package="flexsurv")}. ##' ##' ##' @param formula Survival model formula. The left hand side is a \code{Surv} ##' object specified as in \code{\link{flexsurvreg}}. This may define various ##' kinds of censoring, as described in \code{\link[survival]{Surv}}. Any covariates on ##' the right hand side of this formula will be placed on the location ##' parameter for every component-specific distribution. Covariates on other ##' parameters of the component-specific distributions may be supplied using ##' the \code{anc} argument. ##' ##' Alternatively, \code{formula} may be a list of formulae, with one ##' component for each alternative event. This may be used to specify ##' different covariates on the location parameter for different components. ##' ##' A list of formulae may also be used to indicate that for particular ##' individuals, different events may be observed in different ways, with ##' different censoring mechanisms. Each list component specifies the data ##' and censoring scheme for that mixture component. ##' ##' For example, suppose we are studying people admitted to hospital,and the ##' competing states are death in hospital and discharge from hospital. At ##' time t we know that a particular individual is still alive, but we do not ##' know whether they are still in hospital, or have been discharged. In this ##' case, if the individual were to die in hospital, their death time would be ##' right censored at t. If the individual will be (or has been) discharged ##' before death, their discharge time is completely unknown, thus ##' interval-censored on (0,Inf). Therefore, we need to store different event ##' time and status variables in the data for different alternative events. ##' This is specified here as ##' ##' \code{formula = list("discharge" = Surv(t1di, t2di, type="interval2"), ##' "death" = Surv(t1de, status_de))} ##' ##' where for this individual, \code{(t1di, t2di) = (0, Inf)} and \code{(t1de, ##' status_de) = (t, 0)}. ##' ##' The "dot" notation commonly used to indicate "all remaining variables" in a ##' formula is not supported in \code{flexsurvmix}. ##' ##' ##' @param data Data frame containing variables mentioned in \code{formula}, ##' \code{event} and \code{anc}. ##' ##' @param event Variable in the data that specifies which of the alternative ##' events is observed for which individual. If the individual's follow-up is ##' right-censored, or if the event is otherwise unknown, this variable must ##' have the value \code{NA}. ##' ##' Ideally this should be a factor, since the mixture components can then be ##' easily identified in the results with a name instead of a number. If this ##' is not already a factor, it is coerced to one. Then the levels of the ##' factor define the required order for the components of the list arguments ##' \code{dists}, \code{anc}, \code{inits} and \code{dfns}. Alternatively, if ##' the components of the list arguments are named according to the levels of ##' \code{event}, then the components can be arranged in any order. ##' ##' @param dists Vector specifying the parametric distribution to use for each ##' component. The same distributions are supported as in ##' \code{\link{flexsurvreg}}. ##' ##' @param pformula Formula describing covariates to include on the component ##' membership proabilities by multinomial logistic regression. The first ##' component is treated as the baseline. ##' ##' The "dot" notation commonly used to indicate "all remaining variables" in a ##' formula is not supported. ##' ##' @param anc List of component-specific lists, of length equal to the number ##' of components. Each component-specific list is a list of formulae ##' representing covariate effects on parameters of the distribution. ##' ##' If there are covariates for one component but not others, then a list ##' containing one null formula on the location parameter should be supplied ##' for the component with no covariates, e.g \code{list(rate=~1)} if the ##' location parameter is called \code{rate}. ##' ##' Covariates on the location parameter may also be supplied here instead of ##' in \code{formula}. Supplying them in \code{anc} allows some components ##' but not others to have covariates on their location parameter. If a covariate ##' on the location parameter was provided in \code{formula}, and there are ##' covariates on other parameters, then a null formula should be included ##' for the location parameter in \code{anc}, e.g \code{list(rate=~1)} ##' ##' @param partial_events List specifying the factor levels of \code{event} ##' which indicate knowledge that an individual will not experience particular ##' events, but may experience others. The names of the list indicate codes ##' that indicate partial knowledge for some individuals. The list component ##' is a vector, which must be a subset of \code{levels(event)} defining the ##' events that a person with the corresponding event code may experience. ##' ##' For example, suppose there are three alternative events called ##' \code{"disease1"},\code{"disease2"} and \code{"disease3"}, and for some ##' individuals we know that they will not experience \code{"disease2"}, but ##' they may experience the other two events. In that case we must create a ##' new factor level, called, for example \code{"disease1or3"}, and set the ##' value of \code{event} to be \code{"disease1or3"} for those individuals. ##' Then we use the \code{"partial_events"} argument to tell ##' \code{flexsurvmix} what the potential events are for individuals with this ##' new factor level. ##' ##' \code{partial_events = list("disease1or3" = c("disease1","disease3"))} ##' ##' @param initp Initial values for component membership probabilities. By ##' default, these are assumed to be equal for each component. ##' ##' @param inits List of component-specific vectors. Each component-specific ##' vector contains the initial values for the parameters of the ##' component-specific model, as would be supplied as the \code{inits} argument of ##' \code{\link{flexsurvreg}}. By default, a heuristic is used to obtain ##' initial values, which depends on the parametric distribution being used, ##' but is usually based on the empirical mean and/or variance of the survival ##' times. ##' ##' @param fixedpars Indexes of parameters to fix at their initial values and ##' not optimise. Arranged in the order: baseline mixing probabilities, ##' covariates on mixing probabilities, time-to-event parameters by mixing ##' component. Within mixing components, time-to-event parameters are ordered ##' in the same way as in \code{\link{flexsurvreg}}. ##' ##' If \code{fixedpars=TRUE} then all parameters will be fixed and the ##' function simply calculates the log-likelihood at the initial values. ##' ##' Not currently supported when using the EM algorithm. ##' ##' @param dfns List of lists of user-defined distribution functions, one for ##' each mixture component. Each list component is specified as the ##' \code{dfns} argument of \code{\link{flexsurvreg}}. ##' ##' @param method Method for maximising the likelihood. Either \code{"em"} for ##' the EM algorithm, or \code{"direct"} for direct maximisation. ##' ##' @param em.control List of settings to control EM algorithm fitting. The ##' only options currently available are ##' ##' \code{trace} set to 1 to print the parameter estimates at each iteration ##' of the EM algorithm ##' ##' \code{reltol} convergence criterion. The algorithm stops if the log ##' likelihood changes by a relative amount less than \code{reltol}. The ##' default is the same as in \code{\link{optim}}, that is, ##' \code{sqrt(.Machine$double.eps)}. ##' ##' \code{var.method} method to compute the covariance matrix. \code{"louis"} ##' for the method of Louis (1982), or \code{"direct"}for direct numerical ##' calculation of the Hessian of the log likelihood. ##' ##' \code{optim.p.control} A list that is passed as the \code{control} ##' argument to \code{optim} in the M step for the component membership ##' probability parameters. The optimisation in the M step for the ##' time-to-event parameters can be controlled by the \code{optim.control} ##' argument to \code{flexsurvmix}. ##' ##' For example, \code{em.control = list(trace=1, reltol=1e-12)}. ##' ##' @param optim.control List of options to pass as the \code{control} argument ##' to \code{\link{optim}}, which is used by \code{method="direct"} or in the ##' M step for the time-to-event parameters in \code{method="em"}. By ##' default, this uses \code{fnscale=10000} and \code{ndeps=rep(1e-06,p)} ##' where \code{p} is the number of parameters being estimated, unless the ##' user specifies these options explicitly. ##' ##' ##' @inheritParams flexsurvreg ##' ##' @return List of objects containing information about the fitted model. The ##' important one is \code{res}, a data frame containing the parameter ##' estimates and associated information. ##' ##' ##' @references Jackson, C. H. and Tom, B. D. M. and Kirwan, P. D. and Mandal, S. ##' and Seaman, S. R. and Kunzmann, K. and Presanis, A. M. and De Angelis, D. (2022) ##' A comparison of two frameworks for multi-state modelling, applied to outcomes ##' after hospital admissions with COVID-19. Statistical Methods in Medical Research ##' 31(9) 1656-1674. ##' ##' Larson, M. G., & Dinse, G. E. (1985). A mixture model for the ##' regression analysis of competing risks data. Journal of the Royal ##' Statistical Society: Series C (Applied Statistics), 34(3), 201-211. ##' ##' Lau, B., Cole, S. R., & Gange, S. J. (2009). Competing risk regression ##' models for epidemiologic data. American Journal of Epidemiology, 170(2), ##' 244-256. ##' ##' @export flexsurvmix <- function(formula, data, event, dists, pformula=NULL, anc=NULL, partial_events = NULL, initp=NULL, inits=NULL, fixedpars=NULL, dfns=NULL, method="direct", em.control=NULL, optim.control=NULL, aux=NULL, sr.control=survreg.control(), integ.opts, hess.control=NULL, ...){ call <- match.call() ## Determine names of competing events, and their order, based on event data event <- eval(substitute(event), data, parent.frame()) if (!is.factor(event)) event <- factor(event) ## Determine which of these are codes for partially observed events if (!is.null(partial_events)) { if (!is.list(partial_events)) stop("`partial_events` must be a list") if (!is.null(names(partial_events))) stop("`partial_events` must be a named list") npartials <- length(partial_events) evnames <- setdiff(levels(event), names(partial_events)) for (i in 1:npartials){ badnames <- partial_events[[i]][!(partial_events[[i]] %in% evnames)] badnames <- paste0("\"",badnames,"\"") if (length(badnames) > 0) stop(sprintf("partial_events[[%s]] values %s not in levels(events)", i, paste(badnames,collapse=","))) ## Convert to codes partial_events[[i]] <- match(partial_events[[i]], evnames) } } else npartials <- 0 evnames <- setdiff(levels(event), names(partial_events)) partial_event <- ifelse(event %in% names(partial_events), event, NA) partial_event <- match(partial_event, names(partial_events)) event[event %in% names(partial_events)] <- NA ## For all arguments that are vectors or lists by event, ## make sure their names match names of events ## and reorder if necessary so the order of the names matches too if (missing(dists)) stop("Distributions \"dists\" not specified") dists <- clean_listarg(dists, "dists", evnames) anc <- clean_listarg(anc, "anc", evnames) inits <- clean_listarg(inits, "inits", evnames) dfns <- clean_listarg(dfns, "dfns", evnames) ## Build distribution functions K <- length(dists) dlists <- vector(K, mode="list") if (is.null(dfns)) dfns <- vector(K, mode="list") for (k in 1:K){ dlists[[k]] <- parse.dist(dists[[k]]) dfns[[k]] <- form.dp(dlists[[k]], dfns[[k]], integ.opts) } names(dlists) <- names(dfns) <- names(dists) check.formula.flexsurvmix(formula, dlists[[1]], data) # TESTME if (is.list(formula)) formula <- clean_listarg(formula, "formula", evnames) ## Build covariate model formulae if (!is.null(anc)) { if (!is.list(anc)) stop("`anc` should be a list") } ancm <- vector(K, mode="list") for (k in 1:K){ msg <- sprintf("anc[[%s]] must be a list of formulae", k) fk <- if (is.list(formula)) formula[[k]] else formula ancm[[k]] <- anc_from_formula(fk, anc[[k]], dlists[[k]], msg, data, loc_warn=FALSE) } locform <- forms <- vector(K, mode="list") for (k in 1:K) { ancnames <- setdiff(dlists[[k]]$pars, dlists[[k]]$location) fk <- if (is.list(formula)) formula[[k]] else formula locform[[k]] <- get.locform(fk, ancnames, data) loc <- dlists[[k]]$location if (loc %in% names(ancm[[k]])){ ## Add any extra covariates on the location parameter found in "anc" (usually we'll be adding to ~1) fc <- as.character(ancm[[k]][[loc]]) extraterms <- formula(paste(fc[1], ". +", fc[-1], collapse=" ")) locform[[k]] <- update(locform[[k]], extraterms) ancm[[k]][[loc]] <- anc[[k]][[loc]]<- NULL } forms[[k]] <- c(location=locform[[k]], ancm[[k]]) names(forms[[k]])[[1]] <- loc } ## Build model frame given formulae indx <- match(c("formula", "data", "event"), names(call), nomatch = 0) if (indx[1] == 0) stop("A \"formula\" argument is required") temp <- call[c(1, indx)] temp[[1]] <- as.name("model.frame") temp[["event"]] <- event f1 <- if (is.list(formula)) formula[[1]] else formula if (missing(data)) temp[["data"]] <- environment(f1) temp[["na.action"]] <- na.pass # event will have NAs by design. Or recode them ? TESTME ## one model frame for each component. may be different if different response terms in formula m <- vector(K, mode="list") for (k in 1:K){ f2 <- concat.formulae(locform[[k]], c(unlist(forms), pformula), data=data) temp[["formula"]] <- f2 m[[k]] <- eval(temp, parent.frame()) m[[k]] <- droplevels(m[[k]]) # remove unused factor levels after subset applied } nobs <- nrow(m[[1]]) ## Build design matrices given formulae and model frame mml <- mx <- X <- whichparcov <- vector(K, mode="list") for (k in 1:K) { mml[[k]] <- mx[[k]] <- vector(mode="list", length=length(dlists[[k]]$pars)) names(mml[[k]]) <- names(mx[[k]]) <- c(dlists[[k]]$location, setdiff(dlists[[k]]$pars, dlists[[k]]$location)) for (i in names(forms[[k]])){ mml[[k]][[i]] <- model.matrix(forms[[k]][[i]], m[[k]]) mx[[k]][[i]] <- length(unlist(mx[[k]])) + seq_len(ncol(mml[[k]][[i]][,-1,drop=FALSE])) } X[[k]] <- compress.model.matrices(mml[[k]]) npc <- unlist(lapply(mml[[k]], ncol)) - 1 whichparcov[[k]] <- rep(names(npc), npc) } if (is.null(pformula)) pformula <- ~1 if ("." %in% all.vars(pformula)) stop("`.` in formulae is not supported in flexsurvmix") Xp <- model.matrix(pformula, m[[1]])[,-1,drop=FALSE] ## Convert event internally to numbers based on factor levels event <- model.extract(m[[1]], "event") event <- match(event, evnames, incomparables=NA) ## Count parameters of particular kinds ncoveffsl <- sapply(X, ncol) # number of covariate effects for each component-specific distribution ncoveffs <- sum(ncoveffsl) ncovsp <- ncol(Xp) # number of covariates on mixing probabilities ncoveffsp <- (K-1)*ncovsp # number of covariate effects on mixing probabilities nppars <- length(dists) - 1 + ncoveffsp # number of parameters related to mixing probabilities: baseline probs and covariate effects ## Order of time-to-event parameters: baseline parameters in the order they ## appear in the distribution function (e.g. shape before scale in the ## Weibull), followed by covariate effects on the location parameter, followed ## by covariate effects on the remaining parameters. nthetal <- sapply(dlists, function(x)length(x$pars)) # number of baseline parameters for each component-specific distribution ntparsl <- nthetal + ncoveffsl # total number of time-to-event related pars for each component parindsl <- rep(1:K, ntparsl) # index identifying component for each of those parameters ntpars <- sum(ntparsl) # total number of parameters related to time-to-event distributions npars <- nppars + ntpars # total number of parameters ## identify parameters of particular kinds parclass <- rep(c("prob","time"), c(nppars, ntpars)) # mixing prob or time-to-event related baseorcov <- c(rep(c("pbase","pcov"), c(length(dists) -1, ncoveffsp)), # baseline or covariate effect rep(rep(c("tbase","tcov"), K), as.vector(rbind(nthetal, ncoveffsl)))) parcov <- character(npars) # identify baseline parameter which a covariate effect modifies parcov[parclass=="prob" & baseorcov=="pcov"] <- rep(paste0("prob",2:K), each=ncovsp) parcov[baseorcov=="tcov"] <- unlist(whichparcov) ## Build initial values for each parameter type for optimisation if (is.null(initp)) initp <- rep(1/K, K) alpha <- initp theta_inits <- cov_inits <- covparsl <- vector(K, mode="list") for (k in 1:K) { covparsl[[k]] <- nthetal[k] + seq_len(ncoveffsl[k]) if (is.null(inits[[k]])) { Y <- check.flexsurv.response(model.extract(m[[k]], "response")) yy <- ifelse(Y[,"status"]==3 & is.finite(Y[,"time2"]), (Y[,"time1"] + Y[,"time2"])/2, Y[,"time1"]) yy <- yy[event==k | is.na(event)] # wt <- yy*weights*length(yy)/sum(weights) dlists[[k]]$inits <- expand.inits.args(dlists[[k]]$inits) ## This extra stuff is needed for the Weibull, to use a survreg fit to ## get "initial values" if (dlists[[k]]$name %in% c("exp","weibull.quiet","lnorm","weibullPH","llogis")) inits.aux <- list(forms=forms[[k]], data=if(missing(data)) NULL else data, weights=temp$weights, control=sr.control, counting=(attr(model.extract(m[[k]], "response"), "type")=="counting") ) else inits.aux <- aux[[k]] ## Auto-generate initial values using the heuristic for that distribution auto.inits <- dlists[[k]]$inits(t=yy,mf=m[[k]],mml=mml[[k]],aux=inits.aux) nin <- length(inits) theta_inits[[k]] <- auto.inits[seq_len(nthetal[k])] if ((length(auto.inits) > nthetal[k]) && (ncoveffsl[k] > 0)) { ## e.g for Weibull distributions, initial value fn also estimates covariate effects. cov_inits[[k]] <- auto.inits[nthetal[k] + seq_len(ncoveffsl[k])] } else cov_inits[[k]] <- rep(0, ncoveffsl[k]) } else { theta_inits[[k]] <- inits[[k]][1:nthetal[k]] # baseline pars of parametric survival dists cov_inits[[k]] <- inits[[k]][covparsl[[k]]] } names(theta_inits[[k]]) <- dlists[[k]]$pars names(cov_inits[[k]]) <- colnames(X[[k]]) } ## Transform initial values to log or logit scale for optimisation, if needed. inits_probs <- initp inits_alpha <- if (K==1) numeric() else qmnlogit(inits_probs) inits_covp <- rep( rep(0,ncovsp), K-1) # order by covariate within probability names(inits_covp) <- sprintf("prob%s(%s)", rep(2:K, each=ncovsp), rep(colnames(Xp), K-1)) inits_theta <- numeric() for (k in 1:K){ inits_theta <- c(inits_theta, par.transform(theta_inits[[k]], dlists[[k]]), cov_inits[[k]]) } ## Full loglikelihood function, required for the direct likelihood maximisation ## (note this is different from the "complete data" loglikelihood used in EM) loglik_flexsurvmix <- function(parsopt, ...){ pars <- inits_all pars[optpars] <- parsopt if (K==1) probmat <- pmat <- matrix(1, nrow=nobs, ncol=K) else { ## Apply covariate effects to mixing probabilities by multinomial logistic ## regression alpha <- c(0, pars[1:(K-1)]) alphamat <- matrix(alpha, nrow=nobs, ncol=K, byrow=TRUE) # by individual if (ncovsp > 0) { for (k in 2:K){ cpinds <- K - 1 + (k-2)*ncovsp + 1:ncovsp alphamat[,k] <- alpha[k] + Xp %*% pars[cpinds] } } pmat <- exp(alphamat) pmat <- pmat / rowSums(pmat) probmat <- pmat # this will be 1 or 0 if event observed } ## Remaining parameters are time-to-event stuff parsl <- split(pars[nppars + seq_len(ntpars)], parindsl) theta <- coveffs <- vector(K, mode="list") ## Contribution to likelihood for mixing probabilities for those with known events llp_event_known <- matrix(0, nrow=nobs, ncol=K) # Set membership prob to 0 where there are partially-observed events for (i in seq_len(npartials)){ non_events <- setdiff(1:K, partial_events[[i]]) probmat[!is.na(partial_event) & partial_event==i, non_events] <- 0 } ## Likelihood from times to events or censoring liki <- matrix(0, nrow=nobs, ncol=K) for (k in 1:K){ ## Evaluate likelihood for each component by calling flexsurvreg with ## parameters fixed at initial values. Build this initial values vector. theta[[k]] <- inv.transform(parsl[[k]][seq_len(nthetal[k])], dlists[[k]]) coveffs[[k]] <- parsl[[k]][nthetal[k] + seq_len(ncoveffsl[k])] initsk <- c(theta[[k]], coveffs[[k]]) if (any(is.infinite(log(exp(initsk))))) return(-Inf) ## Event probability is 1 if their event was observed to be k probmat[!is.na(event) & event==k, k] <- 1 ## Event probability is 1 if their event was observed to be one other than k probmat[!is.na(event) & event!=k, k] <- 0 need_lik <- probmat[,k] > 0 liki[need_lik,k] <- exp(do.call("flexsurvreg", list(formula=locform[[k]], data=data, dist=dists[[k]], anc=anc[[k]], inits=initsk, subset=need_lik, aux=aux[[k]], hessian=FALSE, fixedpars=TRUE))$logliki) llp_event_known[,k] <- as.numeric((!is.na(event) & event==k) * log(pmat[,k])) } logliki <- - (log(rowSums(probmat*liki, na.rm=TRUE)) + rowSums(llp_event_known)) res <- sum(logliki) attr(res, "indiv") <- logliki res } # Parameter dictionary to be completed with the estimates distnames <- sapply(dists, function(x){if(is.list(x))x$name else x}) res <- data.frame(component = c(evnames, rep(evnames[setdiff(1:K, 1)], each=ncovsp), rep(evnames, ntparsl)), dist = c(rep("",nppars+1), rep(distnames, ntparsl)), terms = c(paste0("prob",1:K), names(inits_covp), names(inits_theta)), parclass = c("prob", parclass), baseorcov = c("pbase", baseorcov), parcov = c("", parcov)) inits_all <- c(inits_alpha, inits_covp, inits_theta) if (isTRUE(fixedpars)) fixedpars <- seq_len(npars) if (is.logical(fixedpars) && (fixedpars==FALSE)) fixedpars <- NULL if (is.character(fixedpars)){ if (!all(fixedpars %in% res$terms)) { bad_fixedpars <- fixedpars[! fixedpars %in% res$terms[-1]] stop(paste(bad_fixedpars,collapse=","), " not in model terms") } fixedpars <- match(fixedpars, as.character(res$terms[-1])) } if (is.numeric(fixedpars) && !all(fixedpars %in% 1:npars)) stop(sprintf("`fixedpars` should all be in 1,...,%s",npars)) optpars <- setdiff(seq_len(npars), fixedpars) fixed <- (length(optpars) == 0) inits_opt <- inits_all[optpars] if (is.null(optim.control$fnscale)) optim.control$fnscale <- 10000 method <- match.arg(method, c("direct","em")) if (!anyNA(event)) method <- "em" # likelihoods factorise, use EM code with one iteration if (method=="direct"){ if (length(optpars) > 0){ if (is.null(optim.control$ndeps)) optim.control$ndeps = rep(1e-06, length(inits_opt)) opt <- optim(inits_opt, loglik_flexsurvmix, hessian=FALSE, method="BFGS", control=optim.control, ...) if (opt$convergence==1) warning("Iteration limit in optim() reached without convergence. Reported estimates are not the maximum likelihood. Increase \"maxit\" or simplify the model.") } else { opt <- list(par=inits_all, value=loglik_flexsurvmix(inits_all)) } logliki <- -attr(loglik_flexsurvmix(opt$par), "indiv") ## Transform mixing probs back to natural scale for presentation opt_all <- inits_all opt_all[optpars] <- opt$par res_probs <- if (K>1) pmnlogit(opt_all[1:(K-1)]) else 1 res_covp <- if (ncoveffsp>0) opt_all[K:(K-1+ncoveffsp)] else numeric() res_cpars <- split(opt_all[(nppars+1):length(opt_all)], parindsl) res_theta <- res_coveffs <- vector(K, mode="list") for (k in 1:K){ ## Transform time-to-event parameters back to natural scale res_theta[[k]] <- inv.transform(res_cpars[[k]][seq_len(nthetal[k])], dlists[[k]]) res_coveffs[[k]] <- res_cpars[[k]][nthetal[k] + seq_len(ncoveffsl[k])] res_cpars[[k]] <- c(res_theta[[k]], res_coveffs[[k]]) } ## Build tidy data frame of results with one row per parameter. Includes an ## extra row for the probability of the first event (defined as 1 - sum of ## rest) est.t <- c(NA, opt_all) res <- cbind(res, data.frame( est = c(res_probs, res_covp, unlist(res_cpars)), est.t = est.t)) loglik <- - as.vector(opt$value) if (!fixed) { # the hessian computation is potentially extremely time consuming! cov <- .hess_to_cov(.hessian(loglik_flexsurvmix, opt$par), hess.control$tol.solve, hess.control$tol.evalues) } else { cov <- NULL } } else if (method=="em") { if (!is.list(em.control)) em.control <- list() if (is.null(em.control$reltol)) em.control$reltol <- sqrt(.Machine$double.eps) if (is.null(em.control$var.method)) em.control$var.method <- "direct" converged <- FALSE iter <- 0 alpha <- inits_alpha covp <- inits_covp theta <- theta_inits covtheta <- cov_inits fixedpars_em <- split_fixedpars(fixedpars, nppars, ntparsl, K, nthetal) optpars_em <- split_fixedpars(optpars, nppars, ntparsl, K, nthetal) while (!converged) { ## E step alphamat <- matrix(c(0,alpha), nrow=nobs, ncol=K, byrow=TRUE) # by individual if (ncovsp>0){ for (k in 2:K){ cpinds <- (k-2)*ncovsp + 1:ncovsp alphamat[,k] <- alpha[k-1] + Xp %*% covp[cpinds] } } pmat <- exp(alphamat) pmat <- pmat / rowSums(pmat) llmat <- matrix(nrow=nobs, ncol=K) for (k in 1:K) { fs <- flexsurvreg(formula=locform[[k]], data=data, dist=dists[[k]], anc=anc[[k]], inits=theta[[k]], aux=aux[[k]], fixedpars=TRUE, hessian=FALSE) llmat[,k] <- fs$logliki } alphap <- exp(llmat) * pmat w <- alphap / rowSums(alphap) # probability that each observation belongs to each component for (k in 1:K) { w[!is.na(event) & event==k, k] <- 1 w[!is.na(event) & event!=k, k] <- 0 } w ## M step ## estimate component probs and covariate effects on them #alpha <- colMeans(w) loglik_p_em <- function(pars){ parsfull <- numeric(nppars) parsfull[optpars_em$p] <- pars parsfull[fixedpars_em$p] <- c(inits_alpha, inits_covp)[fixedpars_em$p] alphamat <- matrix(c(0,parsfull[1:(K-1)]), nrow=nobs, ncol=K, byrow=TRUE) if (ncovsp > 0) { for (k in 2:K){ cpinds <- K - 1 + (k-2)*ncovsp + 1:ncovsp alphamat[,k] <- alphamat[,k] + Xp %*% parsfull[cpinds] } } pmat <- exp(alphamat) pmat <- pmat / rowSums(pmat) -sum(w*log(pmat)) } # if setting a control argument here in the future, note ndeps has to be different # length from others. alpha <- inits_alpha covp <- inits_covp if (length(fixedpars_em$p) == nppars) { # all prob-related parameters fixed hess_full_p <- matrix(nrow=0,ncol=0) } else { parsp <- optim(c(alpha,covp)[optpars_em$p], loglik_p_em, method="BFGS", hessian=TRUE, control = em.control$optim.p.control) if(any(names(optpars_em$p)=="p")) alpha[optpars_em$p[names(optpars_em$p)=="p"]] <- parsp$par[names(optpars_em$p)=="p"] if(any(names(optpars_em$p)=="pcov")) covp[optpars_em$p[names(optpars_em$p)=="pcov"] - (K-1)] <- parsp$par[names(optpars_em$p)=="pcov"] hess_full_p <- parsp$hessian } probs <- pmnlogit(alpha) ## call flexsurvreg for each component on weighted dataset to estimate component-specific pars thetanew <- covthetanew <- ttepars <- hess_full_t <- vector(K, mode="list") ll <- numeric(K) ctrl <- optim.control for (k in 1:K) { if (is.null(optim.control$ndeps)) ctrl$ndeps = rep(1e-06, length(optpars_em$t[[as.character(k)]])) fs <- do.call("flexsurvreg", # need do.call to avoid environment faff with supplying weights list(formula=locform[[k]], data=data, dist=dists[[k]], anc=anc[[k]], inits=c(theta[[k]],covtheta[[k]]), fixedpars = fixedpars_em$t[[as.character(k)]], weights=w[,k], aux=aux[[k]], subset=w[,k]>0, control=ctrl)) ll[k] <- fs$loglik thetanew[[k]] <- fs$res[seq_len(nthetal[k]),"est"] if (ncoveffsl[k] > 0) covthetanew[[k]] <- fs$res[nthetal[k] + seq_len(ncoveffsl[k]), "est"] ttepars[[k]] <- c(thetanew[[k]], covthetanew[[k]]) hess_full_t[[k]] <- fs$opt$hessian if (is.null(hess_full_t[[k]])) hess_full_t[[k]] <- matrix(nrow=0,ncol=0) } theta <- thetanew covtheta <- covthetanew logliknew <- sum(ll) if (!anyNA(event)) converged <- TRUE else if (iter > 0) converged <- (abs(logliknew / loglik - 1) <= em.control$reltol) loglik <- logliknew est <- c(probs, covp, unlist(ttepars)) theta.t <- parlist.transform(theta,dlists) ttepars.t <- vector(mode="list") for (k in 1:K){ ttepars.t[[k]] <- c(theta.t[[k]], covtheta[[k]]) } est.t <- c(NA, alpha, covp, unlist(ttepars.t)) if (is.numeric(em.control$trace) && em.control$trace > 0) cat(sprintf("loglik=%s\n",loglik)) if (is.numeric(em.control$trace) && em.control$trace > 1) print(est) iter <- iter + 1 } res <- cbind(res, data.frame(est=est, est.t=est.t)) ll <- loglik_flexsurvmix(est.t[-1][optpars]) loglik <- -as.vector(ll) logliki <- -attr(ll, "indiv") if (!anyNA(event)) { hess <- - Matrix::bdiag(hess_full_p, Matrix::bdiag(hess_full_t)) cov <- .hess_to_cov(-hess, hess.control$tol.solve, hess.control$tol.evalues) } else { if (em.control$var.method=="direct"){ hess <- .hessian(loglik_flexsurvmix, est.t[-1][optpars]) cov <- .hess_to_cov(hess, hess.control$tol.solve, hess.control$tol.evalues) } else if (em.control$var.method=="louis") cov <- flexsurvmix_louis(K, nthetal, dlists, ncoveffsl, locform, data, dists, anc, aux, fixedpars_em, optpars_em, inits, optim.control, ttepars.t, nobs, ntparsl, nppars, w, alpha, covp, ncovsp, Xp, hess_full_p, hess_full_t, hess.control) } opt <- NULL } ## Add standard errors to results data frame, given covariance matrix. ## A previous version attempted to calculate a SE for the reference category ## probability as follows, but didn't account for the logit transformation. ## var ( 1 - p1 - p2 - .. ) = var(p1) + var(p2) - cov(p1,p2) - ... res$fixed <- c(NA, rep(FALSE, npars)) res$fixed[1 + fixedpars] <- TRUE optp <- optpars[optpars < K] res$se <- rep(NA, npars + 1) if (!fixed){ if (length(optp) > 0){ covp <- cov[optp, optp, drop=FALSE] res$se[1] <- NA } res$se[1 + optpars] <- sqrt(diag(cov)) } names.first <- c("component","dist","terms","est","est.t","se") res <- res[,c(names.first, setdiff(names(res), names.first)),drop=FALSE] rownames(res) <- NULL mcomb <- do.call("cbind", m) mcomb <- mcomb[,!duplicated(names(mcomb))] attr(mcomb, "covnames") <- unique(unlist(lapply(m, function(x)attr(terms(x),"term.labels")))) attr(mcomb, "covnames.main") <- unique(unlist(lapply(m, function(x)rownames(attr(terms(x),"factors"))[-1]))) res <- list(call=match.call(), res=res, loglik=loglik, cov=cov, npars=npars, AIC=-2*loglik + 2*npars, K=K, dists=distnames, dlists=dlists, dfns=dfns, opt=opt, fixedpars=fixedpars, optpars=optpars, logliki=logliki, evnames=evnames, nthetal=nthetal, parindsl=parindsl, ncoveffsl=ncoveffsl,ncoveffsp=ncoveffsp, covparsl=covparsl, all.formulae=forms, pformula=pformula, data=list(mf=m, mfcomb=mcomb), mx=mx) class(res) <- "flexsurvmix" res } check.formula.flexsurvmix <- function(formula, dlist, data=NULL){ if (!is.list(formula)){ if (!inherits(formula,"formula")) stop("\"formula\" must be a formula object") formula <- list(formula) } for (i in seq_along(formula)){ if (!inherits(formula[[i]],"formula")) stop(sprintf("\"formula[[%s]]\" must be a formula object", i)) if ("." %in% all.vars(formula[[i]])) stop("`.` in formulae is not supported in flexsurvmix") labs <- attr(terms(formula[[i]], data=data), "term.labels") if (!("strata" %in% dlist$pars)){ strat <- grep("strata\\((.+)\\)",labs) if (length(strat) > 0){ cov <- gsub("strata\\((.+)\\)","\\1",labs[strat[1]]) warning("Ignoring \"strata\" function: interpreting \"",cov, "\" as a covariate on \"", dlist$location, "\"") } } if (!("frailty" %in% dlist$pars)){ fra <- grep("frailty\\((.+)\\)",labs) if (length(fra) > 0){ warning("frailty models are not supported and behaviour of frailty() is undefined") } } } } #' @noRd logLik.flexsurvmix <- function(object, ...){ val <- object$loglik attributes(val) <- NULL attr(val, "df") <- object$npars attr(val, "nobs") <- nrow(model.frame(object)) class(val) <- "logLik" val } clean_listarg <- function(arg, argname, evnames){ if (!is.null(arg)){ if (length(arg) != length(evnames)) stop(sprintf("`%s` of length %s, should equal the number of mixture components, assumed to be %s, from the number of levels of factor(event)", argname, length(arg), length(evnames))) narg <- names(arg) if (is.null(narg)) names(arg) <- evnames else { if (!identical(sort(narg), sort(evnames))) stop(sprintf("names(%s) = %s, but this should match levels(factor(event)) = %s", argname, paste(narg, collapse=","), paste(evnames,collapse=","))) arg <- arg[evnames] } } arg } ##' @export print.flexsurvmix <- function(x, ...) { cat("Call:\n") dput(x$call) cat("\n") if (x$npars > 0) { keep.cols <- c("component","dist","terms","est","est.t","se") res <- x$res[,keep.cols,drop=FALSE] cat ("Estimates: \n") args <- list(...) if (is.null(args$digits)) args$digits <- 3 f <- do.call("format", c(list(x=res), args)) print(f, print.gap=2, quote=FALSE, na.print="") } cat("\nLog-likelihood = ", x$loglik, ", df = ", x$npars, "\nAIC = ", x$AIC, "\n\n", sep="") } par.transform <- function(pars, dlist){ pars.t <- numeric(length(pars)) names(pars.t) <- names(pars) for (i in seq_along(pars.t)) pars.t[i] <- dlist$transforms[[i]](pars[i]) pars.t } inv.transform <- function(pars, dlist){ pars.nat <- numeric(length(pars)) names(pars.nat) <- names(pars) for (i in seq_along(pars.nat)) pars.nat[i] <- dlist$inv.transforms[[i]](pars[i]) pars.nat } parlist.transform <- function(parlist, dlists){ parlist.t <- vector(length(parlist), mode="list") for (k in seq_along(parlist.t)) parlist.t[[k]] <- par.transform(parlist[[k]], dlists[[k]]) parlist.t } invlist.transform <- function(parlist, dlists){ parlist.t <- vector(length(parlist), mode="list") for (k in seq_along(parlist.t)) parlist.t[[k]] <- inv.transform(parlist[[k]], dlists[[k]]) parlist.t } ## Transform full vector of estimates back to natural scale. ## Returns Kth baseline prob as well ## TODO can this go into the main flexsurvreg function? Would have to form list first inv.transform.res <- function(x, dlists) { dpars <- x$res$est.t[x$res$dist!=""] dpars <- split(dpars, x$parindsl) dnames <- split(x$res$terms[x$res$dist!=""], x$parindsl) K <- x$K est <- vector(K, mode="list") for (k in 1:K) { bpars <- dpars[[k]][dnames[[k]] %in% x$dlists[[k]]$pars] cpars <- dpars[[k]][!(dnames[[k]] %in% x$dlists[[k]]$pars)] bpars <- inv.transform(bpars, dlists[[k]]) est[[k]] <- c(bpars, cpars) } probs <- if (K==1) 1 else pmnlogit(x$res$est.t[2:K]) pcov <- x$res$est.t[grep("prob[[:digit:]]+\\(.+\\)", x$res$terms)] c(probs, pcov, unlist(est)) } ##' Model frame from a flexsurvmix object ##' ##' Returns a list of data frames, with each component containing the ##' data that were used for the model fit for that mixture component. ##' ##' @param formula Fitted model object from \code{\link{flexsurvmix}}. ##' ##' @param ... Further arguments (currently unused). ##' ##' @return A list of data frames ##' ##' @export model.frame.flexsurvmix <- function(formula, ...) { x <- formula x$data$m } # Multinomial logistic transform and inverse transform # returns transformed probs relative to first component, excluding first component qmnlogit <- function(probs){ if (length(probs) == 1) qlogis(probs) else log(probs[-1] / probs[1]) } # returns probs including first component, given transformed probs with first component excluded pmnlogit <- function(alpha){ c(1, exp(alpha)) / (1 + sum(exp(alpha))) } ## Convert "fixedpars" (vector of parameter indices to fix) from ## joint full MLE form (indices into full parameter vector) to EM form ## (indices of parameters in each submodel to be maximised in the M step) ## e.g. #nppars <- 4 # number of prob pars (including cov effects) #ntparsl <- c(3, 3, 4) # number of time to event pars for each event (including cov effects) #indices 1,2,3,4 are prob pars, 5,6,7 time to event 1 pars # 8,9,10 are time to event 2 pars, and 11,12,13,14 are time to event 3 pars #fixedpars <- c(2,3, 6,7, 9, 12) #correspond to indices 2,3 2,3 2 2) in the four submodels # so function returns list(p=c(2,3), t=list(c(2,3), 2, 2)) # List component will be numeric(0) for prob model, or NULL for time model, if no pars fixed for that model # names of time models will be "1","2",. split_fixedpars <- function(fixedpars, nppars, ntparsl, K, nthetal){ fixedpars_p <- fixedpars[fixedpars <= nppars] if (!is.null(fixedpars_p)) names(fixedpars_p) <- ifelse(fixedpars_p <= K-1, "p", "pcov") ft <- fixedpars[fixedpars >= nppars] - nppars fixedpars_t <- split(sequence(ntparsl)[ft], rep(seq_along(ntparsl), ntparsl)[ft]) for (i in 1:K){ ic <- as.character(i) if (!is.null(fixedpars_t[[ic]])) names(fixedpars_t[[ic]]) <- ifelse(fixedpars_t[[ic]] <= nthetal[i], "theta", "covtheta") else fixedpars_t[[ic]] <- numeric() } fixedpars_t <- fixedpars_t[as.character(1:K)] list(p=fixedpars_p, t=fixedpars_t) } flexsurv/R/summary.flexsurvmix.R0000644000176200001440000005335114607775206016571 0ustar liggesusers##' Mean times to events from a flexsurvmix model ##' ##' This returns the mean of each event-specific parametric time-to-event ##' distribution in the mixture model, which is the mean time to event ##' conditionally on that event being the one that happens. ##' ##' @param x Fitted model object returned from \code{\link{flexsurvmix}}. ##' ##' @param newdata Data frame or list of covariate values. If omitted for a ##' model with covariates, a default is used, defined by all combinations of ##' factors if the only covariates in the model are factors, or all covariate ##' values of zero if there are any non-factor covariates in the model. ##' ##' @param B Number of simulations to use to compute 95\% confidence intervals, ##' based on the asymptotic multivariate normal distribution of the basic ##' parameter estimates. If \code{B=NULL} then intervals are not computed. ##' ##' @return Mean times to next event conditionally on each alternative event, ##' given the specified covariate values. ##' ##' @export mean_flexsurvmix <- function(x, newdata=NULL, B=NULL){ if (is.null(newdata)) newdata <- default_newdata(x) if (!is.null(newdata)){ # mean functions aren't vectorised newdata <- as.data.frame(newdata) nvals <- nrow(newdata) res <- cisumm_flexsurvmix(x, newdata=newdata[1,,drop=FALSE], fnname="mean", fnlist=x$dfns, B=B) if (nvals > 1) { for (i in 2:nvals){ res <- rbind(res, cisumm_flexsurvmix(x, newdata=newdata[i,,drop=FALSE], fnname="mean", fnlist=x$dfns, B=B)) } } } else { res <- cisumm_flexsurvmix(x, newdata=newdata, fnname="mean", fnlist=x$dfns, B=B) } res } ##' Restricted mean times to events from a flexsurvmix model ##' ##' This returns the restricted mean of each event-specific parametric time-to-event ##' distribution in the mixture model, which is the mean time to event ##' conditionally on that event being the one that happens, and conditionally ##' on the event time being less than some time horizon \code{tot}. ##' ##' @param tot Time horizon to compute the restricted mean until. ##' ##' @inheritParams mean_flexsurvmix ##' ##' @return Restricted mean times to next event conditionally on each alternative event, ##' given the specified covariate values. ##' ##' @export rmst_flexsurvmix <- function(x, newdata=NULL, tot=Inf, B=NULL){ if (is.null(newdata)) newdata <- default_newdata(x) if (!is.null(newdata)){ # mean functions aren't vectorised newdata <- as.data.frame(newdata) nvals <- nrow(newdata) res <- cisumm_flexsurvmix(x, newdata=newdata[1,,drop=FALSE], fnname="rmst", fnarg="t", fnargval=tot, fnlist=x$dfns, B=B) if (nvals > 1) { for (i in 2:nvals){ res <- rbind(res, cisumm_flexsurvmix(x, newdata=newdata[i,], fnname="rmst", fnarg="t", fnargval=tot, fnlist=x$dfns, B=B)) } } } else { newdata <- default_newdata(x, zero=TRUE) res <- cisumm_flexsurvmix(x, newdata=newdata, fnname="rmst", fnarg="t", fnargval=tot, fnlist=x$dfns, B=B) } res } ##' Quantiles of time-to-event distributions in a flexsurvmix model ##' ##' This returns the quantiles of each event-specific parametric time-to-event ##' distribution in the mixture model, which describes the time to the event ##' conditionally on that event being the one that happens. ##' ##' @inheritParams mean_flexsurvmix ##' ##' @param probs Vector of alternative quantiles, by default \code{c(0.025, 0.95, 0.975)} ##' giving the median and a 95\% interval. ##' ##' @export quantile_flexsurvmix <- function(x, newdata=NULL, B=NULL, probs=c(0.025, 0.5, 0.975)){ cisumm_flexsurvmix(x, newdata=newdata, fnname="q", fnarg="p", fnargval=probs, fnlist=x$dfns, B=B) } ##' Fitted densities for times to events in a flexsurvmix model ##' ##' This returns an estimate of the probability density for the time to each ##' competing event, at a vector of times supplied by the user. ##' ##' @inheritParams mean_flexsurvmix ##' ##' @param t Vector of times at which to evaluate the probability density ##' ##' @return A data frame with each row giving the fitted density \code{dens} for ##' a combination of covariate values, time and competing event. ##' ##' @export pdf_flexsurvmix <- function(x, newdata=NULL, t=NULL){ if (is.null(t)) { stop("Times `t` to evaluate the density at not supplied") } else { if (!is.numeric(t)) stop("`t` must be numeric") } nt <- length(t) if (!is.null(newdata)) { newdata <- as.data.frame(newdata) ncovs <- nrow(newdata) newdatarep <- newdata[rep(1:ncovs, nt),,drop=FALSE] } else { ncovs <- 1 newdatarep <- NULL } K <- x$K res <- vector(K, mode="list") for (k in 1:K){ pars <- get_basepars(x, newdata=newdatarep, event=k) pars$x <- rep(t, each=ncovs) res[[k]] <- do.call(x$dfns[[k]]$d, pars) } tdf <- data.frame(event = rep(x$evnames, each=length(res[[1]]))) if (!is.null(newdata)) tdf <- cbind(tdf, newdatarep[rep(1:nrow(newdatarep), K),,drop=FALSE]) tdf$t <- rep(rep(t,each=ncovs), K) tdf$dens <- unlist(res) rownames(tdf) <- NULL tdf } ##' Transition probabilities from a flexsurvmix model ##' ##' These quantities are variously known as transition probabilities, or state ##' occupancy probabilities, or values of the "cumulative incidence" function, ##' or values of the "subdistribution" function. They are the probabilities that ##' an individual has experienced an event of a particular kind by time ##' \code{t}. ##' ##' Note that "cumulative incidence" is a misnomer, as "incidence" typically ##' means a hazard, and the quantities computed here are not cumulative hazards, ##' but probabilities. ##' ##' ##' @inheritParams mean_flexsurvmix ##' ##' @param t Vector of times \code{t} to calculate the probabilities of ##' transition by. ##' ##' @param startname Name of the state where individuals start. This considers ##' the model as a multi-state model where people start in this state, and may ##' transition to one of the competing events. ##' ##' @return A data frame with transition probabilities by time, covariate value ##' and destination state. ##' ##' ##' @export p_flexsurvmix <- function(x, newdata=NULL,startname="start", t=1, B=NULL){ fm_p_fn <- function(base,prob,resdf,x,startname) { resdf$val <- base * prob resdf$tval <- resdf$pval <- NULL resdf <- resdf %>% tidyr::pivot_wider(names_from="event", values_from="val") resdf[[startname]] <- 1 - rowSums(resdf[,x$evnames]) statenames <- c(startname,x$evnames) resdf %>% pivot_longer(cols=all_of(statenames), names_to="state", values_to="val") } res <- cisumm_flexsurvmix(x, newdata=newdata, fnname="p", fnarg="q", parclass = c("time", "prob"), fnargval=t, fnlist=x$dfns, combfn = fm_p_fn, B=B, startname=startname) names(res)[names(res)=="q"] <- "t" res } ##' Probabilities of competing events from a flexsurvmix model ##' ##' @inheritParams mean_flexsurvmix ##' ##' @return A data frame containing the probability that each of the competing ##' events will occur next, by event and by any covariate values specified in ##' \code{newdata}. ##' ##' @export probs_flexsurvmix <- function(x, newdata=NULL, B=NULL){ if (!inherits(x, "flexsurvmix")) stop("`x` is not a flexsurvmix object") if (is.null(newdata)) newdata <- default_newdata(x) if (x$K==1) { res <- newdata res$event <- x$evnames res$val <- 1 } else res <- cisumm_flexsurvmix(x, newdata=newdata, parclass="prob", B=B, fnname=NULL) res } default_newdata <- function(x, zero=FALSE){ dat <- x$data$mfcomb covnames <- attr(dat, "covnames") ncovs <- length(covnames) if (ncovs == 0){ newdata <- NULL } else { faccovs <- sapply(dat[,covnames], is.factor) if (!all(faccovs) & !zero) newdata <- matrix(0, nrow=1, ncol=ncovs, dimnames=list(NULL, covnames)) else newdata <- do.call(expand.grid, lapply(dat[,covnames], levels)) newdata <- as.data.frame(newdata) } newdata } cisumm_flexsurvmix <- function(x, newdata=NULL, parclass = "time", fnname, fnarg=NULL, fnargval=NULL, fnlist=NULL, combfn=NULL, B=NULL, ...){ K <- x$K res <- vector(K, mode="list") if (is.null(newdata)) newdata <- default_newdata(x) if ("time" %in% parclass) { nquants <- max(1, length(fnargval)) if (!is.null(newdata)) { newdata <- as.data.frame(newdata) ncovs <- nrow(newdata) newdatarep <- newdata[rep(1:ncovs, nquants),,drop=FALSE] } else { ncovs <- 1 newdatarep <- NULL } fnargvalrep <- rep(fnargval, each=ncovs) for (k in 1:x$K){ pars <- get_basepars(x, newdata=newdatarep, event=k) parnames <- names(pars) if (!is.null(fnarg)) pars[[fnarg]] <- fnargvalrep if (!is.null(fnlist)) fn <- fnlist[[k]][[fnname]] res[[k]] <- do.call(fn, pars) } tdf <- data.frame(event = rep(x$evnames, each=length(res[[1]]))) if (!is.null(fnarg)) tdf[[fnarg]] <- rep(fnargvalrep, K) if (!is.null(newdata)) tdf <- cbind(tdf, newdatarep[rep(1:nrow(newdatarep), K),,drop=FALSE]) tdf$val <- unlist(res) } if ("prob" %in% parclass) { if (!is.null(newdata)) newdata <- as.data.frame(newdata) pdf <- get_probpars(x, newdata=newdata) if (!is.null(newdata)){ # in case there are covariates on times but not probs if (length(intersect(names(pdf), names(newdata)) > 0)) pdf <- dplyr::left_join(pdf, newdata, by=intersect(names(pdf), names(newdata))) else pdf <- tidyr::crossing(pdf, newdata) } } if (setequal(parclass, c("time","prob"))){ tdf <- tdf %>% dplyr::rename(tval="val") pdf <- pdf %>% dplyr::rename(pval="val") resdf <- tdf %>% dplyr::left_join(pdf, by=c("event", names(newdata))) resdf <- combfn(resdf$tval, resdf$pval, resdf, x, ...) resdf$tval <- resdf$pval <- NULL } else if (parclass=="time"){ resdf <- tdf } else if (parclass=="prob") { resdf <- pdf } if (is.numeric(B)) { resm <- array(dim=c(B, nrow(resdf))) resm[1,] <- as.matrix(resdf$val) if (B > 2) { for (b in 2:B){ pars <- list(x = resample_pars(x), newdata=newdata, parclass=parclass, fnname=fnname, fnarg=fnarg, fnargval=fnargval, fnlist=fnlist, combfn=combfn, B = NULL) pars <- c(pars, list(...)) resm[b,]<- do.call(cisumm_flexsurvmix, pars)$val } } qp <- c(0.025, 0.975) ci <- apply(resm, 2, quantile, qp) resdf$lower <- ci[1,] resdf$upper <- ci[2,] } resdf } resample_pars <- function(x){ cov <- matrix(0, x$npars, x$npars) cov[x$optpars, x$optpars] <- x$cov newpars <- rmvnorm(1, x$res$est.t[-1], cov) x$res$est.t <- c(NA, newpars) x$res$est <- inv.transform.res(x, x$dlist) x } ##' Evaluate baseline time-to-event distribution parameters given covariate values in a flexsurvmix model ##' ##' @param x Fitted model object ##' ##' @param newdata Data frame of alternative covariate values ##' ##' @param event Event ##' get_basepars <- function(x, newdata, event){ k <- event kpars <- (x$res$component == x$evnames[k]) & (x$res$dist == x$dists[k]) bpars <- kpars & (x$res$terms %in% x$dlists[[k]]$pars) beta <- if (x$ncoveffsl[k]==0) 0 else x$res[kpars,"est"][x$covparsl[[k]]] if (is.null(newdata) | (x$ncoveffsl[k]==0)) { basepars <- as.list(x$res[bpars,"est"]) names(basepars) <- x$dlists[[k]]$pars if (!is.null(newdata)) # if covariates for one event but not another, stretch out basepars <- lapply(basepars,function(x)x[rep(1,length(newdata[[1]])),drop=FALSE]) } else { basepars <- vector(x$nthetal[k], mode="list") names(basepars) <- x$dlists[[k]]$pars for (j in seq_len(x$nthetal[k])){ parname <- x$dlists[[k]]$pars[j] betainds <- x$res$component == x$evnames[k] & x$res$parcov == x$dlists[[k]]$pars[j] if (any(betainds)) { tm <- delete.response(terms(x$all.formulae[[k]][[parname]])) if (!all(rownames(attr(tm, "factors")) %in% names(newdata))) stop(sprintf("not all required variables supplied in `newdata`")) xlev <- lapply(x$data$mf[[k]], levels)[attr(tm,"term.labels")] ## convert numeric newdata to factor if necessary, ensure ordered status preserved for (i in names(newdata)){ vari <- x$data$mf[[1]][[i]] if (is.factor(vari)) { newdata[[i]] <- factor(as.character(newdata[[i]]), levels=levels(vari), ordered=is.ordered(vari)) } } mf <- model.frame(tm, newdata, xlev = xlev) mm <- model.matrix(tm, mf) basepar <- x$res[bpars,"est.t"][j] beta <- x$res$est.t[betainds] Xb <- as.numeric(mm %*% c(basepar, beta)) basepars[[j]] <- x$dlists[[k]]$inv.transform[[j]](Xb) } else basepars[[j]] <- x$res[bpars,"est"][j] } } basepars } get_probpars <- function(x, newdata=NULL, na.action){ if (is.null(newdata) | (x$ncoveffsp == 0) ) { probpars <- matrix(x$res$est[x$res$baseorcov=="pbase"], nrow=1) } else { tm <- delete.response(terms(x$pformula)) if (!all(rownames(attr(tm, "factors")) %in% names(newdata))) stop(sprintf("not all required variables supplied in `newdata`")) xlev <- lapply(x$data$mf[[1]], levels)[attr(tm,"term.labels")] mf <- model.frame(tm, newdata, xlev = xlev) X <- model.matrix(tm, mf) K <- x$K probpars <- matrix(nrow=nrow(X), ncol=K) for (i in 1:nrow(X)) { logitpcov <- numeric(K-1) for (k in 2:K){ logitpbase <- x$res$est.t[grep(sprintf("prob%s$",k), x$res$terms)] beta <- x$res$est[grep(sprintf("prob%s\\(.+\\)",k), x$res$terms)] logitpcov[k-1] <- X[i,,drop=FALSE] %*% c(logitpbase, beta) } probpars[i,] <- c(1, exp(logitpcov)) / (1 + sum(exp(logitpcov))) } } probpars <- as.data.frame(probpars) names(probpars) <- x$evnames if (!is.null(newdata) && (x$ncoveffsp > 0)) probpars <- cbind(probpars, mf) probpars <- tidyr::pivot_longer(probpars, tidyselect::all_of(x$evnames), names_to="event", values_to="val") probpars } ##' Aalen-Johansen nonparametric estimates comparable to a fitted flexsurvmix ##' model ##' ##' Given a fitted flexsurvmix model, return the Aalen-Johansen estimates of the ##' probability of occupying each state at a series of times covering the ##' observed data. State 1 represents not having experienced any of the ##' competing events, while state 2 and any further states correspond to having ##' experienced each of the competing events respectively. These estimates can ##' be compared with the fitted probabilities returned by ##' \code{\link{p_flexsurvmix}} to check the fit of a \code{flexsurvmix} model. ##' ##' This is only supported for models with no covariates or models containing ##' only factor covariates. ##' ##' For models with factor covariates, the Aalen-Johansen estimates are computed ##' for the subsets of the data defined in \code{newdata}. If \code{newdata} is ##' not supplied, then this function returns state occupancy probabilities for ##' all possible combinations of the factor levels. ##' ##' The Aalen-Johansen estimates are computed using ##' \code{\link[survival]{survfit}} from the \code{survival} package (Therneau ##' 2020). ##' ##' @param x Fitted model returned by \code{\link{flexsurvmix}}. ##' ##' @param newdata Data frame of alternative covariate values to check fit for. ##' Only factor covariates are supported. ##' ##' @param tidy If \code{TRUE} then a single tidy data frame is returned. ##' Otherwise the function returns the object returned by \code{survfit}, or a ##' list of these objects if we are computing subset-specific estimates. ##' ##' @references Therneau T (2020). _A Package for Survival Analysis in R_. R ##' package version 3.2-3, . ##' ##' @export ajfit <- function(x, newdata=NULL, tidy=TRUE){ dat <- x$data$mfcomb covnames <- attr(dat, "covnames.main") ncovs <- length(covnames) if (ncovs == 0){ sf <- sftidy <- ajfit.dat(x$data$mf[[1]], x$evnames) ret <- if (tidy) as.data.frame(unclass(sf)[c("time","pstate","lower","upper")]) else sf } else { faccovs <- sapply(dat[,covnames], is.factor) if (!all(faccovs)) stop("Nonparametric estimation not supported with non-factor covariates") if (is.null(newdata)) { newdata <- do.call(expand.grid, lapply(dat[,covnames,drop=FALSE], levels)) for (i in names(newdata)) class(newdata[[i]]) <- class(x$data$mf[[1]][[i]]) # preserve e.g. ordered factor status } newdata <- as.data.frame(newdata) ncovvals <- nrow(newdata) sf <- sftidy <- vector(ncovvals, mode="list") covnames <- names(newdata) ## TODO error handling for (i in 1:ncovvals) { datsub <- x$data$mf[[1]] # assume any of the mf[[k]] will do for (j in seq_along(covnames)) datsub <- datsub[datsub[,covnames[j]] == newdata[i,covnames[j]],,drop=FALSE] if (nrow(datsub) > 1) { sf[[i]] <- ajfit.dat(datsub, x$evnames) sftidy[[i]] <- as.data.frame(unclass(sf[[i]])[c("time","pstate","lower","upper")]) covvals <- newdata[i,,drop=FALSE][rep(1,nrow(sftidy[[i]])),,drop=FALSE] sftidy[[i]] <- cbind(sftidy[[i]], covvals) } } ret <- if (tidy) do.call("rbind", sftidy) else sf } ret } ajfit.dat <- function(dat,evnames){ intcens <- model.response(dat)[,"status"] == 3 dat <- dat[!intcens,] ## exclude interval-censored data event <- model.extract(dat, "event") # create a multistate outcome for survfit. event <- as.character(event) event[is.na(event)] <- 0 event <- factor(event, levels=c(0,evnames)) Y <- model.response(dat) tname <- if ("time1" %in% colnames(Y)) "time1" else "time" time <- as.numeric(Y[,tname]) sf <- survival::survfit(Surv(time, event) ~ 1) sf } ##' Forms a tidy data frame for plotting the fit of parametric mixture ##' multi-state models against nonparametric estimates ##' ##' This computes Aalen-Johansen estimates of the probability of occupying each ##' state at a series of times, using \code{\link{ajfit}}. The equivalent ##' estimates from the parametric model are then produced using ##' \code{\link{p_flexsurvmix}}, and concatenated with the nonparametric ##' estimates to form a tidy data frame. This data frame can then simply be ##' plotted using \code{\link[ggplot2]{ggplot}}. ##' ##' @param x Fitted model returned by \code{\link{flexsurvmix}}. ##' ##' @param maxt Maximum time to produce parametric estimates for. By default ##' this is the maximum event time in the data, the maximum time we have ##' nonparametric estimates for. ##' ##' @param startname Label to give the state corresponding to "no event happened ##' yet". By default this is \code{"Start"}. ##' ##' @param B Number of simulation replications to use to calculate a confidence ##' interval for the parametric estimates in \code{\link{p_flexsurvmix}}. ##' Comparable intervals for the Aalen-Johansen estimates are returned if this ##' is set. Otherwise if \code{B=NULL} then no intervals are returned. ##' ##' @export ajfit_flexsurvmix <- function(x, maxt=NULL, startname="Start", B=NULL){ nstates <- x$K + 1 dat <- x$data$mfcomb covnames <- attr(dat, "covnames.main") # main effects, excluding interaction terms ncovs <- length(covnames) if (ncovs > 0){ faccovs <- sapply(dat[,covnames,drop=FALSE], is.factor) if (!all(faccovs)) stop("Nonparametric estimation not supported with non-factor covariates") newdata <- do.call(expand.grid, lapply(dat[,covnames,drop=FALSE], levels)) for (i in names(newdata)) class(newdata[[i]]) <- class(dat[[i]]) # preserve e.g. ordered factor status } else newdata <- NULL statenames <- c(startname,x$evnames) ajlong <- ajfit(x) ## survival package changed 04/2024 to include state names in survfit Aalen-Johansen output if (any(names(ajlong)=="pstate..s0.")) # handle both old and new versions ajlong <- ajlong %>% dplyr::rename("pstate._s0_"="pstate..s0.", ## rename name chosen by survfit() "lower._s0_"="lower..s0.", ## since double dot confuses names_sep "upper._s0_"="upper..s0.") ajlong <- ajlong %>% tidyr::pivot_longer(cols = c(tidyselect::starts_with("pstate."), tidyselect::starts_with("lower."), tidyselect::starts_with("upper.")), names_to=c("summary","state"), names_sep="\\.", values_to="prob") %>% tidyr::pivot_wider(names_from="summary", values_from="prob") ajlong$state <- as.character(factor(ajlong$state, labels=statenames)) names(ajlong)[names(ajlong)=="pstate"] <- "val" ajlong$model <- "Aalen-Johansen" if (is.null(B)) { ajlong$lower <- ajlong$upper <- NULL vals <- "val" } else { vals <- c("val","lower","upper") } names(ajlong)[names(ajlong)=="time"] <- "t" if (is.null(maxt)) maxt <- max(ajlong$t) times <- seq(0, maxt, length.out=100) modcomp <- p_flexsurvmix(x, t=times, newdata=newdata, startname=startname, B=B) %>% dplyr::mutate(model="Parametric mixture") %>% dplyr::full_join(ajlong, by = c("t", "state", names(newdata), "model", vals)) %>% dplyr::rename(time="t") modcomp } flexsurv/R/summary.flexsurvreg.R0000644000176200001440000005456214603753361016550 0ustar liggesusers##' Summaries of fitted flexible survival models ##' ##' Return fitted survival, cumulative hazard or hazard at a series of times ##' from a fitted \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} ##' model. ##' ##' Time-dependent covariates are not currently supported. The covariate ##' values are assumed to be constant through time for each fitted curve. ##' ##' @param object Output from \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}}, representing a fitted survival model object. ##' ##' @param newdata Data frame containing covariate values to produce fitted ##' values for. Or a list that can be coerced to such a data frame. There ##' must be a column for every covariate in the model formula, and one row for ##' every combination of covariates the fitted values are wanted for. These ##' are in the same format as the original data, with factors as a single ##' variable, not 0/1 contrasts. ##' ##' If this is omitted, if there are any continuous covariates, then a single ##' summary is provided with all covariates set to their mean values in the ##' data - for categorical covariates, the means of the 0/1 indicator variables ##' are taken. If there are only factor covariates in the model, then all ##' distinct groups are used by default. ##' ##' @param X Alternative way of defining covariate values to produce fitted ##' values for. Since version 0.4, \code{newdata} is an easier way that ##' doesn't require the user to create factor contrasts, but \code{X} has been ##' kept for backwards compatibility. ##' ##' Columns of \code{X} represent different covariates, and rows represent ##' multiple combinations of covariate values. For example ##' \code{matrix(c(1,2),nrow=2)} if there is only one covariate in the model, ##' and we want survival for covariate values of 1 and 2. A vector can also be ##' supplied if just one combination of covariates is needed. ##' ##' For ``factor'' (categorical) covariates, the values of the contrasts ##' representing factor levels (as returned by the \code{\link{contrasts}} ##' function) should be used. For example, for a covariate \code{agegroup} ##' specified as an unordered factor with levels \code{20-29, 30-39, 40-49, ##' 50-59}, and baseline level \code{20-29}, there are three contrasts. To ##' return summaries for groups \code{20-29} and \code{40-49}, supply \code{X = ##' rbind(c(0,0,0), c(0,1,0))}, since all contrasts are zero for the baseline ##' level, and the second contrast is ``turned on'' for the third level ##' \code{40-49}. ##' ##' @param type \code{"survival"} for survival probabilities. ##' ##' \code{"cumhaz"} for cumulative hazards. ##' ##' \code{"hazard"} for hazards. ##' ##' \code{"rmst"} for restricted mean survival. ##' ##' \code{"mean"} for mean survival. ##' ##' \code{"median"} for median survival (alternative to \code{type="quantile"} with \code{quantiles=0.5}). ##' ##' \code{"quantile"} for quantiles of the survival time distribution. ##' ##' \code{"link"} for the fitted value of the location parameter (i.e. the "linear predictor" but on the natural scale of the parameter, not on the log scale) ##' ##' Ignored if \code{"fn"} is specified. ##' ##' @param fn Custom function of the parameters to summarise against time. ##' This has optional first two arguments \code{t} representing time, and ##' \code{start} representing left-truncation points, and any remaining ##' arguments must be parameters of the distribution. It should be vectorised, and ##' return a vector corresponding to the vectors given by \code{t}, \code{start} and ##' the parameter vectors. ##' ##' @param t Times to calculate fitted values for. By default, these are the ##' sorted unique observation (including censoring) times in the data - for ##' left-truncated datasets these are the "stop" times. ##' ##' @param quantiles If \code{type="quantile"}, this specifies the quantiles of the survival time distribution to return estimates for. ##' ##' @template start ##' ##' @param cross If \code{TRUE} (the default) then summaries are calculated for all combinations of times ##' specified in \code{t} and covariate vectors specifed in \code{newdata}. ##' ##' If \code{FALSE}, ##' then the times \code{t} should be of length equal to the number of rows in \code{newdata}, ##' and one summary is produced for each row of \code{newdata} paired with the corresponding ##' element of \code{t}. This is used, e.g. when determining Cox-Snell residuals. ##' ##' @param ci Set to \code{FALSE} to omit confidence intervals. ##' ##' @param se Set to \code{TRUE} to include standard errors. ##' ##' @param B Number of simulations from the normal asymptotic distribution of ##' the estimates used to calculate confidence intervals or standard errors. ##' Decrease for greater ##' speed at the expense of accuracy, or set \code{B=0} to turn off calculation ##' of CIs and SEs. ##' ##' @param cl Width of symmetric confidence intervals, relative to 1. ##' ##' @param tidy If \code{TRUE}, then the results are returned as a tidy data ##' frame instead of a list. This can help with using the \pkg{ggplot2} ##' package to compare summaries for different covariate values. ##' ##' @param na.action Function determining what should be done with missing values in \code{newdata}. If \code{na.pass} (the default) then summaries of \code{NA} are produced for missing covariate values. If \code{na.omit}, then missing values are dropped, the behaviour of \code{summary.flexsurvreg} before \code{flexsurv} version 1.2. ##' ##' @param ... Further arguments passed to or from other methods. Currently ##' unused. ##' ##' @return If \code{tidy=FALSE}, a list with one component for each unique ##' covariate value (if there are only categorical covariates) or one component ##' (if there are no covariates or any continuous covariates). Each of these ##' components is a matrix with one row for each time in \code{t}, giving the ##' estimated survival (or cumulative hazard, or hazard) and 95\% confidence ##' limits. These list components are named with the covariate names and ##' values which define them. ##' ##' If \code{tidy=TRUE}, a data frame is returned instead. This is formed by ##' stacking the above list components, with additional columns to identify the ##' covariate values that each block corresponds to. ##' ##' If there are multiple summaries, an additional list component named ##' \code{X} contains a matrix with the exact values of contrasts (dummy ##' covariates) defining each summary. ##' ##' The \code{\link{plot.flexsurvreg}} function can be used to quickly plot ##' these model-based summaries against empirical summaries such as ##' Kaplan-Meier curves, to diagnose model fit. ##' ##' Confidence intervals are obtained by sampling randomly from the asymptotic ##' normal distribution of the maximum likelihood estimates and then taking quantiles ##' (see, e.g. Mandel (2013)). ##' ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' ##' @seealso \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}. ##' ##' @references Mandel, M. (2013). "Simulation based confidence intervals for ##' functions with complicated derivatives." The American Statistician (in ##' press). ##' ##' @keywords models ##' @export summary.flexsurvreg <- function(object, newdata=NULL, X=NULL, type="survival", fn=NULL, t=NULL, quantiles=0.5, start=0, cross=TRUE, ci=TRUE, se=FALSE, B=1000, cl=0.95, tidy=FALSE, na.action=na.pass, ...){ x <- object X <- newdata_to_X(x, newdata, X, na.action) type <- match.arg(type, c("survival","cumhaz","hazard","rmst","mean","median", "quantile","link")) if (is.null(fn)) { fn <- summary_fns(x, type) } fn <- expand.summfn.args(fn) if (type=="link") x$aux$"(location)" <- x$dlist$location args <- xt_to_fnargs(x, X, t, quantiles, start, type, cross) est <- do.call(fn, args) if (type %in% c("median","mean")) res <- data.frame(est=est) else if (type=="quantile") res <- data.frame(quantile = args$t, est=est) else res <- data.frame(time = args$t, est=est) if (ci || se){ res.ci <- cisumm.flexsurvreg(x, args$t, args$start, attr(args, "X"), fn=fn, B=B, cl=cl) if (ci) { res$lcl <- res.ci[1,] res$ucl <- res.ci[2,] } if (se) res$se <- res.ci[3,] } nodata <- is.null(attr(args, "newdata")) if (x$ncovs > 0 && !nodata) { res <- cbind(res, attr(args, "newdata")) } rownames(res) <- NULL if (!tidy){ ## For backwards compatibility if (x$ncovs == 0 || nodata) res <- list(res) else { nd <- attr(args, "newdata.orig") covnames_untidy <- apply(as.data.frame(nd), 1, function(x)paste0(names(nd), "=", x, collapse=",")) nx <- attr(args, "nx") nt <- attr(args, "nt") resdf <- res[,setdiff(names(res), colnames(nd)),drop=FALSE] res <- split(resdf, rep(1:nx, each=nt)) names(res) <- covnames_untidy res <- lapply(res, function(x)setNames(as.data.frame(x), names(resdf))) for (i in seq_along(res)) row.names(res[[i]]) <- NULL } } if (x$ncovs > 0) attr(res,"X") <- X class(res) <- c("summary.flexsurvreg",class(res)) res } newdata_to_X <- function(x, newdata=NULL, X=NULL, na.action=na.pass){ if (!is.null(X)) { X <- as.matrix(X) if (!is.matrix(X) || (is.matrix(X) && ncol(X) != x$ncoveffs)) { plural <- if (x$ncoveffs > 1) "s" else "" stop("expected X to be a matrix with ", x$ncoveffs, " column", plural, " or a vector with ", x$ncoveffs, " element", plural) } attr(X, "newdata") <- as.data.frame(X) } else if (is.null(newdata)){ if (is.null(x[["data"]])) stop("`newdata` should be supplied if the data have been removed from the model object") Xraw <- model.frame(x)[,unique(attr(model.frame(x),"covnames.orig")),drop=FALSE] isfac <- sapply(Xraw, function(x){is.factor(x) || is.character(x)}) if (is.vector(X)) X <- matrix(X, nrow=1) if (x$ncovs > 0 && is.null(X)) { ## if any continuous covariates, calculate fitted survival for "average" covariate value if (!all(isfac)){ nd <- colMeans(model.matrix(x)) X <- matrix(nd ,nrow=1, dimnames=list(NULL,names(nd))) attr(X, "newdata") <- as.data.frame(X) } ## else calculate for all different factor groupings else { X <- unique(model.matrix(x)) ## build names like "COVA=value1,COVB=value2" nam <- as.matrix(unique(Xraw)) for (i in 1:ncol(nam)) nam[,i] <- paste(colnames(nam)[i], nam[,i], sep="=") rownames(X) <- apply(nam, 1, paste, collapse=",") attr(X, "newdata") <- unique(Xraw) } } else if (is.null(X)) X <- as.matrix(0, nrow=1, ncol=max(x$ncoveffs,1)) else { attr(X, "newdata") <- X colnames(attr(X, "newdata")) <- colnames(model.matrix(x)) } } else X <- form.model.matrix(x, as.data.frame(newdata), na.action=na.action) X } xt_to_fnargs <- function(x, X, t, quantiles=0.5, start=0, type="survival", cross=TRUE){ tstart <- summfn_to_tstart(x, type, t, quantiles, start) t <- tstart$t nd <- ndorig <- attr(X, "newdata") nt <- length(t) nx <- nrow(X) if (!cross){ if (nt != nrow(X)){ stop(sprintf("length(t)=%s, should equal nrow(X)=%s", nt, nrow(X))) } } else { tstart$t <- rep(t, nx) tstart$start <- rep(tstart$start, nx) X <- X[rep(1:nx, each=nt),,drop=FALSE] nd <- nd[rep(1:nx, each=nt),,drop=FALSE] } pbase <- x$res.t[x$dlist$pars,"est"] beta <- if (x$ncovs==0) 0 else x$res[x$covpars,"est"] basepars.mat <- add.covs(x, pbase, beta, X, transform=FALSE) basepars <- as.list(as.data.frame(basepars.mat)) fnargs <- c(tstart, basepars) for (j in seq_along(x$aux)){ fnargs[[names(x$aux)[j]]] <- x$aux[[j]] } attr(fnargs, "newdata") <- nd attr(fnargs, "nx") <- nx attr(fnargs, "nt") <- nt attr(fnargs, "newdata.orig") <- ndorig attr(fnargs, "X") <- X fnargs } summfn_to_tstart <- function(x, type="survival", t=NULL, quantiles=0.5, start=0){ nodata_msg <- "prediction times `t` should be defined explicitly if the data are not included in the model object" if(type == "mean"){ if(!is.null(t)) warning("Mean selected, but time specified. For restricted mean, set type to 'rmst'.") # Type = mean same as RMST w/ time = Inf t <- rep_len(Inf,length(start)) } else if(type == "median"){ if(!is.null(t)) warning("Median selected, but time specified.") t <- rep_len(0.5,length(start)) } else if(type == "link"){ if(!is.null(t)) warning("`link` selected, but time specified.") t <- rep_len(0,length(start)) } else if(type == "quantile"){ t <- quantiles if((any(t<0) | any(t>1))){ stop("Quantiles should not be less than 0 or greater than 1") } maxlen <- max(length(t), length(start)) t <- rep_len(t,maxlen) } else if(type == "rmst"){ if (is.null(x[["data"]])) stop(nodata_msg) if (is.null(t)) t <- max(x$data$Y[,"time1"]) } else if (is.null(t)){ if (is.null(x[["data"]])) stop(nodata_msg) t <- sort(unique(x$data$Y[,"stop"])) } if (length(start)==1) start <- rep_len(start, length(t)) else if (length(start) != length(t)) stop("length of \"start\" is ",length(start),". Should be 1, or length of \"t\" which is ",length(t)) list(t=t, start=start) } cisumm.flexsurvreg <- function(x, t, start, X, fn, B=1000, cl=0.95) { if (all(is.na(x$cov)) || (B==0)) ret <- array(NA, dim=c(2, length(t))) else { sim <- normboot.flexsurvreg(x, B, X=X, tidy=TRUE) args <- list(t = rep(t, each=B), start = rep(start, each=B)) args <- c(args, as.list(as.data.frame(sim))[x$dlist$pars]) for (j in seq_along(x$aux)) args[[names(x$aux)[j]]] <- x$aux[[j]] ret <- do.call(fn, args) ret <- matrix(ret, nrow=B) retci <- apply(ret, 2, function(x)quantile(x, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE)) retse <- apply(ret, 2, sd) ret <- rbind(retci, retse) } ret } #' @noRd summary_fns <- function(x, type){ switch(type, # TODO warn for clashing arguments in dfns "survival" = function(t,start,...) { ret <- (1 - x$dfns$p(t,...))/(1 - x$dfns$p(start,...)) ret[t 0){ pars[,j] <- pars[,j] + beta[,covinds] %*% t(X[,covinds,drop=FALSE]) } if (!transform) pars[,j] <- x$dlist$inv.transforms[[j]](pars[,j]) } colnames(pars) <- x$dlist$pars pars } ## Draw B samples from multivariate normal distribution of baseline ## parameter estimators, for given covariate values ##' Simulate from the asymptotic normal distribution of parameter estimates. ##' ##' Produce a matrix of alternative parameter estimates under sampling ##' uncertainty, at covariate values supplied by the user. Used by ##' \code{\link{summary.flexsurvreg}} for obtaining confidence intervals around ##' functions of parameters. ##' ##' ##' @param x A fitted model from \code{\link{flexsurvreg}} (or \code{\link{flexsurvspline}}). ##' ##' @param B Number of samples. ##' ##' @param newdata Data frame or list containing the covariate values to ##' evaluate the parameters at. If there are covariates in the model, at least ##' one of \code{newdata} or \code{X} must be supplied, unless \code{raw=TRUE}. ##' ##' @param X Alternative (less convenient) format for covariate values: a ##' matrix with one row, with one column for each covariate or factor contrast. ##' Formed from all the "model matrices", one for each named parameter of the ##' distribution, with intercepts excluded, \code{cbind}ed together. ##' ##' @param transform \code{TRUE} if the results should be transformed to the ##' real-line scale, typically by log if the parameter is defined as positive. ##' The default \code{FALSE} returns parameters on the natural scale. ##' ##' @param raw Return samples of the baseline parameters and the covariate ##' effects, rather than the default of adjusting the baseline parameters for ##' covariates. ##' ##' @param rawsim allows input of raw samples from a previous run of ##' \code{normboot.flexsurvreg}. This is useful if running ##' \code{normboot.flexsurvreg} multiple time on the same dataset but with ##' counterfactual contrasts, e.g. treat =0 vs. treat =1. ##' Used in \code{standsurv.flexsurvreg}. ##' ##' @param tidy If \code{FALSE} (the default) then ##' a list is returned. If \code{TRUE} a data frame is returned, consisting ##' of the list elements \code{rbind}ed together, with integer variables ##' labelling the covariate number and simulation replicate number. ##' ##' @return If \code{newdata} includes only one covariate combination, a matrix ##' will be returned with \code{B} rows, and one column for each named ##' parameter of the survival distribution. ##' ##' If more than one covariate combination is requested (e.g. \code{newdata} is ##' a data frame with more than one row), then a list of matrices will be ##' returned, one for each covariate combination. ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @seealso \code{\link{summary.flexsurvreg}} ##' @references Mandel, M. (2013). "Simulation based confidence intervals for ##' functions with complicated derivatives." The American Statistician (in ##' press). ##' @keywords models ##' @examples ##' ##' fite <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist="exp") ##' normboot.flexsurvreg(fite, B=10, newdata=list(age=50)) ##' normboot.flexsurvreg(fite, B=10, X=matrix(50,nrow=1)) ##' normboot.flexsurvreg(fite, B=10, newdata=list(age=0)) ## closer to... ##' fite$res ##' @export normboot.flexsurvreg <- function(x, B, newdata=NULL, X=NULL, transform=FALSE, raw=FALSE, tidy=FALSE, rawsim=NULL){ if (x$ncovs > 0 && !raw) { if (is.null(X)) { if (is.null(newdata)) stop("neither \"newdata\" nor \"X\" supplied") X <- form.model.matrix(x, as.data.frame(newdata)) } } else X <- as.matrix(0, nrow=1, ncol=1) sim <- matrix(nrow=B, ncol=nrow(x$res)) colnames(sim) <- rownames(x$res) if (is.na(x$cov[1])) stop("Covariance matrix not available from non-converged model") if (is.null(rawsim)){ sim[,x$optpars] <- rmvnorm(B, x$opt$par, x$cov) sim[,x$fixedpars] <- rep(x$res.t[x$fixedpars,"est"],each=B) rawsim <- sim } else { sim <- rawsim } if (x$ncovs > 0 && !raw){ beta <- sim[, x$covpars, drop=FALSE] if (nrow(X)==1){ res <- sim[,x$dlist$pars,drop=FALSE] res <- add.covs(x=x, pars=res, beta=beta, X=X, transform=transform) } else { res <- vector(nrow(X), mode="list") for (i in 1:nrow(X)) { res[[i]] <- sim[,x$dlist$pars,drop=FALSE] res[[i]] <- add.covs(x=x, pars=res[[i]], beta=beta, X=X[i,,drop=FALSE], transform=transform) } } } else { res <- sim if (!transform){ for (j in seq_along(x$dlist$pars)){ res[,j] <- x$dlist$inv.transforms[[j]](res[,j]) } } } if (tidy && is.list(res)){ res <- cbind(covno = rep(1:nrow(X), each=B), repno = rep(1:B, nrow(X)), do.call("rbind", res)) res <- as.data.frame(res) } attr(res, "X") <- X attr(res, "rawsim") <- rawsim res } ### Compute CIs for survival, cumulative hazard, hazard, or user ### defined function, at supplied times t and covariates X, using ### random sample of size B from the assumed MVN distribution of MLEs. normbootfn.flexsurvreg <- function(x, t, start, newdata=NULL, X=NULL, fn, B, rawsim=NULL){ sim <- normboot.flexsurvreg(x, B, newdata=newdata, X=X, rawsim=rawsim) X <- attr(sim, "X") if (!is.list(sim)) sim <- list(sim) ret <- array(NA_real_, dim=c(nrow(X), B, length(t))) fncall0 <- list(t,start) for (j in seq_along(x$aux)) fncall0[[names(x$aux)[j]]] <- x$aux[[j]] for (k in 1:nrow(X)){ for (i in seq_len(B)) { fncall <- c(fncall0, lapply(sim[[k]][i,seq_along(x$dlist$pars)], function(z) z)) ret[k,i,] <- do.call(fn, fncall) } } if (nrow(X)==1) ret[1,,,drop=FALSE] else ret } flexsurv/R/residuals.flexsurvreg.R0000644000176200001440000000712414564155207017037 0ustar liggesusers#' Calculate residuals for flexible survival models #' #' Calculates residuals for \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} model fits. #' #' @param object Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object. #' #' @param type Character string for the type of residual desired. Currently only \code{"response"} and \code{"coxsnell"} are supported. More residual types may become available in future versions. #' #' @param ... Not currently used. #' #' @details Residuals of \code{type = "response"} are calculated as the naive difference between the observed survival and the covariate-specific predicted mean survival from \code{\link{predict.flexsurvreg}}, ignoring whether the event time is observed or censored. #' #' \code{type="coxsnell"} returns the Cox-Snell residual, defined as the estimated cumulative hazard at each data point. To check the fit of the #' A more fully featured utility for this is provided in the function \code{\link{coxsnell_flexsurvreg}}. #' #' @return Numeric vector with the same length as \code{nobs(object)}. #' #' @seealso \code{\link{predict.flexsurvreg}} #' #' @importFrom stats residuals #' #' @export #' #' @examples #' #' fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") #' residuals(fitg, type="response") #' #' #' residuals.flexsurvreg <- function(object, type = "response", ...) { type <- match.arg(type, c("response","coxsnell")) if (type=="response"){ obs_surv <- unname(object$data$Y[, 1]) fit_surv <- predict(object, type = type)$.pred_time res <- obs_surv - fit_surv } else if (type=="coxsnell") { cx <- coxsnell_flexsurvreg(object) res <- cx$est } res } ##' Cox-Snell residuals from a parametric survival model ##' ##' @param x Object returned by \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} representing a fitted survival model ##' ##' @return A data frame with a column called \code{est} giving the Cox-Snell residual, defined as the fitted cumulative hazard at each data point. ##' fitted cumulative hazard at the given observed data point, and other columns indicating the observation time, ##' observed event status, and covariate values defining the data at this point. ##' ##' The cumulative hazards \code{est} should form a censored sample from an Exponential(1). ##' Therefore to check the fit of the model, plot a nonparametric estimate of the cumulative ##' hazard curve against a diagonal line through the origin, which is the theoretical cumulative ##' hazard trajectory of the Exponential(1). ##' ##' @examples ##' ##' fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") ##' cs <- coxsnell_flexsurvreg(fitg) ##' ##' ## Model appears to fit well, with some small sample noise ##' surv <- survfit(Surv(cs$est, ovarian$fustat) ~ 1) ##' plot(surv, fun="cumhaz") ##' abline(0, 1, col="red") ##' ##' @export coxsnell_flexsurvreg <- function(x){ mf <- model.frame(x, orig=TRUE) startstop <- "start" %in% colnames(mf[,1]) tind <- if (startstop) "stop" else "time" t <- mf[,1][,tind] start <- if (startstop) mf[,1][,"start"] else 0 covnames <- attr(model.frame(x), "covnames") nd <- mf[,covnames,drop=FALSE] res <- summary(x, type="cumhaz", t=t, start=start, newdata=nd, cross=FALSE, ci=FALSE, se=FALSE, tidy=TRUE) res$status <- mf[,1][,"status"] res <- res[c("time","status", setdiff(names(res), c("time","status","est")), "est")] res } flexsurv/R/hr_flexsurvreg.R0000644000176200001440000000670414603753314015536 0ustar liggesusers##' Hazard ratio as a function of time from a parametric survival model ##' ##' @inheritParams summary.flexsurvreg ##' ##' @param x Object returned by \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}. ##' ##' @param newdata A data frame with two rows, each specifying a set of covariate values. ##' The hazard ratio is calculated as hazard(z2)/hazard(z1), where z1 is the first row ##' of \code{newdata} and z2 is the second row. ##' ##' \code{newdata} must be supplied unless the model \code{x} includes just one covariate. ##' With one covariate, a default is constructed, which defines the hazard ratio between ##' the second and first level of the factor (if the covariate is a factor), or between ##' a value of 1 and a value of 0 (if the covariate is numeric). ##' ##' @return A data frame with estimate and confidence limits for the hazard ratio, and ##' one row for each of the times requested in \code{t}. ##' ##' @export hr_flexsurvreg <- function(x, newdata=NULL, t=NULL, start=0, ci=TRUE, B=1000, cl=0.95, na.action=na.pass){ if (is.null(newdata)){ if (is.null(x$data)) stop("`newdata` must be specified explicitly if the data have been removed from the model object") else newdata <- hr_default_newdata(x) } if (is.null(newdata)) stop("`newdata` must be specified unless the model has a single covariate") newdata <- as.data.frame(newdata) X <- newdata_to_X(x, newdata, na.action=na.action) args1 <- xt_to_fnargs(x, X[2,,drop=FALSE], t, start=start, type="hazard") args0 <- xt_to_fnargs(x, X[1,,drop=FALSE], t, start=start, type="hazard") fn <- expand.summfn.args(summary_fns(x, type="hazard")) est1 <- do.call(fn, args1) est0 <- do.call(fn, args0) tstart <- summfn_to_tstart(x=x, type="hr", t=t) t <- tstart$t; start <- tstart$start res <- data.frame(t = t) res$est <- est1 / est0 if (ci){ argsboth <- xt_to_fnargs(x, X, t, start=start, type="hazard") sim <- normboot.flexsurvreg(x, B, X=attr(argsboth, "X"), tidy=TRUE) sim$"(time)" <- rep(rep(t, each=B), 2) sim$"(cov)" <- rep(c(1,2), each=B*length(t)) sim0 <- sim[sim$"(cov)" == 1,,drop=FALSE] sim1 <- sim[sim$"(cov)" == 2,,drop=FALSE] argst <- list(t = rep(t, each=B), start = start) for (j in seq_along(x$aux)) argst[[names(x$aux)[j]]] <- x$aux[[j]] args1 <- c(argst, as.list(as.data.frame(sim1))[x$dlist$pars]) args0 <- c(argst, as.list(as.data.frame(sim0))[x$dlist$pars]) ret <- do.call(fn, args1) / do.call(fn, args0) ret <- matrix(ret, nrow=B) retci <- apply(ret, 2, function(x)quantile(x, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE)) res$lcl <- retci[1,] res$ucl <- retci[2,] # note it doesn't draw new simulations for each covariate value. OK } res } hr_default_newdata <- function(x){ mf <- model.frame(x) Xraw <- mf[,unique(attr(mf,"covnames.orig")),drop=FALSE] isfac <- sapply(Xraw, function(x){is.factor(x) || is.character(x)}) isnum <- sapply(Xraw, function(x){is.numeric(x)}) ncovs <- ncol(Xraw) if (ncovs == 1) { if (isfac){ levs <- levels(Xraw[,1]) if (length(levs)==1) stop("the covariate has only one one factor level") newdata <- list(levs[1:2]) } else if (isnum) { newdata <- list(c(0,1)) } else newdata <- NULL if (is.list(newdata)) names(newdata) <- attr(mf, "covnames") } else newdata <- NULL newdata } flexsurv/R/spline.R0000644000176200001440000012402214645512110013746 0ustar liggesusers##' Royston/Parmar spline survival distribution ##' ##' Probability density, distribution, quantile, random generation, hazard, ##' cumulative hazard, mean and restricted mean functions for the Royston/Parmar ##' spline model. These functions have all parameters of the distribution collected ##' together in a single argument \code{gamma}. For the equivalent functions with ##' one argument per parameter, see \code{\link{Survsplinek}}. ##' ##' @aliases dsurvspline psurvspline qsurvspline rsurvspline ##' hsurvspline Hsurvspline mean_survspline rmst_survspline ##' ##' @param x,q,t Vector of times. ##' ##' @param p Vector of probabilities. ##' ##' @param n Number of random numbers to simulate. ##' ##' @param gamma Parameters describing the baseline spline function, as ##' described in \code{\link{flexsurvspline}}. This may be supplied as a ##' vector with number of elements equal to the length of \code{knots}, in ##' which case the parameters are common to all times. Alternatively a matrix ##' may be supplied, with rows corresponding to different times, and columns ##' corresponding to \code{knots}. ##' ##' @param start Optional left-truncation time or times. The returned ##' restricted mean survival will be conditioned on survival up to ##' this time. ##' ##' @param beta Vector of covariate effects. Not supported and ignored since version 2.3, and this argument will be removed in 2.4. ##' ##' @param X Matrix of covariate values. Not supported and ignored since version 2.3, and this argument will be removed in 2.4. ##' ##' @param knots Locations of knots on the axis of log time, supplied in ##' increasing order. Unlike in \code{\link{flexsurvspline}}, these include ##' the two boundary knots. If there are no additional knots, the boundary ##' locations are not used. If there are one or more additional knots, the ##' boundary knots should be at or beyond the minimum and maximum values of the ##' log times. In \code{\link{flexsurvspline}} these are exactly at the ##' minimum and maximum values. ##' ##' This may in principle be supplied as a matrix, in the same way as for ##' \code{gamma}, but in most applications the knots will be fixed. ##' ##' @param scale \code{"hazard"}, \code{"odds"}, or \code{"normal"}, as ##' described in \code{\link{flexsurvspline}}. With the default of no knots in ##' addition to the boundaries, this model reduces to the Weibull, log-logistic ##' and log-normal respectively. The scale must be common to all times. ##' ##' @param timescale \code{"log"} or \code{"identity"} as described in ##' \code{\link{flexsurvspline}}. ##' ##' @param spline \code{"rp"} to use the natural cubic spline basis ##' described in Royston and Parmar. \code{"splines2ns"} to use the ##' alternative natural cubic spline basis from the \code{splines2} ##' package (Wang and Yan 2021), which may be better behaved due to ##' the basis being orthogonal. ##' ##' @param offset An extra constant to add to the linear predictor ##' \eqn{\eta}{eta}. Not supported and ignored since version 2.3, and this argument will be removed in 2.4. ##' ##' @param log,log.p Return log density or probability. ##' ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dsurvspline} gives the density, \code{psurvspline} gives the ##' distribution function, \code{hsurvspline} gives the hazard and ##' \code{Hsurvspline} gives the cumulative hazard, as described in ##' \code{\link{flexsurvspline}}. ##' ##' \code{qsurvspline} gives the quantile function, which is computed by crude ##' numerical inversion (using \code{\link{qgeneric}}). ##' ##' \code{rsurvspline} generates random survival times by using ##' \code{qsurvspline} on a sample of uniform random numbers. Due to the ##' numerical root-finding involved in \code{qsurvspline}, it is slow compared ##' to typical random number generation functions. ##' ##' @author Christopher Jackson ##' ##' @seealso \code{\link{flexsurvspline}}. ##' ##' @references Royston, P. and Parmar, M. (2002). Flexible parametric ##' proportional-hazards and proportional-odds models for censored survival ##' data, with application to prognostic modelling and estimation of treatment ##' effects. Statistics in Medicine 21(1):2175-2197. ##' ##' Wang W, Yan J (2021). Shape-Restricted Regression Splines with R ##' Package splines2. Journal of Data Science, 19(3), 498-517. ##' ##' @keywords distribution ##' ##' @examples ##' ##' ## reduces to the weibull ##' regscale <- 0.786; cf <- 1.82 ##' a <- 1/regscale; b <- exp(cf) ##' dweibull(1, shape=a, scale=b) ##' dsurvspline(1, gamma=c(log(1 / b^a), a)) # should be the same ##' ##' ## reduces to the log-normal ##' meanlog <- 1.52; sdlog <- 1.11 ##' dlnorm(1, meanlog, sdlog) ##' dsurvspline(1, gamma = c(-meanlog/sdlog, 1/sdlog), scale="normal") ##' # should be the same ##' @name Survspline NULL ## Things to do that are common to d/p/q functions ## could be generalized to any function with vector of arguments ## TODO more special value handling dbase.survspline <- function(q, gamma, knots, scale, deriv=0, spline="rp"){ if(!is.matrix(gamma)) gamma <- matrix(gamma, nrow=1) if(!is.matrix(knots)) knots <- matrix(knots, nrow=1) anylength0 <- (min(length(q), nrow(gamma), nrow(knots)) == 0) nret <- if (anylength0) 0 else max(length(q), nrow(gamma), nrow(knots)) q <- rep(q, length.out=nret) gamma <- matrix(rep(as.numeric(t(gamma)), length.out = ncol(gamma) * nret), ncol = ncol(gamma), byrow = TRUE) knots <- matrix(rep(as.numeric(t(knots)), length.out = ncol(knots) * nret), ncol = ncol(knots), byrow = TRUE) if (ncol(gamma) != ncol(knots)) { stop("length of gamma should equal number of knots") } scale <- match.arg(scale, c("hazard","odds","normal")) if (deriv==2){ npars <- ncol(gamma) parnames <- paste0("gamma",seq_len(npars)-1) ret <- array(0, dim=c(nret, npars, npars), dimnames = list(NULL, parnames, parnames)) ret[is.na(q),,] <- NA } else if (deriv==1){ ret <- matrix(0, nrow=nret, ncol=ncol(gamma)) ret[is.na(q),] <- NA } else if (deriv==0) { ret <- numeric(nret) ret[is.na(q)] <- NA } ind <- !is.na(q) & q > 0 q <- q[ind] gamma <- gamma[ind,,drop=FALSE] knots <- knots[ind,,drop=FALSE] list(ret=ret, gamma=gamma, q=q, scale=scale, ind=ind, knots=knots) } dlink <- function(scale){ switch(scale, hazard=function(x){exp(x - exp(x))}, odds=function(x){exp(x) / (1 + exp(x))^2}, normal=function(x){dnorm(x)} ) } ldlink <- function(scale){ switch(scale, hazard=function(x){x - exp(x)}, odds=function(x){x - 2*log(1 + exp(x))}, normal=function(x){dnorm(x, log=TRUE)} ) } ## probability density function. ##' @rdname Survspline ##' @export dsurvspline <- function(x, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp", offset=0, log=FALSE){ betax_warn(beta, X, offset) d <- dbase.survspline(q=x, gamma=gamma, knots=knots, scale=scale, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) if (any(ind)){ eta <- rowSums(basis(knots, tsfn(q, timescale), spline=spline) * gamma) # log cumulative hazard/odds eeta <- exp(ldlink(scale)(eta)) ret[ind][eeta==0] <- 0 ret[ind][is.nan(eeta)] <- NaN ind2 <- !(eeta==0 | is.nan(eeta)) q <- q[ind2] gamma <- gamma[ind2,,drop=FALSE] knots <- knots[ind2,,drop=FALSE] eeta <- eeta[ind2] ind[ind] <- ind[ind] & ind2 dsum <- rowSums(dbasis(knots, tsfn(q, timescale), spline=spline) * gamma) # ds/dx ret[ind] <- dtsfn(q,timescale) * dsum * eeta ## derivative of log cum haz cannot be negative by definition, but ## optimisation doesn't constrain gamma to respect this, so set ## likelihood to zero then (assuming at least one death) ret[ind][ret[ind]<=0] <- 0 } if (log) {ret <- log(ret)} as.numeric(ret) } tsfn <- function(x, timescale){ switch(timescale, log = log(x), identity = x) } dtsfn <- function(x, timescale){ switch(timescale, log = 1/x, identity = 1) } Slink <- function(scale){ switch(scale, hazard=function(x){exp(-exp(x))}, odds=function(x){1 / (1 + exp(x))}, normal=function(x){pnorm(-x)} ) } ## cumulative distribution function ##' @rdname Survspline ##' @export psurvspline <- function(q, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp", offset=0, lower.tail=TRUE, log.p=FALSE){ betax_warn(beta, X, offset) d <- dbase.survspline(q=q, gamma=gamma, knots=knots, scale=scale, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) if (any(ind)){ ret[ind][q==0] <- 0 ret[ind][q==Inf] <- 1 finite <- q>0 & q 1) n <- length(n) ret <- qsurvspline(p=runif(n), gamma=gamma, knots=knots, scale=scale, timescale=timescale, spline=spline) ret } Hlink <- function(scale){ switch(scale, hazard=function(x){exp(x)}, # log cum haz, or log cum odds is a spline function of log time odds=function(x){log1p(exp(x))}, normal=function(x){-pnorm(-x, log.p=TRUE)} ) } ## cumulative hazard function ##' @rdname Survspline ##' @export Hsurvspline <- function(x, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp", offset=0){ match.arg(scale, c("hazard","odds","normal")) d <- dbase.survspline(q=x, gamma=gamma, knots=knots, scale=scale, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) if (any(ind)){ eta <- rowSums(basis(knots, tsfn(q,timescale), spline=spline) * gamma) + as.numeric(X %*% beta) ret[ind] <- as.numeric(Hlink(scale)(eta)) } ret } hlink <- function(scale){ switch(scale, hazard=function(x){exp(x)}, odds=function(x){plogis(x)}, normal=function(x){dnorm(-x)/pnorm(-x)} ) } ## hazard function ##' @rdname Survspline ##' @export hsurvspline <- function(x, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp", offset=0){ ## value for x=0? currently zero, should it be limit as x reduces to 0? betax_warn(beta, X, offset) match.arg(scale, c("hazard","odds","normal")) d <- dbase.survspline(q=x, gamma=gamma, knots=knots, scale=scale, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) if (any(ind)){ eta <- rowSums(basis(knots, tsfn(q,timescale), spline=spline) * gamma) + as.numeric(X %*% beta) eeta <- hlink(scale)(eta) ret[ind] <- dtsfn(q, timescale) * rowSums(dbasis(knots, tsfn(q, timescale), spline=spline) * gamma) * eeta ret[ind][ret[ind]<=0] <- 0 # these correspond to invalid decreasing cumulative hazard functions } as.numeric(ret) } ##' @rdname Survspline ##' @export rmst_survspline = function(t, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp", offset=0, start=0){ betax_warn(beta, X, offset) rmst_generic(psurvspline, t, start=start, matargs = c("gamma", "knots"), scalarargs = c("scale", "timescale", "spline"), gamma=gamma, knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survspline ##' @export mean_survspline = function(gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp", offset=0){ betax_warn(beta, X, offset) nt <- if (is.matrix(gamma)) nrow(gamma) else 1 rmst_generic(psurvspline, rep(Inf,nt), start=0, matargs = c("gamma", "knots"), scalarargs = c("scale", "timescale", "spline"), gamma=gamma, knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' Natural cubic spline basis ##' ##' Compute a basis for a natural cubic spline, by default using the ##' parameterisation described by Royston and Parmar (2002). Used for ##' flexible parametric survival models. ##' ##' The exact formula for the basis is given in \code{\link{flexsurvspline}}. ##' ##' @aliases basis dbasis fss dfss ##' ##' @param knots Vector of knot locations in increasing order, including the ##' boundary knots at the beginning and end. ##' ##' @param x Vector of ordinates to compute the basis for. ##' ##' @inheritParams Survspline ##' ##' @return A matrix with one row for each ordinate and one column for each ##' knot. ##' ##' \code{basis} returns the basis, and \code{dbasis} returns its derivative ##' with respect to \code{x}. ##' ##' \code{fss} and \code{dfss} are the same, but with the order of the ##' arguments swapped around for consistency with similar functions in other R ##' packages. ##' ##' @author Christopher Jackson ##' ##' @seealso \code{\link{flexsurvspline}}. ##' ##' @references Royston, P. and Parmar, M. (2002). Flexible parametric ##' proportional-hazards and proportional-odds models for censored survival ##' data, with application to prognostic modelling and estimation of treatment ##' effects. Statistics in Medicine 21(1):2175-2197. ##' ##' Wang W, Yan J (2021). Shape-Restricted Regression Splines with R ##' Package splines2. Journal of Data Science, 19(3), 498-517. ##' ##' @keywords models ##' @export basis <- function(knots, x, spline="rp") { if (spline=="rp") basis_original(knots, x) else if (spline=="splines2ns") basis_splines2ns(knots, x) } basis_splines2ns <- function(knots, x){ if (!isTRUE(requireNamespace("splines2", quietly = TRUE))) stop("spline=\"splines2ns\" needs the splines2 package to be installed") if (is.matrix(knots) && nrow(knots) > 0) basis_splines2ns_matrix(knots, x) else basis_splines2ns_vector(knots, x) } basis_splines2ns_vector <- function(knots, x){ nk <- length(knots) if (nk > 0){ iknots <- knots[-c(1,nk)] bknots <- knots[c(1,nk)] bas <- splines2::naturalSpline(x, knots = iknots, Boundary.knots=bknots, intercept = FALSE) # doesn't handle matrix knots bas <- cbind(1, bas) colnames(bas) <- NULL bas } else numeric(nk) } # Are all rows of a matrix the same as each other [ie the same as the first row] all_rows_same <- function(x){ all(apply(x, 1, function(y)(isTRUE(all.equal(y,x[1,]))))) } basis_splines2ns_matrix <- function(knots, x){ stopifnot(length(x)==nrow(knots)) if (all_rows_same(knots)){ ## Only do basis computation once. bas <- basis_splines2ns_vector(knots[1,], x) stopifnot(length(x)==nrow(bas)) } else { # different basis computation needed for each row bas <- matrix(NA, nrow=length(x), ncol=ncol(knots)) for (i in 1:nrow(knots)){ bas[i,] <- basis_splines2ns_vector(knots[i,], x[i]) } } bas } dbasis_splines2ns <- function(knots, x){ if (!isTRUE(requireNamespace("splines2", quietly = TRUE))) stop("spline=\"splines2ns\" needs the splines2 package to be installed") if (is.matrix(knots) && nrow(knots) > 0) dbasis_splines2ns_matrix(knots, x) else dbasis_splines2ns_vector(knots, x) } dbasis_splines2ns_vector <- function(knots, x){ nk <- length(knots) if (nk > 0){ iknots <- knots[-c(1,nk)] bknots <- knots[c(1,nk)] bas <- splines2::naturalSpline(x, knots = iknots, Boundary.knots=bknots, intercept = FALSE, derivs=1) bas <- cbind(0, bas) colnames(bas) <- NULL bas } else numeric(nk) } dbasis_splines2ns_matrix <- function(knots, x){ stopifnot(length(x)==nrow(knots)) if (all_rows_same(knots)){ ## Only do basis computation once. bas <- dbasis_splines2ns_vector(knots[1,], x) stopifnot(length(x)==nrow(bas)) } else { # different basis computation needed for each row bas <- matrix(NA, nrow=length(x), ncol=ncol(knots)) for (i in 1:nrow(knots)){ bas[i,] <- dbasis_splines2ns_vector(knots[i,], x[i]) } } bas } basis_original <- function(knots, x){ if (is.matrix(knots)) { basis_matrix(knots, x) } else { basis_vector(knots, x) } } ##' @export dbasis <- function(knots, x, spline="rp") { if (spline=="rp") dbasis_original(knots, x) else if (spline=="splines2ns") dbasis_splines2ns(knots, x) } dbasis_original <- function(knots, x){ if (is.matrix(knots)) { dbasis_matrix(knots, x) } else { dbasis_vector(knots, x) } } ##' @export fss <- function(x, knots) { basis(knots, x) } ##' @export dfss <- function(x, knots) { dbasis(knots, x) } flexsurv.splineinits <- function(t=NULL, mf, mml, aux) { Y <- check.flexsurv.response(model.extract(mf, "response")) ## Impute interval-censored data, where Cox doesn't work. intcens <- Y[,"status"]==3 & (Y[,"start"] < Y[,"stop"]) Y[intcens,"status"] <- 1 Y[intcens,"stop"] <- Y[intcens,"start"] + (Y[intcens,"stop"] - Y[intcens,"start"])/2 Y[,"status"] <- ifelse(Y[,"status"]==1, 1, 0) X <- mml[[1]][,-1,drop=FALSE] ## Use only uncensored observations, unless < 5 of those, in which ## case use all (coxph doesn't work if all censored). Impute as ## alternative? dead <- Y[,"status"]==1 inc <- if (sum(dead) >= 5) dead else rep(TRUE, nrow(Y)) inc <- inc & Y[,"start"] < Y[,"stop"] ## Estimate empirical cumulative hazard for each observation formdat <- as.data.frame(cbind(Y, X, weights=model.extract(mf, "weights"))) names(formdat)[1:ncol(Y)] <- colnames(Y) form <- c("Surv(start, stop, status) ~") if (ncol(X)>0){ names(formdat)[ncol(Y) + 1:ncol(X)] <- paste0("X", 1:ncol(X)) form <- paste(form, paste(paste0("X", 1:ncol(X)), collapse=" + ")) } else form <- paste(form, "1") formdat <- formdat[inc,] cox <- coxph(as.formula(form), weights=weights, data=formdat) if (ncol(X)>0){ newdata <- as.data.frame(matrix(rep(0, ncol(X)), nrow=1)) names(newdata) <- paste0("X", 1:ncol(X)) surv <- survfit(cox, newdata=newdata) } else surv <- survfit(cox) surv <- surv$surv[match(Y[inc,"stop"], surv$time)] surv <- surv^exp(cox$linear.predictors) if (aux$scale=="hazard") logH <- log(-log(surv)) else if (aux$scale=="odds") logH <- log((1 - surv)/surv) else if (aux$scale=="normal") logH <- qnorm(1 - surv) x <- tsfn(Y[inc,"time"], aux$timescale) b <- if (!is.null(aux$knots)) basis(aux$knots, x, spline=aux$spline) else cbind(1, x) ## Regress empirical logH on covariates and spline basis to obtain ## initial values. ## Constrain initial spline function to be increasing, using ## quadratic programming Xq <- cbind(b, X[inc,,drop=FALSE]) kx <- x kr <- diff(range(x)) kx[1] <- x[1] - 0.01*kr kx[length(kx)] <- x[length(kx)] + 0.01*kr db <- if (!is.null(aux$knots)) dbasis(aux$knots, kx, spline=aux$spline) else cbind(0, kx) dXq <- cbind(db, matrix(0, nrow=nrow(db), ncol=ncol(X))) nints <- length(mml)-1 for (i in seq_len(nints)){ Xi <- mml[[i+1]][inc,-1,drop=FALSE] Xq <- cbind(Xq, Xi*b[,i+1]) dXq <- cbind(dXq, Xi*db[,i+1]) } y <- logH[is.finite(logH)] Xq <- Xq[is.finite(logH),,drop=FALSE] dXq <- dXq[is.finite(logH),,drop=FALSE] eps <- rep(1e-09, length(y)) # so spline is strictly increasing Dmat <- t(Xq) %*% Xq posdef <- all(eigen(Dmat)$values > 0) # TODO work out why non-positive definite matrices can occur here if (!posdef && is.null(aux$skip.pd.check)) inits <- flexsurv.splineinits.cox(t=t, mf=mf, mml=mml, aux=aux) else if (posdef) inits <- solve.QP(Dmat=Dmat, dvec=t(t(y) %*% Xq), Amat=t(dXq), bvec=eps)$solution else inits <- rep(0, ncol(Xq)) # if Cox fails to get pos def inits } ## Initialise coefficients on spline intercepts (standard hazard ## ratios in PH models) using standard Cox regression, in cases where ## the default inits routine above results in parameters that give a ## zero likelihood, e.g. GBSG2 example flexsurv.splineinits.cox <- function(t=NULL, mf, mml, aux) { aux$skip.pd.check <- TRUE # avoid infinite recursion inits <- flexsurv.splineinits(t=t, mf=mf, mml=mml, aux=aux) Y <- check.flexsurv.response(model.extract(mf, "response")) ## Impute interval-censored data, where Cox doesn't work. intcens <- Y[,"status"]==3 & (Y[,"start"] < Y[,"stop"]) Y[intcens,"status"] <- 1 Y[intcens,"stop"] <- Y[intcens,"start"] + (Y[intcens,"stop"] - Y[intcens,"start"])/2 Y[,"status"] <- ifelse(Y[,"status"]==1, 1, 0) inc <- Y[,"start"] < Y[,"stop"] X <- mml[[1]][,-1,drop=FALSE] formdat <- as.data.frame(cbind(Y, X, weights=model.extract(mf, "weights"))) names(formdat)[1:ncol(Y)] <- colnames(Y) form <- c("Surv(start, stop, status) ~") if (ncol(X)>0){ names(formdat)[ncol(Y) + 1:ncol(X)] <- paste0("X", 1:ncol(X)) form <- paste(form, paste(paste0("X", 1:ncol(X)), collapse=" + ")) formdat <- formdat[inc,] cox <- coxph(as.formula(form), weights=weights, data=formdat) covinds <- length(aux$knots) + 1:ncol(X) inits[covinds] <- coef(cox) } inits } ##' Flexible survival regression using the Royston/Parmar spline model. ##' ##' Flexible parametric modelling of time-to-event data using the spline model ##' of Royston and Parmar (2002). ##' ##' This function works as a wrapper around \code{\link{flexsurvreg}} by ##' dynamically constructing a custom distribution using ##' \code{\link{dsurvspline}}, \code{\link{psurvspline}} and ##' \code{\link{unroll.function}}. ##' ##' In the spline-based survival model of Royston and Parmar (2002), a ##' transformation \eqn{g(S(t,z))} of the survival function is modelled as a ##' natural cubic spline function of log time \eqn{x = \log(t)}{x = log(t)} ##' plus linear effects of covariates \eqn{z}. ##' ##' \deqn{g(S(t,z)) = s(x, \bm{\gamma}) + \bm{\beta}^T \mathbf{z}}{g(S(t,z)) = ##' s(x, gamma) + beta^T z} ##' ##' The proportional hazards model (\code{scale="hazard"}) defines ##' \eqn{g(S(t,\mathbf{z})) = \log(-\log(S(t,\mathbf{z}))) = ##' \log(H(t,\mathbf{z}))}{g(S(t,z)) = log(-log(S(t,z))) = log(H(t,z))}, the ##' log cumulative hazard. ##' ##' The proportional odds model (\code{scale="odds"}) defines ##' \eqn{g(S(t,\mathbf{z})) }{g(S(t,z)) = log(1/S(t,z) - 1)}\eqn{ = ##' \log(S(t,\mathbf{z})^{-1} - 1)}{g(S(t,z)) = log(1/S(t,z) - 1)}, the log ##' cumulative odds. ##' ##' The probit model (\code{scale="normal"}) defines \eqn{g(S(t,\mathbf{z})) = ##' }{g(S(t,z)) = -InvPhi(S(t,z))}\eqn{ -\Phi^{-1}(S(t,\mathbf{z}))}{g(S(t,z)) ##' = -InvPhi(S(t,z))}, where \eqn{\Phi^{-1}()}{InvPhi()} is the inverse normal ##' distribution function \code{\link{qnorm}}. ##' ##' With no knots, the spline reduces to a linear function, and these models ##' are equivalent to Weibull, log-logistic and lognormal models respectively. ##' ##' The spline coefficients \eqn{\gamma_j: j=1, 2 \ldots }{gamma_j: j=1, 2 ##' \ldots}, which are called the "ancillary parameters" above, may also be ##' modelled as linear functions of covariates \eqn{\mathbf{z}}, as ##' ##' \deqn{\gamma_j(\mathbf{z}) = \gamma_{j0} + \gamma_{j1}z_1 + \gamma_{j2}z_2 ##' + ... }{gamma_j(z) = \gamma_{j0} + \gamma_{j1}z_1 + \gamma_{j2}z_2 + ... } ##' ##' giving a model where the effects of covariates are arbitrarily flexible ##' functions of time: a non-proportional hazards or odds model. ##' ##' Natural cubic splines are cubic splines constrained to be linear beyond ##' boundary knots \eqn{k_{min},k_{max}}{kmin,kmax}. The spline function is ##' defined as ##' ##' \deqn{s(x,\boldsymbol{\gamma}) = \gamma_0 + \gamma_1 x + \gamma_2 v_1(x) + \ldots + ##' }{s(x,gamma) = gamma0 + gamma1 x + gamma2 v1(x) + ... + gamma_{m+1} ##' vm(x)}\deqn{ \gamma_{m+1} v_m(x)}{s(x,gamma) = gamma0 + gamma1 x + gamma2 ##' v1(x) + ... + gamma_{m+1} vm(x)} ##' ##' where \eqn{v_j(x)}{vj(x)} is the \eqn{j}th basis function ##' ##' \deqn{v_j(x) = (x - k_j)^3_+ - \lambda_j(x - k_{min})^3_+ - (1 - }{vj(x) = ##' (x - kj)^3_+ - \lambda_j(x - kmin)^3_+ - (1 -\lambda_j) (x - ##' kmax)^3_+}\deqn{ \lambda_j) (x - k_{max})^3_+}{vj(x) = (x - kj)^3_+ - ##' \lambda_j(x - kmin)^3_+ - (1 -\lambda_j) (x - kmax)^3_+} ##' ##' \deqn{\lambda_j = \frac{k_{max} - k_j}{k_{max} - k_{min}}}{\lambda_j = ##' (kmax - kj) / (kmax - kmin)} ##' ##' and \eqn{(x - a)_+ = max(0, x - a)}. ##' ##' @param formula A formula expression in conventional R linear modelling ##' syntax. The response must be a survival object as returned by the ##' \code{\link[survival]{Surv}} function, and any covariates are given on the right-hand ##' side. For example, ##' ##' \code{Surv(time, dead) ~ age + sex} ##' ##' specifies a model where the log cumulative hazard (by default, see ##' \code{scale}) is a linear function of the covariates \code{age} and ##' \code{sex}. ##' ##' If there are no covariates, specify \code{1} on the right hand side, for ##' example \code{Surv(time, dead) ~ 1}. ##' ##' Time-varying covariate effects can be specified using the method described ##' in \code{\link{flexsurvreg}} for placing covariates on ancillary ##' parameters. The ancillary parameters here are named \code{gamma1}, ##' \ldots{}, \code{gammar} where \code{r} is the number of knots \code{k} plus ##' one (the ``degrees of freedom'' as defined by Royston and Parmar). So for ##' the default Weibull model, there is just one ancillary parameter ##' \code{gamma1}. ##' ##' Therefore a model with one internal spline knot, where the equivalents of ##' the Weibull shape and scale parameters, but not the higher-order term ##' \code{gamma2}, vary with age and sex, can be specified as: ##' ##' \code{Surv(time, dead) ~ age + sex + gamma1(age) + gamma1(sex)} ##' ##' or alternatively (and more safely, see \code{flexsurvreg}) ##' ##' \code{Surv(time, dead) ~ age + sex, anc=list(gamma1=~age + sex)} ##' ##' \code{Surv} objects of \code{type="right"},\code{"counting"}, ##' \code{"interval1"} or \code{"interval2"} are supported, corresponding to ##' right-censored, left-truncated or interval-censored observations. ##' @param data A data frame in which to find variables supplied in ##' \code{formula}. If not given, the variables should be in the working ##' environment. ##' @param weights Optional variable giving case weights. ##' ##' @param bhazard Optional variable giving expected hazards for relative ##' survival models. ##' ##' @param rtrunc Optional variable giving individual right-truncation times (see \code{\link{flexsurvreg}}). Note that these models can suffer from weakly identifiable parameters and ##' badly-behaved likelihood functions, and it is advised to compare ##' convergence for different initial values by supplying different ##' \code{inits} arguments to \code{flexsurvspline}. ##' ##' @param subset Vector of integers or logicals specifying the subset of the ##' observations to be used in the fit. ##' @param k Number of knots in the spline. The default \code{k=0} gives a ##' Weibull, log-logistic or lognormal model, if \code{"scale"} is ##' \code{"hazard"}, \code{"odds"} or \code{"normal"} respectively. \code{k} ##' is equivalent to \code{df-1} in the notation of \code{stpm} for Stata. The ##' knots are then chosen as equally-spaced quantiles of the log uncensored ##' survival times, for example, at the median with one knot, or at the 33\% ##' and 67\% quantiles of log time (or time, see \code{"timescale"}) with two ##' knots. To override this default knot placement, specify \code{knots} ##' instead. ##' @param knots Locations of knots on the axis of log time (or time, see ##' \code{"timescale"}). If not specified, knot locations are chosen as ##' described in \code{k} above. Either \code{k} or \code{knots} must be ##' specified. If both are specified, \code{knots} overrides \code{k}. ##' @param bknots Locations of boundary knots, on the axis of log time (or ##' time, see \code{"timescale"}). If not supplied, these are are chosen as ##' the minimum and maximum log death time. ##' @param scale If \code{"hazard"}, the log cumulative hazard is modelled as a ##' spline function. ##' ##' If \code{"odds"}, the log cumulative odds is modelled as a spline function. ##' ##' If \code{"normal"}, \eqn{-\Phi^{-1}(S(t))}{-InvPhi(S(t))} is modelled as a ##' spline function, where \eqn{\Phi^{-1}()}{InvPhi()} is the inverse normal ##' distribution function \code{\link{qnorm}}. ##' ##' @param timescale If \code{"log"} (the default) the log cumulative hazard ##' (or alternative) is modelled as a spline function of log time. If ##' \code{"identity"}, it is modelled as a spline function of time, however ##' this model would not satisfy the desirable property that the cumulative hazard ##' (or alternative) should approach 0 at time zero. ##' ##' @param spline \code{"rp"} to use the natural cubic spline basis ##' described in Royston and Parmar. ##' ##' \code{"splines2ns"} to use the alternative natural cubic spline ##' basis from the \code{splines2} package (Wang and Yan 2021), ##' which may be better behaved due to the basis being orthogonal. ##' ##' @param ... Any other arguments to be passed to or through ##' \code{\link{flexsurvreg}}, for example, \code{anc}, \code{inits}, ##' \code{fixedpars}, \code{weights}, \code{subset}, \code{na.action}, and any ##' options to control optimisation. See \code{\link{flexsurvreg}}. ##' @return A list of class \code{"flexsurvreg"} with the same elements as ##' described in \code{\link{flexsurvreg}}, and including extra components ##' describing the spline model. See in particular: ##' ##' \item{k}{Number of knots.} \item{knots}{Location of knots on the log time ##' axis.} \item{scale}{The \code{scale} of the model, hazard, odds or normal.} ##' \item{res}{Matrix of maximum likelihood estimates and confidence limits. ##' Spline coefficients are labelled \code{"gamma..."}, and covariate effects ##' are labelled with the names of the covariates. ##' ##' Coefficients \code{gamma1,gamma2,...} here are the equivalent of ##' \code{s0,s1,...} in Stata \code{streg}, and \code{gamma0} is the equivalent ##' of the \code{xb} constant term. To reproduce results, use the ##' \code{noorthog} option in Stata, since no orthogonalisation is performed on ##' the spline basis here. ##' ##' In the Weibull model, for example, \code{gamma0,gamma1} are ##' \code{-shape*log(scale), shape} respectively in \code{\link{dweibull}} or ##' \code{\link{flexsurvreg}} notation, or (\code{-Intercept/scale}, ##' \code{1/scale}) in \code{\link[survival]{survreg}} notation. ##' ##' In the log-logistic model with shape \code{a} and scale \code{b} (as in ##' \code{\link[eha:Loglogistic]{eha::dllogis}} from the \pkg{eha} package), \code{1/b^a} is ##' equivalent to \code{exp(gamma0)}, and \code{a} is equivalent to ##' \code{gamma1}. ##' ##' In the log-normal model with log-scale mean \code{mu} and standard ##' deviation \code{sigma}, \code{-mu/sigma} is equivalent to \code{gamma0} and ##' \code{1/sigma} is equivalent to \code{gamma1}. } \item{loglik}{The ##' maximised log-likelihood. This will differ from Stata, where the sum of ##' the log uncensored survival times is added to the log-likelihood in ##' survival models, to remove dependency on the time scale.} ##' ##' @author Christopher Jackson ##' ##' @seealso \code{\link{flexsurvreg}} for flexible survival modelling using ##' general parametric distributions. ##' ##' \code{\link{plot.flexsurvreg}} and \code{\link{lines.flexsurvreg}} to plot ##' fitted survival, hazards and cumulative hazards from models fitted by ##' \code{\link{flexsurvspline}} and \code{\link{flexsurvreg}}. ##' ##' @references Royston, P. and Parmar, M. (2002). Flexible parametric ##' proportional-hazards and proportional-odds models for censored survival ##' data, with application to prognostic modelling and estimation of treatment ##' effects. Statistics in Medicine 21(1):2175-2197. ##' ##' Wang W, Yan J (2021). Shape-Restricted Regression Splines with R ##' Package splines2. Journal of Data Science, 19(3), 498-517. ##' ##' Jackson, C. (2016). flexsurv: A Platform for Parametric Survival Modeling ##' in R. Journal of Statistical Software, 70(8), 1-33. ##' doi:10.18637/jss.v070.i08 ##' ##' @keywords models survival ##' ##' @examples ##' ##' ## Best-fitting model to breast cancer data from Royston and Parmar (2002) ##' ## One internal knot (2 df) and cumulative odds scale ##' ##' spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1, scale="odds") ##' ##' ## Fitted survival ##' ##' plot(spl, lwd=3, ci=FALSE) ##' ##' ## Simple Weibull model fits much less well ##' ##' splw <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=0, scale="hazard") ##' lines(splw, col="blue", ci=FALSE) ##' ##' ## Alternative way of fitting the Weibull ##' ##' \dontrun{ ##' splw2 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") ##' } ##' ##' @export flexsurvspline <- function(formula, data, weights, bhazard, rtrunc, subset, k=0, knots=NULL, bknots=NULL, scale="hazard", timescale="log", spline="rp", ...){ ## Get response matrix from the formula. Only need this to obtain ## default knots. Largely copied from flexsurvreg - ideally ## should be in separate function, but can't make scoping work. call <- match.call() indx <- match(c("formula", "data", "weights", "bhazard", "rtrunc", "subset", "na.action"), names(call), nomatch = 0) if (indx[1] == 0) stop("A \"formula\" argument is required") temp <- call[c(1, indx)] temp[[1]] <- as.name("model.frame") ## remove the predictors f2 <- as.formula(gsub("(.*~).*", "\\1 1", Reduce(paste, deparse(formula)))) environment(f2) <- environment(formula) temp[["formula"]] <- f2 if (missing(data)) temp[["data"]] <- environment(formula) if (missing(data)) data <- environment(formula) # TESTME to pass to flexsurvreg m <- eval(temp, parent.frame()) Y <- check.flexsurv.response(model.extract(m, "response")) deaths <- Y[,"status"]==1 dtimes <- Y[deaths,"stop"] intcens <- Y[,"status"]==3 midpoints <- (Y[,"time2"] + Y[,"time1"])/2 ktimes <- ifelse(deaths, Y[,"stop"], ifelse(intcens, midpoints, NA)) kinds <- deaths | intcens if (is.null(knots)) { is.wholenumber <- function(x, tol = .Machine$double.eps^0.5) abs(x - round(x)) < tol if (is.null(k)) stop("either \"knots\" or \"k\" must be specified") if (!is.numeric(k)) stop("k must be numeric") if (!is.wholenumber(k) || (k<0)) stop("number of knots \"k\" must be a non-negative integer") knots <- quantile_weighted(tsfn(ktimes[kinds],timescale), probs = seq(0, 1, length.out=k+2)[-c(1,k+2)], weights = model.extract(m, "weights")[kinds]) } else { if (!is.numeric(knots)) stop("\"knots\" must be a numeric vector") minlogtime <- min(tsfn(Y[,"stop"], timescale)) if (any(knots <= minlogtime)) { badknots <- knots[knots < min(tsfn(Y[,"stop"],timescale))] plural <- if (length(badknots) > 1) "s" else "" stop(sprintf("knot%s %s less than or equal to minimum %stime", plural, paste(badknots,collapse=", "), (if (timescale=="log") "log " else ""))) } maxlogtime <- max(tsfn(Y[,"stop"], timescale)) if (any(knots >= maxlogtime)) { badknots <- knots[knots > maxlogtime] plural <- if (length(badknots) > 1) "s" else "" stop(sprintf("knot%s %s greater than or equal to maximum %stime", plural, paste(badknots,collapse=", "), (if (timescale=="log") "log " else ""))) } } if (is.null(bknots)) { ## boundary knots chosen from min/max observed death times... if (length(dtimes)>0) { bt <- dtimes } else { ## unless all observations censored, where censoring times used instead ## "time" used with right censoring ## "time1", "time2" used with interval censoring bt <- c(Y[,"time1"], Y[,"time2"], Y[,"time"]) bt <- bt[is.finite(bt)] } bknots <- c(min(tsfn(bt,timescale)), max(tsfn(bt,timescale))) if (bknots[1] == bknots[2]) warning("minimum and maximum log death times are the same: knot and boundary knot locations should be supplied explicitly") } else if (!is.numeric(bknots) || (length(bknots) !=2) ) stop("boundary knots should be a numeric vector of length 2") knots <- c(bknots[1], knots, bknots[2]) nk <- length(knots) custom.fss <- list( name = "survspline", # unused, d,p functions passed through pars = c(paste0("gamma",0:(nk-1))), location = c("gamma0"), transforms = rep(c(identity), nk), inv.transforms=rep(c(identity), nk), inits = flexsurv.splineinits ) aux <- list(knots=knots, scale=scale, timescale=timescale, spline=spline) dfn <- unroll.function(dsurvspline, gamma=0:(nk-1)) pfn <- unroll.function(psurvspline, gamma=0:(nk-1)) rfn <- unroll.function(rsurvspline, gamma=0:(nk-1)) hfn <- unroll.function(hsurvspline, gamma=0:(nk-1)) Hfn <- unroll.function(Hsurvspline, gamma=0:(nk-1)) qfn <- unroll.function(qsurvspline, gamma=0:(nk-1)) meanfn <- unroll.function(mean_survspline, gamma=0:(nk-1)) rmstfn <- unroll.function(rmst_survspline, gamma=0:(nk-1)) Ddfn <- if (scale=="normal") NULL else unroll.function(DLdsurvspline, gamma=0:(nk-1)) DSfn <- if (scale=="normal") NULL else unroll.function(DLSsurvspline, gamma=0:(nk-1)) D2dfn <- if (scale=="normal") NULL else unroll.function(D2Ldsurvspline, gamma=0:(nk-1)) D2Sfn <- if (scale=="normal") NULL else unroll.function(D2LSsurvspline, gamma=0:(nk-1)) args <- c(list(formula=formula, data=data, dist=custom.fss, dfns=list(d=dfn,p=pfn,r=rfn,h=hfn,H=Hfn,rmst=rmstfn,mean=meanfn, q=qfn, DLd=Ddfn,DLS=DSfn,deriv=!(scale=="normal"), D2Ld=D2dfn,D2LS=D2Sfn,hessian=!(scale=="normal") ), aux=aux), list(...)) ## Try an alternative initial value routine if the default one gives zero likelihood fpold <- args$fixedpars args$fixedpars <- TRUE args$weights <- temp$weights args$bhazard <- temp$bhazard args$rtrunc <- temp$rtrunc args$subset <- temp$subset lik_try <- do.call("flexsurvreg", args)$loglik inits_fail <- is.infinite(lik_try) || is.na(lik_try) if (inits_fail){ args$dist$inits <- flexsurv.splineinits.cox } args$fixedpars <- fpold ret <- do.call("flexsurvreg", args) # faff to make ... args work within functions ret <- c(ret, list(k=length(knots) - 2, knots=knots, scale=scale, timescale=timescale, spline=spline)) ret$call <- call class(ret) <- "flexsurvreg" ret } betax_warn <- function(X, beta, offset){ if (!isTRUE(all.equal(X,0)) || !isTRUE(all.equal(beta,0)) || !isTRUE(all.equal(offset,0))) warning("`X`, `beta` and `offset` arguments not supported since v2.3. Instead the first element of `gamma` should be modified to include any covariate effects or offsets.") } ##' Weighted quantile function ##' ##' Works by multiplying the [0,1] weights by a large number ##' `max_rep*length(x)`, then rounding to an integer. Each element of x is ##' duplicated to the length defined by these integers. Then ##' quantiles of x are obtained using the standard `quantile` ##' function. ##' ##' @inheritParams quantile ##' ##' @param weights Vector of non-negative numbers of same length as ##' `x`, in proportion to the weights of `x`. Elements can be greater ##' than 1, since this is normalised to sum to 1 internally. ##' ##' @param `max_rep` is the average number of times that an element of ##' `x` will be replicated. Increasing this will give more accuracy ##' at the cost of bigger memory requirements for longer `x`. The ##' default of 100 is chosen to be rough, given the intended purpose ##' of this function for choosing default knots for a spline to span ##' `x`. ##' ##' @noRd quantile_weighted <- function(x, probs, weights=NULL, max_rep=100, ...){ x_expand <- x if (!is.null(weights)){ weights_int <- round(length(x) * max_rep * (weights/sum(weights))) x_expand <- rep(x, weights_int) } quantile(x_expand, probs) } flexsurv/R/WeibullPH.R0000644000176200001440000000760514171772374014334 0ustar liggesusers##' Weibull distribution in proportional hazards parameterisation ##' ##' Density, distribution function, hazards, quantile function and random ##' generation for the Weibull distribution in its proportional hazards ##' parameterisation. ##' ##' The Weibull distribution in proportional hazards parameterisation with ##' `shape' parameter a and `scale' parameter m has density given by ##' ##' \deqn{f(x) = a m x^{a-1} exp(- m x^a) } ##' ##' cumulative distribution function \eqn{F(x) = 1 - exp( -m x^a )}, survivor ##' function \eqn{S(x) = exp( -m x^a )}, cumulative hazard \eqn{m x^a} and ##' hazard \eqn{a m x^{a-1}}. ##' ##' \code{\link{dweibull}} in base R has the alternative 'accelerated failure ##' time' (AFT) parameterisation with shape a and scale b. The shape parameter ##' \eqn{a} is the same in both versions. The scale parameters are related as ##' \eqn{b = m^{-1/a}}, equivalently m = b^-a. ##' ##' In survival modelling, covariates are typically included through a linear ##' model on the log scale parameter. Thus, in the proportional hazards model, ##' the coefficients in such a model on \eqn{m} are interpreted as log hazard ##' ratios. ##' ##' In the AFT model, covariates on \eqn{b} are interpreted as time ##' acceleration factors. For example, doubling the value of a covariate with ##' coefficient \eqn{beta=log(2)} would give half the expected survival time. ##' These coefficients are related to the log hazard ratios \eqn{\gamma} as ##' \eqn{\beta = -\gamma / a}. ##' ##' @aliases WeibullPH dweibullPH pweibullPH qweibullPH rweibullPH HweibullPH ##' hweibullPH ##' @param x,q Vector of quantiles. ##' @param p Vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the length is ##' taken to be the number required. ##' @param shape Vector of shape parameters. ##' @param scale Vector of scale parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dweibullPH} gives the density, \code{pweibullPH} gives the ##' distribution function, \code{qweibullPH} gives the quantile function, ##' \code{rweibullPH} generates random deviates, \code{HweibullPH} retuns the ##' cumulative hazard and \code{hweibullPH} the hazard. ##' @author Christopher Jackson ##' @seealso \code{\link{dweibull}} ##' @keywords distribution ##' @name WeibullPH NULL ##' @export ##' @rdname WeibullPH dweibullPH <- function(x, shape, scale = 1, log=FALSE) { dweibull(x, shape=shape, scale=scale^{-1/shape}, log=log) } ##' @export ##' @rdname WeibullPH pweibullPH <- function(q, shape, scale = 1, lower.tail=TRUE, log.p=FALSE) { pweibull(q, shape=shape, scale=scale^{-1/shape}, lower.tail=lower.tail, log.p=log.p) } ##' @export ##' @rdname WeibullPH qweibullPH <- function(p, shape, scale = 1, lower.tail=TRUE, log.p=FALSE) { qweibull(p, shape=shape, scale=scale^{-1/shape}, lower.tail=lower.tail, log.p=log.p) } ##' @export ##' @rdname WeibullPH hweibullPH <- function(x, shape, scale = 1, log=FALSE) { hweibull(x, shape=shape, scale=scale^{-1/shape}, log=log) } ##' @export ##' @rdname WeibullPH HweibullPH <- function(x, shape, scale=1, log=FALSE) { Hweibull(x, shape=shape, scale=scale^{-1/shape}, log=log) } ##' @export ##' @rdname WeibullPH rweibullPH <- function(n, shape, scale=1) { rweibull(n, shape=shape, scale=scale^{-1/shape}) } ##' @export ##' @rdname means rmst_weibullPH = function(t, shape, scale=1, start=0){ rmst_generic(pweibullPH, t, start=start, shape=shape, scale=scale) } ##' @export ##' @rdname means mean_weibullPH = function(shape, scale=1){ mean_weibull(shape=shape, scale=scale^{-1/shape}) } flexsurv/R/Weibull.R0000644000176200001440000000710714203141721014057 0ustar liggesusers### Hazard and cumulative hazard functions for R built in ### distributions. Where possible, use more numerically stable ### formulae than d/(1-p) and -log(1-p) ##' @export ##' @rdname hazard hweibull <- function (x, shape, scale = 1, log = FALSE) { h <- dbase("weibull", log=log, x=x, shape=shape, scale=scale) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) if (log) ret[ind] <- log(shape) + (shape-1)*log(x/scale) - log(scale) else ret[ind] <- shape * (x/scale)^(shape - 1)/scale ret } ##' @export ##' @rdname hazard Hweibull <- function (x, shape, scale = 1, log = FALSE) { h <- dbase("weibull", log=log, x=x, shape=shape, scale=scale) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) if (log) ret[ind] <- shape * log(x/scale) else ret[ind] <- (x/scale)^shape ret } check.weibull <- function(shape, scale=1){ ret <- rep(TRUE, length(shape)) if (any(!is.na(shape) & shape<0)) {warning("Negative shape parameter"); ret[!is.na(shape) & shape<0 ] <- FALSE} if (any(!is.na(scale) & scale<0)) {warning("Negative scale parameter"); ret[!is.na(scale) & scale<0 ] <- FALSE} ret } ##' @export ##' @rdname means mean_weibull <- function(shape, scale=1) { scale * gamma(1 + 1/shape) } var.weibull <- function(shape, scale=1) { scale^2 * (gamma(1 + 2/shape) - (gamma(1 + 1/shape))^2) } ##' @export ##' @rdname means rmst_weibull = function(t, shape, scale=1, start=0){ rmst_generic(pweibull, t, start=start, shape=shape, scale=scale) } ##' @export hweibull <- function (x, shape, scale = 1, log = FALSE) { h <- dbase("weibull", log=log, x=x, shape=shape, scale=scale) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) if (log) ret[ind] <- log(shape) + (shape-1)*log(x/scale) - log(scale) else ret[ind] <- shape * (x/scale)^(shape - 1)/scale ret } ##' @export Hweibull <- function (x, shape, scale = 1, log = FALSE) { h <- dbase("weibull", log=log, x=x, shape=shape, scale=scale) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) if (log) ret[ind] <- shape * log(x/scale) else ret[ind] <- (x/scale)^shape ret } ## Don't warn about NaNs when NaNs are produced. This happens for ## extreme parameter values during optimisation. dweibull.quiet <- function(x, shape, scale = 1, log = FALSE) { ret <- suppressWarnings(dweibull(x=x, shape=shape, scale=scale, log=log)) ret } pweibull.quiet <- function(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) { ret <- suppressWarnings(pweibull(q=q, shape=shape, scale=scale, lower.tail=lower.tail, log.p=log.p)) ret } hweibull.quiet <- function(x, shape, scale = 1, log = FALSE) { ret <- suppressWarnings(hweibull(x=x, shape=shape, scale=scale, log=log)) ret } rweibull.quiet <- rweibull hweibull.quiet <- function(x, shape, scale = 1, log = FALSE) { ret <- suppressWarnings(hweibull(x=x, shape=shape, scale=scale, log=log)) ret } Hweibull.quiet <- function(x, shape, scale = 1, log = FALSE) { ret <- suppressWarnings(Hweibull(x=x, shape=shape, scale=scale, log=log)) ret } qweibull.quiet <- function(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) { ret <- suppressWarnings(qweibull(p=p, shape=shape, scale=scale, lower.tail=lower.tail, log.p=log.p)) ret } mean_weibull.quiet <- function(shape, scale=1) { mean_weibull(shape=shape,scale=scale) } var.weibull.quiet <- function(shape, scale=1) { scale^2 * (gamma(1 + 2/shape) - (gamma(1 + 1/shape))^2) } rmst_weibull.quiet = function(t, shape, scale=1, start=0){ rmst_generic(pweibull.quiet, t, start=start, shape=shape, scale=scale) } flexsurv/R/custom.R0000644000176200001440000001555314603725274014011 0ustar liggesusers## Get density, probability, hazard and cumulative hazard functions ## and return them as a list of functions form.dp <- function(dlist, dfns, integ.opts){ ## TODO check for format of dfn (args x, log) ## FIXME bug if object called d is found in global env ## check for existence in current frame. inherits false? name <- dlist$name hname <- paste0("h",name); Hname <- paste0("H",name) dname <- paste0("d",name); pname <- paste0("p",name) rmstname <- paste0("rmst_",name) meanname <- paste0("mean_",name) qname <- paste0("q",name) rname <- paste0("r",name) if (is.function(dfns$d)) d <- dfns$d if (is.function(dfns$p)) p <- dfns$p if (is.function(dfns$h)) h <- dfns$h if (is.function(dfns$H)) H <- dfns$H if (is.function(dfns$r)) r <- dfns$r if (is.function(dfns$q)) q <- dfns$q if (is.function(dfns$mean)) meanf <- dfns$mean if (is.function(dfns$rmst)) rmst <- dfns$rmst if (!exists("h", inherits=FALSE)){ if (exists(hname)) h <- get(hname) else { if (!exists("d")){ if (exists(dname)) d <- get(dname) else stop("Neither density function \"",dname, "\" nor hazard function \"", hname, "\" found") } if (!exists("p")){ if (exists(pname)) p <- get(pname) else { message("Forming cumulative distribution function...") p <- integrate.dh(d, dlist, integ.opts, what="density") } } h <- function(x, ...){ d(x,...)/(1 - p(x,...)) } } } if (!exists("H", inherits=FALSE)){ if (exists(Hname)) H <- get(Hname) else { if (!exists("p")) { if (exists(pname)) p <- get(pname) } if (exists("p")){ H <- function(x, ...){ -log(1 - p(x, ...)) } } else { message("Forming integrated hazard function...") H <- integrate.dh(h, dlist, integ.opts, what="hazard") } } } if (!exists("p", inherits=FALSE)){ if (exists(pname)) p <- get(pname) else { p <- function(q, ...) { ret <- 1 - exp(-H(q, ...)) # ret[q==Inf] <- 1 # should have been handled already in cum.fn # ret[q==0] <- 0 ret ### TODO special values in other functions } } } if (!exists("q", inherits=FALSE)){ if (exists(qname)) q <- get(qname) else { # giving this another name to avoid scoping issues # w/ name p also being an argument to q functions pfun <- p q <- function(p, ...) qgeneric(pfun, p, ...) } } if (!exists("d", inherits=FALSE)){ if (exists(dname)) d <- get(dname) else { d <- function(x, log=FALSE, ...) { if (log) log(h(x,...)) + log(1 - p(x, ...)) else h(x,...) * (1 - p(x, ...)) } } } if (!exists("rmst", inherits=FALSE)){ if (exists(rmstname)) rmst <- get(rmstname) else { message("Forming integrated rmst function...") rmst <- function(t, start=0, ...) rmst_generic(p, t=t, start=start, ...) } } if (!exists("meanf", inherits=FALSE)){ if (exists(rmstname)) meanf <- get(meanname) else { message("Forming integrated mean function...") meanf <- function(start=0, ...) rmst(t=Inf, start=start, ...) } } if (!exists("r", inherits=FALSE)){ if (exists(rname)) r <- get(rname) else r <- NULL ## random sampling function is currently only used for multi-state models } ## Check for existence of derivative functions ## conventionally called DLd, DLs ## dfns$deriv can be set to FALSE by user to ignore any derivatives that exist, but this feature is undocumented/unused. if (is.function(dfns$DLd)) DLd <- dfns$DLd else if (is.null(dfns$deriv) && exists(paste0("DLd",name))) DLd <- get(paste0("DLd",name)) else DLd <- NULL if (is.function(dfns$DLS)) DLS <- dfns$DLS else if (is.null(dfns$deriv) && exists(paste0("DLS",name))) DLS <- get(paste0("DLS",name)) else DLS <- NULL ## Likewise, check for second derivative functions if (is.function(dfns$D2Ld)) D2Ld <- dfns$D2Ld else if (is.null(dfns$hessian) && exists(paste0("D2Ld",name))) D2Ld <- get(paste0("D2Ld",name)) else D2Ld <- NULL if (is.function(dfns$D2LS)) D2LS <- dfns$D2LS else if (is.null(dfns$hessian) && exists(paste0("D2LS",name))) D2LS <- get(paste0("D2LS",name)) else D2LS <- NULL list(p=p, d=d, h=h, H=H, r=r, DLd=DLd, DLS=DLS, D2Ld=D2Ld, D2LS=D2LS, rmst=rmst, mean= meanf, q=q, deriv = !is.null(DLd) && !is.null(DLS), hessian = !is.null(D2Ld) && !is.null(D2LS) ) } ## Produce cumulative version of hazard function or density function ## by numerical integration integrate.dh <- function(fn, dlist, integ.opts, what="dens"){ cum.fn <- function(q, ...){ args <- list(...) pars <- as.list(dlist$pars) names(pars) <- dlist$pars args.done <- numeric() ## if argument is unnamed, assume it is supplied in the default order for (i in seq_along(dlist$pars)){ if(any(names(args)==dlist$pars[i])) { pars[[i]] <- args[[dlist$pars[i]]] args.done <- c(args.done, match(dlist$pars[i], names(args))) } else { pars[[i]] <- args[[i]] args.done <- c(args.done, i) } } ## any auxiliary arguments not in main distribution parameters rest <- args[setdiff(seq_along(args), args.done)] ## replicate all arguments to have the length of the longest one (=n) n <- max(sapply(c(list(q),pars), length)) q <- rep(q, length.out=n) for (i in seq_along(pars)) pars[[i]] <- rep(pars[[i]], length.out=n) ret <- numeric(n) du <- function(u, ...)fn(u,...) ## then return a vector of length n for (i in 1:n){ parsi <- lapply(pars, function(x)x[i]) int.args <- c(list(f=du, lower=0, upper=q[i]), parsi, rest, integ.opts) if (q[i]==0) ret[i] <- 0 else if (q[i]==Inf) { if (what=="density") ret[i] <- 1 else if (what=="hazard") ret[i] <- Inf } else { int <- try(do.call("integrate", int.args)) ret[i] <- int$value } } ret } cum.fn } flexsurv/R/ajfit.R0000644000176200001440000001045614472153214013562 0ustar liggesusers##' Check the fit of Markov flexible parametric multi-state models against ##' nonparametric estimates. ##' ##' Computes both parametric and comparable Aalen-Johansen nonparametric ##' estimates from a flexible parametric multi-state model, and returns them ##' together in a tidy data frame. Only models with no covariates, or only ##' factor covariates, are supported. If there are factor covariates, then the ##' nonparametric estimates are computed for subgroups defined by combinations ##' of the covariates. Another restriction of this function is that all ##' transitions must have the same covariates on them. ##' ##' @param x Object returned by \code{\link{fmsm}} representing a flexible ##' parametric multi-state model. This must be Markov, rather than ##' semi-Markov, and no check is performed for this. Note that all ##' "competing risks" style models, with just one source state and multiple ##' destination states, are Markov, so those are fine here. ##' ##' @param maxt Maximum time to compute parametric estimates to. ##' ##' @param newdata Data frame defining the subgroups to consider. This must ##' have a column for each covariate in the model. If omitted, then all ##' potential subgroups defined by combinations of factor covariates are ##' included. Continuous covariates are not supported. ##' ##' ##' ##' @return Tidy data frame containing both Aalen-Johansen and parametric ##' estimates of state occupancy over time, and by subgroup if subgroups are ##' included. ##' ##' @export ajfit_fmsm <- function(x, maxt=NULL, newdata=NULL){ dat <- x[[1]]$data$m covnames <- attr(dat,"covnames") faccovs <- sapply(dat[,covnames], is.factor) if (!all(faccovs)) stop("Nonparametric estimation not supported with non-factor covariates") covs <- lapply(x, function(x)attr(x$data$m, "covnames")) if (length(covs)>1){ for (i in 2:length(covs)){ if(!identical(covs[[i]], covs[[1]])) stop("Not currently supported with different covariates on different transitions") } } if (is.null(newdata)) newdata <- do.call(expand.grid, lapply(dat[,covnames,drop=FALSE], levels)) else if (is.list(newdata)) newdata <- as.data.frame(newdata) else stop("`newdata` should be a data frame") nmods <- length(x) datlist <- vector(nmods, mode="list") for (j in 1:nmods){ datlist[[j]] <- x[[j]]$data$m names(datlist[[j]])[1] <- "(response)" datlist[[j]]$trans <- j } dat <- do.call(dplyr::bind_rows, datlist) dat$trans <- factor(dat$trans, labels=attr(x,"names")) ## remove interval censored dat <- dat[dat$`(response)`[,"status"] != 3,] dat$time <- dat[,1][,1] dat$status <- dat[,1][,"status"] ncovvals <- nrow(newdata) if (ncovvals==0) ncovvals <- 1 pt <- vector(ncovvals, mode="list") for (i in 1:ncovvals) { datsub <- dat for (j in seq_along(covnames)) datsub <- datsub[datsub[,covnames[j]] == newdata[i,covnames[j]],] cf <- coxph(Surv(time, status) ~ strata(trans), data=datsub) ms <- msfit(cf, trans=attr(x,"trans")) pt[[i]] <- probtrans(ms, predt=0, variance=FALSE)[[1]] covvals <- newdata[i,,drop=FALSE][rep(1,nrow(pt[[i]])),,drop=FALSE] pt[[i]] <- cbind(pt[[i]], covvals) } pt <- do.call(dplyr::bind_rows, pt) nstates <- length(attr(x,"statenames")) names(pt)[names(pt) %in% paste0("pstate",1:nstates)] <- attr(x,"statenames") pt$model <- "Aalen-Johansen" ## Estimates from parametric competing risks model pmat <- vector(ncovvals, mode="list") if (is.null(maxt)) maxt <- max(pt$time) times <- seq(0, maxt, length.out=100) for (i in 1:ncovvals){ # note newdata doesn't support multiple covs pmat[[i]] <- pmatrix.fs(x, newdata=newdata[i,,drop=FALSE], start=1, t=times, tidy=TRUE, ci=FALSE) covvals <- newdata[i,,drop=FALSE][rep(1,nrow(pmat[[i]])),,drop=FALSE] pmat[[i]] <- cbind(pmat[[i]], covvals) } pmat <- do.call(dplyr::bind_rows, pmat) pmat <- pmat[pmat$start==1,,drop=FALSE] pmat$start <- NULL pmat$model <- "Parametric" cols <- c("time",covnames,"model",attr(x,"statenames")) res <- rbind(pt[,cols], pmat[,cols]) res <- tidyr::pivot_longer(res, cols=tidyselect::all_of(attr(x,"statenames")), names_to="state", values_to="val") res } flexsurv/R/Exp.R0000644000176200001440000000231514203407406013211 0ustar liggesusers### Hazard and cumulative hazard functions for R built in ### distributions. Where possible, use more numerically stable ### formulae than d/(1-p) and -log(1-p) ##' @export ##' @rdname hazard hexp <- function(x, rate=1, log=FALSE){ h <- dbase("exp", log=log, x=x, rate=rate) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) ret[ind] <- if (log) log(rate) else rate ret } ##' @export ##' @rdname hazard Hexp <- function(x, rate=1, log=FALSE){ h <- dbase("exp", log=log, x=x, rate=rate) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) ret[ind] <- if (log) {log(rate) + log(x)} else rate*x ret } check.exp <- function(rate=1){ ret <- rep(TRUE, length(rate)) if (any(!is.na(rate) & rate<0)) {warning("Negative rate parameter"); ret[!is.na(rate) & rate<0] <- FALSE} ret } ##' @export ##' @rdname means mean_exp <- function(rate=1) { 1/rate } ##' @export ##' @rdname means rmst_exp <- function(t, rate=1,start=0){ p_start = pexp(start, rate=rate) auc_full = mean_exp(rate=rate) auc_right = auc_full * (1-pexp(t, rate=rate)) auc_left = auc_full * p_start auc_uncond = auc_full - auc_right - auc_left auc_uncond/(1-p_start) } var.exp <- function(rate=1) { 1/rate^2 } flexsurv/R/deriv.R0000644000176200001440000002250214603753150013572 0ustar liggesusers## Deriv of loglik wrt transformed parameters p ## loglik(p|x) = sum(log(f(p|xobs))) + sum(log(S(p|xcens))) - sum(log(S(p|xtrunc))) ## dloglik/dp = sum (df/dp / f(p)) | xobs) + sum(dS/dp / S(p) | xcens) - sum(dS/dp / S(p) | xtrunc) ## = sum(dlogf/dp | xobs) + sum(dlogS/dp | xcens) - sum(dlogS/dp | xtrunc) Dminusloglik.flexsurv <- function(optpars, Y, X=0, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars=NULL) { pars <- inits npars <- length(pars) pars[setdiff(seq_len(npars), fixedpars)] <- optpars nbpars <- length(dlist$pars) pars <- as.list(pars) ncovs <- length(pars) - length(dlist$pars) if (ncovs > 0) beta <- unlist(pars[(nbpars+1):npars]) for (i in dlist$pars) { if (length(mx[[i]]) > 0) pars[[i]] <- pars[[i]] + X[,mx[[i]],drop=FALSE] %*% beta[mx[[i]]] else pars[[i]] <- rep(pars[[i]], length(Y[,"stop"])) } dead <- Y[,"status"]==1 ddcall <- list(t=Y[dead,"stop"]) dsccall <- list(t=Y[!dead,"stop"]) dstcall <- list(t=Y[,"start"]) for (i in 1:nbpars) ddcall[[names(pars)[i]]] <- dsccall[[names(pars)[i]]] <- dstcall[[names(pars)[i]]] <- dlist$inv.transforms[[i]](pars[[i]]) for (i in seq_along(aux)){ ddcall[[names(aux)[i]]] <- dsccall[[names(aux)[i]]] <- dstcall[[names(aux)[i]]] <- aux[[i]] } for (i in dlist$pars) { ddcall[[i]] <- ddcall[[i]][dead] dsccall[[i]] <- dsccall[[i]][!dead] } nobs <- nrow(Y) dloglik <- matrix(nrow=nobs, ncol=npars) dloglik[dead,] <- dderiv(dfns$DLd, ddcall, X[dead,,drop=FALSE], mx, dlist) dloglik[!dead,] <- dderiv(dfns$DLS, dsccall, X[!dead,,drop=FALSE], mx, dlist) dstrunc <- dderiv(dfns$DLS, dstcall, X, mx, dlist) dloglik <- dloglik - dstrunc ## Derivatives with baseline hazard. ## adjust dd, dscens and dstrunc. cens and trunc terms don't depend on pars ## Add deriv of log(1 + (1/h) * bh/w) just for uncensored event ## 1 / (1 + (1/h)*bh/w) * -h^{-2}bh/w * dh ## and h = f * S^-1, so dh = df*s^-1 + f * -s^-2 * ds) if (any(bhazard > 0)) { dcall <- ddcall dcall$x <- ddcall$t; dcall$t <- NULL dens <- do.call(dfns$d, dcall) pcall <- dcall pcall$q <- pcall$x; pcall$x <- NULL surv <- 1 - do.call(dfns$p, pcall) haz <- dens / surv offseti <- 1 / (1 + bhazard[dead] / haz) ## Note d/dx log(x) = 1/x ddx dscense <- dderiv(dfns$DLS, ddcall, X[dead,,drop=FALSE], mx, dlist) doff <- - offseti*bhazard[dead] * (dloglik[dead,] - dscense)/ haz dloglik[dead,] <- dloglik[dead,] + doff } res <- - colSums(dloglik*weights) ## currently wastefully calculates derivs for fixed pars then discards them res[setdiff(1:npars, fixedpars)] } dderiv <- function(ddfn, ddcall, X, mx, dlist){ if (length(ddcall$t) == 0) array(dim=c(0,length(dlist$pars))) else { res.base <- do.call(ddfn, ddcall) res.beta <- Dcov(res.base, X, mx, dlist) cbind(res.base, res.beta) } } ## Derivatives of log density with respect to covariate effects are ## just found by an easy chain rule given the baseline derivatives and ## the covariate value: the parameter on the real-line scale is always ## a linear function of covariates. Dcov <- function(res, X, mx, dlist){ ncoveffs <- length(unlist(mx)) cres <- matrix(nrow=nrow(res), ncol=ncoveffs) inds <- c(0,cumsum(sapply(mx,length))) ## parameters of res ordered as distribution definition, but mx ordered with location first ## mx is a list, with one component per survival distribution parameter ## ith component contains indexes of cols of X that are included in regression for ith parameter for (i in seq_along(mx)) { for (j in seq_along(mx[[i]])){ cres[,inds[i]+j] <- X[,mx[[i]][j]]*res[,match(names(mx)[i], dlist$pars)] } } cres } ## Derivatives of log density and log survival probability with ## respect to baseline parameters for various distributions. Baseline ## parameters are on the real-line scale, commonly the log scale. No ## easy derivatives available for other distributions. ## Naming: names refer to natural scale pars, but derivatives are taken with respect to transformed scale pars ## Transformed scale is log scale for positive pars. Unrestricted pars (e.g. Gompertz shape) not transformed ## Exponential DLdexp <- function(t, rate){ res <- matrix(nrow=length(t), ncol=1) colnames(res) <- c("rate") ts <- 1 - t*rate res[,"rate"] <- ts res } DLSexp <- function(t, rate){ res <- matrix(nrow=length(t), ncol=1) colnames(res) <- c("rate") res[,"rate"] <- -t*rate res } ## Weibull accelerated failure time DLdweibull <- function(t, shape, scale){ res <- matrix(nrow=length(t), ncol=2) colnames(res) <- c("shape","scale") tss <- (t/scale)^shape lts <- log(t/scale) res[,"shape"] <- 1 + shape*lts*(1 - tss) res[,"scale"] <- -1 - (shape-1) + shape*tss res } DLSweibull <- function(t, shape, scale){ res <- matrix(nrow=length(t), ncol=2) colnames(res) <- c("shape","scale") tss <- (t/scale)^shape res[,"shape"] <- ifelse(t==0, 0, -shape*log(t/scale)*tss) res[,"scale"] <- tss*shape res } DLdweibull.quiet <- DLdweibull DLSweibull.quiet <- DLSweibull ## Weibull proportional hazards DLdweibullPH <- function(t, shape, scale){ res <- matrix(nrow=length(t), ncol=2) colnames(res) <- c("shape","scale") res[,"shape"] <- 1 + shape*log(t)*(1 - scale*t^shape) res[,"scale"] <- 1 - scale*t^shape res } DLSweibullPH <- function(t, shape, scale){ res <- matrix(nrow=length(t), ncol=2) colnames(res) <- c("shape","scale") res[,"shape"] <- ifelse(t==0, 0, -scale*shape*log(t)*t^shape) res[,"scale"] <- -scale*t^shape res } ## Gompertz (note this is derivative wrt shape and log rate) DLdgompertz <- function(t, shape, rate){ res <- matrix(nrow=length(t), ncol=2) colnames(res) <- c("shape","rate") res[shape==0,"shape"] <- 0 res[shape==0,"rate"] <- 1 - rate[shape==0] * t[shape==0] sn0 <- (shape!=0) t <- t[sn0]; rate <- rate[sn0]; shape <- shape[sn0] est <- exp(shape*t) res[sn0,"shape"] <- t + -rate/shape*(1/shape*(1 - est) + t*est) res[sn0,"rate"] <- 1 + rate/shape*(1 - est) res } DLSgompertz <- function(t, shape, rate){ res <- matrix(nrow=length(t), ncol=2) colnames(res) <- c("shape","rate") res[shape==0,"shape"] <- 0 res[shape==0,"rate"] <- - rate[shape==0] * t[shape==0] sn0 <- (shape!=0) t <- t[sn0]; rate <- rate[sn0]; shape <- shape[sn0] est <- exp(shape*t) res[sn0,"shape"] <- -rate/shape*(1/shape*(1 - est) + t*est) res[sn0,"rate"] <- rate/shape*(1 - est) res } DLdsurvspline <- function(t, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp"){ d <- dbase.survspline(q=t, gamma=gamma, knots=knots, scale=scale, deriv=1, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]); t <- q b <- basis(knots, tsfn(t,timescale), spline=spline) db <- dbasis(knots, tsfn(t,timescale), spline=spline) eta <- rowSums(b * gamma) + as.numeric(X %*% beta) ds <- rowSums(db * gamma) npars <- ncol(gamma) parnames <- paste0("gamma", seq_len(npars)-1) colnames(ret) <- parnames for (i in 1:ncol(gamma)){ if (scale=="hazard") ret[ind,i] <- db[,i] / ds + b[,i] * (1 - exp(eta)) else if (scale=="odds"){ eeta <- 1 - 2*exp(eta)/(1 + exp(eta)) ret[ind,i] <- db[,i] / ds + b[,i] * eeta } } ret } DLSsurvspline <- function(t, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp"){ d <- dbase.survspline(q=t, gamma=gamma, knots=knots, scale=scale, deriv=1, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]); t <- q b <- basis(knots, tsfn(t,timescale), spline=spline) if (any(ind)){ eta <- rowSums(b * gamma) + as.numeric(X %*% beta) for (i in 1:ncol(gamma)){ if (scale=="hazard") ret[ind,i] <- ifelse(t==0, 0, - b[,i] * exp(eta)) else if (scale=="odds"){ eeta <- exp(eta)/(1 + exp(eta)) ret[ind,i] <- ifelse(t==0, 0, - b[,i] * eeta) } } } ret } #' @noRd deriv_test <- function(optpars, Y, X, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars){ an.d <- Dminusloglik.flexsurv(optpars=optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) if (requireNamespace("numDeriv", quietly = TRUE)) num.d <- numDeriv::grad(minusloglik.flexsurv, optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) else stop("\"numDeriv\" package not available") res <- cbind(analytic=an.d, numeric=as.vector(num.d)) rownames(res) <- names(optpars) list(res=res, error=mean(abs(an.d - num.d))) } flexsurv/R/survsplinek.R0000644000176200001440000005443614603752643015067 0ustar liggesusers##' Royston/Parmar spline survival distribution functions with one argument per parameter ##' ##' Probability density, distribution, quantile, random generation, hazard, ##' cumulative hazard, mean and restricted mean functions for the Royston/Parmar ##' spline model, with one argument per parameter. For the equivalent functions with all parameters collected together in a single argument, see \code{\link{Survspline}}. ##' ##' These functions go up to 7 spline knots, or 9 parameters. ##' ##' @aliases dsurvspline0 dsurvspline1 dsurvspline2 dsurvspline3 dsurvspline4 dsurvspline5 dsurvspline6 dsurvspline7 psurvspline0 psurvspline1 psurvspline2 psurvspline3 psurvspline4 psurvspline5 psurvspline6 psurvspline7 qsurvspline0 qsurvspline1 qsurvspline2 qsurvspline3 qsurvspline4 qsurvspline5 qsurvspline6 qsurvspline7 rsurvspline0 rsurvspline1 rsurvspline2 rsurvspline3 rsurvspline4 rsurvspline5 rsurvspline6 rsurvspline7 hsurvspline0 hsurvspline1 hsurvspline2 hsurvspline3 hsurvspline4 hsurvspline5 hsurvspline6 hsurvspline7 Hsurvspline0 Hsurvspline1 Hsurvspline2 Hsurvspline3 Hsurvspline4 Hsurvspline5 Hsurvspline6 Hsurvspline7 mean_survspline0 mean_survspline1 mean_survspline2 mean_survspline3 mean_survspline4 mean_survspline5 mean_survspline6 mean_survspline7 rmst_survspline0 rmst_survspline1 rmst_survspline2 rmst_survspline3 rmst_survspline4 rmst_survspline5 rmst_survspline6 rmst_survspline7 ##' ##' ##' @param gamma0,gamma1,gamma2,gamma3,gamma4,gamma5,gamma6,gamma7,gamma8 Parameters describing the baseline spline function, as ##' described in \code{\link{flexsurvspline}}. ##' ##' @inheritParams Survspline ##' ##' @author Christopher Jackson ##' ##' @name Survsplinek NULL ##' @rdname Survsplinek ##' @export mean_survspline0 <- function(gamma0, gamma1, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline1 <- function(gamma0, gamma1, gamma2, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline2 <- function(gamma0, gamma1, gamma2, gamma3, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline3 <- function(gamma0, gamma1, gamma2, gamma3, gamma4, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline4 <- function(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline5 <- function(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline6 <- function(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export mean_survspline7 <- function(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp"){ mean_survspline(gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rmst_survspline0 <- function(t, gamma0, gamma1, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline1 <- function(t, gamma0, gamma1, gamma2, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline2 <- function(t, gamma0, gamma1, gamma2, gamma3, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline3 <- function(t, gamma0, gamma1, gamma2, gamma3, gamma4, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline4 <- function(t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline5 <- function(t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline6 <- function(t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export rmst_survspline7 <- function(t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots=c(-10, 10), scale="hazard", timescale="log", spline="rp", start=0){ rmst_survspline(t, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline, start=start) } ##' @rdname Survsplinek ##' @export dsurvspline0 <- function(x, gamma0, gamma1, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline1 <- function(x, gamma0, gamma1, gamma2, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline2 <- function(x, gamma0, gamma1, gamma2, gamma3, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline3 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline4 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline5 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline6 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export dsurvspline7 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale="hazard", timescale="log", spline="rp", log=FALSE){ dsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline, log=log) } ##' @rdname Survsplinek ##' @export psurvspline0 <- function(q, gamma0, gamma1, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline1 <- function(q, gamma0, gamma1, gamma2, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline2 <- function(q, gamma0, gamma1, gamma2, gamma3, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline3 <- function(q, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline4 <- function(q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline5 <- function(q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline6 <- function(q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export psurvspline7 <- function(q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ psurvspline(q, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline0 <- function(p, gamma0, gamma1, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline1 <- function(p, gamma0, gamma1, gamma2, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline2 <- function(p, gamma0, gamma1, gamma2, gamma3, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline3 <- function(p, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline4 <- function(p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline5 <- function(p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline6 <- function(p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export qsurvspline7 <- function(p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale="hazard", timescale="log", spline="rp", lower.tail=TRUE, log.p=FALSE){ qsurvspline(p, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline, lower.tail=lower.tail, log.p=log.p) } ##' @rdname Survsplinek ##' @export rsurvspline0 <- function(n, gamma0, gamma1, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline1 <- function(n, gamma0, gamma1, gamma2, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline2 <- function(n, gamma0, gamma1, gamma2, gamma3, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline3 <- function(n, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline4 <- function(n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline5 <- function(n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline6 <- function(n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export rsurvspline7 <- function(n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale="hazard", timescale="log", spline="rp"){ rsurvspline(n, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline0 <- function(x, gamma0, gamma1, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline1 <- function(x, gamma0, gamma1, gamma2, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline2 <- function(x, gamma0, gamma1, gamma2, gamma3, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline3 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline4 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline5 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline6 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export hsurvspline7 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale="hazard", timescale="log", spline="rp"){ hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline0 <- function(x, gamma0, gamma1, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline1 <- function(x, gamma0, gamma1, gamma2, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline2 <- function(x, gamma0, gamma1, gamma2, gamma3, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline3 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline4 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline5 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline6 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7), knots=knots, scale=scale, timescale=timescale, spline=spline) } ##' @rdname Survsplinek ##' @export Hsurvspline7 <- function(x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale="hazard", timescale="log", spline="rp"){ Hsurvspline(x, gamma=cbind(gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8), knots=knots, scale=scale, timescale=timescale, spline=spline) } flexsurv/R/fracpoly.R0000644000176200001440000000263514471621547014314 0ustar liggesusers### simplified version of gamlss::bfp with no shift or scale #nocov start bfp <- function (x, powers = c(1, 2)) { nobs <- length(x) npoly <- length(powers) X <- matrix(0, nrow = nobs, ncol = npoly) x1 <- ifelse(powers[1] != rep(0, nobs), x^powers[1], log(x)) X[, 1] <- x1 if (npoly >= 2) { for (i in 2:npoly) { if (powers[i] == powers[(i - 1)]) x2 <- log(x) * x1 else x2 <- ifelse(powers[i] != rep(0, nobs), x^powers[i], log(x)) X[, i] <- x2 x1 <- x2 } } X } dbfp <- function (x, powers = c(1, 2)) { nobs <- length(x) npoly <- length(powers) X <- matrix(0, nrow = nobs, ncol = npoly) x1 <- ifelse(powers[1] != rep(0, nobs), x^powers[1], log(x)) dx1 <- ifelse(powers[1] != rep(0, nobs), powers[1]*x^{powers[1]-1}, 1/x) X[, 1] <- dx1 if (npoly >= 2) { for (i in 2:npoly) { if (powers[i] == powers[(i - 1)]) { x2 <- log(x) * x1 dx2 <- log(x) * dx1 + 1/x * x1 } else { x2 <- ifelse(powers[i] != rep(0, nobs), x^powers[i], log(x)) dx2 <- ifelse(powers[i] != rep(0, nobs), powers[i]*x^{powers[i]-1}, 1/x) } X[, i] <- dx2 x1 <- x2 dx1 <- dx2 } } X } #nocov end flexsurv/R/pexp.R0000644000176200001440000000335614155156771013453 0ustar liggesusers## more sensible to reparametersise as baserate, timehr? then trt eff on baserate gives a PH model ## or is trt eff only in first period a sensible model? ## either way might want utilities to describe various kinds of fitted curves hpexp <- function(t, rate, knots){ check_pexp(rate, knots) knots <- sort(knots) rate[findInterval(t, knots) + 1] } ## TODO check t is valid. return zero for zero, other special values? Hpexp <- function(t, rate, knots){ check_pexp(rate, knots) k0 <- c(0,knots) int <- findInterval(t, k0) dk <- diff(k0) cumrate <- c(0, cumsum(dk*rate[-length(rate)])) # cumulative rate up to each knot cumrate[int] + rate[int]*(t - k0[int]) # add on the remainder for each t } ## TODO handle special values for rate check_pexp <- function(rate, knots){ if (!is.numeric(rate)) stop("`rate` should be numeric") if (!is.numeric(knots)) stop("`knots` should be numeric") if (any(knots <= 0)) stop("`knots` should all be positive") nr <- length(rate) nk <- length(knots) if (nr != nk + 1) stop(sprintf("found nr=%s rates and nk=%s knots, should have nr = nk+1", nr, nk)) } hpw <- function(knots){ nk <- length(knots) unroll.function(hpexp, rate=0:nk) } Hpw <- function(knots){ nk <- length(knots) unroll.function(Hpexp, rate=0:nk) } custom_pw <- function(knots){ nk <- length(knots) list(name = "pw", pars = paste0("rate", 0:nk), location = "rate0", transforms = rep(list(log), nk+1), inv.transforms = rep(list(exp), nk+1), inits = function(t,aux) {lam <- sr.exp.inits(t,aux); rep(lam, nk+1)}) } ## todo d, p functions? q? r even? copy from msm? flexsurv/R/deriv2.R0000644000176200001440000002755514603725274013677 0ustar liggesusers## Second derivatives of the log density and log survival ## with respect to parameters on transformed scales ## The transformed scale is log scale for positive parameters ## Gompertz shape is unrestricted D2Ldexp <- function(t, rate){ res <- array(dim=c(length(t), 1, 1)) parnames <- "rate" dimnames(res) <- list(NULL, parnames, parnames) ts <- - t*rate res[,"rate","rate"] <- ts res } D2LSexp <- function(t, rate){ res <- array(dim=c(length(t), 1, 1)) parnames <- "rate" dimnames(res) <- list(NULL, parnames, parnames) res[,"rate","rate"] <- -t*rate res } D2Ldweibull <- function(t, shape, scale){ res <- array(dim=c(length(t), 2, 2)) parnames <- c("shape","scale") dimnames(res) <- list(NULL, parnames, parnames) tss <- (t/scale)^shape lts <- log(t/scale) res[,"shape","shape"] <- ifelse(t==0, 0, shape*lts*(1 - tss - shape*lts*tss)) res[,"scale","scale"] <- -shape^2*tss res[,"shape","scale"] <- res[,"scale","shape"] <- ifelse(t==0, 0, shape*(tss - 1 + shape*lts*tss)) res } D2LSweibull <- function(t, shape, scale){ res <- array(dim=c(length(t), 2, 2)) parnames <- c("shape","scale") dimnames(res) <- list(NULL, parnames, parnames) tss <- (t/scale)^shape lts <- log(t/scale) res[,"shape","shape"] <- ifelse(t==0, 0, -shape*lts*tss*(1 + shape*lts)) res[,"scale","scale"] <- -shape^2*tss res[,"shape","scale"] <- res[,"scale","shape"] <- ifelse(t==0, 0, shape*tss*(1 + shape*lts)) res } D2Ldweibull.quiet <- D2Ldweibull D2LSweibull.quiet <- D2LSweibull D2LdweibullPH <- function(t, shape, scale){ res <- array(dim=c(length(t), 2, 2)) parnames <- c("shape","scale") dimnames(res) <- list(NULL, parnames, parnames) tss <- (t/scale)^shape lts <- log(t/scale) res[,"shape","shape"] <- ifelse(t==0, 0, shape*log(t)*(1 - scale*t^shape*(1 + shape*log(t)))) res[,"scale","scale"] <- -scale*t^shape res[,"shape","scale"] <- res[,"scale","shape"] <- ifelse(t==0, 0, -scale*shape*log(t)*t^shape) res } D2LSweibullPH <- function(t, shape, scale){ res <- array(dim=c(length(t), 2, 2)) parnames <- c("shape","scale") dimnames(res) <- list(NULL, parnames, parnames) res[,"shape","shape"] <- ifelse(t==0, 0, -shape*scale*log(t)*(t^shape + shape*log(t)*t^shape)) res[,"scale","scale"] <- -scale*t^shape res[,"shape","scale"] <- res[,"scale","shape"] <- ifelse(t==0, 0, - scale * shape* log(t) * t^shape) res } D2Ldgompertz <- function(t, shape, rate){ res <- array(dim=c(length(t), 2, 2)) parnames <- c("shape","rate") dimnames(res) <- list(NULL, parnames, parnames) res[shape==0,"shape","shape"] <- 0 res[shape==0,"rate","rate"] <- - rate[shape==0]*t[shape==0] res[shape==0,"shape","rate"] <- res[shape==0,"rate","shape"] <- 0 est <- exp(shape*t) sn0 <- (shape!=0) t <- t[sn0]; rate <- rate[sn0]; shape <- shape[sn0] res[sn0,"shape","shape"] <- 2*rate/shape^3*(1 - est) + 2*rate/shape^2*t*est - rate/shape*t^2*est res[sn0,"rate","rate"] <- rate/shape*(1 - est) res[sn0,"shape","rate"] <- res[sn0,"rate","shape"] <- -rate/shape*(1/shape*(1 - est) + t*est) res } D2LSgompertz <- function(t, shape, rate){ res <- array(dim=c(length(t), 2, 2)) parnames <- c("shape","rate") dimnames(res) <- list(NULL, parnames, parnames) res[shape==0,"shape","shape"] <- 0 res[shape==0,"rate","rate"] <- -rate[shape==0]*t[shape==0] res[shape==0,"shape","rate"] <- res[shape==0,"rate","shape"] <- 0 est <- exp(shape*t) sn0 <- (shape!=0) t <- t[sn0]; rate <- rate[sn0]; shape <- shape[sn0] res[sn0,"shape","shape"] <- 2*rate/shape^3*(1 - est) + 2*rate/shape^2*t*est - rate/shape*t^2*est res[sn0,"rate","rate"] <- rate/shape*(1 - est) res[sn0,"shape","rate"] <- res[sn0,"rate","shape"] <- -rate/shape*(1/shape*(1 - est) + t*est) res } D2Ldsurvspline <- function(t, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp"){ d <- dbase.survspline(q=t, gamma=gamma, knots=knots, scale=scale, deriv=2, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]); t <- q b <- basis(knots, tsfn(t,timescale), spline=spline) db <- dbasis(knots, tsfn(t,timescale), spline=spline) eta <- rowSums(b * gamma) + as.numeric(X %*% beta) ds <- rowSums(db * gamma) if (scale=="odds") { eeta <- 2*exp(eta)/(1 + exp(eta))^2 db <- dbasis(knots, tsfn(t,timescale), spline=spline) } npars <- ncol(gamma) for (i in 1:npars){ for (j in 1:npars){ if (scale=="hazard") ret[ind,i,j] <- -db[,i]*db[,j] / ds^2 - b[,i]*b[,j] * exp(eta) else if (scale=="odds") ret[ind,i,j] <- -db[,i]*db[,j] / ds^2 - b[,i]*b[,j] * eeta } } ret } D2LSsurvspline <- function(t, gamma, beta=0, X=0, knots=c(-10,10), scale="hazard", timescale="log", spline="rp"){ tmp_gamma <- gamma tmp_t <- t tmp_knots <- knots d <- dbase.survspline(q=t, gamma=gamma, knots=knots, scale=scale, deriv=2, spline=spline) for (i in seq_along(d)) assign(names(d)[i], d[[i]]); t <- q b <- basis(knots, tsfn(t,timescale), spline=spline) npars <- ncol(gamma) if (length(t) > 0){ eta <- rowSums(b * gamma) + as.numeric(X %*% beta) if (scale=="odds") { eeta <- exp(eta)/(1 + exp(eta))^2 } for (i in 1:npars){ for (j in 1:npars){ if (scale=="hazard") ret[ind,i,j] <- ifelse(t==0, 0, - b[,i]*b[,j]*exp(eta)) else if (scale=="odds") ret[ind,i,j] <- ifelse(t==0, 0, - b[,i]*b[,j] * eeta) } } } ret } d2deriv <- function(d2dfn, ddcall, X, mx, dlist){ res.base <- do.call(d2dfn, ddcall) res.beta <- D2cov(res.base, X, mx, dlist) # does this have to be in a different function? nobs <- dim(res.base)[1] nbasepars <- dim(res.base)[2] ncoveffs <- dim(res.beta[[1]])[2] npars <- nbasepars + ncoveffs res <- array(dim = c(nobs, npars, npars)) if (length(ddcall$t) > 0){ dimnames(res)[[2]] <- dimnames(res)[[3]] <- c(colnames(res.base), colnames(X)) baseinds <- seq_len(nbasepars) res[,baseinds,baseinds] <- res.base betainds <- nbasepars + seq_len(ncoveffs) res[,betainds,betainds] <- res.beta$ccres res[,baseinds,betainds] <- res.beta$bcres res[,betainds,baseinds] <- aperm(res.beta$bcres,c(1,3,2)) } res } D2cov <- function(res, X, mx, dlist){ ncoveffs <- length(unlist(mx)) nbpars <- length(mx) bcres <- array(dim = c(nrow(res), nbpars, ncoveffs)) basepars <- dimnames(res)[[2]] # ordered as in the distribution (used for baseline pars) basepars_locfirst <- names(mx) # ordered with location parameter first (used for covariate effects) dimnames(bcres)[[2]] <- basepars_locfirst inds <- c(0,cumsum(sapply(mx[basepars_locfirst],length))) ## second derivs wrt two covariate effects ccres <- array(dim = c(nrow(res), ncoveffs, ncoveffs)) for (i in seq_len(nbpars)) { mi <- mx[[basepars_locfirst[i]]] for (j in seq_along(mi)){ for (k in seq_len(nbpars)) { mk <- mx[[basepars_locfirst[k]]] for (l in seq_along(mk)){ ccres[,inds[i]+j,inds[k]+l] <- X[,mi[j]]*X[,mk[l]]*res[,basepars_locfirst[i],basepars_locfirst[k]] } } } } ## second derivs wrt baseline par x covariate effect for (i in seq_len(nbpars)) { for (j in seq_len(nbpars)) { mj <- mx[[basepars_locfirst[j]]] for (k in seq_along(mj)){ bcres[,i,inds[j]+k] <- X[,mj[k]] * res[,basepars[i],basepars_locfirst[j]] } } } list(ccres=ccres, bcres=bcres) } D2minusloglik.flexsurv <- function(optpars, Y, X=0, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars=NULL) { pars <- inits npars <- length(pars) pars[setdiff(seq_len(npars), fixedpars)] <- optpars nbpars <- length(dlist$pars) pars <- as.list(pars) ncovs <- length(pars) - length(dlist$pars) if (ncovs > 0) beta <- unlist(pars[(nbpars+1):npars]) for (i in dlist$pars) { if (length(mx[[i]]) > 0) pars[[i]] <- pars[[i]] + X[,mx[[i]],drop=FALSE] %*% beta[mx[[i]]] else pars[[i]] <- rep(pars[[i]], length(Y[,"stop"])) } dead <- Y[,"status"]==1 ddcall <- list(t=Y[dead,"stop"]) dsccall <- list(t=Y[!dead,"stop"]) dstcall <- list(t=Y[,"start"]) for (i in 1:nbpars) ddcall[[names(pars)[i]]] <- dsccall[[names(pars)[i]]] <- dstcall[[names(pars)[i]]] <- dlist$inv.transforms[[i]](pars[[i]]) for (i in seq_along(aux)){ ddcall[[names(aux)[i]]] <- dsccall[[names(aux)[i]]] <- dstcall[[names(aux)[i]]] <- aux[[i]] } for (i in dlist$pars) { ddcall[[i]] <- ddcall[[i]][dead] dsccall[[i]] <- dsccall[[i]][!dead] } dd <- d2deriv(dfns$D2Ld, ddcall, X[dead,,drop=FALSE], mx, dlist) dscens <- d2deriv(dfns$D2LS, dsccall, X[!dead,,drop=FALSE], mx, dlist) if (sum(dead) > 0) dd <- dd * weights[dead] if (sum(!dead) > 0) dscens <- dscens * weights[!dead] dstrunc <- d2deriv(dfns$D2LS, dstcall, X, mx, dlist) * weights res <- - ( apply(dd,2:3,sum) + apply(dscens,2:3,sum) - apply(dstrunc,2:3,sum) ) if (any(bhazard > 0)) { dcall <- ddcall dcall$x <- ddcall$t; dcall$t <- NULL dens <- do.call(dfns$d, dcall) pcall <- dcall pcall$q <- pcall$x; pcall$x <- NULL surv <- 1 - do.call(dfns$p, pcall) haz <- dens / surv bw <- bhazard[dead] offseti <- 1 / (1 + bw/haz) d1Ld <- dderiv(dfns$DLd, ddcall, X[dead,,drop=FALSE], mx, dlist) d2Ld <- d2deriv(dfns$D2Ld, ddcall, X[dead,,drop=FALSE], mx, dlist) d1LS <- dderiv(dfns$DLS, ddcall, X[dead,,drop=FALSE], mx, dlist) d2LS <- d2deriv(dfns$D2LS, ddcall, X[dead,,drop=FALSE], mx, dlist) dhazinv <- surv/dens*(d1LS - d1Ld) if (any(dead)){ ## given two matrices with dims (n,p), ## return array of dim(n,p,p) with outer product of each pair of matrix rows vouter <- function(y,z){ rows <- seq_len(nrow(y)) res <- mapply(outer, split(y, rows), split(z, rows), SIMPLIFY=FALSE) res <- array(unlist(res), dim=c(dim(res[[1]]), length(res))) # res <- simplify2array(res, except = NULL) # would do this, but needs R >= 4.2.0 aperm(res, c(3,1,2)) } doff <- - offseti*bw*(offseti*vouter(dhazinv, dhazinv)*bw + (d2Ld - d2LS)*surv/dens + vouter(d1Ld - d1LS, dhazinv)) res <- res - apply(doff*weights[dead],2:3,sum) } } ## currently wastefully calculates derivs for fixed pars then discards them optpars <- setdiff(1:npars, fixedpars) res[optpars,optpars] } hess.test <- function(optpars, Y, X, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars){ an.d <- D2minusloglik.flexsurv(optpars=optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) if (requireNamespace("numDeriv", quietly = TRUE)) num.d <- numDeriv::hessian(minusloglik.flexsurv, optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) else stop("\"numDeriv\" package not available") res <- list(analytic=an.d, numeric=num.d) list(res=res, error=mean(abs(an.d - num.d))) } flexsurv/R/fmixmsm.R0000644000176200001440000003012214366216636014147 0ustar liggesusers##' Constructor for a mixture multi-state model based on flexsurvmix ##' ##' @param ... Named arguments. Each argument should be a fitted model as ##' returned by \code{\link{flexsurvmix}}. The name of each argument names ##' the starting state for that model. ##' ##' @return A list of \code{\link{flexsurvmix}} objects, with the following ##' attribute(s): ##' ##' \code{pathways} A list of all potential pathways until absorption, for ##' models without cycles. For models with cycles this will have an element ##' \code{has_cycle=TRUE}, plus the pathways discovered before the function ##' found the cycle and gave up. ##' ##' @export fmixmsm <- function(...){ args <- list(...) starts <- names(args) evlist <- lapply(args, function(x)x$evnames) names(evlist) <- starts plist <- list(transient_unvisited = names(evlist), transient_visited = character(), pathways = list(), pathway_current = character()) pathways <- get_pathways(evlist[1], evlist, plist) ret <- args attr(ret, "pathways") <- pathways$pathways attr(ret, "cycle") <- isTRUE(pathways$has_cycle) attr(ret, "pathway_str") <- sapply(attr(ret, "pathways"), function(x)paste(x,collapse="-")) ret } get_pathways <- function(mod_current, mods, ret){ ## TODO error handling if (isTRUE(ret$has_cycle)) return(ret) fromstate <- names(mod_current) tostates <- mod_current[[1]] absorbing <- setdiff(unlist(mods),names(mods)) ret$transient_visited <- c(ret$transient_visited, fromstate) ret$transient_unvisited <- setdiff(ret$transient_unvisited, fromstate) nd <- length(tostates) pcurr <- c(ret$pathway_current, fromstate) for (j in 1:nd){ pathway_new <- c(pcurr, tostates[j]) if (any(duplicated(pathway_new))){ return(list(has_cycle=TRUE)) # could we carry on, ignore cycles, return all paths to absorption? don't do unless we need. } else if (tostates[j] %in% absorbing){ ret$pathways <- c(ret$pathways, list(pathway_new)) } else { ret$pathway_current <- pcurr ret <- get_pathways(mods[tostates[j]], mods, ret) } } ret } ##' Probability of each pathway taken through a mixture multi-state model ##' ##' ##' @param x Object returned by \code{\link{fmixmsm}}, representing a multi-state ##' model built from piecing together mixture models fitted by ##' \code{\link{flexsurvmix}}. ##' ##' @param final If \code{TRUE} then the probabilities of pathways with the same ##' final state are added together, to produce the probability of each ##' ultimate outcome or absorbing state from the multi-state model. ##' ##' @inheritParams mean_flexsurvmix ##' ##' @return Data frame of pathway probabilities by covariate value and pathway. ##' ##' ##' @export ppath_fmixmsm <- function(x, newdata=NULL, final=FALSE, B=NULL){ pathways <- attr(x, "pathways") if (isTRUE(pathways$has_cycle)) stop("models with cycles not supported in this function") nmods <- length(x) probs <- vector(nmods, mode="list") names(probs) <- names(x) for (i in seq_along(x)){ probs[[i]] <- probs_flexsurvmix(x[[i]], newdata=newdata) } npaths <- length(pathways) ppath <- vector(npaths, mode="list") for (p in seq_along(pathways)){ plen <- length(pathways[[p]]) ppath[[p]] <- 1 for (i in 1:(plen-1)){ cur_state <- pathways[[p]][i] next_state <- pathways[[p]][i+1] cur_prob <- probs[[cur_state]] ppath[[p]] <- ppath[[p]] * cur_prob$val[cur_prob$event==next_state] } } finalstate <- sapply(attr(x, "pathways"), function(x)x[length(x)]) ncovs <- if(is.null(newdata)) 1 else nrow(newdata) finalstate <- rep(finalstate, each=ncovs) pathway <- rep(attr(x, "pathway_str"), each=ncovs) ppath <- data.frame(final=finalstate, pathway=pathway, val = unlist(ppath)) if (!is.null(newdata)) { nd <- newdata[rep(seq_len(ncovs), npaths),,drop=FALSE] ppath <- cbind(nd, ppath) } rownames(ppath) <- NULL if (final) { ppath <- ppath %>% dplyr::group_by(dplyr::across(c(names(newdata), "final"))) %>% dplyr::reframe(val=sum(.data$val)) } if (is.numeric(B) && B > 1){ res <- matrix(nrow=B, ncol=length(ppath$val)) res[1,] <- ppath$val for (i in 2:B){ xrep <- resample_pars_fmixmsm(x) res[i,] <- ppath_fmixmsm(xrep, newdata=newdata, final=final, B=NULL)$val } resci <- apply(res, 2, quantile, c(0.025, 0.975), na.rm=TRUE) ppath$lower <- resci[1,] ppath$upper <- resci[2,] } as.data.frame(ppath) } resample_pars_fmixmsm <- function(x){ xrep <- lapply(x, resample_pars) attributes(xrep) <- attributes(x) xrep } ##' Mean time to final state in a mixture multi-state model ##' ##' Calculate the mean time from the start of the process to a final (or ##' "absorbing") state in a mixture multi-state model. Models with cycles are ##' not supported. ##' ##' @inheritParams ppath_fmixmsm ##' ##' @param final If \code{TRUE} then the mean time to the final state is ##' calculated for each final state, by taking a weighted average of the mean ##' time to travel each pathway ending in that final state, weighted by the ##' probability of the pathway. If \code{FALSE} (the default) then a ##' separate mean is calculated for each pathway. ##' ##' @return A data frame of mean times to absorption, by covariate values and ##' pathway (or by final state) ##' ##' @export meanfinal_fmixmsm <- function(x, newdata=NULL, final=FALSE, B=NULL){ pathways <- attr(x, "pathways") nmods <- length(x) means <- vector(nmods, mode="list") names(means) <- names(x) for (i in seq_along(x)){ means[[i]] <- mean_flexsurvmix(x[[i]], newdata=newdata) } npaths <- length(pathways) meanp <- vector(npaths, mode="list") for (p in seq_along(pathways)){ plen <- length(pathways[[p]]) meanp[[p]] <- 0 for (i in 1:(plen-1)){ cur_state <- pathways[[p]][i] next_state <- pathways[[p]][i+1] cur_mean <- means[[cur_state]] meanp[[p]] <- meanp[[p]] + cur_mean$val[cur_mean$event==next_state] } } finalstate <- sapply(attr(x, "pathways"), function(x)x[length(x)]) ncovs <- if(is.null(newdata)) 1 else nrow(newdata) finalstate <- rep(finalstate, each=ncovs) pathway <- rep(attr(x, "pathway_str"), each=ncovs) meanp <- data.frame(final=finalstate, pathway=pathway, val = unlist(meanp)) if (!is.null(newdata)) { nd <- newdata[rep(seq_len(ncovs), npaths),,drop=FALSE] meanp <- cbind(nd, meanp) } rownames(meanp) <- NULL if (final) { probs <- ppath_fmixmsm(x=x, newdata=newdata, final=FALSE, B=NULL) %>% dplyr::rename(prob="val") meanp <- meanp %>% dplyr::left_join(probs, by=c(names(newdata), "pathway", "final")) %>% dplyr::group_by(dplyr::across(c(names(newdata), "final"))) %>% dplyr::reframe(val=sum(.data$val*.data$prob)/sum(.data$prob)) } if (is.numeric(B) && B > 1){ res <- matrix(nrow=B, ncol=length(meanp$val)) res[1,] <- meanp$val for (i in 2:B){ xrep <- resample_pars_fmixmsm(x) res[i,] <- meanfinal_fmixmsm(xrep, newdata=newdata, final=final, B=NULL)$val } resci <- apply(res, 2, quantile, c(0.025, 0.975), na.rm=TRUE) meanp$lower <- resci[1,] meanp$upper <- resci[2,] } as.data.frame(meanp) } ##' Quantiles of the distribution of the time until reaching a final state in a ##' mixture multi-state model ##' ##' Calculate the quantiles of the time from the start of the process to each ##' possible final (or "absorbing") state in a mixture multi-state model. ##' Models with cycles are not supported. ##' ##' ##' @inheritParams ppath_fmixmsm ##' ##' @param final If \code{TRUE} then the mean time to the final state is ##' calculated for each final state, by taking a weighted average of the mean ##' time to travel each pathway ending in that final state, weighted by the ##' probability of the pathway. If \code{FALSE} (the default) then a ##' separate mean is calculated for each pathway. ##' ##' @param n Number of individual-level simulations to use to characterise the ##' time-to-event distributions ##' ##' @param probs Quantiles to calculate, by default, \code{c(0.025, 0.5, 0.975)} ##' ##' @return Data frame of quantiles of the time to final state by pathway and ##' covariate value, or by final state and covariate value. ##' ##' @export qfinal_fmixmsm <- function(x, newdata=NULL, final=FALSE, B=NULL, n=10000, probs=c(0.025, 0.5, 0.975)){ pathways <- attr(x, "pathways") nmods <- length(x) sims <- vector(nmods, mode="list") names(sims) <- names(x) if (final) { ppath <- ppath_fmixmsm(x=x, newdata=newdata, final=FALSE, B=NULL) %>% dplyr::rename(prob="val") %>% dplyr::mutate(n = round(n * .data$prob)) } for (i in seq_along(x)){ sims[[i]] <- simt_flexsurvmix(x[[i]], newdata=newdata, n=n) } npaths <- length(pathways) simsum <- vector(npaths, mode="list") for (p in seq_along(pathways)){ plen <- length(pathways[[p]]) sm <- 0 for (i in 1:(plen-1)){ cur_state <- pathways[[p]][i] next_state <- pathways[[p]][i+1] sm <- sm + sims[[cur_state]][,next_state] } simsumdf <- sims[[1]][,colnames(newdata),drop=FALSE] simsumdf$pathway <- attr(x,"pathway_str")[[p]] simsumdf$sm <- sm if (final){ simsum[[p]] <- simsumdf %>% dplyr::left_join(ppath, by=c("pathway", colnames(newdata))) %>% dplyr::group_by(dplyr::across(c(colnames(newdata)))) %>% ## Keep only the first n of the sampled rows ## where n is weighted by the prob of the pathway dplyr::group_modify(~{.x[1:.x$n[1],]}) } else { simsum[[p]] <- simsumdf %>% dplyr::group_by(dplyr::across(c("pathway", colnames(newdata)))) %>% dplyr::reframe(probs=probs, val = quantile(.data$sm, p=probs,na.rm=TRUE)) } } resq <- do.call("rbind", simsum) if (final){ resq <- resq %>% dplyr::ungroup() %>% dplyr::group_by(dplyr::across(c("final", colnames(newdata)))) %>% dplyr::reframe(probs=probs, val = quantile(.data$sm, p=probs,na.rm=TRUE)) } rownames(resq) <- NULL if (is.numeric(B) && B > 1){ res <- matrix(nrow=B, ncol=length(resq$val)) res[1,] <- resq$val for (i in 2:B){ xrep <- resample_pars_fmixmsm(x) res[i,] <- qfinal_fmixmsm(xrep, newdata=newdata, final=final, B=NULL, n=n, probs=probs)$val } resci <- apply(res, 2, quantile, c(0.025, 0.975), na.rm=TRUE) resq$lower <- resci[1,] resq$upper <- resci[2,] } as.data.frame(resq) } ##' Simulate times to competing events from a mixture multi-state model ##' ##' @inheritParams probs_flexsurvmix ##' ##' @param n Number of simulations ##' ##' @return Data frame with \code{n*m} rows and a column for each competing ##' event, where \code{m} is the number of alternative covariate values, that ##' is the number of rows of \code{newdata}. The simulated time represents ##' the time to that event conditionally on that event being the one that ##' occurs. This function doesn't simulate which event occurs. ##' simt_flexsurvmix <- function(x, newdata=NULL, n){ if (is.null(newdata)) newdata <- default_newdata(x) if (is.null(newdata)) { ncovvals <- 1 } else { newdata <- as.data.frame(newdata) ncovvals <- nrow(newdata) } simdf <- as.data.frame(matrix(nrow=n*ncovvals, ncol=x$K)) names(simdf) <- x$evnames for (k in 1:x$K){ pars <- get_basepars(x, newdata, k) pars$n <- n*ncovvals simdf[[k]] <- do.call(x$dfns[[k]]$r, pars) } if (!is.null(newdata)){ newdatarep <- newdata[rep(seq_len(ncovvals),n),,drop=FALSE] simdf <- cbind(newdatarep, simdf) simdf <- simdf[do.call("order", newdatarep),,drop=FALSE] } simdf } flexsurv/R/utils.R0000644000176200001440000003674314523727777013656 0ustar liggesusers### Standardised procedure for defining density, cumulative ### distribution, hazard and cumulative hazard functions for ### time-to-event distributions dbase <- function(dname, lower.tail=TRUE, log=FALSE, ...){ args <- list(...) ## Vectorise all arguments, replicating to length of longest argument n <- max(sapply(args, length)) for (i in seq_along(args)) { args[[i]] <- rep(args[[i]], length.out=n) } ret <- numeric(n) ## Check for parameters out of range, give warning and return NaN ## for those check.fn <- paste("check.",dname,sep="") check.ret <- do.call(check.fn, args[-1]) ret[!check.ret] <- NaN for (i in seq_along(args)) ret[is.nan(args[[i]])] <- NaN ## name of first arg is x for PDF, haz, or cum haz, q for CDF and p for quantile function stopifnot( !(names(args)[1]=="x" && lower.tail==FALSE)) if (names(args)[1] %in% c("x","q")){ x <- args[[1]] ## PDF, CDF, hazard and cumulative hazard is 0 for any negative time ret[!is.nan(ret) & (x<0)] <- if (lower.tail) { if (log) -Inf else 0 } else { if (log) 0 else 1 } } if (names(args)[1] == "p") { p <- args[[1]] if (log) p <- exp(p) if (!lower.tail) p <- 1 - p args[[1]] <- p ret[p < 0 | p > 1] <- NaN ## should be 0,Inf for p=0,1, but hopefully always handled anyway ## Result is NA if x or a parameter is NA } ## Result is NA if x or a parameter is NA nas <- rep(FALSE, n) for (i in seq_along(args)) nas <- nas | (is.na(args[[i]]) & !is.nan(args[[i]])) ret[nas] <- NA ind <- !is.nan(ret) & !nas if (names(args)[1] %in% c("x", "q")) ind <- ind & (x>=0) ## Any remaining elements of vector are filled in by standard ## formula for hazard li <- list(ret=ret, ind=ind) for(i in seq_along(args)) args[[i]] <- args[[i]][ind] c(li, args) } ### Standardised procedure for defining random sampling functions rbase <- function(dname, n, ...){ ## Vectorise all arguments, replicating to sample length if (length(n) > 1) n <- length(n) args <- list(...) for (i in seq_along(args)) { args[[i]] <- rep(args[[i]], length.out=n) } ret <- numeric(n) ## Check for parameters out of range, give warning and return NaN ## for those check.fn <- paste("check.",dname,sep="") check.ret <- do.call(check.fn, args) ret[!check.ret] <- NaN for (i in seq_along(args)) ret[is.nan(args[[i]])] <- NaN nas <- rep(FALSE, n) for (i in seq_along(args)) nas <- nas | (is.na(args[[i]]) & !is.nan(args[[i]])) ret[nas] <- NA ind <- !is.nan(ret) & !nas li <- list(ret=ret, ind=ind) for(i in seq_along(args)) args[[i]] <- args[[i]][ind] c(li, args) } ##' Generic function to find restricted mean survival time for some distribution ##' ##' Generic function to find the restricted mean of a distribution, given the ##' equivalent probability distribution function, using numeric integration. ##' ##' This function is used by default for custom distributions for which an ##' \code{rmst} function is not provided. ##' ##' This assumes a suitably smooth, continuous distribution. ##' ##' @param pdist Probability distribution function, for example, ##' \code{\link{pnorm}} for the normal distribution, which must be defined in ##' the current workspace. This should accept and return vectorised parameters ##' and values. It should also return the correct values for the entire real ##' line, for example a positive distribution should have \code{pdist(x)==0} ##' for \eqn{x<0}. ##' ##' @param t Vector of times at which rmst is evaluated ##' ##' @param start Optional left-truncation time or times. The returned ##' restricted mean survival will be conditioned on survival up to ##' this time. ##' ##' @param matargs Character vector giving the elements of \code{...} which ##' represent vector parameters of the distribution. Empty by default. When ##' vectorised, these will become matrices. This is used for the arguments ##' \code{gamma} and \code{knots} in \code{\link{psurvspline}}. ##' ##' @param scalarargs Character vector naming scalar arguments of the distribution function that cannot be vectorised. This is used, for example, for the arguments \code{scale} and \code{timescale} in \code{\link{psurvspline}}. ##' ##' @param ... The remaining arguments define parameters of the distribution ##' \code{pdist}. These MUST be named explicitly. ##' ##' @return Vector of restricted mean survival times of the distribution at ##' \code{p}. ##' ##' @author Christopher Jackson ##' ##' @keywords distribution ##' ##' @examples ##' ##' rmst_lnorm(500, start=250, meanlog=7.4225, sdlog = 1.1138) ##' rmst_generic(plnorm, 500, start=250, meanlog=7.4225, sdlog = 1.1138) ##' # must name the arguments ##' ##' @export rmst_generic <- function(pdist, t, start=0, matargs=NULL, scalarargs=NULL, ...) { args <- list(...) args_mat <- args[matargs] args_scalar <- args[scalarargs] args[c(matargs,scalarargs)] <- NULL matlen <- if(is.null(matargs)) NULL else sapply(args_mat, function(x){if(is.matrix(x))nrow(x) else 1}) veclen <- if (length(args) == 0) NULL else sapply(args, length) t_len <- length(t) maxlen <- max(c(t_len, veclen, matlen)) if(length(start) == 1) start <- rep(start, length.out=maxlen) na_inds <- rep(FALSE, maxlen) for (i in seq_along(args)){ args[[i]] <- rep(args[[i]], length.out=maxlen) na_inds <- na_inds | is.na(args[[i]]) } t <- rep(t, length.out=maxlen) for (i in seq_along(args_mat)){ if (is.matrix(args_mat[[i]])){ args_mat[[i]] <- matrix( apply(args_mat[[i]], 2, function(x)rep(x, length.out=maxlen)), ncol=ncol(args_mat[[i]]), byrow=F ) } else args_mat[[i]] <- matrix(args_mat[[i]], nrow=maxlen, ncol=length(args_mat[[i]]), byrow=TRUE) na_inds <- na_inds | apply(args_mat[[i]], 1, anyNA) } ret <- numeric(maxlen) ret[na_inds] <- NA for (i in seq_len(maxlen)[!na_inds]){ fargs_vec <- lapply(args, function(x)x[i]) fargs_mat <- lapply(args_mat, function(x)x[i,,drop=FALSE]) pdargs <- c(list(start[i]), fargs_vec, fargs_mat, args_scalar) start_p <- 1 - do.call(pdist, pdargs) fn <- function(end){ pdargs <- c(list(end), fargs_vec, fargs_mat, args_scalar) pd <- do.call(pdist, pdargs) (1 - pd) / start_p } ret[i] <- integrate(fn, start[i], t[i])$value } ret[t x].). ##' ##' If the distribution is bounded above or below, then this should contain ##' arguments \code{lbound} and \code{ubound} respectively, and these will be ##' returned if \code{p} is 0 or 1 respectively. Defaults to \code{-Inf} and ##' \code{Inf} respectively. ##' ##' @return Vector of quantiles of the distribution at \code{p}. ##' ##' @author Christopher Jackson ##' ##' @keywords distribution ##' ##' @examples ##' ##' qnorm(c(0.025, 0.975), 0, 1) ##' qgeneric(pnorm, c(0.025, 0.975), mean=0, sd=1) # must name the arguments ##' @export qgeneric <- function(pdist, p, matargs=NULL, scalarargs=NULL, ...) { args <- list(...) if (is.null(args$log.p)) args$log.p <- FALSE if (is.null(args$lower.tail)) args$lower.tail <- TRUE if (is.null(args$lbound)) args$lbound <- -Inf if (is.null(args$ubound)) args$ubound <- Inf if (args$log.p) p <- exp(p) if (!args$lower.tail) p <- 1 - p ret <- numeric(length(p)) ret[p == 0] <- args$lbound ret[p == 1] <- args$ubound ## args containing vector params of the distribution (e.g. gamma and knots in dsurvspline) args.mat <- args[matargs] ## Arguments that cannot be vectorised args.scalar <- args[scalarargs] args[c(matargs,scalarargs,"lower.tail","log.p","lbound","ubound")] <- NULL ## Other args assumed to contain vectorisable parameters of the distribution. ## Replicate all to their maximum length, along with p matlen <- if(is.null(matargs)) NULL else sapply(args.mat, function(x){if(is.matrix(x))nrow(x) else 1}) veclen <- if (length(args) == 0) NULL else sapply(args, length) maxlen <- max(c(length(p), veclen, matlen)) na_inds <- rep(FALSE, length(ret)) for (i in seq_along(args)){ args[[i]] <- rep(args[[i]], length.out=maxlen) na_inds <- na_inds | is.na(args[[i]]) } for (i in seq_along(args.mat)){ if (is.matrix(args.mat[[i]])){ args.mat[[i]] <- matrix( apply(args.mat[[i]], 2, function(x)rep(x, length.out=maxlen)), ncol=ncol(args.mat[[i]]), byrow=F ) } else args.mat[[i]] <- matrix(args.mat[[i]], nrow=maxlen, ncol=length(args.mat[[i]]), byrow=TRUE) na_inds <- na_inds | apply(args.mat[[i]], 1, anyNA) } p <- rep(p, length.out=maxlen) ret[p < 0 | p > 1] <- NaN ret[na_inds] <- NA ind <- (p > 0 & p < 1 & !na_inds) if (any(ind)) { hind <- seq_along(p)[ind] n <- length(p[ind]) ptmp <- numeric(n) interval <- matrix(rep(c(-1, 1), n), ncol=2, byrow=TRUE) h <- function(y) { args <- lapply(args, function(x)x[hind]) args.mat <- lapply(args.mat, function(x)x[hind,]) p <- p[hind] args$q <- y args <- c(args, args.mat, args.scalar) (do.call(pdist, args) - p) } ptmp <- rstpm2::vuniroot(h, interval, tol=.Machine$double.eps, extendInt="yes", maxiter=10000)$root ret[ind] <- ptmp } if (any(is.nan(ret))) warning("NaNs produced") ret } ## suppresses NOTE from checker about variables created with "assign" if(getRversion() >= "2.15.1") utils::globalVariables(c("ind")) ##' helper function to safely convert a Hessian matrix to covariance matrix ##' ##' @param hessian hessian matrix to convert to covariance matrix (must be evaluated at MLE) ##' @param tol.solve tolerance used for solve() ##' @param tol.evalues accepted tolerance for negative eigenvalues of the covariance matrix ##' @param ... arguments passed to Matrix::nearPD ##' ##' @importFrom Matrix nearPD ##' @keywords internal .hess_to_cov <- function(hessian, tol.solve = 1e-9, tol.evalues = 1e-5, ...) { if(is.null(tol.solve)) tol.solve <- .Machine$double.eps if(is.null(tol.evalues)) tol.evalues <- 1e-5 # use solve(.) over chol2inv(chol(.)) to get an inverse even if not PD # less efficient but more stable inv_hessian <- solve(hessian, tol = tol.solve) if (any(is.infinite(inv_hessian))) stop("Inverse Hessian has infinite values. This might indicate that the model is too complex to be identifiable from the data") evalues <- eigen(inv_hessian, symmetric = TRUE, only.values = TRUE)$values if (min(evalues) < -tol.evalues) warning(sprintf( "Hessian not positive definite: smallest eigenvalue is %.1e (threshold: %.1e). This might indicate that the optimization did not converge to the maximum likelihood, so that the results are invalid. Continuing with the nearest positive definite approximation of the covariance matrix.", min(evalues), -tol.evalues )) # make sure we return a plain positive definite symmetric matrix as.matrix(Matrix::nearPD(inv_hessian, ensureSymmetry = TRUE, ...)$mat) } #' Numerical evaluation of the hessian of a function using numDeriv::hessian #' #' We perform a quick check about the expected runtime and adjust the #' precision accordingly. #' #' @param f function to compute Hessian for #' @param x location to evaluate Hessian at #' @param seconds.warning time threshold in seconds to trigger message and #' reduce the number of iterations for Richardson extrapolation of #' numDeriv::hessian #' @param default.r default number of iterations (high-precision recommendation #' of numDeriv) #' @param min.r minial number of iteration, must be at least 2, #' @param ... further arguments passed to method.args of numDeriv::hessian #' #' @importFrom numDeriv hessian #' @keywords internal .hessian <- function(f, x, seconds.warning = 60, default.r = 6, min.r = 2, ...) { # dimensionality of the problem k <- length(x) # estimate evaluation time of f(x) start_time <- Sys.time() for (i in 1:3) f(x) mean_eval_sec <- as.numeric(difftime(Sys.time(), start_time, units = "secs"))/3 default_runtime <- mean_eval_sec * (1 + default.r*(k^2 + k)) # reduce iterations for Richardson extrapolation if (default_runtime > seconds.warning) { r <- default.r runtime <- default_runtime while ((r > min.r) & (runtime > seconds.warning)) { r <- r - 1 runtime <- mean_eval_sec * (1 + r*(k^2 + k)) } message(sprintf( "estimated runtime for evaluating the hessian with r=%i is %i minutes, reducing r to %i, estimated runtime is %i minutes", default.r, round(default_runtime/60), r, round(runtime/60) )) } else { r <- default.r } numDeriv::hessian(f, x, method = "Richardson", method.args = list(r = r, ...)) } check_numeric <- function(...){ args <- list(...) nm <- names(args) for (i in seq_along(args)){ nm <- names(args)[i] nmstr <- if (is.null(nm) || nm=="") "" else sprintf(" for `%s`", nm) if (!is.numeric(args[[i]])) stop(sprintf("Non-numeric value supplied%s", nmstr)) } } flexsurv/R/standsurv.R0000644000176200001440000015526714603753345014537 0ustar liggesusers#' Marginal survival and hazards of fitted flexsurvreg models #' #' Returns a tidy data.frame of marginal survival probabilities, or hazards, #' restricted mean survival, or quantiles of the marginal survival function #' at user-defined time points and covariate patterns. #' Standardization is performed over any undefined covariates in the model. #' The user provides the data to standardize over. Contrasts can be calculated #' resulting in estimates of the average treatment effect or the average #' treatment effect in the treated if a treated subset of the data are supplied. #' #' The syntax of \code{standsurv} follows closely that of Stata's #' \code{standsurv} command written by Paul Lambert and Michael Crowther. The #' function calculates standardized (marginal) measures including standardized #' survival functions, standardized restricted mean survival times, quantiles #' and the hazard of standardized survival. The standardized survival is defined as #' \deqn{S_s(t|X=x) = E(S(t|X=x,Z)) = \frac{1}{N} \sum_{i=1}^N S(t|X=x,Z=z_i)}{S(t|X=x) = E[S(t|X=x,Z)] = 1/N * sum(S(t|X=x,Z=z_i))} #' The hazard of the standardized survival is a weighted average of #' individual hazard functions at time t, weighted by the survival #' function at this time: #' \deqn{h_s(t|X=x) = \frac{\sum_{i=1}^N S(t|X=x,Z=z_i)h(t|X=x,Z=z_i)}{\sum_{i=1}^N S(t|X=x,Z=z_i)}}{h(t|X=x) = sum(S(t|X=x,Z=z_i) * h(t|X=x,Z=z_i)) / sum(S(t|X=x,Z=z_i))} #' Marginal expected survival and hazards can be calculated by providing a #' population-based lifetable of class ratetable in \code{ratetable} and a #' mapping between stratification factors in the lifetable and the user dataset #' using \code{rmap}. If these stratification factors are not in the fitted #' survival model then the user must specify them in \code{newdata} along with #' the covariates of the model. The marginal expected survival is calculated #' using the "Ederer" method that assumes no censoring as this is most relevant #' approach for forecasting (see #' \code{\link[survival]{survexp}}). A worked example is given below. #' #' Marginal all-cause survival and hazards can be calculated after fitting a #' relative survival model, which utilise the expected survival from a population #' ratetable. See Rutherford et al. (Chapter 6) for further details. #' #' #' @param object Output from \code{\link{flexsurvreg}} or #' \code{\link{flexsurvspline}}, representing a fitted survival model object. #' @param newdata Data frame containing covariate values to produce marginal ##' values for. If not specified then the fitted model data.frame is used. ##' There must be a column for every covariate in the model formula ##' for which the user wishes to standardize over. These are in the same format ##' as the original data, with factors as a single variable, not 0/1 contrasts. ##' Any covariates that are to be fixed should be specified in \code{at}. ##' There should be one row for every combination of covariates in which to ##' standardize over. If newdata contains a variable named '(weights)' then a ##' weighted mean will be used to create the standardized estimates. This is the ##' default behaviour if the fitted model contains case weights, which are stored ##' in the fitted model data.frame. #' @param at A list of scenarios in which specific covariates are fixed to #' certain values. Each element of \code{at} must itself be a list. For example, #' for a covariate \code{group} with levels "Good", "Medium" and "Poor", the #' standardized survival plots for each group averaging over all other #' covariates is specified using #' \code{at=list(list(group="Good"), list(group="Medium"), list(group="Poor"))}. #' @param atreference The reference scenario for making contrasts. Default is 1 #' (i.e. the first element of \code{at}). #' @param type \code{"survival"} for marginal survival probabilities. In a #' relative survival framework this returns the marginal all-cause survival #' (see details). ##' ##' \code{"hazard"} for the hazard of the marginal survival probability. In a #' relative survival framework this returns the marginal all-cause hazard #' (see details). ##' ##' \code{"rmst"} for standardized restricted mean survival. ##' ##' \code{"relsurvival"} for marginal relative survival (can only be specified ##' if a relative survival model has been fitted in flexsurv). ##' ##' \code{"excesshazard"} for marginal excess hazards (can only be specified ##' if a relative survival model has been fitted in flexsurv). ##' ##' \code{"quantile"} for quantiles of the marginal all-cause survival ##' distribution. The \code{quantiles} option also needs to be provided. #' @param t Times to calculate marginal values at. #' @param ci Should confidence intervals be calculated? #' Defaults to FALSE #' @param se Should standard errors be calculated? #' Defaults to FALSE #' @param boot Should bootstrapping be used to calculate standard error and #' confidence intervals? Defaults to FALSE, in which case the delta method is #' used #' @param B Number of bootstrap simulations from the normal asymptotic #' distribution of the estimates used to calculate confidence intervals or #' standard errors. Decrease for greater speed at the expense of accuracy. Only #' specify if \code{boot = TRUE} #' @param cl Width of symmetric confidence intervals, relative to 1. #' @param trans Transformation to apply when calculating standard errors via the #' delta method to obtain confidence intervals. The default transformation is #' "log". Other possible names are "none", "loglog", "logit". #' @param contrast Contrasts between standardized measures defined by \code{at} #' scenarios. Options are \code{"difference"} and \code{"ratio"}. There will be #' n-1 new columns created where n is the number of \code{at} scenarios. Default #' is NULL (i.e. no contrasts are calculated). #' @param trans.contrast Transformation to apply when calculating standard errors #' for contrasts via the delta method to obtain confidence intervals. The default #' transformation is "none" for differences in survival, hazard, quantiles, or RMST, #' and "log" for ratios of survival, hazard, quantiles or RMST. #' @param seed The random seed to use (for bootstrapping confidence intervals) #' @param rmap An list that maps data set names to expected ratetable names. #' This must be specified if all-cause survival and hazards are required after #' fitting a relative survival model. This can also be specified if expected #' rates are required for plotting purposes. See the details section below. #' @param ratetable A table of expected event rates #' (see \code{\link[survival]{ratetable}}) #' @param scale.ratetable Transformation from the time scale of the fitted #' flexsurv model to the time scale in \code{ratetable}. For example, if the #' analysis time of the fitted model is in years and the ratetable is in #' units/day then we should use \code{scale.ratetable = 365.25}. This is the #' default as often the ratetable will be in units/day (see example). #' @param n.gauss.quad Number of Gaussian quadrature points used for integrating #' the all-cause survival function when calculating RMST in a relative survival #' framework (default = 100) #' @param quantiles If \code{type="quantile"}, this specifies the quantiles of #' the survival time distribution to return estimates for. #' @param interval Interval of survival times for quantile root finding. #' Default is c(1e-08, 500). #' #' @return A \code{tibble} containing one row for each #' time-point. The column naming convention is \code{at{i}} for the ith scenario #' with corresponding confidence intervals (if specified) named \code{at{i}_lci} #' and \code{at{i}_uci}. Contrasts are named \code{contrast{k}_{j}} for the #' comparison of the kth versus the jth \code{at} scenario. #' #' In addition tidy long-format data.frames are returned in the attributes #' \code{standsurv_at} and \code{standsurv_contrast}. These can be passed to #' \code{ggplot} for plotting purposes (see \code{\link{plot.standsurv}}). #' @importFrom tibble as_tibble #' @importFrom rlang := #' @importFrom dplyr bind_cols #' @importFrom dplyr inner_join #' @export #' @author Michael Sweeting #' @references Paul Lambert, 2021. "STANDSURV: Stata module to compute #' standardized (marginal) survival and related functions," #' Statistical Software Components S458991, Boston College Department of #' Economics. https://ideas.repec.org/c/boc/bocode/s458991.html #' #' Rutherford, MJ, Lambert PC, Sweeting MJ, Pennington B, Crowther MJ, Abrams KR, #' Latimer NR. 2020. "NICE DSU Technical Support Document 21: Flexible Methods #' for Survival Analysis" #' https://nicedsu.sites.sheffield.ac.uk/tsds/flexible-methods-for-survival-analysis-tsd #' #' @examples #'## mean age is higher in those with smaller observed survival times #' newbc <- bc #' set.seed(1) #' newbc$age <- rnorm(dim(bc)[1], mean = 65-scale(newbc$recyrs, scale=FALSE), #' sd = 5) #' #' ## Fit a Weibull flexsurv model with group and age as covariates #' weib_age <- flexsurvreg(Surv(recyrs, censrec) ~ group+age, data=newbc, #' dist="weibull") #' #'## Calculate standardized survival and the difference in standardized survival #'## for the three levels of group across a grid of survival times #'standsurv_weib_age <- standsurv(weib_age, #' at = list(list(group="Good"), #' list(group="Medium"), #' list(group="Poor")), #' t=seq(0,7, length.out=100), #' contrast = "difference", ci=FALSE) #'standsurv_weib_age #' #'## Calculate hazard of standardized survival and the marginal hazard ratio #'## for the three levels of group across a grid of survival times #'## 10 bootstraps for confidence intervals (this should be larger) #'\dontrun{ #'haz_standsurv_weib_age <- standsurv(weib_age, #' at = list(list(group="Good"), #' list(group="Medium"), #' list(group="Poor")), #' t=seq(0,7, length.out=100), #' type="hazard", #' contrast = "ratio", boot = TRUE, #' B=10, ci=TRUE) #'haz_standsurv_weib_age #'plot(haz_standsurv_weib_age, ci=TRUE) #'## Hazard ratio plot shows a decreasing marginal HR #'## Whereas the conditional HR is constant (model is a PH model) #'plot(haz_standsurv_weib_age, contrast=TRUE, ci=TRUE) #' #'## Calculate standardized survival from a Weibull model together with expected #'## survival matching to US lifetables #' #'# age at diagnosis in days. This is required to match to US ratetable, whose #'# timescale is measured in days #'newbc$agedays <- floor(newbc$age * 365.25) #'## Create some random diagnosis dates centred on 01/01/2010 with SD=1 year #'## These will be used to match to expected rates in the lifetable #'newbc$diag <- as.Date(floor(rnorm(dim(newbc)[1], #' mean = as.Date("01/01/2010", "%d/%m/%Y"), sd=365)), #' origin="1970-01-01") #'## Create sex (assume all are female) #'newbc$sex <- factor("female") #'standsurv_weib_expected <- standsurv(weib_age, #' at = list(list(group="Good"), #' list(group="Medium"), #' list(group="Poor")), #' t=seq(0,7, length.out=100), #' rmap=list(sex = sex, #' year = diag, #' age = agedays), #' ratetable = survival::survexp.us, #' scale.ratetable = 365.25, #' newdata = newbc) #'## Plot marginal survival with expected survival superimposed #'plot(standsurv_weib_expected, expected=TRUE) #'} standsurv <- function(object, newdata = NULL, at = list(list()), atreference = 1, type = "survival", t = NULL, ci = FALSE, se = FALSE, boot = FALSE, B = NULL, cl =0.95, trans = "log", contrast = NULL, trans.contrast = NULL, seed = NULL, rmap, ratetable, scale.ratetable = 365.25, n.gauss.quad = 100, quantiles = 0.5, interval = c(1e-08, 500)) { x <- object if(!is.null(seed)) set.seed(seed) ## Add checks ## Currently type is restricted to survival, hazard, rmst, quantile, or relsurvival or excesshazard (for relative survival models) type <- match.arg(type, c("survival", "hazard", "rmst", "quantile", "relsurvival", "excesshazard")) # Check that models is a relative survival model if relsurv or excesshazard are specified if(type %in% c("relsurvival", "excesshazard") & !("bhazard" %in% names(x$call))){ stop(paste0(type, " can only be specified for a relative survival flexsurv model")) } type2 <- type ## Checks for relative survival models if("bhazard" %in% names(x$call)){ if(type %in% c("quantile", "survival", "hazard") & (missing(rmap) | missing(ratetable))) stop("'rmap' and 'ratetable' must be specified to calculate all-cause survival/hazard in a relative survival model") # Swap type to acsurvival (all-cause survival) or achazard (all-cause hazard) if survival or hazard is specified # Swap type to survival or hazard if relsurv or excesshazard are specified type2 <- switch(type, "survival"= "acsurvival", "hazard"= "achazard", "quantile" = "acquantile", "relsurvival" = "survival", "excesshazard" = "hazard", "rmst" = "acrmst" ) if(type2 == "acsurvival") message("Marginal all-cause survival will be calculated") if(type2 == "achazard") message("Marginal all-cause hazard will be calculated") if(type2 == "acquantile") message("Quantiles of marginal all-cause survival will be calculated") if(type2 == "acrmst"){ message("Marginal restricted mean survival will be calculated") if(length(t)>2){ message("Marginal RMST is currently slow. We suggest using only one or two time points") } } if(!missing(rmap) & is.null(newdata)) stop("Must provide a 'newdata' data.frame containing all covariates and matching variables with 'rmap'") } # checks for type="quantile" if(type == "quantile" & !is.numeric(quantiles)) stop("'quantiles' argument must be provided as a numeric vector for type='quantile'") if(!is.null(contrast)) { contrast <- match.arg(contrast, c("difference", "ratio")) if(is.null(trans.contrast)){ trans.contrast <- ifelse(contrast=="difference", "none", "log") trans.contrast <- match.arg(trans.contrast, c("log", "none", "loglog", "logit")) } } trans <- match.arg(trans, c("log", "none", "loglog", "logit")) ## Check that at is a list and that all elements of at are lists if(!is.list(at)){ stop("'at' must be at list") } if (!all(sapply(at, is.list))) { stop("All elements of 'at' must be lists") } ## Check sensible transformations have been specified for type if(boot == F & type %in% c("hazard", "rmst", "quantile") & trans %in% c("loglog", "logit")){ warning(paste0("type ",type, " with transformation ",trans, " may not be sensible")) } if(boot == F & !is.null(B)){ stop(paste0("'boot'=FALSE but 'B' is non-null")) } if(boot == T & is.null(B)){ stop(paste("'B' must be specified if 'boot'=TRUE")) } ## Contrast numbers cnums <- (1:length(at))[-atreference] ## If no contrasts (i.e. only one at() list) then 'contrast' should be NULL if(length(cnums)==0 & !is.null(contrast)){ stop("'contrast' cannot be specified if length of 'at' < 2") } ## Standardize over fitted dataset by default if(is.null(newdata)){ data <- model.frame(x) } else{ data <- newdata } ## Was weighted regression used, and do these weights feature in newdata? weighted <- FALSE if("(weights)" %in% names(data)){ if(var(data$`(weights)`)!=0){ weighted <- TRUE message("Weighted regression was used, standardization will be weighted accordingly") } } ## Set t to be unique event times if NULL if(is.null(t)) t <- sort(unique(x$data$Y[,"stop"])) ## Calculate individual expected survival and expected hazard if((!missing(rmap) & !missing(ratetable))){ message("Calculating marginal expected survival and hazard") expsurv <- expsurv.fn(t, substitute(rmap), ratetable, data, weighted, scale.ratetable) } else expsurv <- NULL ## Loop over at() stand.pred.list <- dat.list <- list() for(i in 1:length(at)){ dat <- data covs <- at[[i]] covnames <- names(covs) ## If all covariates have been specified in 'at' then we have no further covariates ## to standardize over, so just use 1 row of data ## do not use this shortcut for type2 = "acsurvival", type2 = "achazard", type = "acrmst" ## or type = "acquantile" as we require individual expected survivals for these methods allcovs <- all.vars(formula(x)[-2]) if(all(allcovs %in% covnames) & !weighted & !(type2 %in% c("acsurvival", "achazard", "acrmst", "acquantile"))){ dat <- dat[1,,drop=F] } ## If at is not specified then no further manipulation of data is required, ## we standardize over original or passes dataset if(!is.null(covnames)){ for(j in 1:length(covnames)) dat[, covnames[j]] <- covs[j] } dat.list[[i]] <- dat predsum <- standsurv.fn(object, type = type2, newdata=dat, t=t, i=i, weighted=weighted, expsurv=expsurv, rmap=substitute(rmap), ratetable=ratetable, scale.ratetable=scale.ratetable, quantiles=quantiles, interval=interval, n.gauss.quad=n.gauss.quad) if(ci == TRUE | se == TRUE){ if(boot == TRUE){ if(i==1) message("Calculating bootstrap standard errors / confidence intervals") rawsim <- NULL bootresults <- boot.standsurv(object, B, dat, i, t, type, type2, weighted, se, ci, cl, rawsim, predsum, expsurv, rmap=substitute(rmap), ratetable=ratetable, scale.ratetable=scale.ratetable, quantiles=quantiles, interval=interval, n.gauss.quad=n.gauss.quad) stand.pred.list[[i]] <- bootresults$stand.pred predsum <- bootresults$predsum if(is.null(rawsim)) rawsim <- bootresults$rawsim } else{ if(i==1) message("Calculating standard errors / confidence intervals using delta method") predsum <- deltamethod.standsurv(object, newdata=dat, type2, t, i, se, ci, predsum, trans, cl, weighted, expsurv, rmap=substitute(rmap), ratetable=ratetable, scale.ratetable=scale.ratetable, quantiles=quantiles, interval=interval, n.gauss.quad=n.gauss.quad) } } if(i == 1) { standpred <- predsum } else { by <- ifelse(type2 %in% c("quantile","acquantile"), "probability", "time") standpred <- standpred %>% inner_join(predsum, by = by) } } if (anyNA(standpred)) warning("Missing values present in newdata") if(!is.null(contrast)){ if(boot == TRUE){ if(ci==TRUE | se==TRUE) message("Calculating bootstrap standard errors / confidence intervals for contrasts") if(contrast == "difference"){ for(i in cnums){ standpred <- standpred %>% mutate("contrast{i}_{atreference}" := .data[[paste0("at", i)]] - .data[[paste0("at", atreference)]]) if(ci == TRUE){ stand.pred.quant <- apply(stand.pred.list[[i]] - stand.pred.list[[atreference]], 2, function(x)quantile(x, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE)) stand.pred.quant <- as_tibble(t(stand.pred.quant)) %>% rename("contrast{i}_{atreference}_lci" := "2.5%", "contrast{i}_{atreference}_uci" := "97.5%") standpred <- standpred %>% bind_cols(stand.pred.quant) } if(se == TRUE){ stand.pred.se <- tibble("contrast{i}_{atreference}_se" := apply(stand.pred.list[[i]] - stand.pred.list[[atreference]], 2, sd, na.rm=TRUE)) standpred <- standpred %>% bind_cols(stand.pred.se) } } } if(contrast == "ratio"){ for(i in cnums){ standpred <- standpred %>% mutate("contrast{i}_{atreference}" := .data[[paste0("at", i)]] / .data[[paste0("at", atreference)]]) if(ci == TRUE){ stand.pred.quant <- apply(stand.pred.list[[i]] / stand.pred.list[[atreference]], 2, function(x)quantile(x, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE)) stand.pred.quant <- as_tibble(t(stand.pred.quant)) %>% rename("contrast{i}_{atreference}_lci" := "2.5%", "contrast{i}_{atreference}_uci" := "97.5%") standpred <- standpred %>% bind_cols(stand.pred.quant) } if(se == TRUE){ stand.pred.se <- tibble("contrast{i}_{atreference}_se" := apply(stand.pred.list[[i]] / stand.pred.list[[atreference]], 2, sd, na.rm=TRUE)) standpred <- standpred %>% bind_cols(stand.pred.se) } } } } else { if(ci==TRUE | se==TRUE) message("Calculating standard errors / confidence intervals for contrasts using delta method") for(i in cnums){ standpred <- deltamethod.contrast.standsurv(object, dat=dat.list[[i]], dat.ref=dat.list[[atreference]], type2, t, i, atreference, se, ci, standpred, trans.contrast, cl, contrast, weighted, expsurv, rmap=substitute(rmap), ratetable=ratetable, scale.ratetable=scale.ratetable, quantiles=quantiles, interval=interval, n.gauss.quad=n.gauss.quad) } } } label <- unlist(lapply(at,function(k){paste(names(k),k,sep="=",collapse=", ")})) attr(standpred, "label") <- label attr(standpred, "type") <- type attr(standpred, "contrast") <- contrast attr(standpred, "at") <- at attr(standpred, "atreference") <- atreference if(!is.null(expsurv)){ attr(standpred, "expected") <- expsurv$marginal } class(standpred) <- c("standsurv", class(standpred)) ## Create tidy versions of the data.frame and store as attributes standpred <- tidy(standpred) standpred } #' @importFrom dplyr group_by #' @importFrom dplyr summarise #' @importFrom dplyr left_join #' @importFrom dplyr slice #' @importFrom dplyr n #' @importFrom dplyr ungroup #' @importFrom statmod gauss.quad #' @import rlang standsurv.fn <- function(object, type, newdata, t, i, trans="none", weighted, expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad){ tr.fun <- tr(trans) if(! type %in% c("hazard", "acsurvival", "achazard", "acrmst", "quantile", "acquantile")){ predsum <- standsurv.fn.generic(t, object, type, newdata, i, weighted, tr.fun) } else if(type == "hazard"){ predsum <- standsurv.fn.hazard(t, object, newdata, i, weighted, tr.fun) } else if(type == "quantile"){ predsum <- standsurv.fn.quantile(object, newdata, i, weighted, tr.fun, quantiles, interval) } else if(type=="acsurvival"){ predsum <- standsurv.fn.acsurvival(t, object, newdata, i, weighted, tr.fun, expsurv) } else if(type=="achazard"){ predsum <- standsurv.fn.achazard(t, object, newdata, i, weighted, tr.fun, expsurv) } else if(type=="acrmst"){ pred <- standsurv.fn.acrmst(t, object, newdata, i, rmap, ratetable, scale.ratetable, weighted, tr.fun, n.gauss.quad) predsum <- tibble(time=t, "at{i}":=pred) } else if(type=="acquantile"){ predsum <- standsurv.fn.acquantile(t, object, newdata, i, rmap, ratetable, scale.ratetable, weighted, tr.fun, quantiles, interval) } predsum } # generic standardisation function, for use with types "survival", "relsurv", "excesshazard" standsurv.fn.generic <- function(t, object, type, newdata, i, weighted, tr.fun){ pred <- summary(object, type = type, tidy = T, newdata=newdata, t=t, ci=F) pred$levels.fct <- factor(seq_along(t)) if(weighted){ pred$weights <- rep(newdata$`(weights)`, each=length(t)) predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(weighted.mean(.data$est, .data$weights))) %>% ungroup() %>% select(-levels.fct) } else{ predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(mean(.data$est))) %>% ungroup() %>% select(-levels.fct) } predsum } # hazard standardisation function, for use with type "hazard" standsurv.fn.hazard <- function(t, object, newdata, i, weighted, tr.fun){ pred <- summary(object, type = "hazard", tidy = T, newdata=newdata, t=t, ci=F) names(pred)[names(pred)=="est"] <- "h" pred <- cbind(pred, S = summary(object, type = "survival", tidy = T, newdata=newdata, t=t, ci=F)[,"est"]) pred$levels.fct <- factor(seq_along(t)) if(weighted){ pred$weights <- rep(newdata$`(weights)`, each=length(t)) predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(weighted.mean(.data$h,.data$S * .data$weights))) %>% ungroup() %>% select(-levels.fct) } else{ predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(weighted.mean(.data$h,.data$S))) %>% ungroup() %>% select(-levels.fct) } } # quantile standardisation function, for use with type "quantile" standsurv.fn.quantile <- function(object, newdata, i, weighted, tr.fun, quantiles, interval){ quantile.root.fn <- function(t, q, object, newdata, i, weighted){ as.numeric(standsurv.fn.generic(t, object, type = "survival", newdata, i, weighted, tr.fun=tr("none"))[1,2]) - (1-q) } predsum <- tibble() for(q in quantiles){ root <- uniroot(quantile.root.fn, interval = interval, q=q, object=object, newdata=newdata, i=i, weighted=weighted)$root predsum <- predsum %>% bind_rows(tibble(probability = q) %>% mutate("at{i}" := tr.fun(root))) } predsum } # acsurvival standardisation function, for use with type "acsurvival" standsurv.fn.acsurvival <- function(t, object, newdata, i, weighted, tr.fun, expsurv){ rs <- summary(object, type = "survival", tidy = T, newdata=newdata, t=t, ci=F) ## this gives predictions of relative survival for each individual rs$id <- rep(1:dim(newdata)[1],each=length(t)) names(rs)[names(rs)=="est"] <- "rs" pred <- rs %>% left_join(expsurv$expsurv, by=c("id","time")) pred$levels.fct <- factor(seq_along(t)) if(weighted){ pred$weights <- rep(newdata$`(weights)`, each=length(t)) predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(weighted.mean(.data$rs*.data$es, .data$weights))) %>% ungroup() %>% select(-levels.fct) } else { predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(mean(.data$rs*.data$es))) %>% ungroup() %>% select(-levels.fct) } predsum } # achazard standardisation function, for use with type "achazard" standsurv.fn.achazard <- function(t, object, newdata, i, weighted, tr.fun, expsurv){ rs <- summary(object, type = "survival", tidy = T, newdata=newdata, t=t, ci=F) ## this gives predictions of relative survival for each individual rs$id <- rep(1:dim(newdata)[1],each=length(t)) names(rs)[names(rs)=="est"] <- "rs" excessh <- summary(object, type = "hazard", tidy = T, newdata=newdata, t=t, ci=F) ## this gives excess hazard excessh$id <- rep(1:dim(newdata)[1],each=length(t)) names(excessh)[names(excessh)=="est"] <- "excessh" pred <- rs %>% left_join(excessh, by=c("id", "time")) %>% left_join(expsurv$expsurv, by=c("id","time")) pred$levels.fct <- factor(seq_along(t)) if(weighted){ pred$weights <- rep(newdata$`(weights)`, each=length(t)) predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(weighted.mean(.data$excessh*.data$eh, .data$rs*.data$es * .data$weights))) %>% ungroup() %>% select(-levels.fct) } else { predsum <- pred %>% group_by(levels.fct, time) %>% summarise("at{i}" := tr.fun(weighted.mean(.data$excessh + .data$eh, .data$rs*.data$es))) %>% ungroup() %>% select(-levels.fct) } } standsurv.fn.acrmst <- function(t, object, newdata, i, rmap, ratetable, scale.ratetable, weighted, tr.fun = tr("none"), n.gauss.quad = 100){ # Using Gauss-Legendre quadrature newdata$id <- 1:dim(newdata)[1] gaussxw <- gauss.quad(n.gauss.quad) pred <- vector() for(j in seq_along(t)){ if(t[j]==0){ pred[j] <- 0 } else { scale <- t[j]/2 points <- scale*(gaussxw$nodes + 1) eval_fn <- acsurv.int.fn(points, object, newdata, rmap, ratetable, scale.ratetable, weighted) pred[j] <- tr.fun(scale*sum(gaussxw$weights * eval_fn)) } } pred } # Function to marginal all-cause survival at any given time points average(S*(t)R*(t)) acsurv.int.fn <- function(t1, object, newdata, rmap, ratetable, scale.ratetable, weighted){ # Relative survival rs <- summary(object, type = "survival", tidy = T, newdata=newdata, t=t1, ci=F) rs$id <- rep(1:dim(newdata)[1],each=length(t1)) rs <- rs %>% left_join(newdata, by="id") ## Expected survival rs$t1.scale <- rs$time * scale.ratetable rs$es <- do.call("survexp", list(formula = t1.scale~1, rmap = rmap, method="individual.s", ratetable = ratetable, data=rs )) rs$levels.fct <- factor(seq_along(t)) if(weighted){ rssum <- rs %>% group_by(levels.fct, time) %>% summarise(acsurv = weighted.mean(.data$est*.data$es, .data$weights)) %>% ungroup() %>% select(-levels.fct) } else { rssum <- rs %>% group_by(levels.fct, time) %>% summarise(acsurv = mean(.data$est*.data$es)) %>% ungroup() %>% select(-levels.fct) } rssum$acsurv } # acquantile standardisation function, for use with type "acquantile" standsurv.fn.acquantile <- function(t, object, newdata, i, rmap, ratetable, scale.ratetable, weighted, tr.fun, quantiles, interval){ newdata$id <- 1:dim(newdata)[1] quantile.root.fn <- function(t, q, object, newdata, i, weighted){ acsurv.int.fn(t, object, newdata, rmap, ratetable, scale.ratetable, weighted) - (1-q) } predsum <- tibble() for(q in quantiles){ root <- uniroot(quantile.root.fn, interval = interval, q=q, object=object, newdata=newdata, i=i, weighted=weighted)$root predsum <- predsum %>% bind_rows(tibble(probability = q) %>% mutate("at{i}" := tr.fun(root))) } predsum } tr <- function(trans){ switch(trans, "log"= log, "none"= function(x) x, "loglog" = function(x) log(-log(1-x)), "logit" = qlogis ) } inv.tr <- function(trans){ switch(trans, "log"= exp, "none"= function(x) x, "loglog" = function(x) 1-exp(-exp(x)), "logit" = plogis ) } #' @importFrom dplyr pull boot.standsurv <- function(object, B, dat, i, t, type, type2, weighted, se, ci, cl, rawsim, predsum, expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad){ if(is.null(rawsim)) rawsim <- attributes(normboot.flexsurvreg(object, B=B, raw=T))$rawsim ## only run this once, not for every specified _at X <- form.model.matrix(object, as.data.frame(dat), na.action=na.pass) if(!(type2 %in% c("acrmst","quantile","acquantile"))){ if(!(type2 %in% c("acsurvival", "achazard"))){ sim.pred <- normbootfn.flexsurvreg(object, t=t, start=0, X=X, fn=summary_fns(object, type2), B=B, rawsim=rawsim) # pts, sims, times } else { sim.pred <- normbootfn.flexsurvreg(object, t=t, start=0, X=X, fn=summary_fns(object, type), B=B, rawsim=rawsim) # pts, sims, times } if(weighted){ weights <- array(dat$`(weights)`, dim(sim.pred)) } else { weights <- array(1, dim(sim.pred)) } if(type2=="hazard"){ # Weight individual hazards by survival function to get hazard of the standardized survival haz <- sim.pred surv <- normbootfn.flexsurvreg(object, t=t, start=0, X=X, fn=summary_fns(object, "survival"), B=B, rawsim=rawsim) # pts, sims, times stand.pred <- apply(haz*surv*weights, c(2,3),sum) / apply(surv*weights,c(2,3),sum) } else if(type2=="acsurvival"){ rs <- sim.pred es <- array(expsurv$expsurv$es, dim= dim(rs)[c(1,3,2)]) es <- aperm(es, c(1, 3, 2)) stand.pred <- apply(es*rs*weights, c(2,3),sum) / apply(weights,c(2,3),sum) } else if(type2=="achazard"){ excessh <- sim.pred rs <- normbootfn.flexsurvreg(object, t=t, start=0, X=X, fn=summary_fns(object, "survival"), B=B, rawsim=rawsim) # pts, sims, times es <- array(expsurv$expsurv$es, dim= dim(rs)[c(1,3,2)]) es <- aperm(es, c(1, 3, 2)) eh <- array(expsurv$expsurv$eh, dim= dim(rs)[c(1,3,2)]) eh <- aperm(eh, c(1, 3, 2)) stand.pred <- apply(rs*es*weights*(excessh+eh), c(2,3),sum) / apply(rs*es*weights,c(2,3),sum) } else { stand.pred <- apply(sim.pred*weights, c(2,3), sum) / apply(weights,c(2,3),sum) } } if(type2=="acrmst") { ## if type2=="acrmst" ## This for now manipulates rawsim within standsurv.fn.acrmst. This code could be made more slick. stand.pred <- matrix(nrow=B, ncol=length(t)) for(b in seq(length.out=B)) { newobject <- object newobject$res.t[,"est"] <- rawsim[b,] newobject$res[newobject$covpars,"est"] <- rawsim[b, newobject$covpars] newobject$res[newobject$dlist$pars,"est"] <- NA ## setting to NA to be safe newobject$res.t[,-1] <- newobject$res[,-1] <- NA ## setting to NA to be safe ## standardisation (averaging across patients) is done within acrmst itself stand.pred[b,] <- standsurv.fn.acrmst(t, newobject, newdata=dat, i, rmap, ratetable, scale.ratetable, weighted, tr.fun=tr("none"), n.gauss.quad) } } if(type2=="quantile"){ ## This for now manipulates rawsim within standsurv.fn.quantile. This code could be made more slick. stand.pred <- matrix(nrow=B, ncol=length(quantiles)) for(b in seq(length.out=B)) { newobject <- object newobject$res.t[,"est"] <- rawsim[b,] newobject$res[newobject$covpars,"est"] <- rawsim[b, newobject$covpars] newobject$res[newobject$dlist$pars,"est"] <- NA ## setting to NA to be safe newobject$res.t[,-1] <- newobject$res[,-1] <- NA ## setting to NA to be safe ## standardisation (averaging across patients) is done within standsurv.fn.quantile itself stand.pred[b,] <- pull(standsurv.fn.quantile(newobject, newdata=dat, i, weighted, tr.fun=tr("none"), quantiles, interval)[,2]) } } if(type2=="acquantile"){ stop("bootstrap not yet applied with acquantile") } if(se == TRUE){ stand.pred.se <- tibble("at{i}_se" := apply(stand.pred, 2, sd, na.rm=TRUE)) predsum <- predsum %>% bind_cols(stand.pred.se) } if(ci == TRUE){ stand.pred.quant <- apply(stand.pred, 2, function(x)quantile(x, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE) ) stand.pred.quant <- as_tibble(t(stand.pred.quant)) %>% rename("at{i}_lci" := "2.5%", "at{i}_uci" := "97.5%") predsum <- predsum %>% bind_cols(stand.pred.quant) } return(list(predsum = predsum, stand.pred=stand.pred, rawsim=rawsim)) } #' @importFrom numDeriv grad deltamethod.standsurv <- function(object, newdata, type2, t, i, se, ci, predsum, trans, cl, weighted, expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad){ if(!(type2 %in% c("quantile","acquantile"))){ g1 <- function(coef, t, trans) { object$res[,"est"] <- object$res.t[,"est"] <- coef standsurv.fn(object, type=type2, newdata=newdata, t=t, i=i, trans, weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad)[,2,drop=T] } } else { g2 <- function(coef, quantiles, trans) { object$res[,"est"] <- object$res.t[,"est"] <- coef standsurv.fn(object, type=type2, newdata=newdata, t=t, i=i, trans, weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles=quantiles, interval, n.gauss.quad)[,2,drop=T] } } est <- standsurv.fn(object, type=type2, newdata=newdata, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad)[,2,drop=T] var.none <- NULL if(se==TRUE){ # Calculate for each value of t the untransformed standardized measure if(!(type2 %in% c("quantile","acquantile"))){ var.none <- sapply(t, function(ti){ gd <- grad(g1, coef(object), method="simple" ,t=ti, trans="none") gd %*% vcov(object) %*% gd }) } else { var.none <- sapply(quantiles, function(q){ gd <- grad(g2, coef(object), method="simple" ,quantiles=q, trans="none") gd %*% vcov(object) %*% gd }) } stand.pred.se <- as_tibble(sqrt(var.none)) %>% rename("at{i}_se" := "value") predsum <- predsum %>% bind_cols(stand.pred.se) } if(ci==TRUE){ # Calculate for each value of t the transformed standardized measure if(trans=="none" & !is.null(var.none)){ var.trans <- var.none ## use already calculated variances } else { if(!(type2 %in% c("quantile","acquantile"))){ var.trans <- sapply(t, function(ti){ gd <- grad(g1, coef(object), method="simple" ,t=ti, trans=trans) gd %*% vcov(object) %*% gd }) } else { var.trans <- sapply(quantiles, function(q){ gd <- grad(g2, coef(object), method="simple" ,quantiles=q, trans=trans) gd %*% vcov(object) %*% gd }) } } tr.fun <- tr(trans) inv.tr.fun <- inv.tr(trans) stand.pred.lcl <- as_tibble(inv.tr.fun(tr.fun(est)+qnorm((1-cl)/2, lower.tail=T)*sqrt(var.trans))) %>% rename("at{i}_lci" := "value") stand.pred.ucl <- as_tibble(inv.tr.fun(tr.fun(est)+qnorm((1-cl)/2, lower.tail=F)*sqrt(var.trans))) %>% rename("at{i}_uci" := "value") predsum <- predsum %>% bind_cols(stand.pred.lcl, stand.pred.ucl) } predsum } #' @importFrom numDeriv grad deltamethod.contrast.standsurv <- function(object, dat, dat.ref, type2, t, i, atreference, se, ci, predsum, trans.contrast, cl, contrast, weighted, expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad){ tr.fun <- tr(trans.contrast) inv.tr.fun <- inv.tr(trans.contrast) contrast.fn <- switch(contrast, "difference"= `-`, "ratio"= `/` ) if(!(type2 %in% c("quantile","acquantile"))){ g1 <- function(coef, t, tr.fun, contrast.fn) { object$res[,"est"] <- object$res.t[,"est"] <- coef tr.fun(contrast.fn(standsurv.fn(object, type=type2, newdata=dat, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad)[,2,drop=T], standsurv.fn(object, type=type2, newdata=dat.ref, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad)[,2,drop=T])) } } else { g2 <- function(coef, quantiles, tr.fun, contrast.fn) { object$res[,"est"] <- object$res.t[,"est"] <- coef tr.fun(contrast.fn(standsurv.fn(object, type=type2, newdata=dat, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles=quantiles, interval, n.gauss.quad)[,2,drop=T], standsurv.fn(object, type=type2, newdata=dat.ref, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles=quantiles, interval, n.gauss.quad)[,2,drop=T])) } } est <- contrast.fn(standsurv.fn(object, type=type2, newdata=dat, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad)[,2,drop=T], standsurv.fn(object, type=type2, newdata=dat.ref, t=t, i=i, trans="none", weighted=weighted, expsurv=expsurv, rmap, ratetable, scale.ratetable, quantiles, interval, n.gauss.quad)[,2,drop=T]) stand.pred <- as_tibble(est) %>% rename("contrast{i}_{atreference}" := "value") predsum <- predsum %>% bind_cols(stand.pred) var.none <- NULL if(se==TRUE){ # Calculate for each value of t the untransformed standardized measure if(!(type2 %in% c("quantile","acquantile"))){ var.none <- sapply(t, function(ti){ gd <- grad(g1, coef(object), method="simple" ,t=ti, tr.fun=function(x) x, contrast.fn=contrast.fn) gd %*% vcov(object) %*% gd }) } else { var.none <- sapply(quantiles, function(q){ gd <- grad(g2, coef(object), method="simple" ,quantiles=q, tr.fun=function(x) x, contrast.fn=contrast.fn) gd %*% vcov(object) %*% gd }) } stand.pred.se <- as_tibble(sqrt(var.none)) %>% rename("contrast{i}_{atreference}_se" := "value") predsum <- predsum %>% bind_cols(stand.pred.se) } if(ci==TRUE){ # Calculate for each value of t the transformed standardized measure if(trans.contrast=="none" & !is.null(var.none)){ var.trans <- var.none ## use already calculated variances } else { if(!(type2 %in% c("quantile","acquantile"))){ var.trans <- sapply(t, function(ti){ gd <- grad(g1, coef(object), method="simple" ,t=ti, tr.fun=tr.fun, contrast.fn=contrast.fn) gd %*% vcov(object) %*% gd }) } else { var.trans <- sapply(quantiles, function(q){ gd <- grad(g2, coef(object), method="simple" ,quantiles=q, tr.fun=tr.fun, contrast.fn=contrast.fn) gd %*% vcov(object) %*% gd }) } } stand.pred.lcl <- as_tibble(inv.tr.fun(tr.fun(est)+qnorm((1-cl)/2, lower.tail=T)*sqrt(var.trans))) %>% rename("contrast{i}_{atreference}_lci" := "value") stand.pred.ucl <- as_tibble(inv.tr.fun(tr.fun(est)+qnorm((1-cl)/2, lower.tail=F)*sqrt(var.trans))) %>% rename("contrast{i}_{atreference}_uci" := "value") predsum <- predsum %>% bind_cols(stand.pred.lcl, stand.pred.ucl) } predsum } #' Tidy a standsurv object. #' #' This function is used internally by \code{standsurv} and tidy #' data.frames are automatically returned by the function. #' #' @param x A standsurv object. #' @param ... Not currently used. #' #' @return Returns additional tidy data.frames (tibbles) #' stored as attributes named standpred_at and standpred_contrast. #' @importFrom dplyr select #' @importFrom dplyr inner_join #' @importFrom dplyr mutate #' @importFrom tidyr pivot_longer #' @importFrom tidyselect matches #' @export #' tidy.standsurv <- function(x, ...){ standpred <- x at <-attributes(standpred)$at atreference <- attributes(standpred)$atreference type <- attributes(standpred)$type label <- attributes(standpred)$label contrast <- attributes(standpred)$contrast ci <- any(grepl("_lci",names(standpred))) by <- ifelse(type == "quantile", "probability", "time") class(standpred) <- class(standpred)[class(standpred)!="standsurv"] standpred_at <- standpred %>% select(c(all_of(by), matches("at[0-9]+$"))) %>% pivot_longer(cols=matches("at[0-9]+$"), names_to = "at", values_to = type, names_prefix = "at") if(ci){ standpred_at_lci <- standpred %>% select(c(all_of(by), matches("at[0-9]+_lci"))) %>% pivot_longer(cols=matches("at[0-9]+_lci"), names_to = "at", names_pattern = "at(.+)_lci", values_to = paste0(type,"_lci")) %>% distinct() standpred_at_uci <- standpred %>% select(c(all_of(by), matches("at[0-9]+_uci"))) %>% pivot_longer(cols=matches("at[0-9]+_uci"), names_to = "at", names_pattern = "at(.+)_uci", values_to = paste0(type,"_uci")) %>% distinct() standpred_at <- standpred_at %>% inner_join(standpred_at_lci, by=c(by,"at")) %>% inner_join(standpred_at_uci, by=c(by, "at")) } for(i in 1:length(at)){ standpred_at <- standpred_at %>% mutate(at = replace(at, at==i, label[i])) } attr(standpred,"standpred_at") <- standpred_at if(!is.null(contrast)){ ## Contrast numbers cnums <- (1:length(at))[-atreference] standpred_contrast <- standpred %>% select(c(all_of(by), matches("contrast[0-9]+_[0-9]+$"))) %>% pivot_longer(cols=matches("contrast[0-9]+_[0-9]+$"), names_to = "contrast", values_to = contrast, names_prefix = "contrast") if(ci){ standpred_contrast_lci <- standpred %>% select(c(all_of(by), matches("contrast[0-9]+_[0-9]+_lci"))) %>% pivot_longer(cols=matches("contrast[0-9]+_[0-9]+_lci"), names_to = "contrast", names_pattern = "contrast(.+)_lci", values_to = paste0(contrast,"_lci")) %>% distinct() standpred_contrast_uci <- standpred %>% select(c(all_of(by), matches("contrast[0-9]+_[0-9]+_uci"))) %>% pivot_longer(cols=matches("contrast[0-9]+_[0-9]+_uci"), names_to = "contrast", names_pattern = "contrast(.+)_uci", values_to = paste0(contrast,"_uci")) %>% distinct() standpred_contrast <- standpred_contrast %>% inner_join(standpred_contrast_lci, by=c(by, "contrast")) %>% inner_join(standpred_contrast_uci, by=c(by, "contrast")) } for(i in cnums){ standpred_contrast <- standpred_contrast %>% mutate(contrast = replace(contrast, contrast==paste0(i,"_",atreference), paste0(label[i]," vs ",label[atreference]))) } attr(standpred,"standpred_contrast") <- standpred_contrast } class(standpred) <- c("standsurv",class(standpred)) standpred } #' Plot standardized metrics from a fitted flexsurv model #' #' Plot standardized metrics such as the marginal survival, restricted mean #' survival and hazard, based on a fitted flexsurv model. #' #' @param x A standsurv object returned by \code{standsurv} #' @param contrast Should contrasts of standardized metrics be plotted. Defaults #' to FALSE #' @param ci Should confidence intervals be plotted (if calculated in #' \code{standsurv})? #' @param expected Should the marginal expected survival / hazard also be #' plotted? This can only be invoked if \code{rmap} and \code{ratetable} have #' been passed to \code{standsurv} #' @param ... Not currently used #' #' @return A ggplot showing the standardized metric calculated by #' \code{standsurv} over time. Modification of the plot is #' possible by adding further ggplot objects, see Examples. #' @import ggplot2 #' @export #' #' @examples #'## Use bc dataset, with an age variable appended #'## mean age is higher in those with smaller observed survival times #'newbc <- bc #'newbc$age <- rnorm(dim(bc)[1], mean = 65-scale(newbc$recyrs, scale=FALSE), #' sd = 5) #' #'## Fit a Weibull flexsurv model with group and age as covariates #'weib_age <- flexsurvreg(Surv(recyrs, censrec) ~ group+age, data=newbc, #' dist="weibull") #'## Calculate standardized survival and the difference in standardized survival #'## for the three levels of group across a grid of survival times #'standsurv_weib_age <- standsurv(weib_age, #' at = list(list(group="Good"), #' list(group="Medium"), #' list(group="Poor")), #' t=seq(0,7, length=100), #' contrast = "difference", ci=TRUE, #' boot = TRUE, B=10, seed=123) #'plot(standsurv_weib_age) #'plot(standsurv_weib_age) + ggplot2::theme_bw() + ggplot2::ylab("Survival") + #' ggplot2::xlab("Time (years)") + #' ggplot2::guides(color=ggplot2::guide_legend(title="Prognosis"), #' fill=ggplot2::guide_legend(title="Prognosis")) #'plot(standsurv_weib_age, contrast=TRUE, ci=TRUE) + #' ggplot2::ylab("Difference in survival") plot.standsurv <- function(x, contrast = FALSE, ci = FALSE, expected = FALSE, ...){ if(!contrast){ obj <- attributes(x)$standpred_at obj <- obj %>% mutate(Population = "Study") y <- attributes(x)$type if(y=="quantile") stop("plot method not configured for type='quantile'") group <- "at" if(expected){ if(is.null(attributes(x)$expected)) stop("Expected survival/hazards have not been calculated by standsurv") if(!(y %in% c("hazard", "achazard", "survival", "acsurvival"))) stop(paste0("Expected survival/hazards cannot be plotted with type = ",y)) if(y %in% c("hazard", "achazard")) y2 <- "exphaz" if(y %in% c("survival", "acsurvival")) y2 <- "expsurv" obj2 <- attributes(x)$expected[,c("time",y2)] %>% rename({{y}} := all_of(y2)) %>% mutate({{group}} := "Expected", Population = "Expected") obj <- obj %>% bind_rows(obj2) } } else { if(is.null(attributes(x)$standpred_contrast)) stop("Contrasts have not been calculated by standsurv") obj <- attributes(x)$standpred_contrast obj <- obj %>% mutate(Population = "Study") y <- attributes(x)$contrast group <- "contrast" if(expected) stop("Expected survival/hazard cannot be plotted with contrasts") } linetype <- c("Study" = "solid", "Expected" = "dashed") p <- ggplot() + geom_line(aes(x=.data[["time"]], y=.data[[y]], color=.data[[group]], linetype= .data[["Population"]]), data=obj) + xlab("Time") + scale_linetype_manual(values = linetype, guide="none") if(ci){ if(any(grepl("_lci",names(obj)))){ p <- p + geom_ribbon(aes(x= .data[["time"]], ymin=.data[[paste0(y,"_lci")]], ymax=.data[[paste0(y,"_uci")]], fill= .data[[group]]), data = obj, alpha=0.2) } else warning("Confidence intervals have not been calculated in standsurv. None will be plotted") } p } #' @importFrom dplyr bind_rows expsurv.fn <- function(t, rmap, ratetable, data, weighted, scale.ratetable){ expsurv <- exphaz <- tibble() for(l in 1:length(t)){ data$t.temp <- t[l] * scale.ratetable es <- do.call("survexp", list(formula = t.temp~1, rmap = rmap, method="individual.s", ratetable = ratetable, data = data )) expsurv <- expsurv %>% bind_rows(tibble(time = t[l], es = es, id = 1:dim(data)[1])) # individual hazards from difference in cumulative hazards / epsilon epsilon <- 0.001 data$t.temp.epsilon <- data$t.temp + epsilon eh.epsilon <- do.call("survexp", list(formula = t.temp.epsilon~1, rmap = rmap, method="individual.h", ratetable = ratetable, data = data )) eh.epsilon0 <- do.call("survexp", list(formula = t.temp~1, rmap = rmap, method="individual.h", ratetable = ratetable, data=data )) eh <- scale.ratetable * (eh.epsilon - eh.epsilon0) / epsilon exphaz <- exphaz %>% bind_rows(tibble(time = t[l], eh=eh, id=1:dim(data)[1])) } expsurv <- expsurv %>% inner_join(exphaz, by= c("id", "time")) if(weighted){ expsurv$weights <- rep(data$`(weights)`, each=length(t)) marginal <- expsurv %>% group_by(time) %>% summarise("expsurv" = weighted.mean(.data$es, .data$weights), "exphaz" = weighted.mean(.data$eh, .data$es * .data$weights)) } else { marginal <- expsurv %>% group_by(time) %>% summarise("expsurv" = mean(.data$es), "exphaz" = weighted.mean(.data$eh, .data$es)) } return(list(marginal=marginal, expsurv=expsurv)) } ## to remove R CMD check NOTE utils::globalVariables(c("levels.fct")) flexsurv/R/simulate_flexsurvreg.R0000644000176200001440000000770414632364677016765 0ustar liggesusers##' Simulate censored time-to-event data from a fitted flexsurvreg model ##' ##' @param object Object returned by \code{\link{flexsurvreg}}. ##' ##' @param nsim Number of simulations per row in \code{newdata}. ##' ##' @param seed Random number seed. This is returned with the result of this ##' function, as described in \code{\link{simulate}} for the \code{lm} method. ##' ##' @param newdata Data frame defining alternative sets of covariate values to simulate with. ##' If omitted, this defaults to the data originally used to fit the model. ##' ##' @template start ##' ##' @param censtime A right-censoring time, or vector of times matching the rows ##' of \code{newdata}. If \code{NULL} (the default) then uncensored times to events ##' are simulated. ##' ##' @param tidy If \code{TRUE} then a "tidy" or "long"-format data frame is ##' returned, with rows defined by combinations of covariates and simulation ##' replicates. The simulation replicate is indicated in the column named \code{i}. ##' ##' If \code{FALSE}, then a data frame is returned with one row per set of ##' covariate values, and different columns for different simulation ##' replicates. This is the traditional format for `simulate` methods in base ##' R. ##' ##' In either case, the simulated time and indicator for whether the time is ##' an event time (rather than a time of right-censoring) are returned in ##' different columns. ##' ##' @param ... Other arguments (not currently used). ##' ##' @return A data frame, with format determined by whether \code{tidy} was specified. ##' ##' @examples ##' fit <- flexsurvreg(formula = Surv(futime, fustat) ~ rx, data = ovarian, dist="weibull") ##' fit2 <- flexsurvspline(formula = Surv(futime, fustat) ~ rx, data = ovarian, k=3) ##' nd = data.frame(rx=1:2) ##' simulate(fit, seed=1002, newdata=nd) ##' simulate(fit, seed=1002, newdata=nd, start=500) ##' simulate(fit2, nsim=3, seed=1002, newdata=nd) ##' simulate(fit2, nsim=3, seed=1002, newdata=nd, start=c(500,1000)) ##' ##' @export simulate.flexsurvreg <- function(object, nsim=1, seed=NULL, newdata=NULL, start=NULL, censtime=NULL, tidy=FALSE,...) { if (is.null(newdata)) newdata <- model.frame(object) else if (!is.data.frame(newdata)) stop("`newdata` should be a data frame") if (!is.null(seed)) { set.seed(seed) attr(seed, "kind") <- as.list(RNGkind()) seed_attr <- seed } else seed_attr <- .Random.seed nd <- nrow(newdata) if (!is.numeric(nsim) || (nsim < 1)) stop("`nsim` should be a number >= 1") n <- nd*nsim if (!is.null(start)) { if(!(length(start) %in% c(1, nd))) stop(sprintf("`start` of length %s, should be of length 1 or %s = nrow(newdata)"), length(start), nd) if (length(start)==1) start <- rep(start, length.out=n) else start <- rep(start, each=nsim) } else start <- 0 U <- runif(n, 0, 1) newdata <- newdata[rep(1:nd, each=nsim), , drop=FALSE] time <- summary(object, newdata=newdata, start=start, type="quantile", quantiles=U, cross=FALSE, ci=FALSE, se=FALSE, tidy=TRUE)$est if (is.null(censtime)) censtime <- rep(Inf, nd) if (length(censtime) ==1) censtime <- rep(censtime, nd) if (length(censtime)!=nd) stop(sprintf("`censtime` of length %s, should be of length %s = nrow(newdata)", length(censtime), nd)) censtime <- rep(censtime, each = nsim) event <- as.numeric(time <= censtime) time <- ifelse(event, time, censtime) if (tidy) { res <- cbind(newdata, i=rep(1:nsim, nd), time=time, event=event) rownames(res) <- NULL } else { time <- matrix(time, nrow=nd, ncol=nsim, byrow=TRUE) event <- matrix(event, nrow=nd, ncol=nsim, byrow=TRUE) colnames(time) <- paste0("time_",1:nsim) colnames(event) <- paste0("event_",1:nsim) res <- as.data.frame(cbind(time, event)) } attr(res, "seed") <- seed_attr res } flexsurv/R/flexsurvreg.R0000644000176200001440000020640314644755325015054 0ustar liggesusers## sinh(log(y)) logh <- function(x) { 0.5 * (x - 1/x) } buildTransformer <- function(inits, nbpars, dlist) { par.transform <- lapply(seq_len(nbpars), function(ind) { xform <- dlist$inv.transforms[[ind]] function(pars) { xform(pars[[ind]]) } }) names(par.transform) <- names(inits)[seq_len(nbpars)] function(pars) { lapply(par.transform, function(item, par) { item(par) }, pars) } } buildAuxParms <- function(aux, dlist) { aux.transform <- list() for (ind in seq_along(aux)) { name <- names(aux)[[ind]] if (!(name %in% dlist$pars)) { aux.transform[[name]] <- aux[[ind]] } } aux.transform } ## Filter out warnings produced during fitting, when the optimiser visits ## parameters are on the boundary of the parameter space, as the optimiser will ## move on in these cases, and the message is unhelpful to users. call_distfn_quiet <- function(fn, args){ res <- withCallingHandlers( do.call(fn, args), warning=function(w) { if (grepl(x = w$message, pattern = "NaNs produced")) invokeRestart("muffleWarning") } ) res } logLikFactory <- function(Y, X=0, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars=NULL) { pars <- inits npars <- length(pars) nbpars <- length(dlist$pars) insert.locations <- setdiff(seq_len(npars), fixedpars) ## which are the subjects with known event times event <- Y[,"status"] == 1 event.times <- Y[event, "time1"] lcens.times <- Y[!event, "time2"] rcens.times <- Y[!event, "time1"] par.transform <- buildTransformer(inits, nbpars, dlist) aux.pars <- buildAuxParms(aux, dlist) do.bhazard <- any(bhazard > 0) loglik <- rep.int(0, nrow(Y)) ## the ... here is to work around optim function(optpars, ...) { pars[insert.locations] <- optpars raw.pars <- pars pars <- as.list(pars) pars.event <- pars.nevent <- pars if (npars > nbpars) { beta <- raw.pars[(nbpars+1):npars] for (i in dlist$pars){ pars[[i]] <- pars[[i]] + X[,mx[[i]],drop=FALSE] %*% beta[mx[[i]]] pars.event[[i]] <- pars[[i]][event] pars.nevent[[i]] <- pars[[i]][!event] } } fnargs <- c(par.transform(pars), aux.pars) fnargs.event <- c(par.transform(pars.event), aux.pars) fnargs.nevent <- c(par.transform(pars.nevent), aux.pars) ## Generic survival model likelihood contributions ## Observed deaths dargs <- fnargs.event dargs$x <- event.times dargs$log <- TRUE logdens <- call_distfn_quiet(dfns$d, dargs) ## Left censoring times (upper bound for event time) if (!all(event)){ pmaxargs <- fnargs.nevent pmaxargs$q <- lcens.times # Inf if right-censored, giving pmax=1 pmax <- call_distfn_quiet(dfns$p, pmaxargs) pmax[pmaxargs$q==Inf] <- 1 # in case user-defined function doesn't already do this ## Right censoring times (lower bound for event time) pargs <- fnargs.nevent pargs$q <- rcens.times pmin <- call_distfn_quiet(dfns$p, pargs) } targs <- fnargs ## Left-truncation targs$q <- Y[,"start"] plower <- call_distfn_quiet(dfns$p, targs) ## Right-truncation targs$q <- rtrunc pupper <- call_distfn_quiet(dfns$p, targs) pupper[rtrunc==Inf] <- 1 # in case the user's function doesn't already do this pobs <- pupper - plower # prob of being observed = 1 - 0 if no truncation if (do.bhazard){ # Adjust for background hazard in relative survival models pargs <- fnargs.event pargs$q <- event.times pminb <- call_distfn_quiet(dfns$p, pargs) logsurv_excess <- log(1 - pminb) loghaz_excess <- logdens - logsurv_excess haz_excess <- exp(loghaz_excess) logdens_offset <- log(1 + bhazard[event] / haz_excess) # = log(haz_allcause / haz_excess) if (!all(event)) { # background survival S* and left or interval censoring b_condsurv <- 1 - bhazard[!event] # this is S*(end) / S*(start) b_condsurv[lcens.times==Inf] <- 0 # when end=Inf, i.e. right censoring } if (any(is.finite(rtrunc))) stop("models with both right truncation and background hazards not supported") } else { logdens_offset <- 0 } ## Express as vector of individual likelihood contributions loglik[event] <- (logdens + logdens_offset) if (!all(event)){ if (do.bhazard) loglik[!event] <- log((pmax - 1)*b_condsurv + 1 - pmin) else loglik[!event] <- log(pmax - pmin) } loglik <- loglik - log(pobs) ret <- -sum(loglik*weights) attr(ret, "indiv") <- loglik ret } } minusloglik.flexsurv <- function(optpars, Y, X=0, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars=NULL) { logLikFactory(Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars)(optpars) } parse.dist <- function(dist){ if (is.character(dist)) { # Added: case insensitve matching of distributions # Step 1: Use match.arg on lowercase argument, dists. # Step 2: Use match to get index in distribution list from # value obtained in step 1, and grab corresponding element. dist <- match.arg(tolower(dist), tolower(names(flexsurv.dists))) dist <- names(flexsurv.dists)[match(dist,tolower(names(flexsurv.dists)))] dlist <- flexsurv.dists[[dist]] } else if (is.list(dist)) { dlist <- check.dlist(dist) } else stop("\"dist\" should be a string for a built-in distribution, or a list for a custom distribution") dlist } check.dlist <- function(dlist){ ## put tests in testthat if (is.null(dlist$name)) stop("\"name\" element of custom distribution list not given") if (!is.character(dlist$name)) stop("\"name\" element of custom distribution list should be a string") if (is.null(dlist$pars)) stop("parameter names \"pars\" not given in custom distribution list") if (!is.character(dlist$pars)) stop("parameter names \"pars\" should be a character vector") npars <- length(dlist$pars) if (is.null(dlist$location)) { warning("location parameter not given, assuming it is the first one") dlist$location <- dlist$pars[1] } if (!(dlist$location %in% dlist$pars)) { stop(sprintf("location parameter \"%s\" not in list of parameters", dlist$location)) } if (is.null(dlist$transforms)) stop("transforms not given in custom distribution list") if (is.null(dlist$inv.transforms)) stop("inverse transforms not given in custom distribution list") if (!is.list(dlist$transforms)) stop("\"transforms\" must be a list of functions") if (!is.list(dlist$inv.transforms)) stop("\"inv.transforms\" must be a list of functions") if (!all(sapply(dlist$transforms, is.function))) stop("some of \"transforms\" are not functions") if (!all(sapply(dlist$inv.transforms, is.function))) stop("some of \"inv.transforms\" are not functions") if (length(dlist$transforms) != npars) stop("transforms vector of length ",length(dlist$transforms),", parameter names of length ",npars) if (length(dlist$inv.transforms) != npars) stop("inverse transforms vector of length ",length(dlist$inv.transforms),", parameter names of length ",npars) # for (i in 1:npars){ if (is.character(dlist$transforms[[i]])) dlist$transforms[[i]] <- get(dlist$transforms[[i]]) if (is.character(dlist$inv.transforms[[i]])) dlist$inv.transforms[[i]] <- get(dlist$inv.transforms[[i]]) if (!is.function(dlist$transforms[[i]])) stop("Transformation function for parameter ", i, " not defined") if (!is.function(dlist$inv.transforms[[i]])) stop("Inverse transformation function for parameter ", i, " not defined") } if (!is.null(dlist$inits) && !is.function(dlist$inits)) stop("\"inits\" element of custom distribution list must be a function") dlist } ## Return formula for linear model on parameter called "par" ## Parameters should not have the same name as anything that might ## appear as a function in a formula (such as "I", "strata", or ## "factor"). If any parameters of the distribution being used are ## named like this, then such model functions will be interpreted as ## parameters and will not work check.formula <- function(formula, dlist, data = NULL){ if (!inherits(formula,"formula")) stop("\"formula\" must be a formula object") labs <- as.character(attr(terms(formula, data = data), "variables"))[-c(1,2)] if (!("strata" %in% dlist$pars)){ strat <- grep("strata\\((.+)\\)",labs) if (length(strat) > 0){ cov <- gsub("strata\\((.+)\\)","\\1",labs[strat[1]]) warning("Ignoring \"strata\" function: interpreting \"",cov, "\" as a covariate on \"", dlist$location, "\"") } } if (!("frailty" %in% dlist$pars)){ fra <- grep("frailty\\((.+)\\)",labs) if (length(fra) > 0){ stop("frailty models are not supported and behaviour of frailty() is undefined") } } if (!("offset" %in% dlist$pars)){ fra <- grep("offset\\((.+)\\)",labs) if (length(fra) > 0){ stop("offset() terms are not supported in formulae. To fit a model with a covariate coefficient fixed to 1, use the `inits` and `fixedpars` arguments") } } } check.fixedpars <- function(fixedpars, npars) { if (!is.null(fixedpars) && !is.logical(fixedpars) && (!is.numeric(fixedpars) || !all(fixedpars %in% 1:npars))) { dots <- if(npars>2) "...," else "" stop("fixedpars must be TRUE/FALSE or a vector of indices in 1,",dots,npars) } } anc_from_formula <- function(formula, anc, dlist, msg = "\"anc\" must be a list of formulae", data = NULL, loc_warn=TRUE) { parnames <- dlist$pars ancnames <- setdiff(parnames, dlist$location) if (is.null(anc)){ anc <- vector(mode="list", length=length(ancnames)) names(anc) <- ancnames for (i in ancnames){ anc[[i]] <- ancpar.formula(formula, i, data) } ancpar.formula(formula, dlist$location, data, location=TRUE) } else { if (!is.list(anc) || !all(sapply(anc, function(x)inherits(x, "formula")))) stop(msg) badnames <- names(anc)[!(names(anc) %in% dlist$pars)] if (length(badnames) > 0) stop(sprintf("There is no parameter of distribution `%s` called `%s`", dlist$name, badnames[1])) ## reorder components of anc to canonical order anc <- anc[dlist$pars[dlist$pars %in% names(anc)]] if (dlist$location %in% names(anc) && loc_warn) warning(sprintf("Ignoring location parameter `%s` in ancillary formula", dlist$location)) } anc } ancpar.formula <- function(formula, par, data = NULL, location=FALSE){ labs <- attr(terms(formula, data = data), "term.labels") pattern <- paste0(par,"\\((.+)\\)") labs <- grep(pattern,labs,value=TRUE) if (length(labs)==0) return(NULL) else if (location) warning(sprintf("Ignoring location parameter `%s` in ancillary formula", par)) labs <- gsub(pattern, "\\1", labs) f2 <- reformulate(labs) environment(f2) <- environment(formula) f2 } ## Omit formula terms containing ancillary parameters, leaving only ## the formula for the location parameter get.locform <- function(formula, ancnames, data = NULL){ labs <- attr(terms(formula, data = data), "term.labels") dropx <- unlist(lapply(ancnames, function(x){grep(paste0(x,"\\((.+)\\)"),labs)})) formula(terms(formula, data = data)[c(0,setdiff(seq_along(labs),dropx))]) } ## Concatenate location formula (that includes Surv response term) ## with list of ancillary formulae, giving a merged formula to obtain ## the model frame concat.formulae <- function(formula,forms, data = NULL){ covnames <- unlist(lapply(forms, function(x)attr(terms(x, data = data),"term.labels"))) covform <- if(length(covnames)==0) "1" else paste(covnames, collapse=" + ") respname <- as.character(formula[2]) form <- paste0(respname, " ~ ", covform) f2 <- eval(parse(text=form)) environment(f2) <- environment(formula) ## names of variables in the data, not the formula, with functions such as factor() stripped ## used for error message with incomplete "newdata" in summary() covnames.bare <- unlist(lapply(forms, function(x)all.vars(delete.response(terms(x, data = data))))) attr(f2, "covnames") <- covnames.bare attr(f2, "covnames.orig") <- covnames f2 } ## User-supplied initial value functions don't have to include all ## four possible arguments: this expands them if they don't #' @noRd expand.inits.args <- function(inits){ inits2 <- inits formals(inits2) <- alist(t=,mf=,mml=,aux=) body(inits2) <- body(inits) inits2 } ## User-supplied summary output functions don't have to include all ## two possible arguments: this expands them if they don't #' @noRd expand.summfn.args <- function(summfn){ summfn2 <- summfn args <- c(alist(t=,start=), formals(summfn)) formals(summfn2) <- args[!duplicated(names(args))] body(summfn2) <- body(summfn) summfn2 } ### On entry: ### event (status=1) time1=event time ### right-censoring (status=0) time1=lower bound ### left-censoring (status=2) time1=upper bound ### interval-censoring (status=3) time1=lower, time2=upper ### On exit ### time1=lower bound or event time ### time2=upper bound ### start=left truncation time ### so meaning of time1,time2 reversed with left-censoring check.flexsurv.response <- function(Y){ if (!inherits(Y, "Surv")) stop("Response must be a survival object") ### convert Y from Surv object to numeric matrix type <- attr(Y, "type") ### though "time" only used for initial values, printed time at risk, empirical hazard if (type == "counting") Y <- cbind(Y, time=Y[,"stop"] - Y[,"start"], time1=Y[,"stop"], time2=Inf) else if (type == "interval"){ # Surv() converts interval2 to interval Y[,"time2"][Y[,"status"]==0] <- Inf # upper bound with right censoring Y[,"time2"][Y[,"status"]==1] <- Y[,"time1"][Y[,"status"]==1] # event time Y[,"time2"][Y[,"status"]==2] <- Y[,"time1"][Y[,"status"]==2] Y[,"time1"][Y[,"status"]==2] <- 0 # Y <- cbind(Y, start=0, stop=Y[,"time1"], time=Y[,"time1"]) } else if (type == "right") Y <- cbind(Y, start=0, stop=Y[,"time"], time1=Y[,"time"], time2=Inf) else stop("Survival object type \"", attr(Y, "type"), "\"", " not supported") if (any(Y[,"time1"]<0)){ stop("Negative survival times in the data") } attr(Y, "type") <- type Y } compress.model.matrices <- function(mml){ cbind.drop.intercept <- function(...)do.call("cbind", lapply(list(...), function(x)x[,-1,drop=FALSE])) X <- do.call("cbind.drop.intercept",mml) loc.cnames <- colnames(mml[[1]])[-1] anc.cnames <- unlist(mapply(function(x,y)sprintf("%s(%s)",x,y), names(mml[-1]), lapply(mml[-1], function(x)colnames(x)[-1]))) cnames <- c(loc.cnames, anc.cnames) colnames(X) <- cnames X } ##' Flexible parametric regression for time-to-event data ##' ##' Parametric modelling or regression for time-to-event data. Several built-in ##' distributions are available, and users may supply their own. ##' ##' Parameters are estimated by maximum likelihood using the algorithms ##' available in the standard R \code{\link{optim}} function. Parameters ##' defined to be positive are estimated on the log scale. Confidence intervals ##' are estimated from the Hessian at the maximum, and transformed back to the ##' original scale of the parameters. ##' ##' The usage of \code{\link{flexsurvreg}} is intended to be similar to ##' \code{\link[survival]{survreg}} in the \pkg{survival} package. ##' ##' @aliases flexsurvreg flexsurv.dists ##' @param formula A formula expression in conventional R linear modelling ##' syntax. The response must be a survival object as returned by the ##' \code{\link[survival]{Surv}} function, and any covariates are given on the ##' right-hand side. For example, ##' ##' \code{Surv(time, dead) ~ age + sex} ##' ##' \code{Surv} objects of \code{type="right"},\code{"counting"}, ##' \code{"interval1"} or \code{"interval2"} are supported, corresponding to ##' right-censored, left-truncated or interval-censored observations. ##' ##' If there are no covariates, specify \code{1} on the right hand side, for ##' example \code{Surv(time, dead) ~ 1}. ##' ##' If the right hand side is specified as \code{.} all remaining variables are ##' included as covariates. For example, \code{Surv(time, dead) ~ .} ##' corresponds to \code{Surv(time, dead) ~ age + sex} if \code{data} contains ##' the variables \code{time}, \code{dead}, \code{age}, and \code{sex}. ##' ##' By default, covariates are placed on the ``location'' parameter of the ##' distribution, typically the "scale" or "rate" parameter, through a linear ##' model, or a log-linear model if this parameter must be positive. This ##' gives an accelerated failure time model or a proportional hazards model ##' (see \code{dist} below) depending on how the distribution is ##' parameterised. ##' ##' Covariates can be placed on other (``ancillary'') parameters by using the ##' name of the parameter as a ``function'' in the formula. For example, in a ##' Weibull model, the following expresses the scale parameter in terms of age ##' and a treatment variable \code{treat}, and the shape parameter in terms of ##' sex and treatment. ##' ##' \code{Surv(time, dead) ~ age + treat + shape(sex) + shape(treat)} ##' ##' However, if the names of the ancillary parameters clash with any real ##' functions that might be used in formulae (such as \code{I()}, or ##' \code{factor()}), then those functions will not work in the formula. A ##' safer way to model covariates on ancillary parameters is through the ##' \code{anc} argument to \code{\link{flexsurvreg}}. ##' ##' \code{\link[survival]{survreg}} users should also note that the function ##' \code{strata()} is ignored, so that any covariates surrounded by ##' \code{strata()} are applied to the location parameter. Likewise the ##' function \code{frailty()} is not handled. ##' ##' @param anc An alternative and safer way to model covariates on ancillary ##' parameters, that is, parameters other than the main location parameter of ##' the distribution. This is a named list of formulae, with the name of each ##' component giving the parameter to be modelled. The model above can also ##' be defined as: ##' ##' \code{Surv(time, dead) ~ age + treat, anc = list(shape = ~ sex + ##' treat)} ##' @param data A data frame in which to find variables supplied in ##' \code{formula}. If not given, the variables should be in the ##' working environment. ##' ##' @param weights Optional numeric variable giving weights for each ##' individual in the data. The fitted model is then defined by ##' maximising the weighted sum of the individual-specific log-likelihoods. ##' ##' @param bhazard Optional variable giving expected hazards for relative ##' survival models. The model is described by Nelson et al. (2007). ##' ##' \code{bhazard} should contain a vector of values for each person in ##' the data. ##' ##' \itemize{ ##' \item For people with observed events, \code{bhazard} refers to the ##' hazard at the observed event time. ##' ##' \item For people whose event time is ##' left-censored or interval-censored, \code{bhazard} should contain the ##' probability of dying by the end of the corresponding interval, ##' conditionally on being alive at the start. ##' ##' \item For people whose event time ##' is right-censored, the value of \code{bhazard} is ignored and does not ##' need to be specified. ##' } ##' ##' If \code{bhazard} is supplied, then the parameter estimates returned by ##' \code{flexsurvreg} and the outputs returned by \code{summary.flexsurvreg} ##' describe the parametric model for relative survival. ##' ##' For relative survival models, the log-likelihood returned by \code{flexsurvreg} is a partial ##' log-likelihood, which omits a constant term defined by the sum of the ##' cumulative hazards at the event or censoring time for each individual. ##' Hence this constant must be added if a full likelihood is needed. ##' ##' @param rtrunc Optional variable giving individual-specific right-truncation ##' times. Used for analysing data with "retrospective ascertainment". For ##' example, suppose we want to estimate the distribution of the time from ##' onset of a disease to death, but have only observed cases known to have ##' died by the current date. In this case, times from onset to death for ##' individuals in the data are right-truncated by the current date minus the ##' onset date. Predicted survival times for new cases can then be described ##' by an un-truncated version of the fitted distribution. ##' ##' These models can suffer from weakly identifiable parameters and ##' badly-behaved likelihood functions, and it is advised to compare ##' convergence for different initial values by supplying different ##' \code{inits} arguments to \code{flexsurvreg}. ##' ##' @param subset Vector of integers or logicals specifying the subset of the ##' observations to be used in the fit. ##' @param na.action a missing-data filter function, applied after any 'subset' ##' argument has been used. Default is \code{options()$na.action}. ##' @param dist Typically, one of the strings in the first column of the ##' following table, identifying a built-in distribution. This table also ##' identifies the location parameters, and whether covariates on these ##' parameters represent a proportional hazards (PH) or accelerated failure ##' time (AFT) model. In an accelerated failure time model, the covariate ##' speeds up or slows down the passage of time. So if the coefficient ##' (presented on the log scale) is log(2), then doubling the covariate value ##' would give half the expected survival time. ##' ##' \tabular{llll}{ \code{"gengamma"} \tab Generalized gamma (stable) \tab mu ##' \tab AFT \cr \code{"gengamma.orig"} \tab Generalized gamma (original) \tab ##' scale \tab AFT \cr \code{"genf"} \tab Generalized F (stable) \tab mu \tab ##' AFT \cr \code{"genf.orig"} \tab Generalized F (original) \tab mu \tab AFT ##' \cr \code{"weibull"} \tab Weibull \tab scale \tab AFT \cr \code{"gamma"} ##' \tab Gamma \tab rate \tab AFT \cr \code{"exp"} \tab Exponential \tab rate ##' \tab PH \cr \code{"llogis"} \tab Log-logistic \tab scale \tab AFT \cr ##' \code{"lnorm"} \tab Log-normal \tab meanlog \tab AFT \cr \code{"gompertz"} ##' \tab Gompertz \tab rate \tab PH \cr } ##' ##' \code{"exponential"} and \code{"lognormal"} can be used as aliases for ##' \code{"exp"} and \code{"lnorm"}, for compatibility with ##' \code{\link[survival]{survreg}}. ##' ##' Alternatively, \code{dist} can be a list specifying a custom distribution. ##' See section ``Custom distributions'' below for how to construct this list. ##' ##' Very flexible spline-based distributions can also be fitted with ##' \code{\link{flexsurvspline}}. ##' ##' The parameterisations of the built-in distributions used here are the same ##' as in their built-in distribution functions: \code{\link{dgengamma}}, ##' \code{\link{dgengamma.orig}}, \code{\link{dgenf}}, ##' \code{\link{dgenf.orig}}, \code{\link{dweibull}}, \code{\link{dgamma}}, ##' \code{\link{dexp}}, \code{\link{dlnorm}}, \code{\link{dgompertz}}, ##' respectively. The functions in base R are used where available, ##' otherwise, they are provided in this package. ##' ##' A package vignette "Distributions reference" lists the survivor functions ##' and covariate effect parameterisations used by each built-in distribution. ##' ##' For the Weibull, exponential and log-normal distributions, ##' \code{\link{flexsurvreg}} simply works by calling \code{\link[survival]{survreg}} to ##' obtain the maximum likelihood estimates, then calling \code{\link{optim}} ##' to double-check convergence and obtain the covariance matrix for ##' \code{\link{flexsurvreg}}'s preferred parameterisation. ##' ##' The Weibull parameterisation is different from that in ##' \code{\link[survival]{survreg}}, instead it is consistent with ##' \code{\link{dweibull}}. The \code{"scale"} reported by ##' \code{\link[survival]{survreg}} is equivalent to \code{1/shape} as defined ##' by \code{\link{dweibull}} and hence \code{\link{flexsurvreg}}. The first ##' coefficient \code{(Intercept)} reported by \code{\link[survival]{survreg}} ##' is equivalent to \code{log(scale)} in \code{\link{dweibull}} and ##' \code{\link{flexsurvreg}}. ##' ##' Similarly in the exponential distribution, the rate, rather than the mean, ##' is modelled on covariates. ##' ##' The object \code{flexsurv.dists} lists the names of the built-in ##' distributions, their parameters, location parameter, functions used to ##' transform the parameter ranges to and from the real line, and the ##' functions used to generate initial values of each parameter for ##' estimation. ##' @param inits An optional numeric vector giving initial values for each ##' unknown parameter. These are numbered in the order: baseline parameters ##' (in the order they appear in the distribution function, e.g. shape before ##' scale in the Weibull), covariate effects on the location parameter, ##' covariate effects on the remaining parameters. This is the same order as ##' the printed estimates in the fitted model. ##' ##' If not specified, default initial values are chosen from a simple summary ##' of the survival or censoring times, for example the mean is often used to ##' initialize scale parameters. See the object \code{flexsurv.dists} for the ##' exact methods used. If the likelihood surface may be uneven, it is ##' advised to run the optimisation starting from various different initial ##' values to ensure convergence to the true global maximum. ##' @param fixedpars Vector of indices of parameters whose values will be fixed ##' at their initial values during the optimisation. The indices are ordered ##' as in \code{inits}. For example, in a stable generalized Gamma model with ##' two covariates, to fix the third of three generalized gamma parameters ##' (the shape \code{Q}, see the help for \code{\link{GenGamma}}) and the ##' second covariate, specify \code{fixedpars = c(3, 5)} ##' @param dfns An alternative way to define a custom survival distribution (see ##' section ``Custom distributions'' below). A list whose components may ##' include \code{"d"}, \code{"p"}, \code{"h"}, or \code{"H"} containing the ##' probability density, cumulative distribution, hazard, or cumulative hazard ##' functions of the distribution. For example, ##' ##' \code{list(d=dllogis, p=pllogis)}. ##' ##' If \code{dfns} is used, a custom \code{dlist} must still be provided, but ##' \code{dllogis} and \code{pllogis} need not be visible from the global ##' environment. This is useful if \code{flexsurvreg} is called within other ##' functions or environments where the distribution functions are also ##' defined dynamically. ##' @param aux A named list of other arguments to pass to custom distribution ##' functions. This is used, for example, by \code{\link{flexsurvspline}} to ##' supply the knot locations and modelling scale (e.g. hazard or odds). This ##' cannot be used to fix parameters of a distribution --- use ##' \code{fixedpars} for that. ##' @param cl Width of symmetric confidence intervals for maximum likelihood ##' estimates, by default 0.95. ##' @param integ.opts List of named arguments to pass to ##' \code{\link{integrate}}, if a custom density or hazard is provided without ##' its cumulative version. For example, ##' ##' \code{integ.opts = list(rel.tol=1e-12)} ##' ##' @param sr.control For the models which use \code{\link[survival]{survreg}} to find the ##' maximum likelihood estimates (Weibull, exponential, log-normal), this list ##' is passed as the \code{control} argument to \code{\link[survival]{survreg}}. ##' ##' @param ... Optional arguments to the general-purpose optimisation routine ##' \code{\link{optim}}. For example, the BFGS optimisation algorithm is the ##' default in \code{\link{flexsurvreg}}, but this can be changed, for example ##' to \code{method="Nelder-Mead"} which can be more robust to poor initial ##' values. If the optimisation fails to converge, consider normalising the ##' problem using, for example, \code{control=list(fnscale = 2500)}, for ##' example, replacing 2500 by a number of the order of magnitude of the ##' likelihood. If 'false' convergence is reported with a ##' non-positive-definite Hessian, then consider tightening the tolerance ##' criteria for convergence. If the optimisation takes a long time, ##' intermediate steps can be printed using the \code{trace} argument of the ##' control list. See \code{\link{optim}} for details. ##' ##' @param hessian Calculate the covariances and confidence intervals for the ##' parameters. Defaults to \code{TRUE}. ##' ##' @param hess.control List of options to control covariance matrix computation. ##' Available options are: ##' ##' \code{numeric}. If \code{TRUE} then numerical methods are used ##' to compute the Hessian for models where an analytic Hessian is ##' available. These models include the Weibull (both versions), ##' exponential, Gompertz and spline models with hazard or odds ##' scale. The default is to use the analytic Hessian for these ##' models. For all other models, numerical methods are always used ##' to compute the Hessian, whether or not this option is set. ##' ##' \code{tol.solve}. The tolerance used for \code{\link{solve}} ##' when inverting the Hessian (default \code{.Machine$double.eps}) ##' ##' \code{tol.evalues} The accepted tolerance for negative ##' eigenvalues in the covariance matrix (default \code{1e-05}). ##' ##' The Hessian is positive definite, thus invertible, at the maximum ##' likelihood. If the Hessian computed after optimisation convergence can't ##' be inverted, this is either because the converged result is not the ##' maximum likelihood (e.g. it could be a "saddle point"), or because the ##' numerical methods used to obtain the Hessian were inaccurate. If you ##' suspect that the Hessian was computed wrongly enough that it is not ##' invertible, but not wrongly enough that the nearest valid inverse would be ##' an inaccurate estimate of the covariance matrix, then these tolerance ##' values can be modified (reducing \code{tol.solve} or increasing ##' \code{tol.evalues}) to allow the inverse to be computed. ##' ##' ##' @return A list of class \code{"flexsurvreg"} containing information about ##' the fitted model. Components of interest to users may include: ##' \item{call}{A copy of the function call, for use in post-processing.} ##' \item{dlist}{List defining the survival distribution used.} ##' \item{res}{Matrix of maximum likelihood estimates and confidence limits, ##' with parameters on their natural scales.} \item{res.t}{Matrix of maximum ##' likelihood estimates and confidence limits, with parameters all ##' transformed to the real line (using a log transform for all built-in ##' models where this is necessary). The ##' \code{\link{coef}}, \code{\link{vcov}} ##' and \code{\link{confint}} methods for \code{flexsurvreg} objects work on ##' this scale.} \item{coefficients}{The transformed maximum likelihood ##' estimates, as in \code{res.t}. Calling \code{coef()} on a ##' \code{\link{flexsurvreg}} object simply returns this component.} ##' \item{loglik}{Log-likelihood. This will differ from Stata, where the sum ##' of the log uncensored survival times is added to the log-likelihood in ##' survival models, to remove dependency on the time scale. ##' ##' For relative survival models specified with \code{bhazard}, this is a partial ##' log-likelihood which omits a constant term defined by the sum of the ##' cumulative hazards over all event or censoring times. ##' } ##' \item{logliki}{Vector of individual contributions to the log-likelihood} ##' \item{AIC}{Akaike's information criterion (-2*log likelihood + 2*number of ##' estimated parameters)} \item{cov}{Covariance matrix of the parameters, on ##' the real-line scale (e.g. log scale), which can be extracted with ##' \code{\link{vcov}}.} \item{data}{Data used in the model fit. To extract ##' this in the standard R formats, use use ##' \code{\link{model.frame.flexsurvreg}} or ##' \code{\link{model.matrix.flexsurvreg}}.} ##' ##' @section Custom distributions: \code{\link{flexsurvreg}} is intended to be ##' easy to extend to handle new distributions. To define a new distribution ##' for use in \code{\link{flexsurvreg}}, construct a list with the following ##' elements: ##' ##' \describe{ \item{\code{"name"}}{A string naming the distribution. If this ##' is called \code{"dist"}, for example, then there must be visible in the ##' working environment, at least, either ##' ##' a) a function called \code{ddist} which defines the probability density, ##' ##' or ##' ##' b) a function called \code{hdist} which defines the hazard. ##' ##' Ideally, in case a) there should also be a function called \code{pdist} ##' which defines the probability distribution or cumulative density, and in ##' case b) there should be a function called \code{Hdist} defining the ##' cumulative hazard. If these additional functions are not provided, ##' \pkg{flexsurv} attempts to automatically create them by numerically ##' integrating the density or hazard function. However, model fitting will ##' be much slower, or may not even work at all, if the analytic versions of ##' these functions are not available. ##' ##' The functions must accept vector arguments (representing different times, ##' or alternative values for each parameter) and return the results as a ##' vector. The function \code{\link{Vectorize}} may be helpful for doing ##' this: see the example below. ##' These functions may be in an add-on package (see below for an example) or ##' may be user-written. If they are user-written they must be defined in the ##' global environment, or supplied explicitly through the \code{dfns} argument ##' to \code{flexsurvreg}. The latter may be useful if the functions are ##' created dynamically (as in the source of \code{flexsurvspline}) and thus ##' not visible through R's scoping rules. ##' ##' Arguments other than parameters must be named in the conventional way -- ##' for example \code{x} for the first argument of the density function or ##' hazard, as in \code{\link{dnorm}(x, ...)} and \code{q} for the first ##' argument of the probability function. Density functions should also have ##' an argument \code{log}, after the parameters, which when \code{TRUE}, ##' computes the log density, using a numerically stable additive formula if ##' possible. ##' ##' Additional functions with names beginning with \code{"DLd"} and ##' \code{"DLS"} may be defined to calculate the derivatives of the log density ##' and log survival probability, with respect to the parameters of the ##' distribution. The parameters are expressed on the real line, for example ##' after log transformation if they are defined as positive. The first ##' argument must be named \code{t}, representing the time, and the remaining ##' arguments must be named as the parameters of the density function. The ##' function must return a matrix with rows corresponding to times, and columns ##' corresponding to the parameters of the distribution. The derivatives are ##' used, if available, to speed up the model fitting with \code{\link{optim}}. ##' } \item{\code{"pars"}}{Vector of strings naming the parameters of the ##' distribution. These must be the same names as the arguments of the density ##' and probability functions. } ##' \item{\code{"location"}}{Name of the main parameter governing the mean of ##' the distribution. This is the default parameter on which covariates are ##' placed in the \code{formula} supplied to \code{flexsurvreg}. } ##' \item{\code{"transforms"}}{List of R ##' functions which transform the range of values taken by each parameter onto ##' the real line. For example, \code{c(log, log)} for a distribution with two ##' positive parameters. } ##' \item{\code{"inv.transforms"}}{List of R functions defining the ##' corresponding inverse transformations. Note these must be lists, even for ##' single parameter distributions they should be supplied as, e.g. ##' \code{c(exp)} or \code{list(exp)}. } ##' \item{\code{"inits"}}{A function of the ##' observed survival times \code{t} (including right-censoring times, and ##' using the halfway point for interval-censored times) which returns a vector ##' of reasonable initial values for maximum likelihood estimation of each ##' parameter. For example, \code{function(t){ c(1, mean(t)) }} will always ##' initialize the first of two parameters at 1, and the second (a scale ##' parameter, for instance) at the mean of \code{t}. } } ##' ##' For example, suppose we want to use an extreme value survival distribution. ##' This is available in the CRAN package \pkg{eha}, which provides ##' conventionally-defined density and probability functions called ##' \code{\link[eha:EV]{eha::dEV}} and \code{\link[eha:EV]{eha::pEV}}. See the Examples below ##' for the custom list in this case, and the subsequent command to fit the ##' model. ##' @author Christopher Jackson ##' @seealso \code{\link{flexsurvspline}} for flexible survival modelling using ##' the spline model of Royston and Parmar. ##' ##' \code{\link{plot.flexsurvreg}} and \code{\link{lines.flexsurvreg}} to plot ##' fitted survival, hazards and cumulative hazards from models fitted by ##' \code{\link{flexsurvreg}} and \code{\link{flexsurvspline}}. ##' @references Jackson, C. (2016). flexsurv: A Platform for Parametric ##' Survival Modeling in R. Journal of Statistical Software, 70(8), 1-33. ##' doi:10.18637/jss.v070.i08 ##' ##' Cox, C. (2008) The generalized \eqn{F} distribution: An umbrella for ##' parametric survival analysis. Statistics in Medicine 27:4301-4312. ##' ##' Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007) Parametric survival ##' analysis and taxonomy of hazard functions for the generalized gamma ##' distribution. Statistics in Medicine 26:4252-4374 ##' ##' Jackson, C. H. and Sharples, L. D. and Thompson, S. G. (2010) Survival ##' models in health economic evaluations: balancing fit and parsimony to ##' improve prediction. International Journal of Biostatistics 6(1):Article 34. ##' ##' Nelson, C. P., Lambert, P. C., Squire, I. B., & Jones, D. R. (2007). ##' Flexible parametric models for relative survival, with application in ##' coronary heart disease. Statistics in medicine, 26(30), 5486-5498. ##' ##' @keywords models survival ##' @examples ##' ##' ## Compare generalized gamma fit with Weibull ##' fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gengamma") ##' fitg ##' fitw <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="weibull") ##' fitw ##' plot(fitg) ##' lines(fitw, col="blue", lwd.ci=1, lty.ci=1) ##' ## Identical AIC, probably not enough data in this simple example for a ##' ## very flexible model to be worthwhile. ##' ##' ## Custom distribution ##' ## make "dEV" and "pEV" from eha package (if installed) ##' ## available to the working environment ##' if (require("eha")) { ##' custom.ev <- list(name="EV", ##' pars=c("shape","scale"), ##' location="scale", ##' transforms=c(log, log), ##' inv.transforms=c(exp, exp), ##' inits=function(t){ c(1, median(t)) }) ##' fitev <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, ##' dist=custom.ev) ##' fitev ##' lines(fitev, col="purple", col.ci="purple") ##' } ##' ##' ##' ## Custom distribution: supply the hazard function only ##' hexp2 <- function(x, rate=1){ rate } # exponential distribution ##' hexp2 <- Vectorize(hexp2) ##' custom.exp2 <- list(name="exp2", pars=c("rate"), location="rate", ##' transforms=c(log), inv.transforms=c(exp), ##' inits=function(t)1/mean(t)) ##' flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.exp2) ##' flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="exp") ##' ## should give same answer ##' ##' @export flexsurvreg <- function(formula, anc=NULL, data, weights, bhazard, rtrunc, subset, na.action, dist, inits, fixedpars=NULL, dfns=NULL, aux=NULL, cl=0.95, integ.opts=NULL, sr.control=survreg.control(), hessian=TRUE, hess.control=NULL, ...) { call <- match.call() if (missing(data)) data <- NULL if (missing(dist)) stop("Distribution \"dist\" not specified") dlist <- parse.dist(dist) dfns <- form.dp(dlist, dfns, integ.opts) parnames <- dlist$pars check.formula(formula, dlist, data) anc <- anc_from_formula(formula, anc, dlist, data = data) ancnames <- setdiff(parnames, dlist$location) forms <- c(location=get.locform(formula, ancnames, data), anc) names(forms)[[1]] <- dlist$location ## a) calling model.frame() directly doesn't work. it only looks in ## "data" or the environment of "formula" for extra variables like ## "weights". needs to also look in environment of flexsurvreg. ## should handle calling flexsurvreg within a function ## Make model frame indx <- match(c("formula", "data", "weights", "bhazard", "rtrunc", "subset", "na.action"), names(call), nomatch = 0) if (indx[1] == 0) stop("A \"formula\" argument is required") temp <- call[c(1, indx)] temp[[1]] <- as.name("model.frame") f2 <- concat.formulae(formula,forms, data) temp[["formula"]] <- terms(f2) if (missing(data)) temp[["data"]] <- environment(formula) m <- eval(temp, parent.frame()) m <- droplevels_keepcontrasts(m) # remove unused factor levels after subset applied attr(m,"covnames") <- attr(f2, "covnames") # for "newdata" in summary attr(m,"covnames.orig") <- intersect(colnames(m), attr(f2, "covnames.orig")) # for finding factors in plot method Y <- check.flexsurv.response(model.extract(m, "response")) mml <- mx <- vector(mode="list", length=length(dlist$pars)) names(mml) <- names(mx) <- c(dlist$location, setdiff(dlist$pars, dlist$location)) for (i in names(forms)){ mml[[i]] <- model.matrix(forms[[i]], m) mx[[i]] <- length(unlist(mx)) + seq_len(ncol(mml[[i]][,-1,drop=FALSE])) } X <- compress.model.matrices(mml) contr.save <- lapply(mml, function(x)attr(x,"contrasts")) weights <- model.extract(m, "weights") if (is.null(weights)) weights <- m$"(weights)" <- rep(1, nrow(X)) bhazard <- model.extract(m, "bhazard") if (is.null(bhazard)) bhazard <- rep(0, nrow(X)) rtrunc <- model.extract(m, "rtrunc") if (is.null(rtrunc)) rtrunc <- rep(Inf, nrow(X)) dat <- list(Y=Y, m=m, mml=mml) ncovs <- length(attr(m, "covnames.orig")) ncoveffs <- ncol(X) nbpars <- length(parnames) # number of baseline parameters npars <- nbpars + ncoveffs if (missing(inits) && is.null(dlist$inits)) stop("\"inits\" not supplied, and no function to estimate them found in the custom distribution list") if (missing(inits) || anyNA(inits)) { yy <- ifelse(Y[,"status"]==3 & is.finite(Y[,"time2"]), (Y[,"time1"] + Y[,"time2"])/2, Y[,"time1"]) wt <- yy*weights*length(yy)/sum(weights) dlist$inits <- expand.inits.args(dlist$inits) inits.aux <- c(aux, list(forms=forms, data=if(missing(data)) NULL else data, weights=temp$weights, control=sr.control, counting=(attr(model.extract(m, "response"), "type")=="counting") )) auto.inits <- dlist$inits(t=wt,mf=m,mml=mml,aux=inits.aux) if (!missing(inits) && anyNA(inits)) inits[is.na(inits)] <- auto.inits[is.na(inits)] else inits <- auto.inits } if (!is.numeric(inits)) stop ("initial values must be a numeric vector") nin <- length(inits) if (nin < npars && ncoveffs > 0) inits <- c(inits, rep(0,length.out=npars-nin)) else if (nin > npars){ inits <- inits[1:npars] warning("Initial values are a vector length > ", npars, ": using only the first ", npars) } else if (nin < nbpars){ stop("Initial values are a vector length ", nin, ", but distribution has ",nbpars, " parameters") } for (i in 1:nbpars) inits[i] <- dlist$transforms[[i]](inits[i]) outofrange <- which(is.nan(inits) | is.infinite(inits)) if (any(outofrange)){ plural <- if(length(outofrange) > 1) "s" else "" stop("Initial value", plural, " for parameter", plural, " ", paste(outofrange,collapse=","), " out of range") } names(inits) <- c(parnames, colnames(X)) check.fixedpars(fixedpars, npars) if ((is.logical(fixedpars) && fixedpars==TRUE) || (is.numeric(fixedpars) && identical(as.vector(fixedpars), 1:npars))) { minusloglik <- minusloglik.flexsurv(inits, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx) res.t <- matrix(inits, ncol=1) inits.nat <- inits for (i in 1:nbpars) inits.nat[i] <- dlist$inv.transforms[[i]](inits[i]) res <- matrix(inits.nat, ncol=1) dimnames(res) <- dimnames(res.t) <- list(names(inits), "est") ret <- list(res=res, res.t=res.t, npars=0, loglik=-as.vector(minusloglik), logliki=attr(minusloglik,"indiv")) } else { optpars <- inits[setdiff(1:npars, fixedpars)] optim.args <- list(...) if (is.null(optim.args$method)){ optim.args$method <- "BFGS" } gr <- if (dfns$deriv && deriv_supported(Y)) Dminusloglik.flexsurv else NULL has_analytic_hessian <- dfns$hessian && !isTRUE(hess.control$numeric) && deriv_supported(Y) optim.args <- c(optim.args, list(par=optpars, fn=logLikFactory(Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, inits=inits, dlist=dlist, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars), gr=gr, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars, hessian = hessian && !has_analytic_hessian)) opt <- do.call("optim", optim.args) est <- opt$par if (has_analytic_hessian) opt$hessian <- D2minusloglik.flexsurv(est, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) if (hessian && all(is.finite(opt$hessian))) { cov <- .hess_to_cov(opt$hessian, hess.control$tol.solve, hess.control$tol.evalues) se <- sqrt(diag(cov)) if (!is.numeric(cl) || length(cl)>1 || !(cl>0) || !(cl<1)) stop("cl must be a number in (0,1)") lcl <- est - qnorm(1 - (1-cl)/2)*se ucl <- est + qnorm(1 - (1-cl)/2)*se } else { if (hessian) warning("Optimisation has probably not converged to the maximum likelihood - Hessian is not finite. ") cov <- lcl <- ucl <- se <- NA } res <- cbind(est=inits, lcl=NA, ucl=NA, se=NA) res[setdiff(1:npars, fixedpars),] <- cbind(est, lcl, ucl, se) colnames(res) <- c("est", paste(c("L","U"), round(cl*100), "%", sep=""), "se") res.t <- res # results on transformed (log) scale for (i in 1:nbpars){ # results on natural scale res[i,1:3] <- dlist$inv.transforms[[i]](res[i,1:3]) if (identical(body(dlist$transforms[[i]]), body(log))) res[i,"se"] <- exp(res.t[i,"est"])*res.t[i,"se"] else if (identical(body(dlist$transforms[[i]]), body(logh))) res[i,"se"] <- dexph(res.t[i,"est"])*res.t[i,"se"] else if (!identical(dlist$transforms[[i]], identity)) res[i,"se"] <- NA ## theoretically could also do logit SE(g(x) = exp(x)/(1 + exp(x))) = g'(x) SE(x); g'(x) = exp(x)/(1 + exp(x))^2 ## or any interval scale (dglogit) as in msm } minusloglik <- minusloglik.flexsurv(res.t[,"est"], Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx) ret <- list(res=res, res.t=res.t, cov=cov, coefficients=res.t[,"est"], npars=length(est), fixedpars=fixedpars, optpars=setdiff(1:npars, fixedpars), loglik=-opt$value, logliki=attr(minusloglik,"indiv"), cl=cl, opt=opt) } covdata <- list(covnames = attr(dat$m, "covnames"), isfac = sapply(dat$m[,attr(dat$m,"covnames.orig"),drop=FALSE], is.factor), terms = attr(dat$m, "terms"), xlev = .getXlevels(attr(dat$m, "terms"), dat$m)) ret <- c(list(call=call, dlist=dlist, aux=aux, ncovs=ncovs, ncoveffs=ncoveffs, mx=mx, basepars=1:nbpars, covpars=if (ncoveffs>0) (nbpars+1):npars else NULL, AIC = -2*ret$loglik + 2*ret$npars, data = dat, datameans = colMeans(X), N=nrow(dat$Y), events=sum(dat$Y[,"status"]==1), trisk=sum(dat$Y[,"time"]), concat.formula=f2, all.formulae=forms, dfns=dfns), ret, list(all.contrasts=contr.save, covdata = covdata)) # temporary position so cyclomort doesn't break ret$BIC <- BIC.flexsurvreg(ret, cens=TRUE) ret <- c(ret, check_deriv(optpars=optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars)) class(ret) <- "flexsurvreg" ret } check_deriv <- function(optpars, Y, X, weights, bhazard, rtrunc, dlist, inits, dfns, aux, mx, fixedpars){ if (isTRUE(getOption("flexsurv.test.analytic.derivatives")) && deriv_supported(Y)){ if (is.logical(fixedpars) && fixedpars==TRUE) { optpars <- inits; fixedpars=FALSE } if (dfns$deriv) deriv.test <- deriv_test(optpars=optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) if (dfns$hessian) hess.test <- hess.test(optpars=optpars, Y=Y, X=X, weights=weights, bhazard=bhazard, rtrunc=rtrunc, dlist=dlist, inits=inits, dfns=dfns, aux=aux, mx=mx, fixedpars=fixedpars) res <- list(deriv.test=deriv.test, hess.test=hess.test) } else res <- NULL res } ##' @export print.flexsurvreg <- function(x, ...) { covs <- names(x$datameans) covinds <- match(covs, rownames(x$res)) cat("Call:\n") dput(x$call) cat("\n") if (x$npars > 0) { res <- x$res cat ("Estimates: \n") if (any(covinds)) { ecoefs <- matrix(NA, nrow=nrow(x$res), ncol=3) colnames(ecoefs) <- c("exp(est)", colnames(res)[2:3]) means <- rep(NA,nrow(x$res)) ecoefs[covinds,] <- exp(x$res[covinds,1:3,drop=FALSE]) means[covinds] <- x$datameans res <- cbind(means, res, ecoefs) colnames(res)[1] <- "data mean" } args <- list(...) if (is.null(args$digits)) args$digits <- 3 f <- do.call("format", c(list(x=res), args)) print(f, print.gap=2, quote=FALSE, na.print="") } llname <- if (all(x$bhazard == 0)) "Log-likelihood" else "Partial log-likelihood" llname <- sprintf("\n%s = ", llname) aicname <- if (all(x$bhazard == 0)) "AIC" else "Partial AIC" aicname <- sprintf("\n%s = ", aicname) cat("\nN = ", x$N, ", Events: ", x$events, ", Censored: ", x$N - x$events, "\nTotal time at risk: ", x$trisk, llname, x$loglik, ", df = ", x$npars, aicname, x$AIC, "\n\n", sep="") } form.model.matrix <- function(object, newdata, na.action=na.pass, forms=NULL){ ## If required covariate missing, give a slightly more informative error message than, e.g. ## "Error in eval(expr, envir, enclos) (from flexsurvreg.R#649) : object 'sex' not found" covnames <- object$covdata$covnames missing.covs <- unique(covnames[!covnames %in% names(newdata)]) if (length(missing.covs) > 0){ missing.covs <- sprintf("\"%s\"", missing.covs) plural <- if (length(missing.covs)>1) "s" else "" stop(sprintf("Value%s of covariate%s ",plural,plural), paste(missing.covs, collapse=", "), " not supplied in \"newdata\"") } ## as in predict.lm Terms <- delete.response(object$covdata$terms) mf <- model.frame(Terms, newdata, xlev = object$covdata$xlev, na.action=na.action) if (!is.null(cl <- attr(Terms, "dataClasses"))) .checkMFClasses(cl, mf) if (is.null(forms)) forms <- object$all.formulae mml <- vector(mode="list", length=length(forms)) names(mml) <- names(forms) forms[[1]] <- delete.response(terms(forms[[1]])) for (i in seq_along(forms)){ mml[[i]] <- model.matrix(forms[[i]], mf, contrasts.arg = object$all.contrasts[[i]]) } X <- compress.model.matrices(mml) attr(X, "newdata") <- mf # newdata with any extra variables stripped. Used to name components of summary list X } ##' Variance-covariance matrix from a flexsurvreg model ##' ##' @inheritParams logLik.flexsurvreg ##' ##' @return Variance-covariance matrix of the estimated parameters, on ##' the scale that they were estimated on (for positive parameters ##' this is the log scale). ##' ##' @export vcov.flexsurvreg <- function (object, ...) { object$cov } .onLoad <- function(libname, pkgname) { assign("flexsurv.dfns", new.env(), envir=parent.env(environment())) } ##' Extract original data from \code{flexsurvreg} objects. ##' ##' Extract the data from a model fitted with \code{flexsurvreg}. ##' ##' ##' @aliases model.frame.flexsurvreg model.matrix.flexsurvreg ##' @param formula A fitted model object, as returned by ##' \code{\link{flexsurvreg}}. ##' @param object A fitted model object, as returned by ##' \code{\link{flexsurvreg}}. ##' @param par String naming the parameter whose linear model matrix is ##' desired. ##' ##' The default value of \code{par=NULL} returns a matrix consisting of the ##' model matrices for all models in the object \code{cbind}ed together, with ##' the intercepts excluded. This is not really a ``model matrix'' in the ##' usual sense, however, the columns directly correspond to the covariate ##' coefficients in the matrix of estimates from the fitted model. ##' @param ... Further arguments (not used). ##' @return \code{model.frame} returns a data frame with all the original ##' variables used for the model fit. ##' ##' \code{model.matrix} returns a design matrix for a part of the model that ##' includes covariates. The required part is indicated by the \code{"par"} ##' argument (see above). ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @seealso \code{\link{flexsurvreg}}, \code{\link{model.frame}}, ##' \code{\link{model.matrix}}. ##' @keywords models ##' @export model.frame.flexsurvreg <- function(formula, ...) { x <- formula x$data$m } ##' @export ##' @rdname model.frame.flexsurvreg model.matrix.flexsurvreg <- function(object, par=NULL, ...) { x <- object if (is.null(par)) compress.model.matrices(x$data$mml) else x$data$mml[[par]] } ##' Log likelihood from a flexsurvreg model ##' ##' @param object A fitted model object of class ##' \code{\link{flexsurvreg}}, e.g. as returned by ##' \code{flexsurvreg} or \code{flexsurvspline}. ##' ##' @param ... Other arguments (currently unused). ##' ##' @return Log-likelihood (numeric) with additional attributes \code{df} (degrees of freedom, or number ##' of parameters that were estimated), and number of observations \code{nobs} (including observed ##' events and censored observations). ##' ##' @export logLik.flexsurvreg <- function(object, ...){ val <- object$loglik attr(val, "df") <- object$npars attr(val, "nobs") <- object$N class(val) <- "logLik" val } ##' Extract model coefficients from fitted flexible survival models ##' ##' Extract model coefficients from fitted flexible survival models. This ##' presents all parameter estimates, transformed to the real line if necessary. ##' For example, shape or scale parameters, which are constrained to be ##' positive, are returned on the log scale. ##' ##' This matches the behaviour of \code{coef.default} for standard R model ##' families such as \code{\link[stats]{glm}}, where intercepts in regression ##' models are presented on the same scale as the covariate effects. Note that ##' any parameter in a distribution fitted by \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvreg}} may be an intercept in a regression model. #' ##' @param object Output from \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}}, representing a fitted survival model object. ##' @param ... Further arguments passed to or from other methods. Currently ##' unused. ##' @return This returns the \code{mod$res.t[,"est"]} component of the fitted ##' model object \code{mod}. See \code{\link{flexsurvreg}}, ##' \code{\link{flexsurvspline}} for full documentation of all components. ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' @seealso \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}. ##' @keywords models ##' @export coef.flexsurvreg <- function(object, ...){ object$coefficients } ##' Number of observations contributing to a fitted flexible survival model ##' ##' Number of observations contributing to a fitted flexible survival model ##' ##' By default, this matches the behaviour of the \code{nobs} method for \code{\link[survival]{survreg}} objects, including both censored and uncensored observations. ##' ##' If a weighted \code{flexsurvreg} analysis was done, then this function returns the sum of the weights. ##' ##' @param object Output from \code{\link{flexsurvreg}} or ##' \code{\link{flexsurvspline}}, representing a fitted survival model object. ##' ##' @param cens Include censored observations in the number. \code{TRUE} by default. ##' If \code{FALSE} then the number of observed events is returned. See ##' \code{\link{BIC.flexsurvreg}} for a discussion of the issues ##' with defining the sample size for censored data. ##' ##' @param ... Further arguments passed to or from other methods. Currently ##' unused. ##' ##' @return This returns the \code{mod$N} component of the fitted ##' model object \code{mod}. See \code{\link{flexsurvreg}}, ##' \code{\link{flexsurvspline}} for full documentation of all components. ##' ##' @author C. H. Jackson \email{chris.jackson@@mrc-bsu.cam.ac.uk} ##' ##' @seealso \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}. ##' ##' @keywords models ##' ##' @export nobs.flexsurvreg <- function(object, cens=TRUE, ...){ if (cens) ind <- seq(length.out=nrow(object$data$Y)) else ind <- which(object$data$Y[,"status"] == 1) sum(object$data$m[ind,"(weights)"]) } ##' Bayesian Information Criterion (BIC) for comparison of flexsurvreg models ##' ##' Bayesian Information Criterion (BIC) for comparison of flexsurvreg models ##' ##' @param object Fitted model returned by \code{\link{flexsurvreg}} ##' (or \code{\link{flexsurvspline}}). ##' ##' @param cens Include censored observations in the sample size term ##' (\code{n}) used in the calculation of BIC. ##' ##' @return The BIC of the fitted model. This is minus twice the log likelihood plus \code{p*log(n)}, where ##' \code{p} is the number of parameters and \code{n} is the sample ##' size of the data. If \code{weights} was supplied to ##' \code{flexsurv}, the sample size is defined as the sum of the ##' weights. ##' ##' @param ... Other arguments (currently unused). ##' ##' @details There is no "official" definition of what the sample size ##' should be for the use of BIC in censored survival analysis. BIC ##' is based on an approximation to Bayesian model comparison using ##' Bayes factors and an implicit vague prior. Informally, the ##' sample size describes the number of "units" giving rise to a ##' distinct piece of information (Kass and Raftery 1995). However ##' censored observations provide less information than observed ##' events, in principle. The default used here is the number of ##' individuals, for consistency with more familiar kinds of ##' statistical modelling. However if censoring is heavy, then the ##' number of events may be a better represent the amount of ##' information. Following these principles, the best approximation ##' would be expected to be somewere in between. ##' ##' AIC and BIC are intended to measure different things. Briefly, ##' AIC measures predictive ability, whereas BIC is expected to choose ##' the true model from a set of models where one of them is the ##' truth. Therefore BIC chooses simpler models for all but the ##' tiniest sample sizes (\eqn{log(n)>2}, \eqn{n>7}). AIC might be preferred in the ##' typical situation where ##' "all models are wrong but some are useful". AIC also gives similar ##' results to cross-validation (Stone 1977). ##' ##' @references Kass, R. E., & Raftery, A. E. (1995). Bayes ##' factors. Journal of the American Statistical Association, ##' 90(430), 773-795. ##' ##' @references Stone, M. (1977). An asymptotic equivalence of choice ##' of model by crossâ€validation and Akaike's criterion. Journal of ##' the Royal Statistical Society: Series B (Methodological), 39(1), ##' 44-47. ##' ##' @seealso \code{\link{BIC}}, \code{\link{AIC}}, \code{\link{AICC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}} ##' ##' @export BIC.flexsurvreg <- function(object, cens = TRUE, ...){ n <- nobs.flexsurvreg(object, cens=cens) -2*object$loglik + object$npars * log(n) } ##' Second-order Akaike information criterion ##' ##' Second-order or "corrected" Akaike information criterion, often ##' known as AICc (see, e.g. Burnham and Anderson 2002). This is ##' defined as -2 log-likelihood + \code{(2*p*n)/(n - p -1)}, whereas ##' the standard AIC is defined as -2 log-likelihood + \code{2*p}, ##' where \code{p} is the number of parameters and \code{n} is the ##' sample size. The correction is intended to adjust AIC for ##' small-sample bias, hence it only makes a difference to the result ##' for small \code{n}. ##' ##' This can be spelt either as \code{AICC} or \code{AICc}. ##' ##' @param object Fitted model returned by \code{\link{flexsurvreg}} ##' (or \code{\link{flexsurvspline}}). ##' ##' @param cens Include censored observations in the sample size term ##' (\code{n}) used in this calculation. See ##' \code{\link{BIC.flexsurvreg}} for a discussion of the issues ##' with defining the sample size. ##' ##' @param ... Other arguments (currently unused). ##' ##' @references Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York. ##' ##' @return The second-order AIC of the fitted model. ##' ##' @seealso \code{\link{BIC}}, \code{\link{AIC}}, \code{\link{BIC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}} ##' ##' @export AICc.flexsurvreg <- function(object, cens=TRUE, ...){ n <- nobs.flexsurvreg(object, cens=cens) p <- object$npars ## equivalently: object$AIC + ((2 * p) * (p + 1) / (n - p - 1)) -2*object$loglik + (2*p*n) / (n - p - 1) } ##' @rdname AICc.flexsurvreg ##' @export AICC.flexsurvreg <- AICc.flexsurvreg ##' Second-order Akaike information criterion ##' ##' Generic function for the second-order Akaike information criterion. ##' The only current implementation of this in \pkg{flexsurv} is ##' in \code{\link{AICc.flexsurvreg}}, see there for more details. ##' ##' This can be spelt either as \code{AICC} or \code{AICc}. ##' ##' @param object Fitted model object. ##' ##' @param ... Other arguments (currently unused). ##' ##' @export AICc <- function (object, ...) UseMethod("AICc") ##' @rdname AICc ##' @export AICC <- AICc deriv_supported <- function(Y){ event <- Y[,"status"] == 1 left_cens <- is.finite(Y[!event, "time2"]) !any(left_cens) } droplevels_factor_keepcontrasts <- function (x, exclude = if (anyNA(levels(x))) NULL else NA, ...) { ct <- attr(x, "contrasts") x <- factor(x, exclude = exclude) contrasts(x) <- ct x } droplevels_keepcontrasts <- function (x, except = NULL, exclude, ...) { ix <- vapply(x, is.factor, NA) if (!is.null(except)) ix[except] <- FALSE x[ix] <- if (missing(exclude)) lapply(x[ix], droplevels_factor_keepcontrasts) else lapply(x[ix], droplevels_factor_keepcontrasts, exclude = exclude) x } flexsurv/R/broom-funs.R0000644000176200001440000002350414644755103014560 0ustar liggesusers#' Tidy a flexsurv model object #' #' Tidy summarizes information about the components of the model into a tidy data frame. #' #' @param x Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object. #' #' @param conf.int Logical. Should confidence intervals be returned? Default is \code{FALSE}. #' #' @param conf.level The confidence level to use for the confidence interval if \code{conf.int = TRUE}. Default is \code{0.95}. #' #' @param pars One of \code{"all"}, \code{"baseline"}, or \code{"coefs"} for all parameters, baseline distribution parameters, or covariate effects (i.e. regression betas), respectively. Default is \code{"all"}. #' #' @param transform Character vector of transformations to apply to requested \code{pars}. Default is \code{"none"}, which returns \code{pars} as-is. #' #' Users can specify one or both types of transformations: #' #' * \code{"baseline.real"} which transforms the baseline distribution parameters to the real number line used for estimation. #' #' * \code{"coefs.exp"} which exponentiates the covariate effects. #' #' See \code{Details} for a more complete explanation. #' #' @param ... Not currently used. #' #' @details \code{flexsurvreg} models estimate two types of coefficients, baseline distribution parameters, and covariate effects which act on the baseline distribution. By design, \code{flexsurvreg} returns distribution parameters on the same scale as is found in the relevant \code{d/p/q/r} functions. Covariate effects are returned on the log-scale, which represents either log-time ratios (accelerated failure time models) or log-hazard ratios for proportional hazard models. By default, \code{tidy()} will return baseline distribution parameters on their natural scale and covariate effects on the log-scale. #' #' To transform the baseline distribution parameters to the real-value number line (the scale used for estimation), pass the character argument \code{"baseline.real"} to \code{transform}. To get time ratios or hazard ratios, pass \code{"coefs.exp"} to \code{transform}. These transformations may be done together by submitting both arguments as a character vector. #' #' @return A \code{\link[tibble]{tibble}} containing the columns: \code{term}, \code{estimate}, \code{std.error}, \code{statistic}, \code{p.value}, \code{conf.low}, and \code{conf.high}, by default. #' #' \code{statistic} and \code{p.value} are only provided for covariate effects (\code{NA} for baseline distribution parameters). These are computed as Wald-type test statistics with p-values from a standard normal distribution. #' #' @importFrom purrr map2_dbl #' #' @md #' #' @export #' #' @examples #' #' fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") #' tidy(fitg) #' tidy(fitg, pars = "coefs", transform = "coefs.exp") #' tidy.flexsurvreg <- function(x, conf.int = FALSE, conf.level = 0.95, pars = "all", transform = "none", ...) { assertthat::assert_that(is.logical(conf.int)) if (conf.int) assertthat::assert_that(is.numeric(conf.level), conf.level > 0, conf.level < 1, length(conf.level) == 1, msg = "`conf.level` must be length one and between 0 and 1") pars <- match.arg(pars, c("all", "coefs", "baseline")) transform <- match.arg(transform, c("none", "baseline.real", "coefs.exp"), several.ok = TRUE) dist_pars <- x$dlist$pars if ("baseline.real" %in% transform) vals <- x$res.t else vals <- x$res coefs <- vals[, "est"] terms <- rownames(vals) ses <- vals[, "se"] stats <- coefs / ses; stats[names(stats) %in% dist_pars] <- NA pvals <- 2 * pnorm(abs(stats), lower.tail = FALSE) coef_pars <- terms[which(!terms %in% dist_pars)] if (conf.int) cis <- confint(x, level = conf.level) else cis <- NULL if (!"baseline.real" %in% transform && any(rownames(cis) %in% dist_pars)) { cis[rownames(cis) %in% dist_pars, 1] <- purrr::map2_dbl(cis[rownames(cis) %in% dist_pars, 1], x$dlist$inv.transforms, ~.y(.x)) cis[rownames(cis) %in% dist_pars, 2] <- purrr::map2_dbl(cis[rownames(cis) %in% dist_pars, 2], x$dlist$inv.transforms, ~.y(.x)) } if ("coefs.exp" %in% transform & conf.int) { coefs[terms %in% coef_pars] <- exp(coefs[terms %in% coef_pars]) ses[terms %in% coef_pars] <- exp(ses[terms %in% coef_pars]) cis[terms %in% coef_pars] <- exp(cis[terms %in% coef_pars]) } else if ("coefs.exp" %in% transform) { coefs[terms %in% coef_pars] <- exp(coefs[terms %in% coef_pars]) ses[terms %in% coef_pars] <- exp(ses[terms %in% coef_pars]) } lcl <- cis[, 1] ucl <- cis[, 2] res <- tibble::tibble( term = terms, estimate = coefs, std.error = ses, statistic = stats, p.value = pvals, conf.low = !!lcl, conf.high = !!ucl ) if (pars == "coefs") { return(res[res$term %in% coef_pars, ]) } else if (pars == "baseline") { return(res[res$term %in% dist_pars, ]) } else { res } } #' @importFrom generics tidy #' @export generics::tidy #' Glance at a flexsurv model object #' #' Glance accepts a model object and returns a tibble with exactly one row of model summaries. #' #' @param x Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object. #' #' @param ... Not currently used. #' #' @return A one-row \code{\link[tibble]{tibble}} containing columns: #' #' * \code{N} Number of observations used in fitting #' #' * \code{events} Number of events #' #' * \code{censored} Number of censored events #' #' * \code{trisk} Total length of time-at-risk (i.e. follow-up) #' #' * \code{df} Degrees of freedom (i.e. number of estimated parameters) #' #' * \code{logLik} Log-likelihood #' #' * \code{AIC} Akaike's "An Information Criteria" #' #' * \code{BIC} Bayesian Information Criteria #' #' @export #' #' @md #' #' @examples #' fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") #' glance(fitg) #' glance.flexsurvreg <- function(x, ...) { tibble::tibble( N = x$N, events = x$events, censored = x$N - x$events, trisk = x$trisk, df = x$npars, # global test statistic? # global p.value? logLik = x$loglik, AIC = x$AIC, BIC = BIC(x) ) } #' @importFrom generics glance #' @export generics::glance #' Augment data with information from a flexsurv model object #' #' Augment accepts a model object and a dataset and adds information about each observation in the dataset. Most commonly, this includes predicted values in the \code{.fitted} column, residuals in the \code{.resid} column, and standard errors for the fitted values in a \code{.se.fit} column. New columns always begin with a . prefix to avoid overwriting columns in the original dataset. #' #' @param x Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object. #' #' @param data A \code{\link{data.frame}} or \code{\link[tibble]{tibble}} containing the original data that was used to produce the object \code{x}. #' #' @param newdata A \code{\link{data.frame}} or \code{\link[tibble]{tibble}} containing all the original predictors used to create \code{x}. Defaults to \code{NULL}, indicating that nothing has been passed to \code{newdata}. If \code{newdata} is specified, the \code{data} argument will be ignored. #' #' @param type.predict Character indicating type of prediction to use. Passed to the \code{type} argument of the \code{\link{predict}} generic. Allowed arguments vary with model class, so be sure to read the \code{predict.my_class} documentation. #' #' @param type.residuals Character indicating type of residuals to use. Passed to the type argument of \code{\link{residuals}} generic. Allowed arguments vary with model class, so be sure to read the \code{residuals.my_class} documentation. #' #' @param ... Additional arguments. Not currently used. #' #' @details If neither of \code{data} or \code{newdata} are specified, then \code{model.frame(x)} will be used. It is worth noting that \code{model.frame(x)} will include a \code{\link[survival]{Surv}} object and not the original time-to-event variables used when fitting the \code{flexsurvreg} object. If the original data is desired, specify \code{data}. #' #' @return A \code{\link[tibble]{tibble}} containing \code{data} or \code{newdata} and possible additional columns: #' #' * \code{.fitted} Fitted values of model #' #' * \code{.se.fit} Standard errors of fitted values #' #' * \code{.resid} Residuals (not present if \code{newdata} specified) #' #' @importFrom tidyr unnest #' #' @md #' #' @export #' #' @examples #' fit <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "exp") #' augment(fit, data = ovarian) #' augment.flexsurvreg <- function(x, data = NULL, newdata = NULL, type.predict = "response", type.residuals = "response", ...) { if (is.null(data) && is.null(newdata)) { data <- model.frame(x) } type.predict <- match.arg(type.predict, c("response")) type.residuals <- match.arg(type.residuals, c("response")) if (is.null(newdata)) { preds <- predict(x, type = type.predict, se.fit = TRUE) res <- tibble::as_tibble(data) res <- dplyr::bind_cols( res, preds, .resid = residuals(x, type = type.residuals) ) } else { preds <- predict(x, type = type.predict, se.fit = TRUE, newdata = newdata) res <- tibble::as_tibble(newdata) res <- dplyr::bind_cols(res, preds) } res } utils::globalVariables(".pred") #' @importFrom generics augment #' @export generics::augment flexsurv/R/Llogis.R0000644000176200001440000001236414472142637013725 0ustar liggesusers##' The log-logistic distribution ##' ##' Density, distribution function, hazards, quantile function and ##' random generation for the log-logistic distribution. ##' ##' The log-logistic distribution with \code{shape} parameter ##' \eqn{a>0} and \code{scale} parameter \eqn{b>0} has probability ##' density function ##' ##' \deqn{f(x | a, b) = (a/b) (x/b)^{a-1} / (1 + (x/b)^a)^2} ##' ##' and hazard ##' ##' \deqn{h(x | a, b) = (a/b) (x/b)^{a-1} / (1 + (x/b)^a)} ##' ##' for \eqn{x>0}. The hazard is decreasing for shape \eqn{a\leq 1}{a ##' <= 1}, and unimodal for \eqn{a > 1}. ##' ##' The probability distribution function is \deqn{F(x | a, b) = 1 - 1 ##' / (1 + (x/b)^a)} ##' ##' If \eqn{a > 1}, the mean is \eqn{b c / sin(c)}, and if \eqn{a > 2} ##' the variance is \eqn{b^2 * (2*c/sin(2*c) - c^2/sin(c)^2)}, where ##' \eqn{c = \pi/a}, otherwise these are undefined. ##' ##' @aliases Llogis dllogis pllogis qllogis hllogis Hllogis rllogis ##' @param x,q vector of quantiles. ##' @param p vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the ##' length is taken to be the number required. ##' @param shape,scale vector of shape and scale parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as ##' log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are ##' \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dllogis} gives the density, \code{pllogis} gives the ##' distribution function, \code{qllogis} gives the quantile function, ##' \code{hllogis} gives the hazard function, \code{Hllogis} gives the ##' cumulative hazard function, and \code{rllogis} generates random ##' deviates. ##' @note Various different parameterisations of this distribution are ##' used. In the one used here, the interpretation of the parameters ##' is the same as in the standard Weibull distribution ##' (\code{\link{dweibull}}). Like the Weibull, the survivor function ##' is a transformation of \eqn{(x/b)^a} from the non-negative real line to [0,1], ##' but with a different link function. Covariates on \eqn{b} ##' represent time acceleration factors, or ratios of expected ##' survival. ##' ##' The same parameterisation is also used in ##' \code{\link[eha:Loglogistic]{eha::dllogis}} in the \pkg{eha} package. ##' @author Christopher Jackson ##' @seealso \code{\link{dweibull}} ##' @references Stata Press (2007) Stata release 10 manual: Survival analysis ##' and epidemiological tables. ##' @keywords distribution ##' @name Llogis NULL ##' @export ##' @rdname Llogis dllogis <- function(x, shape=1, scale=1, log = FALSE) { check_numeric(x=x, shape=shape, scale=scale) dllogis_work(x, shape, scale, log) } ##' @export ##' @rdname Llogis pllogis <- function(q, shape=1, scale=1, lower.tail = TRUE, log.p = FALSE) { check_numeric(q=q, shape=shape, scale=scale) pllogis_work(q, shape, scale, lower.tail, log.p) } ##' @export ##' @rdname Llogis qllogis <- function(p, shape=1, scale=1, lower.tail = TRUE, log.p = FALSE) { d <- dbase("llogis", lower.tail=lower.tail, log=log.p, p=p, shape=shape, scale=scale) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) # lower.tail is handled in dbase() by transforming p to 1-p ret[ind] <- exp(qlogis(p, log(scale), 1/shape, lower.tail=TRUE, log.p)) ret } ##' @export ##' @rdname Llogis rllogis <- function(n, shape=1, scale=1){ r <- rbase("llogis", n=n, shape=shape, scale=scale) for (i in seq_along(r)) assign(names(r)[i], r[[i]]) ret[ind] <- qllogis(p=runif(sum(ind)), shape=shape, scale=scale) ret } ##' @export ##' @rdname Llogis hllogis <- function(x, shape=1, scale=1, log = FALSE) { h <- dbase("llogis", log=log, x=x, shape=shape, scale=scale) for (i in seq_along(h)) assign(names(h)[i], h[[i]]) if (log) ret[ind] <- log(shape) - log(scale) + (shape-1)*(log(x) - log(scale)) - log(1 + (x/scale)^shape) else ret[ind] <- (shape/scale) * (x/scale)^{shape-1} / (1 + (x/scale)^shape) ret } ##' @export ##' @rdname Llogis Hllogis <- function(x, shape=1, scale=1, log = FALSE) { ret <- - pllogis(x, shape, scale, lower.tail=FALSE, log.p=TRUE) if (log) ret <- log(ret) ret } DLdllogis <- function(t, shape, scale){ res <- matrix(nrow=length(t), ncol=2) tss <- (t/scale)^shape ilt <- tss / (1 + tss) res[,1] <- 1 + (1 - 2*ilt)*shape*log(t/scale) res[,2] <- - shape + 2*ilt*shape res } DLSllogis <- function(t, shape, scale){ res <- matrix(nrow=length(t), ncol=2) tss <- (t/scale)^shape ilt <- tss / (1 + tss) res[,1] <- ifelse(t==0, 0, -ilt*log(t/scale)*shape) res[,2] <- shape*ilt res } ##' @export ##' @rdname means mean_llogis <- function(shape=1, scale=1){ ifelse(shape > 1, {b <- pi/shape scale*b / sin(b)}, NaN) } ##' @export ##' @rdname means rmst_llogis = function(t, shape=1, scale=1, start=0){ rmst_generic(pllogis, t, start=start, shape=shape, scale=scale) } var.llogis <- function(shape=1, scale=1){ ifelse(shape > 2, {b <- pi/shape scale^2 * (2*b/sin(2*b) - b^2/sin(b)^2)}, NaN) } flexsurv/R/GenF.R0000644000176200001440000003306714603767312013315 0ustar liggesusers##' Generalized F distribution (original parameterisation) ##' ##' Density, distribution function, quantile function and random ##' generation for the generalized F distribution, using the less ##' flexible original parameterisation described by Prentice (1975). ##' ##' If \eqn{y \sim F(2s_1, 2s_2)}{y ~ F(2*s1, 2*s2)}, and \eqn{w = \log(y)}{w = ##' log(y)} then \eqn{x = \exp(w\sigma + \mu)}{x = ##' exp(w*sigma + mu)} has the original generalized F distribution with ##' location parameter \eqn{\mu}{mu}, scale parameter \eqn{\sigma>0}{sigma>0} ##' and shape parameters \eqn{s_1>0,s_2>0}{s1>0,s2>0}. The probability density ##' function of \eqn{x} is ##' ##' \deqn{f(x | \mu, \sigma, s_1, s_2) = \frac{(s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 + s_2)} B(s_1, s_2)}}{ ##' f(x | mu, sigma, s_1, s_2) = ((s1/s2)^{s1} e^{s1 w}) / (sigma x (1 + s1 e^w/s2) ^ (s1 + s2) B(s1, s2))} ##' ##' where \eqn{w = (\log(x) - \mu)/\sigma}{w = (log(x) - mu)/sigma}, and ##' \eqn{B(s_1,s_2) = \Gamma(s_1)\Gamma(s_2)/\Gamma(s_1+s_2)}{B(s1,s2) = ##' \Gamma(s1)\Gamma(s2)/\Gamma(s1+s2)} is the beta function. ##' ##' As \eqn{s_2 \rightarrow \infty}{s2 -> infinity}, the distribution ##' of \eqn{x} tends towards an original generalized gamma ##' distribution with the following parameters: ##' ##' \code{\link{dgengamma.orig}(x, shape=1/sigma, scale=exp(mu) / ##' s1^sigma, k=s1)} ##' ##' See \code{\link{GenGamma.orig}} for how this includes several ##' other common distributions as special cases. ##' ##' The alternative parameterisation of the generalized F ##' distribution, originating from Prentice (1975) and given in this ##' package as \code{\link{GenF}}, is preferred for statistical ##' modelling, since it is more stable as \eqn{s_1}{s1} tends to ##' infinity, and includes a further new class of distributions with ##' negative first shape parameter. The original is provided here for ##' the sake of completion and compatibility. ##' ##' @aliases GenF.orig dgenf.orig pgenf.orig qgenf.orig rgenf.orig Hgenf.orig ##' hgenf.orig ##' @param x,q vector of quantiles. ##' @param p vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the length is ##' taken to be the number required. ##' @param mu Vector of location parameters. ##' @param sigma Vector of scale parameters. ##' @param s1 Vector of first F shape parameters. ##' @param s2 vector of second F shape parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dgenf.orig} gives the density, \code{pgenf.orig} gives the ##' distribution function, \code{qgenf.orig} gives the quantile function, ##' \code{rgenf.orig} generates random deviates, \code{Hgenf.orig} retuns the ##' cumulative hazard and \code{hgenf.orig} the hazard. ##' @author Christopher Jackson ##' @seealso \code{\link{GenF}}, \code{\link{GenGamma.orig}}, ##' \code{\link{GenGamma}} ##' @references R. L. Prentice (1975). Discrimination among some parametric ##' models. Biometrika 62(3):607-614. ##' @keywords distribution ##' @name GenF.orig NULL ##' Generalized F distribution ##' ##' Density, distribution function, hazards, quantile function and ##' random generation for the generalized F distribution, using the ##' reparameterisation by Prentice (1975). ##' ##' If \eqn{y \sim F(2s_1, 2s_2)}{y ~ F(2*s1, 2*s2)}, and \eqn{w = }{w = ##' log(y)}\eqn{ \log(y)}{w = log(y)} then \eqn{x = \exp(w\sigma + \mu)}{x = ##' exp(w*sigma + mu)} has the original generalized F distribution with ##' location parameter \eqn{\mu}{mu}, scale parameter \eqn{\sigma>0}{sigma>0} ##' and shape parameters \eqn{s_1,s_2}{s1,s2}. ##' ##' In this more stable version described by Prentice (1975), ##' \eqn{s_1,s_2}{s1,s2} are replaced by shape parameters \eqn{Q,P}, with ##' \eqn{P>0}, and ##' ##' \deqn{s_1 = 2(Q^2 + 2P + Q\delta)^{-1}, \quad s_2 = 2(Q^2 + 2P - ##' Q\delta)^{-1}}{s1 = 2 / (Q^2 + 2P + Q*delta), s2 = 2 / (Q^2 + 2P - ##' Q*delta)} equivalently \deqn{Q = \left(\frac{1}{s_1} - ##' \frac{1}{s_2}\right)\left(\frac{1}{s_1} + \frac{1}{s_2}\right)^{-1/2}, ##' \quad P = \frac{2}{s_1 + s_2} }{Q = (1/s1 - 1/s2) / (1/s1 + 1/s2)^{-1/2}, P ##' = 2 / (s1 + s2) } ##' ##' Define \eqn{\delta = (Q^2 + 2P)^{1/2}}{delta = (Q^2 + 2P)^{1/2}}, and ##' \eqn{w = (\log(x) - \mu)\delta /\sigma}{w = (log(x) - mu)delta / sigma}, ##' then the probability density function of \eqn{x} is \deqn{ f(x) = ##' \frac{\delta (s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 ##' + s_2)} B(s_1, s_2)} }{ f(x) = (delta (s1/s2)^{s1} e^{s1 w}) / (sigma t (1 ##' + s1 e^w/s2) ^ {(s1 + s2)} B(s1, s2)) } The ##' original parameterisation is available in this package as ##' \code{\link{dgenf.orig}}, for the sake of completion / compatibility. With ##' the above definitions, ##' ##' \code{dgenf(x, mu=mu, sigma=sigma, Q=Q, P=P) = dgenf.orig(x, mu=mu, ##' sigma=sigma/delta, s1=s1, s2=s2)} ##' ##' The generalized F distribution with \code{P=0} is equivalent to the ##' generalized gamma distribution \code{\link{dgengamma}}, so that ##' \code{dgenf(x, mu, sigma, Q, P=0)} equals \code{dgengamma(x, mu, sigma, ##' Q)}. The generalized gamma reduces further to several common ##' distributions, as described in the \code{\link{GenGamma}} help page. ##' ##' The generalized F distribution includes the log-logistic distribution (see ##' \code{\link[eha:Loglogistic]{eha::dllogis}}) as a further special case: ##' ##' \code{dgenf(x, mu=mu, sigma=sigma, Q=0, P=1) = \link[eha:Loglogistic]{eha::dllogis}(x, ##' shape=sqrt(2)/sigma, scale=exp(mu))} ##' ##' The range of hazard trajectories available under this distribution are ##' discussed in detail by Cox (2008). Jackson et al. (2010) give an ##' application to modelling oral cancer survival for use in a health economic ##' evaluation of screening. ##' ##' @aliases GenF dgenf pgenf qgenf rgenf Hgenf hgenf ##' @param x,q Vector of quantiles. ##' @param p Vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the length is ##' taken to be the number required. ##' @param mu Vector of location parameters. ##' @param sigma Vector of scale parameters. ##' @param Q Vector of first shape parameters. ##' @param P Vector of second shape parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dgenf} gives the density, \code{pgenf} gives the distribution ##' function, \code{qgenf} gives the quantile function, \code{rgenf} generates ##' random deviates, \code{Hgenf} retuns the cumulative hazard and \code{hgenf} ##' the hazard. ##' @note The parameters \code{Q} and \code{P} are usually called \eqn{q} and ##' \eqn{p} in the literature - they were made upper-case in these R functions ##' to avoid clashing with the conventional arguments \code{q} in the ##' probability function and \code{p} in the quantile function. ##' @author Christopher Jackson ##' @seealso \code{\link{GenF.orig}}, \code{\link{GenGamma}} ##' @references R. L. Prentice (1975). Discrimination among some parametric ##' models. Biometrika 62(3):607-614. ##' ##' Cox, C. (2008). The generalized \eqn{F} distribution: An umbrella for ##' parametric survival analysis. Statistics in Medicine 27:4301-4312. ##' ##' Jackson, C. H. and Sharples, L. D. and Thompson, S. G. (2010). Survival ##' models in health economic evaluations: balancing fit and parsimony to ##' improve prediction. International Journal of Biostatistics 6(1):Article ##' 34. ##' @keywords distribution ##' @name GenF NULL ## Generalized F distribution (Prentice 1975 parameterisation) ## For P=0 this is equivalent to the generalized (log-)gamma (Prentice 1974) ## P=Q=0, lognormal ## P=0, Q=1, Weibull ## Equation 2 in C.Cox (2008) is wrong, delta*beta*m1 not beta*m1 in first exponent in numerator ##' @export ##' @rdname GenF dgenf <- function(x, mu=0, sigma=1, Q, P, log=FALSE) { check_numeric(x=x, mu=mu, sigma=sigma, Q=Q, P=P) dgenf_work(x, mu, sigma, Q, P, log) } ##' @export ##' @rdname GenF pgenf <- function(q, mu=0, sigma=1, Q, P, lower.tail = TRUE, log.p = FALSE) { check_numeric(q=q, mu=mu, sigma=sigma, Q=Q, P=P) pgenf_work(q, mu, sigma, Q, P, lower.tail, log.p) } ##' @export ##' @rdname GenF Hgenf <- function(x, mu=0, sigma=1, Q, P) { -log(pgenf(q=x, mu=mu, sigma=sigma, Q=Q, P=P, lower.tail=FALSE)) } ##' @export ##' @rdname GenF hgenf <- function(x, mu=0, sigma=1, Q, P) { logdens <- dgenf(x = x, mu = mu, sigma = sigma, Q = Q, P = P, log=TRUE) logsurv <- pgenf(q = x, mu = mu, sigma = sigma, Q = Q, P = P, lower.tail = FALSE, log.p=TRUE) loghaz <- logdens - logsurv exp(loghaz) } ##' @export ##' @rdname GenF qgenf <- function(p, mu=0, sigma=1, Q, P, lower.tail = TRUE, log.p = FALSE) { d <- dbase("genf", lower.tail=lower.tail, log=log.p, p=p, mu=mu, sigma=sigma, Q=Q, P=P) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) ret[ind][P==0] <- qgengamma(p[P==0], mu[P==0], sigma[P==0], Q[P==0]) pn0 <- P!=0 if (any(pn0)) { mu <- mu[pn0]; sigma <- sigma[pn0]; Q <- Q[pn0]; P <- P[pn0] tmp <- Q^2 + 2*P delta <- sqrt(tmp) s1 <- 2 / (tmp + Q*delta) s2 <- 2 / (tmp - Q*delta) w <- log(qf(p, 2*s1, 2*s2)) ret[ind][pn0] <- exp(w*sigma/delta + mu) } ret } ##' @export ##' @rdname GenF rgenf <- function(n, mu=0, sigma=1, Q, P) { r <- rbase("genf", n=n, mu=mu, sigma=sigma, Q=Q, P=P) for (i in seq_along(r)) assign(names(r)[i], r[[i]]) ret[ind][P==0] <- rgengamma(sum(P==0), mu[P==0], sigma[P==0], Q[P==0]) pn0 <- P!=0 if (any(pn0)) { mu <- mu[pn0]; sigma <- sigma[pn0]; Q <- Q[pn0]; P <- P[pn0] tmp <- Q^2 + 2*P delta <- sqrt(tmp) s1 <- 2 / (tmp + Q*delta) s2 <- 2 / (tmp - Q*delta) w <- log(rf(sum(pn0), 2*s1, 2*s2)) ret[ind][pn0] <- exp(w*sigma/delta + mu) } ret } ##' @export ##' @rdname means rmst_genf= function(t, mu, sigma, Q, P, start=0){ rmst_generic(pgenf, t, start=start, mu=mu, sigma=sigma, Q=Q, P=P) } ##' @export ##' @rdname means mean_genf = function(mu, sigma, Q, P){ rmst_generic(pgenf, Inf, start=0, mu=mu, sigma=sigma, Q=Q, P=P) } ##' @export ##' @rdname GenF.orig dgenf.orig <- function(x, mu=0, sigma=1, s1, s2, log=FALSE) { d <- dbase("genf.orig", log=log, x=x, mu=mu, sigma=sigma, s1=s1, s2=s2) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) w <- (log(x) - mu)/sigma expw <- x^(1/sigma)*exp(-mu/sigma) logdens <- -log(sigma*x) + s1*(log(s1) + w - log(s2)) - (s1+s2)*log(1 + s1*expw/s2) - lbeta(s1, s2) ret[ind] <- if (log) logdens else exp(logdens) ret } ##' @export ##' @rdname GenF.orig pgenf.orig <- function(q, mu=0, sigma=1, s1, s2, lower.tail = TRUE, log.p = FALSE) { d <- dbase("genf.orig", lower.tail=lower.tail, log=log.p, q=q, mu=mu, sigma=sigma, s1=s1, s2=s2) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) w <- (log(q) - mu)/sigma prob <- 1 - pbeta(s2/(s2 + s1*exp(w)), s2, s1) if (!lower.tail) prob <- 1 - prob if (log.p) prob <- log(prob) ret[ind] <- prob ret } ##' @export ##' @rdname GenF.orig Hgenf.orig <- function(x, mu=0, sigma=1, s1, s2) { -log(pgenf.orig(q=x, mu=mu, sigma=sigma, s1=s1, s2=s2, lower.tail=FALSE)) } ##' @export ##' @rdname GenF.orig hgenf.orig <- function(x, mu=0, sigma=1, s1, s2) { logdens <- dgenf.orig(x = x, mu = mu, sigma = sigma, s1 = s1, s2 = s2, log=TRUE) logsurv <- pgenf.orig(q = x, mu = mu, sigma = sigma, s1 = s1, s2 = s2, lower.tail = FALSE, log.p=TRUE) loghaz <- logdens - logsurv exp(loghaz) } ##' @export ##' @rdname GenF.orig qgenf.orig <- function(p, mu=0, sigma=1, s1, s2, lower.tail = TRUE, log.p = FALSE) { d <- dbase("genf.orig", lower.tail=lower.tail, log=log.p, p=p, mu=mu, sigma=sigma, s1=s1, s2=s2) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) w <- log(qf(p, 2*s1, 2*s2)) ret[ind] <- exp(w*sigma + mu) ret } ##' @export ##' @rdname GenF.orig rgenf.orig <- function(n, mu=0, sigma=1, s1, s2) { r <- rbase("genf.orig", n=n, mu=mu, sigma=sigma, s1=s1, s2=s2) for (i in seq_along(r)) assign(names(r)[i], r[[i]]) w <- log(rf(n, 2*s1, 2*s2)) ret[ind] <- exp(w*sigma + mu) ret } ##' @export ##' @rdname means rmst_genf.orig= function(t, mu, sigma, s1, s2, start=0){ rmst_generic(pgenf.orig, t, start=start, mu=mu, sigma=sigma, s1=s1, s2=s2) } ##' @export ##' @rdname means mean_genf.orig = function(mu, sigma, s1, s2){ rmst_generic(pgenf.orig, Inf, start=0, mu=mu, sigma=sigma, s1=s1, s2=s2) } check.genf.orig <- function(mu, sigma, s1, s2){ ret <- rep(TRUE, length(mu)) if (missing(s1)) stop("shape parameter \"s1\" not given") if (missing(s2)) stop("shape parameter \"s2\" not given") if (any(!is.na(sigma) & sigma < 0)) { warning("Negative scale parameter \"sigma\"") ret[!is.na(sigma) & sigma < 0] <- FALSE } if (any(!is.na(s1) & s1 < 0)) { warning("Negative shape parameter \"s1\""); ret[!is.na(s1) & s1 < 0] <- FALSE } if (any(!is.na(s2) & s2 < 0)) { warning("Negative shape parameter \"s2\""); ret[!is.na(s2) & s2 < 0] <- FALSE } ret } ## Thanks to Skif Pankov ## currently undocumented and unused! ## Only defined for s2 > sigma ## mean for gengamma.orig will follow ## TODO replace integrate version with this, check equal #mean_genf.orig <- function(mu, sigma, s1, s2){ # if (s2 <= sigma) NaN else exp(mu) * (s2/s1)^sigma * gamma(s1 + sigma)*gamma(s2 - sigma) / (gamma(s1)*gamma(s2)) #} flexsurv/R/GenGamma.R0000644000176200001440000003261114472142603014136 0ustar liggesusers##' Generalized gamma distribution (original parameterisation) ##' ##' Density, distribution function, hazards, quantile function and ##' random generation for the generalized gamma distribution, using ##' the original parameterisation from Stacy (1962). ##' ##' If \eqn{w \sim Gamma(k,1)}{w ~ Gamma(k, 1)}, then \eqn{x = ##' \exp(w/shape + \log(scale))}{x = exp(w/shape + log(scale))} ##' follows the original generalised gamma distribution with the ##' parameterisation given here (Stacy 1962). Defining ##' \code{shape}\eqn{=b>0}, \code{scale}\eqn{=a>0}, \eqn{x} has ##' probability density ##' ##' \deqn{f(x | a, b, k) = \frac{b}{\Gamma(k)} \frac{x^{bk - 1}}{a^{bk}} }{ f(x ##' | a, b, k) = (b / \Gamma(k)) (x^{bk -1} / a^{bk}) exp(-(x/a)^b)}\deqn{ ##' \exp(-(x/a)^b)}{ f(x | a, b, k) = (b / \Gamma(k)) (x^{bk -1} / a^{bk}) ##' exp(-(x/a)^b)} ##' ##' The original generalized gamma distribution simplifies to the ##' gamma, exponential and Weibull distributions with the following ##' parameterisations: ##' ##' \tabular{lcl}{ \code{dgengamma.orig(x, shape, scale, k=1)} \tab \code{=} ##' \tab \code{\link{dweibull}(x, shape, scale)} \cr \code{dgengamma.orig(x, ##' shape=1, scale, k)} \tab \code{=} \tab \code{\link{dgamma}(x, shape=k, ##' scale)} \cr \code{dgengamma.orig(x, shape=1, scale, k=1)} \tab \code{=} ##' \tab \code{\link{dexp}(x, rate=1/scale)} \cr } ##' ##' Also as k tends to infinity, it tends to the log normal (as in ##' \code{\link{dlnorm}}) with the following parameters (Lawless, ##' 1980): ##' ##' \code{dlnorm(x, meanlog=log(scale) + log(k)/shape, ##' sdlog=1/(shape*sqrt(k)))} ##' ##' For more stable behaviour as the distribution tends to the log-normal, an ##' alternative parameterisation was developed by Prentice (1974). This is ##' given in \code{\link{dgengamma}}, and is now preferred for statistical ##' modelling. It is also more flexible, including a further new class of ##' distributions with negative shape \code{k}. ##' ##' The generalized F distribution \code{\link{GenF.orig}}, and its similar ##' alternative parameterisation \code{\link{GenF}}, extend the generalized ##' gamma to four parameters. ##' ##' @aliases GenGamma.orig dgengamma.orig pgengamma.orig qgengamma.orig ##' rgengamma.orig Hgengamma.orig hgengamma.orig ##' @param x,q vector of quantiles. ##' @param p vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the length is ##' taken to be the number required. ##' @param shape vector of ``Weibull'' shape parameters. ##' @param scale vector of scale parameters. ##' @param k vector of ``Gamma'' shape parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dgengamma.orig} gives the density, \code{pgengamma.orig} ##' gives the distribution function, \code{qgengamma.orig} gives the quantile ##' function, \code{rgengamma.orig} generates random deviates, ##' \code{Hgengamma.orig} retuns the cumulative hazard and ##' \code{hgengamma.orig} the hazard. ##' @author Christopher Jackson ##' @seealso \code{\link{GenGamma}}, \code{\link{GenF.orig}}, ##' \code{\link{GenF}}, \code{\link{Lognormal}}, \code{\link{GammaDist}}, ##' \code{\link{Weibull}}. ##' @references Stacy, E. W. (1962). A generalization of the gamma ##' distribution. Annals of Mathematical Statistics 33:1187-92. ##' ##' Prentice, R. L. (1974). A log gamma model and its maximum likelihood ##' estimation. Biometrika 61(3):539-544. ##' ##' Lawless, J. F. (1980). Inference in the generalized gamma and log gamma ##' distributions. Technometrics 22(3):409-419. ##' @keywords distribution ##' @name GenGamma.orig NULL ##' Generalized gamma distribution ##' ##' Density, distribution function, hazards, quantile function and ##' random generation for the generalized gamma distribution, using ##' the parameterisation originating from Prentice (1974). Also known ##' as the (generalized) log-gamma distribution. ##' ##' If \eqn{\gamma \sim Gamma(Q^{-2}, 1)}{g ~ Gamma(Q^{-2}, 1)} , and \eqn{w = ##' log(Q^2 \gamma) / Q}{w = log(Q^2*g) / Q}, then \eqn{x = \exp(\mu + \sigma ##' w)}{x = exp(mu + sigma w)} follows the generalized gamma distribution with ##' probability density function ##' ##' \deqn{f(x | \mu, \sigma, Q) = \frac{|Q|(Q^{-2})^{Q^{-2}}}{\sigma x ##' \Gamma(Q^{-2})} \exp(Q^{-2}(Qw - \exp(Qw)))}{ f(x | mu, sigma, Q) = |Q| ##' (Q^{-2})^{Q^{-2}} / (sigma * x * Gamma(Q^{-2})) exp(Q^{-2}*(Q*w - ##' exp(Q*w)))} ##' ##' This parameterisation is preferred to the original ##' parameterisation of the generalized gamma by Stacy (1962) since it ##' is more numerically stable near to \eqn{Q=0} (the log-normal ##' distribution), and allows \eqn{Q<=0}. The original is available ##' in this package as \code{\link{dgengamma.orig}}, for the sake of ##' completion and compatibility with other software - this is ##' implicitly restricted to \code{Q}>0 (or \code{k}>0 in the original ##' notation). The parameters of \code{\link{dgengamma}} and ##' \code{\link{dgengamma.orig}} are related as follows. ##' ##' \code{dgengamma.orig(x, shape=shape, scale=scale, k=k) = } ##' ##' \code{dgengamma(x, mu=log(scale) + log(k)/shape, sigma=1/(shape*sqrt(k)), ##' Q=1/sqrt(k))} ##' ##' The generalized gamma distribution simplifies to the gamma, ##' log-normal and Weibull distributions with the following ##' parameterisations: ##' ##' \tabular{lcl}{ \code{dgengamma(x, mu, sigma, Q=0)} \tab \code{=} \tab ##' \code{dlnorm(x, mu, sigma)} \cr \code{dgengamma(x, mu, sigma, Q=1)} \tab ##' \code{=} \tab \code{dweibull(x, shape=1/sigma, scale=exp(mu))} \cr ##' \code{dgengamma(x, mu, sigma, Q=sigma)} \tab \code{=} \tab \code{dgamma(x, ##' shape=1/sigma^2, rate=exp(-mu) / sigma^2)} \cr } The properties of the ##' generalized gamma and its applications to survival analysis are discussed ##' in detail by Cox (2007). ##' ##' The generalized F distribution \code{\link{GenF}} extends the generalized ##' gamma to four parameters. ##' ##' @aliases GenGamma dgengamma pgengamma qgengamma rgengamma Hgengamma ##' hgengamma ##' @param x,q vector of quantiles. ##' @param p vector of probabilities. ##' @param n number of observations. If \code{length(n) > 1}, the length is ##' taken to be the number required. ##' @param mu Vector of ``location'' parameters. ##' @param sigma Vector of ``scale'' parameters. Note the inconsistent ##' meanings of the term ``scale'' - this parameter is analogous to the ##' (log-scale) standard deviation of the log-normal distribution, ``sdlog'' in ##' \code{\link{dlnorm}}, rather than the ``scale'' parameter of the gamma ##' distribution \code{\link{dgamma}}. Constrained to be positive. ##' @param Q Vector of shape parameters. ##' @param log,log.p logical; if TRUE, probabilities p are given as log(p). ##' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P(X ##' \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}. ##' @return \code{dgengamma} gives the density, \code{pgengamma} gives the ##' distribution function, \code{qgengamma} gives the quantile function, ##' \code{rgengamma} generates random deviates, \code{Hgengamma} retuns the ##' cumulative hazard and \code{hgengamma} the hazard. ##' @author Christopher Jackson ##' @seealso \code{\link{GenGamma.orig}}, \code{\link{GenF}}, ##' \code{\link{Lognormal}}, \code{\link{GammaDist}}, \code{\link{Weibull}}. ##' @references Prentice, R. L. (1974). A log gamma model and its maximum ##' likelihood estimation. Biometrika 61(3):539-544. ##' ##' Farewell, V. T. and Prentice, R. L. (1977). A study of ##' distributional shape in life testing. Technometrics 19(1):69-75. ##' ##' Lawless, J. F. (1980). Inference in the generalized gamma and log ##' gamma distributions. Technometrics 22(3):409-419. ##' ##' Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007). ##' Parametric survival analysis and taxonomy of hazard functions for ##' the generalized gamma distribution. Statistics in Medicine ##' 26:4252-4374 ##' ##' Stacy, E. W. (1962). A generalization of the gamma distribution. ##' Annals of Mathematical Statistics 33:1187-92 ##' @keywords distribution ##' @name GenGamma NULL ## Log-gamma or generalized gamma distribution (parameterisation as in Farewell and Prentice, Technometrics 1977) ### FIXME value for x = 0 ##' @export ##' @rdname GenGamma dgengamma <- function(x, mu=0, sigma=1, Q, log=FALSE) { check_numeric(x=x, mu=mu, sigma=sigma, Q=Q) dgengamma_work(x, mu, sigma, Q, log) } ##' @export ##' @rdname GenGamma pgengamma <- function(q, mu=0, sigma=1, Q, lower.tail = TRUE, log.p = FALSE) { check_numeric(q=q, mu=mu, sigma=sigma, Q=Q) pgengamma_work(q, mu, sigma, Q, lower.tail, log.p) } ##' @export ##' @rdname GenGamma Hgengamma <- function(x, mu=0, sigma=1, Q) { -pgengamma(q=x, mu=mu, sigma=sigma, Q=Q, lower.tail=FALSE, log.p=TRUE) } ##' @export ##' @rdname GenGamma hgengamma <- function(x, mu=0, sigma=1, Q) { logdens <- dgengamma(x = x, mu = mu, sigma = sigma, Q = Q, log=TRUE) logsurv <- pgengamma(q = x, mu = mu, sigma = sigma, Q = Q, lower.tail = FALSE, log.p=TRUE) loghaz <- logdens - logsurv exp(loghaz) } ##' @export ##' @rdname GenGamma qgengamma <- function(p, mu=0, sigma=1, Q, lower.tail = TRUE, log.p = FALSE) { d <- dbase("gengamma", lower.tail=lower.tail, log=log.p, p=p, mu=mu, sigma=sigma, Q=Q) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) p[Q<0] <- 1 - p[Q<0] ret[ind] <- numeric(sum(ind)) ret[ind][Q==0] <- qlnorm(p[Q==0], mu[Q==0], sigma[Q==0]) qn0 <- Q!=0 p <- p[qn0]; mu <- mu[qn0]; sigma <- sigma[qn0]; Q <- Q[qn0] ret[ind][qn0] <- exp(mu + sigma*(log(Q^2*qgamma(p, 1/Q^2, 1)) / Q)) ret } ##' @export ##' @rdname GenGamma rgengamma <- function(n, mu=0, sigma=1, Q) { r <- rbase("gengamma", n=n, mu=mu, sigma=sigma, Q=Q) for (i in seq_along(r)) assign(names(r)[i], r[[i]]) ret[ind][Q==0] <- rlnorm(n, mu, sigma) qn0 <- Q!=0 if (any(qn0)) { mu <- mu[qn0]; sigma <- sigma[qn0]; Q <- Q[qn0] w <- log(Q^2*rgamma(n, 1/Q^2, 1)) / Q ret[ind][qn0] <- exp(mu + sigma*w) } ret } ##' @export ##' @rdname means rmst_gengamma = function(t, mu=0, sigma=1, Q, start=0){ rmst_generic(pgengamma, t, start=start, mu=mu, sigma=sigma, Q=Q) } ##' @export ##' @rdname means mean_gengamma = function(mu=0, sigma=1, Q){ rmst_generic(pgengamma, Inf, start=0, mu=mu, sigma=sigma, Q=Q) } ### FIXME limiting value for x=0: 0 if bk >1, 1 if b=k=1, ... ? ##' @export ##' @rdname GenGamma.orig dgengamma.orig <- function(x, shape, scale=1, k, log=FALSE){ d <- dbase("gengamma.orig", log=log, x=x, shape=shape, scale=scale, k=k) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) logdens <- log(shape) - lgamma(k) + (shape*k - 1)*log(x) - shape*k*log(scale) - (x/scale)^shape ret[ind] <- if (log) logdens else exp(logdens) ret } ##' @export ##' @rdname GenGamma.orig pgengamma.orig <- function(q, shape, scale=1, k, lower.tail = TRUE, log.p = FALSE) { d <- dbase("gengamma.orig", lower.tail=lower.tail, log=log.p, q=q, shape=shape, scale=scale, k=k) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) y <- log(q) w <- (y - log(scale))*shape prob <- pgamma(exp(w), shape=k) if (!lower.tail) prob <- 1 - prob if (log.p) prob <- log(prob) ret[ind] <- prob ret } ##' @export ##' @rdname GenGamma.orig Hgengamma.orig <- function(x, shape, scale=1, k) { -log(pgengamma.orig(q=x, shape=shape, scale=scale, k=k, lower.tail=FALSE)) } ##' @export ##' @rdname GenGamma.orig hgengamma.orig <- function(x, shape, scale=1, k) { logdens <- dgengamma.orig(x = x, shape = shape, scale = scale, k = k, log=TRUE) logsurv <- pgengamma.orig(q = x, shape = shape, scale = scale, k = k, lower.tail = FALSE, log.p=TRUE) loghaz <- logdens - logsurv exp(loghaz) } ##' @export ##' @rdname GenGamma.orig qgengamma.orig <- function(p, shape, scale=1, k, lower.tail = TRUE, log.p = FALSE) { d <- dbase("gengamma.orig", lower.tail=lower.tail, log=log.p, p=p, shape=shape, scale=scale, k=k) for (i in seq_along(d)) assign(names(d)[i], d[[i]]) w <- log(qgamma(p, shape=k)) y <- w / shape + log(scale) ret[ind] <- exp(y) ret } ##' @export ##' @rdname GenGamma.orig rgengamma.orig <- function(n, shape, scale=1, k) { r <- rbase("gengamma.orig", n=n, shape=shape, scale=scale, k=k) for (i in seq_along(r)) assign(names(r)[i], r[[i]]) w <- log(rgamma(n, shape=k)) y <- w / shape + log(scale) ret[ind] <- exp(y) ret } ##' @export ##' @rdname means rmst_gengamma.orig = function(t, shape, scale=1, k, start=0){ rmst_generic(pgengamma.orig, t, start=start, shape=shape, scale=scale, k=k) } ##' @export ##' @rdname means mean_gengamma.orig = function(shape, scale=1, k){ rmst_generic(pgengamma.orig, Inf, start=0, shape=shape, scale=scale, k=k) } check.gengamma.orig <- function(shape, scale, k){ ret <- rep(TRUE, length(shape)) if (missing(shape)) stop("shape parameter \"shape\" not given") if (missing(k)) stop("shape parameter \"k\" not given") if (any(!is.na(shape) & shape < 0)) { warning("Negative shape parameter \"shape\"") ret[!is.na(shape) & shape < 0] <- FALSE } if (any(!is.na(scale) & scale < 0)) { warning("Negative scale parameter"); ret[!is.na(scale) & scale < 0] <- FALSE } if (any(!is.na(k) & k < 0)) { warning("Negative shape parameter \"k\""); ret[!is.na(k) & k < 0] <- FALSE } ret } flexsurv/R/distributions.R0000644000176200001440000001434614632521533015372 0ustar liggesuserssurvreg_wrap <- function(args){ opts <- options() on.exit(options(opts)) options( warnPartialMatchArgs = FALSE, warnPartialMatchAttr = FALSE, warnPartialMatchDollar = FALSE ) do.call(survreg, args) } ## covr doesn't detect when these are used, as they are manipulated dynamically # nocov start sr.weib.inits <- function(t,aux){ if (aux$counting){ lt <- log(t[t>0]) ### c(1, exp(median(lt)) / log(2)) c(1.64/var(lt), exp(mean(lt)+0.572)) # from survreg } else { aux$formula <- aux$forms[[1]] aux$forms <- NULL aux$dist <- "weibull" sr <- survreg_wrap(aux) sr2fswei(sr) } } sr.weibPH.inits <- function(aux){ if (aux$counting){ lt <- log(t[t>0]) shape <- 1.64/var(lt) scale <- exp(mean(lt)+0.572) c(shape, scale^{-shape}) } else { aux$formula <- aux$forms[[1]] aux$forms <- NULL aux$dist <- "weibull" sr <- survreg_wrap(aux) sr2fswei(sr, ph=TRUE) } } sr.exp.inits <- function(t,aux){ if (aux$counting){ 1 / mean(t) } else { aux$formula <- aux$forms[[1]] aux$forms <- NULL aux$dist <- "exponential" sr <- survreg_wrap(aux) sr2fsexp(sr) } } sr.ln.inits <- function(t,aux){ if (aux$counting){ lt <- log(t[t>0]) c(mean(lt), sd(lt)) } else { aux$formula <- aux$forms[[1]] aux$forms <- NULL aux$dist <- "lognormal" sr <- survreg_wrap(aux) sr2fsln(sr) } } sr.llog.inits <- function(t,aux){ if (aux$counting){ scale <- median(t) shape <- 1 / log(quantile(t, 0.25)/scale, base=3) if (shape < 0) shape <- 1 c(shape, scale) } else { aux$formula <- aux$forms[[1]] aux$forms <- NULL aux$dist <- "loglogistic" sr <- survreg_wrap(aux) sr2fsllog(sr) } } # nocov end ## Convert parameters of survreg models to flexsurvreg ## parameterisation, for use as initial values sr2fswei <- function(sr, ph=FALSE){ scale <- exp(coef(sr)[1]) beta.scale <- coef(sr)[-1] shape <- mean(1/sr$scale) beta.shape <- if (length(sr$scale)>1) log(sr$scale[1]/sr$scale[-1]) else numeric() if (ph) c(shape, scale^{-shape}, -beta.scale*shape, beta.shape) else c(shape, scale, beta.scale, beta.shape) } sr2fsexp <- function(sr){ rate <- exp(-coef(sr)[1]) beta <- -coef(sr)[-1] c(rate, beta) } sr2fsln <- function(sr){ meanlog <- coef(sr)[1] sdlog <- sr$scale beta <- coef(sr)[-1] c(meanlog, sdlog, beta) } sr2fsllog <- function(sr){ shape <- 1/sr$scale scale <- exp(coef(sr)[1]) beta <- coef(sr)[-1] c(shape, scale, beta) } ##' @export flexsurv.dists <- list(genf = list( name="genf", pars=c("mu","sigma","Q","P"), location="mu", transforms=c(identity, log, identity, log), inv.transforms=c(identity, exp, identity, exp), inits=function(t){ lt <- log(t[t>0]) c(mean(lt), sd(lt), 0, 1) } ), genf.orig = list( name="genf.orig", pars=c("mu","sigma","s1","s2"), location="mu", transforms=c(identity, log, log, log), inv.transforms=c(identity, exp, exp, exp), inits=function(t){ lt <- log(t[t>0]) c(mean(lt), sd(lt), 1, 1) } ), gengamma = list( name="gengamma", pars=c("mu","sigma","Q"), location="mu", transforms=c(identity, log, identity), inv.transforms=c(identity, exp, identity), inits=function(t){ lt <- log(t[t>0]) c(mean(lt), sd(lt), 0) } ), gengamma.orig = list( name="gengamma.orig", pars=c("shape","scale","k"), location="scale", transforms=c(log, log, log), inv.transforms=c(exp, exp, exp), inits=function(t){c(1, mean(t), 1)} ), exp = list( name="exp", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=sr.exp.inits ), weibull = list( name = "weibull.quiet", pars=c("shape","scale"), location="scale", transforms=c(log, log), inv.transforms=c(exp, exp), inits=sr.weib.inits ), weibullPH = list( name="weibullPH", pars=c("shape","scale"), location="scale", transforms=c(log, log), inv.transforms=c(exp, exp), inits = sr.weibPH.inits ), lnorm = list( name="lnorm", pars=c("meanlog","sdlog"), location="meanlog", transforms=c(identity, log), inv.transforms=c(identity, exp), inits=sr.ln.inits ), gamma = list( name="gamma", pars=c("shape","rate"), location="rate", transforms=c(log, log), inv.transforms=c(exp, exp), inits=function(t){ m=mean(t); v=var(t); c(m^2/v, m/v) } ), gompertz = list( name="gompertz", pars=c("shape","rate"), location="rate", transforms=c(identity, log), inv.transforms=c(identity, exp), inits=function(t){c(0.001,1 / mean(t))} ), llogis = list( name="llogis", pars=c("shape","scale"), location="scale", transforms=c(log, log), inv.transforms=c(exp, exp), inits=sr.llog.inits ) ) flexsurv.dists$exponential <- flexsurv.dists$exp flexsurv.dists$lognormal <- flexsurv.dists$lnorm flexsurv/R/summary.flexsurvrtrunc.R0000644000176200001440000000773414603753373017312 0ustar liggesusers##' Summarise quantities of interest from fitted flexsurvrtrunc models ##' ##' This function extracts quantities of interest from the untruncated ##' version of a model with individual-specific right truncation points ##' fitted by \code{\link{flexsurvrtrunc}}. Note that covariates are ##' currently not supported by \code{\link{flexsurvrtrunc}}. ##' ##' ##' @param type \code{"survival"} for survival probabilities. ##' ##' \code{"cumhaz"} for cumulative hazards. ##' ##' \code{"hazard"} for hazards. ##' ##' \code{"rmst"} for restricted mean survival. ##' ##' \code{"mean"} for mean survival. ##' ##' \code{"median"} for median survival (alternative to \code{type="quantile"} with \code{quantiles=0.5}). ##' ##' \code{"quantile"} for quantiles of the survival time distribution. ##' ##' Ignored if \code{"fn"} is specified. ##' ##' @param fn Custom function of the parameters to summarise against time. ##' This has optional first argument \code{t} representing time, and any remaining ##' arguments must be parameters of the distribution. It should return a ##' vector of the same length as \code{t}. ##' ##' ##' @inheritParams summary.flexsurvreg ##' ##' @export ##' summary.flexsurvrtrunc <- function(object, type="survival", fn=NULL, t=NULL, quantiles=0.5, ci=TRUE, se=FALSE, B=1000, cl=0.95, ...) { x <- object dat <- x$data type <- match.arg(type, c("survival","cumhaz","hazard","rmst","mean","median", "quantile","link")) start <- 0 if(type == "mean"){ if(!is.null(t)) warning("Mean selected, but time specified. For restricted mean, set type to 'rmst'.") # Type = mean same as RMST w/ time = Inf t <- rep(Inf,length(start)) } else if(type == "median"){ if(!is.null(t)) warning("Median selected, but time specified.") t <- rep(0.5,length(start)) } else if(type == "quantile"){ t <- quantiles if((any(t<0) | any(t>1))){ stop("Quantiles should not be less than 0 or greater than 1") } t <- rep(t,length(start)) } else if(type == "rmst"){ if (is.null(t)) t <- max(dat$t) } else if (is.null(t)) t <- sort(unique(dat$t)) if (is.null(fn)) { fn <- summary_fns(x, type) } fn <- expand.summfn.args(fn) fncall <- list(t,start) dlist <- x$dlist basepars <- x$res[dlist$pars,"est"] names(basepars) <- dlist$pars basepars <- as.list(basepars) fncall[dlist$pars] <- basepars y <- do.call(fn, fncall) if (ci){ res.ci <- cisumm.flexsurvreg.old(x, t, start, X=NULL, fn=fn, B=B, cl=cl) ly <- res.ci[,1] uy <- res.ci[,2] } if (se){ res.se <- sesumm.flexsurvreg.old(x, t, start, X=NULL, fn=fn, B=B) } if (type %in% c("median","mean")) ret <- data.frame(est=y, row.names=NULL) else if (type == "quantile") ret <- data.frame(quantile=t, est=y, row.names=NULL) else ret <- data.frame(time=t, est=y, row.names=NULL) if (ci) { ret$lcl <- ly; ret$ucl <- uy} if (se) { ret$se <- res.se } class(ret) <- c("summary.flexsurvrtrunc", class(ret)) ret } cisumm.flexsurvreg.old <- function(x, t, start, X, fn, B=1000, cl=0.95) { if (all(is.na(x$cov)) || (B==0)) ret <- array(NA, dim=c(length(t), 2)) else { ret <- normbootfn.flexsurvreg(x=x, t=t, start=start, X=X, fn=fn, B=B) ret <- apply(ret, c(1,3), function(x)quantile(x, c((1-cl)/2, 1 - (1-cl)/2), na.rm=TRUE)) ret <- t(ret[,1,]) } ret } sesumm.flexsurvreg.old <- function(x, t, start, X, fn, B=1000) { if (all(is.na(x$cov)) || (B==0)) ret <- numeric(length(t)) else { ret <- normbootfn.flexsurvreg(x=x, t=t, start=start, X=X, fn=fn, B=B) ret <- apply(ret, c(1,3), sd, na.rm=TRUE) ret <- ret[1,] } ret } flexsurv/R/flexsurvrtrunc.R0000644000176200001440000002670614174025364015611 0ustar liggesusers##' Flexible parametric models for right-truncated, uncensored data defined by times of initial and final events. ##' ##' This function estimates the distribution of the time between an initial and final event, in situations where individuals are only observed if they have experienced both events before a certain time, thus they are right-truncated at this time. The time of the initial event provides information about the time from initial to final event, given the truncated observation scheme, and initial events are assumed to occur with an exponential growth rate. ##' ##' Covariates are not currently supported. ##' ##' Note that \code{\link{flexsurvreg}}, with an \code{rtrunc} argument, can fit models for a similar kind of data, but those models ignore the information provided by the time of the initial event. ##' ##' A nonparametric estimator of survival under right-truncation is also provided in \code{\link{survrtrunc}}. See Seaman et al. (2020) for a full comparison of the alternative models. ##' ##' ##' @param t Vector of time differences between an initial and final event for a set of individuals. ##' ##' @param tinit Absolute time of the initial event for each individual. ##' ##' @param rtrunc Individual-specific right truncation points on the same scale as \code{t}, so that each individual's survival time \code{t} would not have been observed if it was greater than the corresponding element of \code{rtrunc}. Only used in \code{method="joint"}. In \code{method="final"}, the right-truncation is implicit. ##' ##' @param tmax Maximum possible time between initial and final events that could have been observed. This is only used in \code{method="joint"}, and is ignored in \code{method="final"}. ##' ##' @param data Data frame containing \code{t}, \code{rtrunc} and \code{tinit}. ##' ##' @param method If \code{"joint"} then the "joint-conditional" method is used. If \code{"final"} then the "conditional-on-final" method is used. The "conditional-on-initial" method can be implemented by using \code{\link{flexsurvreg}} with a \code{rtrunc} argument. These methods are all described in Seaman et al. (2020). ##' ##' @param theta Initial value (or fixed value) for the exponential growth rate \code{theta}. Defaults to 1. ##' ##' @param inits Initial values for the parameters of the parametric survival distributon. If not supplied, a heuristic is used. as is done in \code{\link{flexsurvreg}}. ##' ##' @param fixedpars Integer indices of the parameters of the survival distribution that should be fixed to their values supplied in \code{inits}. Same length as \code{inits}. ##' ##' @param fixed.theta Should \code{theta} be fixed at its initial value or estimated. This only applies to \code{method="joint"}. For \code{method="final"}, \code{theta} must be fixed. ##' ##' @param optim_control List to supply as the \code{control} argument to \code{\link{optim}} to control the likelihood maximisation. ##' ##' @inheritParams flexsurvreg ##' ##' @seealso \code{\link{flexsurvreg}}, \code{\link{survrtrunc}}. ##' ##' @examples ##' set.seed(1) ##' ## simulate time to initial event ##' X <- rexp(1000, 0.2) ##' ## simulate time between initial and final event ##' T <- rgamma(1000, 2, 10) ##' ##' ## right-truncate to keep only those with final event time ##' ## before tmax ##' tmax <- 40 ##' obs <- X + T < tmax ##' rtrunc <- tmax - X ##' dat <- data.frame(X, T, rtrunc)[obs,] ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gamma", theta=0.2) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gamma", theta=0.2, fixed.theta=FALSE) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gamma", theta=0.2, inits=c(1, 8)) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gamma", theta=0.2, method="final") ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gamma", fixed.theta=TRUE) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="weibull", fixed.theta=TRUE) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="lnorm", fixed.theta=TRUE) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gengamma", fixed.theta=TRUE) ##' ##' flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, ##' dist="gompertz", fixed.theta=TRUE) ##' ##' @references Seaman, S., Presanis, A. and Jackson, C. (2020) Estimating a Time-to-Event ##' Distribution from Right-Truncated Data in an Epidemic: a Review of Methods ##' ##' @export flexsurvrtrunc <- function(t, tinit, rtrunc, tmax, data=NULL, method="joint", dist, theta=NULL, fixed.theta=TRUE, inits=NULL, fixedpars=NULL, dfns=NULL, integ.opts=NULL, cl=0.95, optim_control = list()){ tdelay <- eval(substitute(t), data, parent.frame()) rtrunc <- eval(substitute(rtrunc), data, parent.frame()) tinit <- eval(substitute(tinit), data, parent.frame()) dlist <- parse.dist(dist) dfns <- form.dp(dlist, dfns, integ.opts) if (is.null(inits)){ if (is.null(theta)) theta <- 1 ## FIXME for aux arguments. pop out a function for this ## what is this for. to fit a survreg weibull and use their heiurisitic ## shdnt be a problem, just build the formula up build_inits_aux <- function() { list(forms = list(Surv(tdelay) ~ 1), control = list(), counting = FALSE ) } aux <- build_inits_aux() dlist$inits <- expand.inits.args(dlist$inits) initsd <- dlist$inits(t=tdelay, aux=aux) names(initsd) <- dlist$pars inits <- c(initsd, theta=theta) } else { if (!is.numeric(inits)) stop("`inits` should be numeric") if (length(inits) != length(dlist$pars)) stop(sprintf("%s values supplied in `inits`, but %s parameters in distribution \"%s\"", length(inits), length(dlist$pars), dlist$name)) inits <- c(inits, theta) } npars <- length(inits) nbpars <- npars - 1 if (method=="final") { if (!fixed.theta) warning("theta cannot be estimated in method=\"final\"") fixed.theta <- TRUE } check.fixedpars(fixedpars, nbpars) if (isTRUE(fixedpars)) fixedpars <- 1:nbpars if (fixed.theta) fixedpars <- unique(c(fixedpars, npars)) names(inits) <- c(dlist$pars, "theta") for (i in 1:nbpars){ inits[i] <- dlist$transforms[[i]](inits[i]) } inits[nbpars+1] <- inits[nbpars+1] optpars <- setdiff(1:npars, fixedpars) optvals <- inits[optpars] fixed <- length(fixedpars)==npars if (!fixed) { opt <- optim(optvals, frtrunc_loglik_factory(inits=inits,tinit=tinit, tdelay=tdelay, tmax=tmax, method=method, dlist=dlist, dfns=dfns, fixedpars=fixedpars), control=optim_control, hessian=TRUE) est <- opt$par covar <- solve(opt$hessian) se <- sqrt(diag(covar)) loglik <- - opt$value } else { opt <- NULL est <- inits se <- covar <- NA loglik <- - frtrunc_loglik_factory(inits=inits, tinit=tinit, tdelay=tdelay, tmax=tmax, method=method,dlist=dlist, dfns=dfns, fixedpars=fixedpars)(inits) } if (!is.numeric(cl) || length(cl)>1 || !(cl>0) || !(cl<1)) stop("cl must be a number in (0,1)") lcl <- est - qnorm(1 - (1-cl)/2)*se ucl <- est + qnorm(1 - (1-cl)/2)*se est.opt <- cbind(estlog=est, selog=se, lcllog=lcl, ucllog=ucl) res <- matrix(nrow=npars, ncol=ncol(est.opt), dimnames=list(names(inits), colnames(est.opt))) res[optpars,] <- est.opt res[fixedpars,"estlog"] <- inits[fixedpars] res <- as.data.frame(res) res$ucl <- res$lcl <- res$est <- numeric(npars) for (i in 1:npars){ trf <- if (i==npars) exp else dlist$inv.transforms[[i]] res$est[i] <- trf(res$estlog[i]) res$lcl[i] <- trf(res$lcllog[i]) res$ucl[i] <- trf(res$ucllog[i]) } res$pars <- c(dlist$pars, "theta") est <- res[,c("pars","est","lcl","ucl","estlog","selog")] npars <- length(optpars) res <- list(call=match.call(), res=est, loglik=loglik, data=data.frame(t=tdelay, tinit=tinit, rtrunc=rtrunc), dfns=dfns, dlist=dlist, ncovs=0, cov=covar, opt=opt, optpars=optpars, fixedpars=fixedpars, npars=npars, AIC = -2*loglik + 2*npars, res.t=est) class(res) <- "flexsurvrtrunc" res } ##' @export print.flexsurvrtrunc <- function(x, ...) { cat("Call:\n") dput(x$call) cat("\n") if (x$npars > 0) { res <- x$res cat ("Estimates: \n") args <- list(...) if (is.null(args$digits)) args$digits <- 3 f <- do.call("format", c(list(x=res), args)) print(f, print.gap=2, quote=FALSE, na.print="") } cat("\nLog-likelihood = ", x$loglik, ", df = ", x$npars, "\nAIC = ", x$AIC, "\n\n", sep="") } frtrunc_loglik_factory <- function(inits, tinit, tdelay, tmax, method, dlist, dfns, fixedpars){ pars <- inits insert.locations <- setdiff(seq_along(pars), fixedpars) frtrunc_intfn_joint <- function(a, dpars, theta) { pargs <- as.list(dpars) pargs$q <- tmax - a exp(theta*a) * do.call(dfns$p, pargs) } frtrunc_intfn_final <- function(a, dpars, theta, log=FALSE){ dargs <- as.list(dpars) dargs$x <- a dargs$log <- log ret <- do.call(dfns$d, dargs) if (log) ret <- ret - theta*a else ret <- ret * exp( - theta*a) ret } function(optpars, ...) { pars[insert.locations] <- optpars nbpars <- length(pars) - 1 ## NO COVARIATES SO FAR . this needed if covariates for (i in 1:nbpars){ pars[i] <- dlist$inv.transforms[[i]](pars[i]) } dpars <- pars[1:nbpars] theta <- pars[nbpars+1] nv <- length(tinit) dargs <- as.list(dpars) dargs$x <- tdelay dargs$log <- TRUE if (method=="joint") { log.numer <- theta*tinit + do.call(dfns$d, dargs) integ <- integrate(frtrunc_intfn_joint, lower=0, upper=tmax, dpars = dpars, theta=theta)$value logl <- sum(log.numer) - log(integ) * nv } else if (method=="final") { if (dlist$name=="gamma") { logl <- loglik_final_gamma(tdelay, tinit, dpars, theta) } else { log.numer <- frtrunc_intfn_final(tdelay, dpars, theta, log=TRUE) integ <- numeric(nv) y <- tinit + tdelay for (i in 1:nv){ integ[i] <- integrate(frtrunc_intfn_final, lower=0, upper=y[i], dpars = dpars, theta=theta)$value } logl <- sum(log.numer) - sum(log(integ)) } } - logl } } loglik_final_gamma <- function(tdelay, tinit, dpars, theta){ sum(dgamma(tdelay, dpars["shape"], dpars["rate"]+theta, log=TRUE) - pgamma(tinit + tdelay, dpars["shape"], dpars["rate"]+theta, log.p=TRUE)) } flexsurv/R/unroll.function.R0000644000176200001440000001217213231112051015603 0ustar liggesusers##' Convert a function with matrix arguments to a function with vector ##' arguments. ##' ##' Given a function with matrix arguments, construct an equivalent function ##' which takes vector arguments defined by the columns of the matrix. The new ##' function simply uses \code{cbind} on the vector arguments to make a matrix, ##' and calls the old one. ##' ##' ##' @param mat.fn A function with any number of arguments, some of which are ##' matrices. ##' @param \dots A series of other arguments. Their names define which ##' arguments of \code{mat.fn} are matrices. Their values define a vector of ##' strings to be appended to the names of the arguments in the new function. ##' For example ##' ##' \code{fn <- unroll.function(oldfn, gamma=1:3, alpha=0:1)} ##' ##' will make a new function \code{fn} with arguments ##' \code{gamma1},\code{gamma2},\code{gamma3},\code{alpha0},\code{alpha1}. ##' ##' Calling ##' ##' \code{fn(gamma1=a,gamma2=b,gamma3=c,alpha0=d,alpha1=e)} ##' ##' should give the same answer as ##' ##' \code{oldfn(gamma=cbind(a,b,c),alpha=cbind(d,e))} ##' @return The new function, with vector arguments. ##' @section Usage in \pkg{flexsurv}: ##' ##' This is used by \code{\link{flexsurvspline}} to allow spline models, which ##' have an arbitrary number of parameters, to be fitted using ##' \code{\link{flexsurvreg}}. ##' ##' The ``custom distributions'' facility of \code{\link{flexsurvreg}} ##' expects the user-supplied probability density and distribution ##' functions to have one explicitly named argument for each scalar ##' parameter, and given R vectorisation, each of those arguments ##' could be supplied as a vector of alternative parameter values. ##' ##' However, spline models have a varying number of scalar parameters, ##' determined by the number of knots in the spline. ##' \code{\link{dsurvspline}} and \code{\link{psurvspline}} have an ##' argument called \code{gamma}. This can be supplied as a matrix, ##' with number of columns \code{n} determined by the number of knots ##' (plus 2), and rows referring to alternative parameter values. The ##' following statements are used in the source of ##' \code{flexsurvspline}: \preformatted{ dfn <- ##' unroll.function(dsurvspline, gamma=0:(nk-1)) pfn <- ##' unroll.function(psurvspline, gamma=0:(nk-1)) } ##' ##' to convert these into functions with arguments \code{gamma0}, ##' \code{gamma1},\ldots{},\code{gamman}, corresponding to the columns ##' of \code{gamma}, where \code{n = nk-1}, and with other arguments ##' in the same format. ##' @author Christopher Jackson ##' @seealso \code{\link{flexsurvspline}},\code{\link{flexsurvreg}} ##' @examples ##' ##' fn <- unroll.function(ncol, x=1:3) ##' fn(1:3, 1:3, 1:3) # equivalent to... ##' ncol(cbind(1:3,1:3,1:3)) ##' @export unroll.function <- function(mat.fn, ...){ fargs <- formals(mat.fn) vargs <- list(...) # list of names and numbers if (length(vargs)==0) return(mat.fn) badargs <- paste0("\"",names(vargs)[!(names(vargs) %in% names(fargs))],"\"") argerr <- if (length(badargs) > 1) "arguments" else "an argument" if (badargs!="\"\"") stop("\"",deparse(substitute(mat.fn)),"\" does not have ",argerr, " named ", paste(badargs,collapse=",")) sargs <- fargs[setdiff(names(fargs), names(vargs))] # arguments to not change ## converts e.g. list(gamma=2,knots=2) to c("gamma1","gamma2","knots1","knots2") unames <- mapply(function(x,y)paste0(x, y), names(vargs), vargs) unamesv <- as.vector(unames) ## makes an alist(gamma1=,gamma2=,knots1=,knots2=) uargs <- eval(parse(text=paste0("alist(",paste(unamesv, collapse="=, "),"=)"))) args <- as.pairlist(c(sargs,uargs)) ## copy the old function definition into the body of the new one ## so it remains visible dpa <- deparse(args(mat.fn)) basefn.lines <- paste("base.fn <-", paste(paste(dpa[-length(dpa)]), collapse="\n"), paste(deparse(body(mat.fn)), collapse="\n")) ## build the function body cbind.lines <- character(length=length(vargs)) for (i in seq_along(vargs)){ ## make statements like: gamma <- do.call("cbind", list(gamma1, gamma2)) cbind.lines[i] <- sprintf("%s <- do.call(\"cbind\", list(%s))", names(vargs)[i], paste(unames[,i],collapse=",")) } ## make the return statement of the new function sargsn <- paste(paste(names(sargs),names(sargs),sep="="), collapse=", ") vargsn <- paste(paste0(names(vargs),"=",names(vargs)), collapse=", ") ret.line <- if (sargsn=="") sprintf("do.call(base.fn, list(%s))",vargsn) else sprintf("do.call(base.fn, list(%s, %s))",sargsn,vargsn) body <- as.call(c(as.name("{"), parse(text = paste( basefn.lines, paste(cbind.lines, collapse="\n"), ret.line, sep="\n") ))) ## thanks to http://adv-r.had.co.nz/Expressions.html#pairlists for this res <- eval(call("function", args, body), envir=parent.frame()) environment(res) <- environment(mat.fn) res } flexsurv/vignettes/0000755000176200001440000000000014657665315014162 5ustar liggesusersflexsurv/vignettes/standsurv.Rmd0000644000176200001440000010446014417276462016657 0ustar liggesusers--- title: "Calculating standardized survival measures in flexsurv" author: "Michael Sweeting^[mikesweeting79@gmail.com]" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Calculating standardized survival measures in flexsurv} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} bibliography: "standsurv.bib" --- ```{r, include = FALSE} knitr::opts_chunk$set( fig.dim = c(8, 6), collapse = TRUE, comment = "#>" ) ``` # Background ## Standardized survival measures `standsurv` is a post-estimation command that takes a `flexsurvreg` object and calculates standardized survival measures. After fitting a parametric survival model in `flexsurv` it is often useful to compute and visualise the marginal (or standardized) survival. For example, suppose a survival model is fitted adjusted for treatment group, age, and sex. A separate predicted survival curve can be obtained for each individual based on their covariate pattern or a prediction can be obtained by setting covariates to their mean values (both can be obtained using `summary.flexsurvreg`), but it may be more useful to obtain the marginal survival for each treatment group. Regression standardization achieves this by fitting a regression model including the treatment group $Z$, covariates $X$ and possible interactions between $X$ and $Z$. The standardized survival can be estimated by obtaining predictions for every individual in the study under each fixed treatment arm and averaging these individual-specific estimates. The marginal survival over the distribution of covariates in the study assuming all participants were assigned to arm $Z=z$ is: \begin{equation} S_s(t|Z=z) = E[S(t | Z=z, X)] = \frac{1}{N} \sum_{i=1}^{N} S(t | Z=z, X=x_i) \end{equation} for covariate values (vectors) $x_1,...,x_{N}$. Here standarization is done over all $N$ patients in the study and provides a counterfactual marginal estimate when setting $Z=z$. The standardized survival is therefore an estimate of the marginal survival if all study patients had been assigned to group $z$. Under certain assumptions, differences in marginal survival provide estimates of causal effects (@syriopoulou_inverse_2021) and certain estimands such as the average treatment effect (ATE) can be targeted: $$ ATE = S_s(t|Z=z_1) - S_s(t|Z=z_0)]$$ Alternatively, an average treatment effect in the treated (ATET) estimand can be targeted by averaging over only patients who were in the intervention treatment arm $Z=z_1$. Standardization estimates can also be obtained for other target populations of interest. For example it may be important to predict survival in an external population with different characteristics to the study population. The hazard function for the standardized survival can be obtained to understand how the shape of the hazard changes over time. This provides an estimate of the marginal hazard. It can be shown (@rutherford_nice_2020, Appendix I) that the hazard of the standardized survival can be calculated as \begin{equation} h_s(t|Z=z) = \frac{\sum_{i=1}^{N} S(t|Z=z,X=x_i)h(t|Z=z,X=x_i)}{\sum_{i=1}^{N} S(t | Z=z, X=x_i)} \end{equation} This is a weighted average of the $N$ individual hazard functions, weighted by the probability of survival at time $t$. Patients who are unlikely to have survived to $t$ will contribute less weight to this hazard function. ## Calculating marginal expected survival and hazard In economic evaluations parametric survival models are used to extrapolate clinical trial data to estimate lifetime benefits. In this context it is often useful to plot marginal 'expected' (general population) survival alongside parametric models fitted and extrapolated from trial data in order to aid interpretation and for a visual comparison between the trial subjects and the population at large. Displaying expected survival and hazard functions can aid understanding of whether the assumed hazard and survival functions are credible (@rutherford_nice_2020). Expected survival is defined as the all-cause survival in a general population with the same key characteristics as the study subjects. General population mortality rates are often taken from national lifetables that are stratified by age, sex, calendar year and occasionally other prognostic factors (e.g. deprivation indices). The Ederer or "exact" method for estimating expected survival assumes subjects in the trial population are not censored before the end of a stated follow-up time [@ederer_relative_1961]. The expected survival is then the survival we would expect to see in an age-sex matched general population if all patients are continuously followed-up. This is the approach used by `standsurv` to calculate expected survival and is the "most appropriate when doing forcasting, sample size calculations or other predictions of the 'future' where censoring is not an issue" [@therneau_1999]. Based on the exact method, the marginal expected survival using background mortality rates is calculated using all $N$ patients in the trial at any time point $t$: \begin{equation} S^*(t) = \frac{1}{N} \sum_{i=1}^N S_i^*(t) \end{equation} where $S_i^*(t)$ is the expected survival for the $i$th subject at time $t$. It follows that the marginal expected hazard is a weighted average of the expected hazard rates: \begin{equation} h^*(t) = \frac{ \sum_{i=1}^N S_i^*(t) h_i^*(t)}{\sum_{i=1}^N S_i^*(t)} \end{equation} The expected survival for the $i$th subject at follow-up time $t$ is calculated based on matching to the general population hazard rates. If lifetables are utilised these often provide mortality rates by sex ($s$), age ($a$) and calendar year ($y$), in yearly or 5-yearly categories. In practice the expected survival at time $t$ for a given subject is calculated from the cumulative hazard. At a given follow-up time $t$ this is the sum of $h^*_{asy} \times \textrm{Number of days in state } (a,s,y)$ in the follow-up where $h^*_{asy}$ is the expected hazard for age $a$, sex $s$, year $y$. This requires follow-up time for each individual in the study dataset to be split by multiple timescales (e.g. age and year) into time epochs, which can be visualised as a Lexis diagram. Each epoch can then be matched to a corresponding expected mortality rate. ## Incorporation of background mortality into survival models Incorporating background mortality into survival models directly is recommended as it helps avoid extremely implausible projections (@rutherford_nice_2020). This can be done using an excess mortality / relative survival model where population based 'expected' rates, often from life tables, are introduced to explain background mortality. The concept behind these models is to partition the all-cause mortality into excess mortality caused by the disease of interest and that due to other causes. A parametric model can then be applied to the isolated excess mortality. This may be particularly useful when making long-term extrapolations as the pattern of disease-specific mortality and other cause mortality are likely to be very different over time. Alternatively, if cause of death information is available and reliable, a separate cause-specific model can be fitted to the disease-specific mortality and other cause mortality. The all-cause mortality rate at time $t$ for individual $i$ can be partitioned into two constituent parts: \begin{equation} h_i(t) = h^*_i(t) + \lambda_i(t) \end{equation} where $h_i(t)$ is the all-cause mortality rate (hazard), $h^*_i(t)$ is the expected or background mortality rate and $\lambda_i(t)$ is the excess mortality rate. Equivalently, the hazard rates can be transformed to the survival scale which gives the all-cause survival at time $t$ as the product of the expected survival and the relative survival: \begin{equation} S_i(t) = S^*_i(t) R_i(t) \end{equation} The relative survival, $R_i(t)$, is therefore the ratio of all-cause survival and the expected survival in the background population. Typically, $h_i^*(t)$ (and hence $S_i^*(t)$) are obtained from population lifetables. The expected mortality rates are assumed to be fixed and known and a parametric model is then used to estimate the relative survival (or equivalently excess hazard). # `standsurv` `standsurv` is a post-estimation command that takes a `flexsurv` regression and calculates standardized survival measures and contrasts. Expected mortality rates and survival can also be obtained. The main features of the command are that it enables the calculation and plotting over any specified follow-up times of 1. Marginal survival, hazard and restricted mean survival time (RMST) metrics 2. Marginal expected (population) survival and hazard functions matched to the study population 3. Marginal all-cause survival and all-cause hazard after fitting relative survival models 4. Contrasts in survival, hazard and RMST metrics (e.g. marginal hazard ratio, differences in marginal RMST) 5. Confidence intervals and standard errors for all measures and contrasts using either the delta method or bootstrapping Through a simple syntax the user can specify the groups that they wish to calculate the marginal metrics. These groups can be formed by any combination of covariate values. ## A worked example: the pbc dataset For this example we will use data from the German Breast Cancer Study Group 1984-1989, which is the R dataset `bc` found in the `flexsurv` package. This dataset has death, or censoring times for 686 primary node positive breast cancer patients together with a 3-level prognostic group variable with levels "Good", "Medium" and "Poor". For this demonstration we collapse the prognostic variable into 2 levels: "Good" and "Medium/Poor". We also create some artificial ages and diagnosis dates for the patients, along with assuming all patients are female. We allow a correlation between the age at diagnosis for a patient and their survival time so that age is a prognostic variable. The mean age is 65 with a standard deviation of 5. We load this dataset and create these additional variables. ```{r, message = FALSE, warning = FALSE} library(flexsurv) library(flexsurvcure) library(ggplot2) library(dplyr) library(survminer) ``` ```{r} data(bc) set.seed(236236) ## Age at diagnosis is correlated with survival time. A longer survival time ## gives a younger mean age bc$age <- rnorm(dim(bc)[1], mean = 65 - scale(bc$recyrs, scale=F), sd = 5) ## Create age at diagnosis in days - used later for matching to expected rates bc$agedays <- floor(bc$age * 365.25) ## Create some random diagnosis dates between 01/01/1984 and 31/12/1989 bc$diag <- as.Date(floor(runif(dim(bc)[1], as.Date("01/01/1984", "%d/%m/%Y"), as.Date("31/12/1989", "%d/%m/%Y"))), origin="1970-01-01") ## Create sex (assume all are female) bc$sex <- factor("female") ## 2-level prognostic variable bc$group2 <- ifelse(bc$group=="Good", "Good", "Medium/Poor") head(bc) ``` A plot of the Kaplan-Meier shows a clear separation in the survival curves between the two prognostic groups. ```{r} km <- survfit(Surv(recyrs, censrec)~group2, data=bc) kmsurvplot <- ggsurvplot(km) kmsurvplot + xlab("Time from diagnosis (years)") ``` ## A stratified Weibull model We start by fitting a Weibull model to each group separately. One way to do this is to fit a single saturated model whereby group affects both the scale and shape parameters of the Weibull distribution. This effectively means we have a separate scale and shape parameter for each group, which is equivalent to fitting two separate models. Such a model does not make a proportional hazards assumption and hence the hazard ratio will change over time. The saturated model approach has advantages as we can use the model to easily investigate treatment effects using `standsurv` as we shall see later. Including group in the main formula of `flexsurvreg` allows group to affect the scale parameter of the Weibull distribution whilst we use the `anc` argument in `flexsurvreg` to additionally allow group to affect the shape parameter. ```{r} model.weibull.sep <- flexsurvreg(Surv(recyrs, censrec)~group2, anc = list(shape = ~ group2), data=bc, dist="weibullPH") model.weibull.sep ``` Given that the model only contains `group2` and no other covariates we can obtain the predicted (fitted) survival for each of the two groups using the `summary` function and storing these predictions in a tidy data.frame with the argument `tidy=T`. ```{r} predictions <- summary(model.weibull.sep, type = "survival", tidy=T) ggplot() + geom_line(aes(x=time, y=est, color = group2), data=predictions) + geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot) ``` The Weibull model does not appear to fit the data very well and so we should try other parametric distributions. However, for illustration purposes we shall continue using the Weibull model. We will now show that the same predictions can be obtained from `standsurv` but with the benefit of addition flexibility. ## Using `standsurv` to calculate marginal survival `standsurv` works similarly to the `margins` command in `R` and `standsurv` in Stata by allowing the user to specify a list of scenarios in which specific covariates are fixed to certain values. This is done using the `at` argument of `standsurv` to provide the list of scenarios where each scenario is itself a list containing covariates that are to be fixed. In our worked example the two scenarios are `list(group2 = "Good")` and `list(group2 = "Medium/Poor")`. Any covariates not specified in the `at` scenarios are averaged over, hence creating marginal, or standardized, estimates of the metric of interest. In the example above, there are no other covariates in the model so we will get the same answer as obtained from `summary`. But the later worked example extends this to models containing other covariates. The default is to calculate survival probabilities at the event times in the data but this can be changed with the `type` and `t` arguments, respectively. The returned object is a tidy data.frame with columns named `at1` up to `atn` for the n scenarios specified in the `at` argument. ```{r} ss.weibull.sep.surv <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) ss.weibull.sep.surv ``` Further details such as labels for the `at` scenarios are stored in attributes of the `standsurv` object. These are utilised by the `plot` function. A plot of the marginal estimates can be easily produced using the `plot` function, which produces a `ggplot` object. ```{r} plot(ss.weibull.sep.surv) ``` The plot can be easily further manipulated, for example by changing axis labels and adding further plots. ```{r} plot(ss.weibull.sep.surv) + xlab("Time since diagnosis (years)") + geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot) ``` ## Other metrics: marginal hazards and marginal RMST We can use the `type` argument to calculate marginal hazards or restricted mean survival time (RMST). For example a plot of the hazard functions for the two groups is obtained as follows: ```{r} ss.weibull.sep.haz <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) plot(ss.weibull.sep.haz) + xlab("Time since diagnosis (years)") ``` Whilst a plot of RMST is given by ```{r} ss.weibull.sep.rmst <- standsurv(model.weibull.sep, type = "rmst", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) plot(ss.weibull.sep.rmst) + xlab("Time since diagnosis (years)") ``` ## Calculating contrasts The advantage of fitting a saturated model now becomes clear as we can calculate contrasts between our `at` scenarios. Suppose we are interested in the difference in the survival functions between the two groups. This is easily calculated using the `contrast = "difference"` argument, and a plot of the contrast can be obtained using `contrast = TRUE` argument in the `plot` function. ```{r} ss.weibull.sep.3 <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), contrast = "difference") plot(ss.weibull.sep.3, contrast=TRUE) + xlab("Time since diagnosis (years)") + ylab("Difference in survival probabilities") + geom_hline(yintercept = 0) ``` Alternatively, we may wish to visualise the implied hazard ratio from fitting separate Weibull models to the two groups. In the breast cancer example we see that the hazard ratio (treatment effect) starts very high before decreasing, suggesting that those with Medium/Poor prognosis start with a high elevated risk but have a continued excess risk up to the end of follow-up, compared to those with Good prognosis. ```{r} ss.weibull.sep.4 <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), contrast = "ratio") plot(ss.weibull.sep.4, contrast=TRUE) + xlab("Time since diagnosis (years)") + ylab("Hazard ratio") + geom_hline(yintercept = 1) ``` ## Confidence intervals and standard errors Confidence intervals and standard errors for both the metric of interest and contrasts can be obtained either through bootstrapping or using the delta method. Bootstrap confidence intervals are calculated by specifying `ci = TRUE`, `boot = TRUE`, and providing the number of bootstrap samples using `B`. We can also set the seed using the `seed` argument to allow reproducibility. If instead the delta method is to be used to obtain confidence intervals then we specify `ci = TRUE`, `boot = FALSE`. The delta method obtains confidence intervals by calculating standard errors for a given transformation of the metric of interest and then assuming normality. The default is to use a log transformation; hence if `type = "survival"` the confidence intervals are symmetric for the log survival probabilities. Alternative transformations can be specified using the `trans` argument. The code below shows confidence intervals for marginal survival calculated through a bootstrap method (with `B = 100`) compared to a delta method. For computational efficiency here we only predict for 10 time points. ```{r} ss.weibull.sep.boot <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=10), ci = TRUE, boot = TRUE, B = 100, seed = 2367) ss.weibull.sep.deltam <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=10), ci = TRUE, boot = FALSE) plot(ss.weibull.sep.boot, ci = TRUE) + geom_ribbon(aes(x=time, ymin=survival_lci, ymax=survival_uci, color=at, linetype = "Delta method"), fill=NA, data=attr(ss.weibull.sep.deltam,"standpred_at")) + scale_linetype_manual(values = c("Bootstrap" = "solid", "Delta method"= "dashed")) + ggtitle("Comparison of bootstrap and delta method confidence intervals") ``` ## Adding age as a covariate Suppose age has been added as a covariate to the survival model. If age is not included in our `at` scenarios `standsurv` will by default produce standardized estimates of survival averaged over the age distribution in our study population. Alternatively we could pass a new prediction dataset to `standsurv` and obtain standardized estimates for this population. As an example, we obtain marginal survival estimates after fitting a stratified Weibull model, firstly standardized to the age-distribution of our study population and secondly standardized to an older population with mean age of 75 and standard deviation 5. ```{r} model.weibull.age.sep <- flexsurvreg(Surv(recyrs, censrec)~group2 + age, anc = list(shape = ~ group2 + age), data=bc, dist="weibullPH") ## Marginal survival standardized to age distribution of study population ss.weibull.age.sep.surv <- standsurv(model.weibull.age.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50) ) ## Marginal survival standardized to an older population # create a new prediction dataset as a copy of the bc data but whose ages are drawn from # a normal distribution with mean age 75, sd 5. newpred.data <- bc set.seed(247) newpred.data$age = rnorm(dim(bc)[1], 75, 5) ss.weibull.age2.sep.surv <- standsurv(model.weibull.age.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), newdata=newpred.data) ## Overlay both marginal survival curves plot(ss.weibull.age.sep.surv) + geom_line(aes(x=time, y=survival, color=at, linetype = "Older population"), data = attr(ss.weibull.age2.sep.surv, "standpred_at") ) + scale_linetype_manual(values = c("Study" = "solid", "Older population"= "dashed")) ``` ## Calculating expected survival and hazard in `standsurv` To overlay marginal expected survival or hazard curves we require a lifetable of population hazard rates. To demonstrate we use the US lifetable that comes with the `survival` package, called `survexp.us`. Other lifetables can be obtained directly from the Human Mortality Database (HMD) using the `HMDHFDplus` package. The `survexp.us` lifetable is a `ratetable` object with stratification factors age, sex and year. It gives rates of mortality per person-day for combinations of the stratification factors. A summary of the `survexp.us` object shows that the time-scale is in days. ```{r} summary(survexp.us) ``` To use the lifetable to get expected rates for our trial population we need to match age, sex and year variables in our dataset to those in the ratetable. We can use the `rmap` argument to do this. `standsurv` utilises the `survexp` function in the `survival` package to calculate expected survival over the times specified in `t` using the 'exact' method of Ederer. We note that sex in our data is coded the same as in the `ratetable` ("male" and "female") and importantly that we have variables that record both age at diagnosis and diagnosis date in days. It is important that the user ensures that the study data are correctly coded and have variables on the same timescale as in the `ratetable` so that matching is successful. The code below demonstrates that for our data we therefore need to match the `year` variable in the `ratetable` to the `diag` variable in our study data, and the `age` variable in the `ratetable` to the `agedays` variable in our study data. We need to specify three more arguments in `standsurv`. First, the lifetable, which must be a `ratetable` object and is specified using the `ratetable` argument. Second, we may need to pass our trial dataset to `standsurv` if the stratifying factors do not appear as covariates in the `flexsurv` model. Finally, we need to be careful to tell `standsurv` what the time scale transformation is between the fitted `flexsurv` model and the time scale in `ratetable`. We can use the `scale.ratetable` argument to do this. Typically ratetable objects are expressed in days (e.g. rates per person-day). The default is therefore `scale.ratetable = 365.25`, which indicates that the survival model was fitted in years but the ratetable is in days. After running `standsurv` we can plot the expected survival (or hazard) by using the argument `expected = TRUE` in the `plot()` function. ```{r} ss.weibull.sep.expected <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.expected, expected = T) ``` We can see that the marginal expected survival is much higher than the marginal (predicted) survival for our breast cancer population. We can also obtain the expected hazards: ```{r} ss.weibull.sep.expectedh <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.expectedh, expected = T) ``` The hazard plot shows that our model is predicting an increasing hazard over time for the cancer population, which remains significantly higher than the expected hazard in the general population. The monotonically increasing hazard imposed by the Weibull distribution may be implausible and this may make us question the suitability of a Weibull model if we wish to extrapolate. ## Incorporation of background mortality A relative survival model can be fitted using `flexsurv` by incorporating background mortality rates. The model then estimates excess hazard rates and relative survival measures. For prediction purposes, following the fitting of a relative survival model, `standsurv` allows the user to either obtain marginal predictions of relative survival / excess hazard or of all-cause survival / all-cause hazard. The latter are calculated by multiplying relative survival estimates with expected survival to get all-cause survival, or by adding excess hazard rates to expected hazard to get all-cause hazard. We demonstrate this by fitting a relative survival cure model to the breast cancer data and obtaining predicted all-cause survival and all-cause hazard up to 30-years after diagnosis. A mixture cure model makes the assumption that a proportion of the study population will never experience the event. In a relative survival framework the cure model assumes that the excess mortality rate approaches zero (or equivalently the relative survival reaches an asymptote determined by the cure fraction). We fit a relative survival cure model with a Weibull distribution assumed for the uncured. The relative survival mixture-cure model is fitted below. We must pass to `flexsurvcure` the expected hazard rates at the event / censoring time for each individual, as it is the expected rates at the event times that are used in the likelihood function for a parametric relative survival model. For this we need to initally do some data wrangling. Firstly, we calculate attained age and attained year (in whole years) at the event time for all study subjects. Secondly, we join the data with the expected rates using the matching variables attained age, attained year and sex. In the example, we express the expected rate as per person-year as this is the timescale used in the flexsurv regression model. ```{r} ## reshape US lifetable to be a tidy data.frame, and convert rates to per person-year as flexsurv regression is in years survexp.us.df <- as.data.frame.table(survexp.us, responseName = "exprate") %>% mutate(exprate = 365.25 * exprate) survexp.us.df$age <- as.numeric(as.character(survexp.us.df$age)) survexp.us.df$year <- as.numeric(as.character(survexp.us.df$year)) ## Obtain attained age and attained calendar year in (whole) years bc <- bc %>% mutate(attained.age.yr = floor(age + recyrs), attained.year = lubridate::year(diag + rectime)) ## merge in (left join) expected rates at event time bc <- bc %>% left_join(survexp.us.df, by = c("attained.age.yr"="age", "attained.year"="year", "sex"="sex")) # A stratified relative survival mixture-cure model model.weibull.sep.rs <- flexsurvcure(Surv(recyrs, censrec)~group2, anc = list(shape = ~ group2, scale = ~ group2), data=bc, dist="weibullPH", bhazard=exprate) model.weibull.sep.rs ``` We can now use `standsurv` to obtain all-cause survival and hazard predictions using `type = "survival"` and `type = "hazard"`. If instead we had wanted predictions of relative survival or excess hazards we would use `type = "relsurvival"` and `type = "excesshazard"`, respectively. ```{r} ## All-cause survival ss.weibull.sep.rs.surv <- standsurv(model.weibull.sep.rs, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.surv, expected = T) # All-cause hazard ss.weibull.sep.rs.haz <- standsurv(model.weibull.sep.rs, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.haz, expected = T) ``` The marginal excess hazard is now unimodal since the cure model is forcing the initially increasing excess hazard to tend to zero in the long-term where only 'cured' subjects remain. The marginal all-cause hazard tends to the expected hazard and follows it thereafter. A plot of the excess hazard confirms this. ```{r} # Excess hazard ss.weibull.sep.rs.excesshaz <- standsurv(model.weibull.sep.rs, type = "excesshazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.excesshaz) ``` # Conclusions `standsurv` is a powerful post-estimation command that allows easy calculation of a number of useful prediction metrics. Contrasts can be made between any counterfactual populations of interest and, through regression standardisation, allows the targeting of marginal estimands. Confidence intervals, via the delta method or bootstrapping, are available and benchmarking against or incorporating background mortality rates is also supported. # References flexsurv/vignettes/multistate.Rnw0000644000176200001440000014302114471114027017025 0ustar liggesusers%\VignetteIndexEntry{Multi-state modelling with flexsurv} %\VignetteEngine{knitr::knitr} % \documentclass[article,shortnames]{jss} \documentclass[article,shortnames,nojss,nofooter]{jss} \usepackage{bm} \usepackage{tabularx} \usepackage{graphics} \usepackage{alltt} \usepackage[utf8]{inputenc} <>= options(width=60) options(prompt="R> ") library(knitr) opts_chunk$set(fig.path="flexsurv-") render_sweave() @ %% need no \usepackage{Sweave.sty} \author{Christopher H. Jackson \\ MRC Biostatistics Unit, Cambridge, UK} \title{Flexible parametric multi-state modelling with flexsurv} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Address{ Christopher Jackson\\ MRC Biostatistics Unit\\ Cambridge Institute of Public Health\\ Robinson Way\\ Cambridge, CB2 0SR, U.K.\\ E-mail: \email{chris.jackson@mrc-bsu.cam.ac.uk} } \Abstract{ A \emph{multi-state model} represents how an individual moves between multiple states in continuous time. Survival analysis is a special case with two states, ``alive'' and ``dead''. \emph{Competing risks} are a further special case, where there are multiple causes of death, that is, one starting state and multiple possible destination states. This vignette describes the two forms of multi-state or competing risks models that can be implemented in \pkg{flexsurv}. Section~\ref{sec:causespec} describes models based on \emph{cause-specific hazards}. Section~\ref{sec:mixture} describes a less commonly-used approach based on \emph{mixture models}. Cause-specific hazards models tend to be faster to fit, whereas the parameters of the mixture models are easier to interpret. } \Keywords{multi-state models, multistate models, competing risks} \begin{document} \section{Overview} \label{sec:multistate} This vignette describes multi-state models for data where there are a series of event times $t_{1},\dots, t_{n}$ for an individual, corresponding to changes of state. The last of these may be an observed or right-censored event time. Note \emph{panel data} are not considered here --- that is, observations of the state of the process at an arbitrary set of times \citep{kalbfleisch:lawless}. In panel data, we do not necessarily know the time of each transition, or even whether transitions of a certain type have occurred at all between a pair of observations. Multi-state models for that type of data (and also exact event times) can be fitted with the \pkg{msm} package for \proglang{R} \citep{msmjss}, but are restricted to (piecewise) exponential event time distributions. Knowing the exact event times enables much more flexible models, which \pkg{flexsurv} can fit. The \pkg{flexsurv} package provides two general frameworks for multi-state modelling. \begin{enumerate} \item The most common framework is based on \emph{cause-specific hazards} of competing risks. This is an extension of standard survival modelling, and is explained in Section~\ref{sec:causespec}. \item An alternative approach is based on \emph{mixture models}. For example, suppose there are three competing states that an individual in state $r$ may move to next. People are then classified into three \emph{mixture components}, defined by the state the person moves to. The probabilities of each next state, and the distribution of the time of moving to each state, are estimated jointly. These quantities are easier to interpret than cause specific hazards. This approach was originally described by \citet{larson1985mixture}. In Section~\ref{sec:mixture} we explain how to implement it using the \code{flexsurvmix} function. \end{enumerate} \section{Multi-state modelling using cause-specific hazards} \label{sec:causespec} Given that an individual is in state $X(t)$ at time $t$, their next state, and the time of the change, are governed by a set of \emph{transition intensities} or \emph{transition hazards} \[q_{rs}(t,\mathbf{z}(t),\mathcal{F}_t) = \lim_{\delta t \rightarrow 0} \Prob(X(t+\delta t) = s | X(t) = r, \mathbf{z}(t), \mathcal{F}_t) / \delta t \] for states $r, s = 1,\dots,R$, which for a survival model are equivalent to the hazard $h(t)$. The intensity represents the instantaneous risk of moving from state $r$ to state $s$, and is zero if the transition is impossible. It may depend on covariates $\mathbf{z}(t)$, the time $t$ itself, and possibly also the ``history'' of the process up to that time, $\mathcal{F}_t$: the states previously visited or the length of time spent in them. \paragraph{Alternative time scales} In semi-Markov (``clock-reset'') models, $q_{rs}(t)$ is defined as a function of the time $t$ since entry into the current state. Any software to fit survival models can also fit this kind of multi-state model, as the following sections will explain. In an inhomogeneous Markov model, $t$ represents the time since the beginning of the process (that is, a ``clock-forward'' scale is used), but the intensity $q_{rs}(t)$ does not depend further on $\mathcal{F}_t$. Again, standard survival modelling software can be used, with the additional requirement that it can deal with left-truncation or \emph{counting process} data, which \code{survreg}, for example, does not currently support. These approaches are equivalent for competing risks models, since there is at most one transition for each individual, so that the time since the beginning of the process equals the time spent in the current state. Therefore no left-truncation is necessary. Note also that in a clock-reset model, the time since the beginning of the process may enter the model as a covariate. Likewise, in a clock-forward model, the time spent in the current state may enter as a covariate, in which case the model is no longer Markov. \paragraph{Example} For illustration, consider a simple three-state example, previously studied by \citet{heng:paper}. Recipients of lung transplants are are risk of bronchiolitis obliterans syndrome (BOS). This was defined as a decrease in lung function to below 80\% of a baseline value defined in the six months following transplant. A three-state ``illness-death'' model represents the risk of developing BOS, the risk of dying before developing BOS, and the risk of death after BOS. BOS is assumed to be irreversible, so there are only three allowed transitions (Figure \ref{fig:bosmsm}), each with an intensity function $q_{rs}(t)$. \begin{figure}[h] \centering \scalebox{0.6}{\includegraphics{bosmsm.pdf}} \caption{Three-state multi-state model for bronchiolitis obliterans syndrome (BOS).} \label{fig:bosmsm} \end{figure} \subsection{Representing multi-state data as survival data} \label{sec:multistate:data} \citet{andersen:keiding} and \citet{putter:mstate} explain how to implement multi-state models by manipulating the data into a suitable form for survival modelling software --- an overview is given here. For each permitted $r \rightarrow s$ transition in the multi-state model, there is a corresponding ``survival'' (time-to-event) model, with hazard rates defined by $q_{rs}(t)$. For a patient who enters state $r$ at time $t_{j}$, their next event at $t_{j+1}$ is defined by the model structure to be one of a set of competing events $s_1,\ldots,s_{n_r}$. This implies there are $n_r$ corresponding survival models for this state $r$, and $\sum_r n_r$ models over all states $r$. In the BOS example, there are $n_1=2,n_2=1$ and $n_3=0$ possible transitions from states 1, 2 and 3 respectively. The data to inform the $n_r$ models from state $r$ consists firstly of an indicator for whether the transition to the corresponding state $s_1,\ldots,s_{n_r}$ is observed or censored at $t_{j+1}$. If the individual moves to state $s_k$, the transitions to all other states in this set are censored at this time. This indicator is coupled with: \begin{itemize} \item (for a semi-Markov model) the time elapsed $dt_{j} = t_{j+1} - t_{j}$ from state $r$ entry to state $s$ entry. The ``survival'' model for the $r \rightarrow s$ transition is fitted to this time. \item (for an inhomogeneous Markov model) the start and stop time $(t_j,t_{j+1})$, as in \S\ref{sec:censtrunc}. The $r \rightarrow s$ model is fitted to the right-censored time $t_{j+1}$ from the \emph{start of the process}, but is conditional on not experiencing the $r \rightarrow s$ transition until after the state $r$ entry time. In other words, the $r \rightarrow s$ transition model is \emph{left-truncated} at the state $r$ entry time. \end{itemize} In this form, the outcomes of two patients in the BOS data are <<>>= library(flexsurv) bosms3[18:22, ] @ Each row represents an observed (\code{status = 1}) or censored (\code{status = 0}) transition time for one of three time-to-event models indicated by the categorical variable \code{trans} (defined as a factor). Times are expressed in years, with the baseline time 0 representing six months after transplant. Values of \code{trans} of 1, 2, 3 correspond to no BOS$\rightarrow$BOS, no BOS$\rightarrow$death and BOS$\rightarrow$death respectively. The first row indicates that the patient (\code{id} 7) moved from state 1 (no BOS) to state 2 (BOS) at 0.17 years, but (second row) this is also interpreted as a censored time of moving from state 1 to state 3, potential death before BOS onset. This patient then died, given by the third row with \code{status} 1 for \code{trans} 3. Patient 8 died before BOS onset, therefore at 8.2 years their potential BOS onset is censored (fourth row), but their death before BOS is observed (fifth row). The \pkg{mstate} \proglang{R} package \citep{mstate:cmpb,mstate:jss} has a utility \code{msprep} to produce data of this form from ``wide-format'' datasets where rows represent individuals, and times of different events appear in different columns. \pkg{msm} has a similar utility \code{msm2Surv} for producing the required form given longitudinal data where rows represent state observations. \subsection{Multi-state model likelihood with cause-specific hazards} \label{sec:multistate:lik} After forming survival data as described above, a multi-state model can be fitted by maximising the standard survival model likelihood~(given at the start of the main \pkg{flexsurv} vignette), $l(\bm{\theta} | \mathbf{x}) = \prod_i l_i(\bm{\theta}|x_i)$, where $\mathbf{x}$ is the data, and $i$ now indexes multiple observations for multiple individuals. This can also be written as a product over the $K=\sum_r n_r$ transitions $k$, and the $m_k$ observations $j$ pertaining to the $k$th transition. The transition type will typically enter this model as a categorical covariate --- see the examples in the next section. \begin{equation} \label{eq:lik:multistate} l(\bm{\theta} | \mathbf{x}) = \prod_{k=1}^K \prod_{j=1}^{m_k} l_{jk}(\bm{\theta}|\mathbf{x}_{jk}) \end{equation} Therefore if the parameter vector $\bm{\theta}$ can be partitioned as $(\bm{\theta}_1|\ldots|\bm{\theta}_K)$, independent components for each transition $k$, the likelihood becomes the product of $K$ independent transition-specific likelihoods \citep{andersen:keiding}. The full multi-state model can then be fitted by maximising each of these independently, using $K$ separate calls to a survival modelling function such as \code{flexsurvreg}. This can give vast computational savings over maximising the joint likelihood for $\bm{\theta}$ with a single fit. For example, \citet{francesca:smmr} used \pkg{flexsurv} to fit a parametric multi-state model with 21 transitions and 84 parameters for over 30,000 observations, which was computationally impractical via the joint likelihood, whereas it only took about a minute to perform 21 transition-specific fits. On the other hand, if any parameters are constrained between transitions (e.g. if hazards are proportional between transitions, or the effects of covariates on different transitions are the same) then it is necessary to maximise the joint likelihood~(\ref{eq:lik:multistate}) with a single call. \subsection{Fitting parametric multi-state models with cause-specific hazards} \label{sec:multistate:fitting} \paragraph{Joint likelihood} Three multi-state models are fitted to the BOS data using \code{flexsurvreg}, firstly using a single likelihood maximisation for each model. The first two use the ``clock-reset'' time scale. \code{crexp} is a simple time-homogeneous Markov model where all transition intensities are constant through time, so that the clock-forward and clock-reset scales are identical. The time to the next event is exponentially-distributed, but with a different rate $q_{rs}$ for each transition type \code{trans}. \code{crwei} is a semi-Markov model where the times to BOS onset, death without BOS and the time from BOS onset to death all have Weibull distributions, with a different shape and scale for each transition type. \code{cfwei} is a clock-forward, inhomogeneous Markov version of the Weibull model: the 1$\rightarrow$2 and 1$\rightarrow$3 transition models are the same, but the third has a different interpretation, now the time \emph{from baseline} to death with BOS has a Weibull distribution. <<>>= crexp <- flexsurvreg(Surv(years, status) ~ trans, data = bosms3, dist = "exp") crwei <- flexsurvreg(Surv(years, status) ~ trans + shape(trans), data = bosms3, dist = "weibull") cfwei <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans + shape(trans), data = bosms3, dist = "weibull") @ \paragraph{Semi-parametric equivalents} The equivalent Cox models are also fitted using \code{coxph} from the \pkg{survival} package. These specify a different baseline hazard for each transition type through a function \code{strata} in the formula, so since there are no other covariates, they are essentially non-parametric. Note that the \code{strata} function is not currently understood by \code{flexsurvreg} --- the user must say explicitly what parameters, if any, vary with the transition type, as in \code{crwei}. <<>>= crcox <- coxph(Surv(years, status) ~ strata(trans), data = bosms3) cfcox <- coxph(Surv(Tstart, Tstop, status) ~ strata(trans), data = bosms3) @ In all cases, if there were other covariates, they could simply be included in the model formula. Typically, covariate effects will vary with the transition type, so that an interaction term with \code{trans} would be included. Some post-processing might then be needed to combine the main covariate effects and interaction terms into an easily-interpretable quantity (such as the hazard ratio for the $r,s$ transition). Alternatively, \pkg{mstate} has a utility \code{expand.covs} to expand a single covariate in the data into a set of transition-specific covariates, to aid interpretation \citep[see][]{mstate:jss}. \paragraph{Transition-specific models} In this small example, the joint likelihood can be maximised easily with a single function call, but for larger models and datasets, this may be unfeasible. A more computationally-efficient approach is to fit a list of transition-specific models, as follows. <<>>= mod_nobos_bos <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data = bosms3, dist = "weibull") mod_nobos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "weibull") mod_bos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==3), data = bosms3, dist = "weibull") @ We then define a matrix \code{tmat} describes the transition structure of the multi-state model , as a matrix of integers whose $r,s$ entry is $i$ if the $i$th transition type is $r,s$, and has \code{NA}s on the diagonal and where the $r,s$ transition is disallowed. <<>>= tmat <- rbind(c(NA, 1, 2), c(NA, NA, 3), c(NA, NA, NA)) crfs <- fmsm(mod_nobos_bos, mod_nobos_death, mod_bos_death, trans = tmat) @ The three transition models are then grouped together, and the transition matrix is attached, using the \code{fmsm} function. This constructs an R object, \code{crfs}, that fully describes the multistate model. The \code{fmsm} object can be supplied to the output and prediction functions described in the subsequent sections, instead of a single \code{flexsurvreg} object. However, this approach is not possible if there are constraints in the parameters across transitions, such as common covariate effects. \begin{sloppypar} Any parametric distribution can be employed in a multi-state model, just as for standard survival models, with \code{flexsurvreg}. Spline models may also be fitted with \code{flexsurvspline}, and if hazards are assumed proportional, they are expected to give similar results to the Cox model. Since \pkg{flexsurv} version 2.0, different parametric families can be used for different transitions, though in earlier versions, the same family had to be used. \end{sloppypar} \subsection{Obtaining cumulative transition-specific hazards} Multi-state models can be characterised by their cumulative $r \rightarrow s$ transition-specific hazard functions $H_{rs}(t) = \int_0^t q_{rs}(u)du$. For \emph{semi-parametric} multi-state models fitted with \code{coxph}, the function \code{msfit} in \pkg{mstate} \citep{mstate:cmpb,mstate:jss} provides piecewise-constant estimates and covariances for $H_{rs}(t)$. For the Cox models for the BOS data, <<>>= require("mstate") mrcox <- msfit(crcox, trans = tmat) mfcox <- msfit(cfcox, trans = tmat) @ \pkg{flexsurv} provides an analogous function \code{msfit.flexsurvreg} to produce cumulative hazards from \emph{fully-parametric} multi-state models in the same format. This is a short wrapper around \code{summary.flexsurvreg(..., type = "cumhaz")}, previously mentioned in \S\ref{sec:plots}. The difference from \pkg{mstate}'s method is that hazard estimates can be produced for any grid of times \code{t}, at any level of detail and even beyond the range of the data, since the model is fully parametric. The argument \code{newdata} can be used in the same way to specify a desired covariate category, though in this example there are no covariates in addition to the transition type. The name of the (factor) covariate indicating the transition type can also be supplied through the \code{tvar} argument, in this case it is the default, \code{"trans"}. <<>>= tgrid <- seq(0, 14, by = 0.1) mrwei <- msfit.flexsurvreg(crwei, t = tgrid, trans = tmat) mrexp <- msfit.flexsurvreg(crexp, t = tgrid, trans = tmat) mfwei <- msfit.flexsurvreg(cfwei, t = tgrid, trans = tmat) @ These can be plotted (Figure \ref{fig:bos:cumhaz}) to show the fit of the parametric models compared to the non-parametric estimates. Both models appear to fit adequately, though give diverging extrapolations after around 6 years when the data become sparse. The Weibull clock-reset model has an improved AIC of \Sexpr{round(crwei$AIC)}, compared to \Sexpr{round(crexp$AIC)} for the exponential model. For the $2\rightarrow 3$ transition, the clock-forward and clock-reset models give slightly different hazard trajectories. <>= cols <- c("black", "#E495A5", "#86B875", "#7DB0DD") # colorspace::rainbow_hcl(3) plot(mrcox, xlab = "Years after baseline", lwd = 3, xlim = c(0, 14), cols = cols[1:3]) for (i in 1:3){ lines(tgrid, mrexp$Haz$Haz[mrexp$Haz$trans == i], col = cols[i], lty = 2, lwd = 2) lines(tgrid, mrwei$Haz$Haz[mrwei$Haz$trans == i], col = cols[i], lty = 3, lwd = 2) } lines(mfcox$Haz$time[mfcox$Haz$trans == 3], mfcox$Haz$Haz[mfcox$Haz$trans == 3], type = "s", col = cols[4], lty = 1, lwd = 2) lines(tgrid, mfwei$Haz$Haz[mfwei$Haz$trans == 3], col = cols[4], lty = 3, lwd = 2) legend("topleft", inset = c(0, 0.2), lwd = 2, col = cols[4], c("2 -> 3 (clock-forward)"), bty = "n") legend("topleft", inset = c(0, 0.3), c("Non-parametric", "Exponential", "Weibull"), lty = c(1, 2, 3), lwd = c(3, 2, 2), bty = "n") @ \begin{figure}[h] \includegraphics{flexsurv-cumhaz-1} \caption{Cumulative hazards for three transitions in the BOS multi-state model (clock-reset), under non-parametric, exponential and Weibull models. For the $2\rightarrow 3$ transition, an alternative clock-forward scale is shown for the non-parametric and Weibull models.} \label{fig:bos:cumhaz} \end{figure} \subsection{Prediction from parametric multi-state models with cause-specific hazards} The \emph{transition probabilities} of the multi-state model are the probabilities of occupying each state $s$ at time $t > t_0$, given that the individual is in state $r$ at time $t_0$. \[ P(t_0, t) = \Prob(X(t) = s | X(t_0) = r) \] \paragraph{Markov models} For a time-inhomogeneous Markov model, these are related to the transition intensities via the Kolmogorov forward equation \[ \frac{d P(t_0,t)}{dt} = P(t_0,t) Q(t) \] with initial condition $P(t_0,t_0) = I$ \citep{cox:miller}. This can be solved numerically, as in \citet{titman:nonhomog}. This is implemented in the function \code{pmatrix.fs}, using the \pkg{deSolve} package \citep{deSolve}. This returns the full transition probability matrix $P(t_0,t)$ from time $t_0=0$ to a time or set of times $t$ specified in the call. Under the Weibull model, the probability of remaining alive and free of BOS is estimated at 0.3 at 5 years and 0.09 at 10 years: <<>>= pmatrix.fs(cfwei, t = c(5, 10), trans = tmat) @ Confidence intervals can be obtained by simulation from the asymptotic distribution of the maximum likelihood estimates --- see \code{help(pmatrix.fs)} for full details. A similar function \code{totlos.fs} is provided to estimate the expected total amount of time spent in state $s$ up to time $t$ for a process that starts in state $r$, defined as $\int_{u=0}^tP(0,u)_{rs}du$. \paragraph{Semi-Markov models} For semi-Markov models, the Kolmogorov equation does not apply, since the transition intensity matrix $Q(t)$ is no longer a deterministic function of $t$, but depends on when the transitions occur between time $t_0$ and $t$. Predictions can then be made by simulation. The function \code{sim.fmsm} simulates trajectories from parametric semi-Markov models by repeatedly generating the time to the next transition until the individual reaches an absorbing state or a specified censoring time. This requires the presence of a function to generate random numbers from the underlying parametric distribution --- and is fast for built-in distributions which use vectorised functions such as \code{rweibull}. \code{pmatrix.simfs} calculates the transition probability matrix by using \code{sim.fmsm} to simulate state histories for a large number of individuals, by default 100000. Simulation-based confidence-intervals are also available in \code{pmatrix.simfs}, at an extra computational cost, and the expected total length of stay in each state is available from \code{totlos.simfs}. <>= pmatrix.simfs(crwei, trans = tmat, t = 5) pmatrix.simfs(crwei, trans = tmat, t = 10) @ \paragraph{Prediction via mstate} Alternatively, predictions can be made by supplying the cumulative transition-specific hazards, calculated with \code{msfit.flexsurvreg}, to functions in the \pkg{mstate} package. For Markov models, the solution to the Kolmogorov equation \citep[e.g.,][]{aalen:process} is given by a product integral, which can be approximated as \[ P(t_0, t) = \prod_{i=0}^{m-1} \left\{ I + Q(t_i)dt \right\} \] where a fine grid of times $t_0,t_1,\ldots,t_m=t$ is chosen to span the prediction interval, and $Q(t_i)dt$ is the increment in the cumulative hazard matrix between times $t_i$ and $t_{i+1}$. $Q$ may also depend on other covariates, as long as these are known in advance. In \pkg{mstate}, these can be calculated with the \code{probtrans} function, applied to the cumulative hazards returned by \code{msfit}. For Cox models, the time grid is naturally defined by the observed survival times, giving the Aalen-Johansen estimator \citep{andersen}. Here, the probability of remaining alive and free of BOS is estimated at 0.27 at 5 years and 0.17 at 10 years. <<>>= ptc <- probtrans(mfcox, predt = 0, direction = "forward")[[1]] round(ptc[c(165, 193),], 3) @ For parametric models, using a similar discrete-time approximation was suggested by \citet{cook:lawless}. This is achieved by passing the object returned by \code{msfit.flexsurvreg} to \code{probtrans} in \pkg{mstate}. It can be made arbitrarily accurate by choosing a finer resolution for the grid of times when calling \code{msfit.flexsurvreg}. <<>>= ptw <- probtrans(mfwei, predt = 0, direction = "forward")[[1]] round(ptw[ptw$time %in% c(5, 10),], 3) @ \code{pstate1}--\code{pstate3} are close to the first rows of the matrices returned by \code{pmatrix.fs}. The discrepancy from the Cox model is more marked at 10 years when the data are more sparse (Figure \ref{fig:bos:cumhaz}). A finer time grid would be required to achieve a similar level of accuracy to \code{pmatrix.fs} for the point estimates, at the cost of a slower run time than \code{pmatrix.fs}. However, an advantage of \code{probtrans} is that standard errors are available more cheaply. For semi-Markov models, \pkg{mstate} provides the function \code{mssample} to produce both simulated trajectories and transition probability matrices from semi-Markov models, given the estimated piecewise-constant cumulative hazards \citep{fiocco:mstatepred}, produced by \code{msfit} or \code{msfit.flexsurvreg}, though this is generally less efficient than \code{pmatrix.simfs}. In this example, 1000 samples from \code{mssample} give estimates of transition probabilities that are accurate to within around 0.02. However with \code{pmatrix.simfs}, greater precision is achieved by simulating 100 times as many trajectories in a shorter time. <>= mssample(mrcox$Haz, trans = tmat, clock = "reset", M = 1000, tvec = c(5, 10)) mssample(mrwei$Haz, trans = tmat, clock = "reset", M = 1000, tvec = c(5, 10)) @ \subsection{Next-state probabilities} \label{sec:nextstate} In a multi-state situation we are usually interested in the probability that a person in one state will move to a specific state next, rather than to the other competing states. In the BOS example we might want to estimate the probability that a patient will die before getting BOS, or get BOS before dying. In a mixture multi-state model (Section~\ref{sec:mixture}), these are explicit parameters of the model. In a multi-state model parameterised by cause-specific hazards, these probabilities are related to the hazards through the Kolmogorov forward equation. To obtain these, we consider the full multi-state model as a set of \emph{competing risks submodels}. There is one submodel for each state a person can transition from (the "transient" states of the model). In the BOS example, there is one submodel for the transitions from no BOS (with two competing risks: BOS and death), and a second submodel for the single transition from BOS to death. The probability that the the next state after $r$ is $s$ can then be obtained in practice as the transition probability $P(X(t)=s | X(t_0)=r)$, under the submodel for transient state $r$, for a very large time $t$. \code{pmatrix.fs} can be used for this. <<>>= tmat_nobos <- rbind("No BOS"=c(NA,1,2), "BOS"=c(NA,NA,NA),"Death"=c(NA,NA,NA)) crfs_nobos <- fmsm(mod_nobos_bos, mod_nobos_death, trans = tmat_nobos) pmatrix.fs(crfs_nobos, from=1, t=100000)["No BOS",c("BOS","Death")] @ In a time-homogeneous Markov model, i.e. where the times from state $r$ to state $s$ are all exponentially distributed with a constant rate $\lambda_{rs}$, the probability that the next state after $r$ is $s$ is simply $\lambda_{rs} / \sum_u \lambda_{ru}$, where the sum is taken over all possible next states after $r$. We can check the result from \code{pmatrix.fs} agrees with this: <<>>= modexp_nobos_bos <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data = bosms3, dist = "exponential") modexp_nobos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "exponential") crfs_nobos <- fmsm(modexp_nobos_bos, modexp_nobos_death, trans=tmat_nobos) pmatrix.fs(crfs_nobos, from=1, t=100000)["No BOS",c("BOS","Death")] rate12 <- modexp_nobos_bos$res["rate","est"] rate13 <- modexp_nobos_death$res["rate","est"] rate12 / (rate12 + rate13) @ \subsection{Distribution of the time to the next state} \label{sec:nexttime} Under the cause-specific hazards model, the time until the next observed transition can be considered to equal the \emph{minimum} of a set of latent times --- one latent time for each potential transition whose cause-specific hazard defines the multi-state model. The distribution of this time is not generally known analytically, given a set of parametric distributions defining the cause-specific hazards. For example, if there were two competing latent event times $T_1$, $T_2$ with cause-specific hazards distributed as Gamma$(a_1,b_1)$ and Weibull$(a_2,b_2)$ respectively, then the equivalent mixture model would be specified by the conditional distributions of $T_1|T_1 T_2$, which wouldn't have a standard form. Instead this time can be computed using simulation, via \code{sim.fmsm}. The function \code{simfinal_fmsm} wraps \code{sim.fmsm} to summarise the distribution of the time to each absorbing state in a multi-state model, conditionally on that state occurring. If this is applied to a \emph{competing-risks submodel} for state $r$ of a multi-state model, this simply produces the time to the \emph{next} state in the full model, since the absorbing states of the submodel define the potential next states after state $r$. This is done here to calculate the mean, median and interquartile range for the time to BOS (given survival) and the time to death (given no BOS before death). The function also produces estimates of the probability of each of these states, though as we saw in Section~\ref{sec:nextstate}, this is available more efficiently via \code{pmatrix.fs}. Note the number of simulated individuals $M$ can be increased for more accuracy, and optionally the $B$ argument can be supplied to obtain simulation-based confidence intervals around the estimates. <<>>= crfs_nobos <- fmsm(mod_nobos_bos, mod_nobos_death, trans = tmat_nobos) simfinal_fmsm(crfs_nobos, probs = c(0.25, 0.5, 0.75), M=10000) @ \subsection{Obtaining probabilities of, and times to, a final absorbing state} \label{sec:ultimate} As the previous section mentioned, \code{simfinal_fmsm} can be applied to any multi-state model with an absorbing state, to estimate the distribution of the time from the start of the process to the absorbing state. If there are multiple absorbing states, it can also estimate the probability that the individual ends up in each one. For the BOS model, there is only one absorbing state, death, so the function returns a probability of 1 that the patient will eventually die, and summaries of the distribution of the time from transplant to death. <<>>= simfinal_fmsm(crfs, probs = c(0.25, 0.5, 0.75), M=10000) @ \code{simfinal_fmsm} requires a semi-Markov multi-state model, or a simple competing risks model, constructed through \code{fmsm}. Though for a simple competing risks model, \code{pmatrix.fs} can be used to get the probability of each competing state, as in~\ref{sec:nextstate}. \section{Multi-state modelling using mixtures} \label{sec:mixture} \subsection{Definitions} A ``mixture'' multi-state model, first described for competing risks models by \citet{larson1985mixture} is described in terms of: \begin{itemize} \item the probability $\pi_{rs}$ that the next state after state $r$ is state $s$ \item the distribution of the time $T_{rs}$ from state $r$ entry to state $s$ entry, given that the next state after $r$ is state $s$. \end{itemize} In other words, the transition intensity is defined by \[ q_{rs}(t) = \left\{ \begin{array}{ll} q^*_{rs}(t) & \mbox{if } I_{r} = s \\ 0 & \mbox{if } I_{r} \neq s\\ \end{array} \right. \] where $I_{r}$ is a latent categorical variable that determines which transition will happen next for an individual in state $r$, governed by probabilities $\pi_{r,s} = P(I_{r} = s)$, with $\sum_{s \in \mathcal{S}_r} \pi_{r,s} = 1$ over the potential next state $\mathcal{S}_r$ after state $r$. The transition intensity $q^*_{rs}(t) $ is defined by the hazard function of a parametric distribution that governs the time $S_{rs}$ from state $r$ entry until the transition to state $s$, \emph{given that this is the transition that occurs}. The mixture model describes a mechanism where the transition that happens is determined ``in advance" at time zero, whereas in the cause-specific hazards model, the risks of different events ``compete" with each other as time proceeds. However, in practice, both models can represent situations where individuals can experience any of the competing events. In the mixture model, we only specify a distribution for the time to the event \emph{that happens first} among the competing risks, and do not model events that don't occur. As discussed by \citet{cox1959analysis}, if the time-to-event distributions are specified correctly in both frameworks, then they can both represent the same process. In practice however, they will differ. As discussed in Section~\ref{sec:nexttime}, given a particular parametric form for a set of cause-specific hazards, the form of the distribution for the \emph{minimum} of the potential event times, the one that actually happens, won't be available. The main advantage of the mixture model is that it is parameterised in terms of quantities that have an easy, direct interpretation. In the mixture model, we specify a parametric distribution with density $f_{r,s}(|\theta_{r,s})$ (and CDF $F_{r,s}()$) for the time of transition to state $s$ for a person in state $r$, conditionally on this transition being the one that occurs. We have data consisting of state transitions, indexed by $j$, experienced by individuals $i$. This can either be \begin{itemize} \item \emph{an exact transition time:} $\{y_{i,j}, r_{i,j}, s_{i,j}, \delta_{i,j}=1\}$, where a transition to state $s_{i,j}$ is known to occur at a time $y_{i,j}$ after entry to state $r_{i,j}$. \item \emph{right censoring} $\{y_{i,j},r_{i,j},\delta_{i,j}=2\}$, where an individual's follow-up ends while they are in state $r_{i,j}$, at time $y_{i,j}$ after entering this state, thus the next state and the time of transition to it are unknown. \end{itemize} Therefore, for an exact time of transition to a known state $s_{i,j}$, i.e. $\delta_{i,j}=1$, the likelihood contribution is simply \[ l_{i,j} = \pi_{r_{i,j}s_{i,j}} f_{r_{i,j},s_{i,j}}(y_{i,j} | \theta_{r_{i,j},s_{i,j}}) \] For observations $j$ of right-censoring at $y_{i,j}$, the state that the person will move to, and the time of that transition, is unknown. Thus it is unknown which of the distributions $f_{r,s}$ the transition time will obey, and the likelihood contribution is of the form of a mixture model, that sums over the set $\mathcal{S}_r$ of potential next states after $r$: \[ l_{i,j} = \sum_{s \in \mathcal{S}_r} \pi_{r_{i,j}s} (1 - F_{r_{i,j},s}(y_{i,j} | \theta_{r_{i,j},s})) \] \subsection{Data for mixture competing risks models} The required data format for the mixture model is shown for the BOS data in the object \code{bosmx3}. This has \begin{itemize} \item one row for each observed event time \item one row for each ``end of follow-up" time where we know an individual was still at risk of making a transition, but we don't know which transition will occur. \end{itemize} Recall that in the data \code{bosms3} used to implement the cause-specific hazards model, a individual ``censored" at time $t$ contributed a row in the data \emph{for each} of the events that might have occurred after $t$. The difference from \code{bosmx3} is that for these individuals, \code{bosmx3} only has \emph{one} row per ``censored" individual. For example, patient 5 is censored at 11 years, when they were still at risk of either BOS or death. Also we do not include censoring times for events competing with events that were observed, e.g. when patient 4 below got BOS (state 2) at year 2, thus were ``censored" at the same time for the transition from state 1 (no BOS) to state 3 (death). The process of transforming the cause-specific dataset to the mixture dataset is shown below. Multiple censoring records, for different destination states, are condensed to a single censoring record. Each row of \code{bosmx3} then corresponds to a transition. A new column called \code{event} is created, which should be a factor that identifies the terminal event of the transition, which takes the value \code{NA} in cases of censoring where the transition that will happen is unknown. Columns not needed for the mixture model are removed. Informative labels for the factor levels of \code{event} are added to identify the states. <<>>= bosms3[bosms3$id %in% c(4,5),] bosmx3 <- bosms3 bosmx3$Tstart <- bosmx3$Tstop <- bosmx3$trans <- NULL bosmx3 <- bosmx3[!(bosmx3$status==0 & duplicated(paste(bosmx3$id, bosmx3$from))),] bosmx3$event <- ifelse(bosmx3$status==0, NA, bosmx3$to) bosmx3$event <- factor(bosmx3$event, labels=c("BOS","Death")) bosmx3$to <- NULL bosmx3[bosmx3$id %in% c(4,5),] @ \subsection{Fitting mixture competing risks models} The \code{flexsurvmix} function fits a mixture model to competing risks data. To fit a full multi-state mixture model, we fit one mixture competing risks model for each transient state in the multi-state structure. The models are then grouped together (Section~\ref{sec:fmixmsm}) to form the full multi-state model. The mixture model for the event following transplant (BOS or death before BOS, the 1-2 and 1-3 transitions in the multi-state structure) is fitted as follows. A Weibull distribution is fitted for the time to BOS given BOS onset, and an exponential distribution is fitted for the time to death given death before BOS onset. These distributions are specified in the \code{dists} argument. The same distributions as in \code{flexsurvreg} are supported (including custom distributions, in the same way). <<>>= bosfs <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) bosfs @ The printed results object shows the two event probabilities $\pi_{rs}$ in the first two rows, and the parameters of the time-to-event distributions in the remaining rows. The maximum likelihood estimates are in column \code{est}, and estimates on a (multinomial) logit or log transformed scale are in column \code{est.t}, with standard errors on the transformed scale in \code{se}. Covariates can be included on the event probabilities through multinomial logistic regression. For illustration, we just simulate some fake covariate data in the variable \code{x}. The log odds ratio for this covariate on the odds of death (with the first category, BOS here, always taken as the baseline) is shown in the row with \code{terms} labelled \code{prob2(x)}. <<>>= set.seed(1) bosmx3$x <- rnorm(nrow(bosmx3),0,1) bosfsp <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential"), pformula = ~ x) bosfsp @ Covariates may also be included on any parameter of any time-to-event distribution, as in \code{flexsurvreg}. If the covariate is named on the right hand side of the \code{Surv} formula in the first argument, then it is included on the location parameter of all distributions. <<>>= bosfst <- flexsurvmix(Surv(years, status) ~ x, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) @ The first argument may be a list of formulae, to indicate that different covariates are included on the location parameter for different events. <<>>= flexsurvmix(list(Surv(years, status) ~ x, Surv(years, status) ~ 1), event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) @ An argument \code{anc} is used to supply covariates on ancillary parameters (e.g. shape parameters). This must be a list of length matching the number of competing events, each component being a named list in the format used for the \code{anc} argument in \code{flexsurvreg}. If there are no covariates for a particular component, just specify a null formula on the location parameter (as below, \code{rate=~1}). <<>>= flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential"), anc = list(BOS=list(shape=~x), Death=list(rate=~1))) @ \subsection{Predictions from mixture competing risks models} A few functions have been supplied to extract estimates and confidence intervals for interpretable quantities, for given covariate values. Here we extract estimates of various quantities for covariate values of \code{x=0} and \code{x=1}. These values are provided in a data frame \code{nd} that will be supplied as the \code{newdata} argument to various extractor functions. The first extractor function \code{probs_flexsurvmix} gives the fitted event probabilities, by event and covariate value. This is applied here to the fitted model \code{bosfsp} that included a covariate on the event probabilities. All these functions take an argument \code{B} which specifies the number of samples to use for calculating bootstrap-like confidence limits --- increase this for more accurate limits. <<>>= nd <- data.frame(x=c(0,1)) probs_flexsurvmix(bosfsp, newdata=nd, B=50) @ \code{mean_flexsurvmix} extracts the mean time to each event conditionally on that event occurring, from the mean of the fitted time-to-event distribution. \code{quantile_flexsurvmix} extracts the quantiles of these distributions, e.g. the interquartile range in this example summarises the variability between individuals for this time. <<>>= mean_flexsurvmix(bosfst, newdata=nd) quantile_flexsurvmix(bosfst, B=50, newdata=nd, probs=c(0.25, 0.5, 0.75)) @ \code{p_flexsurvmix} extracts the probability of being in each of the states at a time $t$ in the future, shown for $t=5,10$ here. The \code{startname} argument supplies an informative name to the ``starting" state that the model \code{bosfst} describes transitions from. <<>>= p_flexsurvmix(bosfst, t=c(5, 10), B=10, startname="No BOS") @ \subsection{Forming a mixture multi-state model} \label{sec:fmixmsm} We supplement the mixture model for the event following state 1 (no BOS) with a second model \code{bosfst_bos} for the events following BOS (the other transient state in the multi-state model). Although this is fitted with \code{flexsurvmix}, there is only one potential next state after BOS, which is death, so internally this just fits a standard survival model using \code{flexsurvreg}. The two mixture models are then coupled together using the \code{fmixmsm} function, which returns an object containing the entire multi-state model, here named \code{bosfmix}. This object contains attributes listing the potential pathways that an individual can take through the states. These pathways are identified automatically by naming the arguments to \code{fmixmsm} with the label of the state that each model describes transitions from --- here the first model \code{bosfst} describes transitions from ``No BOS" and the second describes transitions from BOS. (Note we redefine the \code{event} factor so that empty levels are dropped) <<>>= bdat <- bosmx3[bosmx3$from==2,] bdat$event <- factor(bdat$event) bosfst_bos <- flexsurvmix(Surv(years, status) ~ x, event=event, data=bdat, dists = c(Death="exponential")) bosfmix <- fmixmsm("No BOS"=bosfst, "BOS"=bosfst_bos) @ Now we can predict outcomes from the full multi-state model. All these functions work by simulating a large population of individuals from the model, by default \code{M=10000}, so increase this for more accuracy. A cut-off time \code{t=1000} is also applied to the simulated data that assumes people have all reached the absorbing state by this time -- increase this if necessary. These functions currently require models to have at least one absorbing state, and no ``cycles" in their transition structure. The function \code{ppath_fmixmsm} returns the probability of following each of the potential pathways through the model. For this example, they are the same for both covariate values \code{x=0} and \code{x=1}. Setting \code{final=TRUE} aggregates the pathway probabilities by the final (absorbing) state, returning the probability of ending in each of the potential final states, which is trivially 1 in this case for the single absorbing state of death. <<>>= ppath_fmixmsm(bosfmix, B=20) ppath_fmixmsm(bosfmix, B=20, final=TRUE) @ To estimate the mean time to the final state for individuals following each pathway, use \code{meanfinal_fmixmsm}, and for the quantiles of the distribution of this time over individuals (by default the median and a 95\% interval), use \code{qfinal_fmixmsm}. Supplying \code{final=TRUE} in these functions summarises the mean time to the final state, averaged over all potential pathways (according to the probability of following those pathways). Again, covariate values can be supplied in the \code{newdata} argument if needed. <<>>= meanfinal_fmixmsm(bosfmix, B=10) qfinal_fmixmsm(bosfmix, B=10) meanfinal_fmixmsm(bosfmix, B=10, final=TRUE) @ \subsection{Goodness of fit checking} The fit of mixture competing risks models can be checked by comparing predictions of the state occupancy probabilities (as returned by \code{p_flexsurvmix}) with nonparametric estimates of these quantities \citep{aalen:johansen}. This is only supported for models with no covariates or only factor covariates (where subgroup-specific predictions are compared with stratified nonparametric estimates). The function \code{ajfit_flexsurvmix} derives these estimates from both the mixture model and the Aalen-Johansen method, and collects them in a tidy data frame ready for plotting, e.g. with the \pkg{ggplot2} package. The mixture models fit nicely here. A \code{start} argument is supplied to give an informative label to the starting state in the plots. Note we are plotting not probability of \emph{being in} a state at time $t$, but the probability of \emph{having made} the respective transition --- here we are checking the competing risks submodels one at time. <>= aj <- ajfit_flexsurvmix(bosfs, start="No BOS") bosfs_bos <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bdat, dists = c(Death="exponential")) aj2 <- ajfit_flexsurvmix(bosfs_bos, start="BOS") library(ggplot2) ggplot(aj, aes(x=time, y=val, lty=model, col=state)) + geom_line() + xlab("Years after transplant") + ylab("Probability of having moved to state") ggplot(aj2, aes(x=time, y=val, lty=model, col=state)) + xlab("Years after transplant") + ylab("Probability of having moved to state") + geom_line() @ Checking against Aalen-Johansen estimates is also supported for cause-specific hazards models that are grouped together using \code{fmsm}. Thus we can compare cause-specific hazards and mixture models that have been fitted to the same data. We do this here for the \code{fmsm} object \code{crfs_nobos} created in Section~\ref{sec:nextstate}. <>= library(dplyr) aj3 <- ajfit_fmsm(crfs_nobos) %>% filter(model=="Parametric") %>% mutate(model = "Cause specific hazards") %>% mutate(state = factor(state, labels=c("No BOS","BOS","Death"))) %>% full_join(aj) ggplot(aj3, aes(x=time, y=val, lty=model, col=state)) + xlab("Years after transplant") + ylab("Probability of having moved to state") + geom_line() @ \section{Comparison of frameworks for parametric multi-state modelling} As the mixture model is described by the probabilities of observable events and the times to those events, it is somewhat easier to interpret then the cause-specific hazards model. While those quantities can be computed under the cause-specific hazards model, they require potentially-expensive simulation. An advantage of the cause-specific hazards model is that it tends to be faster to \emph{fit}, if the transition-specific models are fitted independently. Another competing-risks modelling framework not implemented here is typically referred to as \emph{subdistribution} hazard modelling --- essentially covariate effects are applied to the probabilities of occupying different states at time $t$, rather than to the cause-specific hazards. This leads to covariate effects that are easier to interpret compared to, e.g. cause-specific hazard ratios. The method has been implemented semiparametrically~\citep{fine1999proportional} and parametrically~\citep{lambert2017flexible}. A further framework referred to as ``vertical" modelling \citep{nicolaie2010vertical} involves factorising the joint distribution of events and event times as $P(time)P(event|time)$, whereas the mixture modelling framework uses $P(event)P(time|event)$. \bibliography{flexsurv} \end{document} flexsurv/vignettes/standsurv.bib0000644000176200001440000000326714252566476016700 0ustar liggesusers@article{therneau_1999, title = {A package for survival analysis in {S}}, author = {Therneau, Terry M.}, year = {1999}, month = {February}, url = {https://www.mayo.edu/research/documents/tr53pdf/doc-10027379} } @article{syriopoulou_inverse_2021, title = {Inverse probability weighting and doubly robust standardization in the relative survival framework}, volume = {40}, issn = {1097-0258}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9171}, OPTdoi = {10.1002/sim.9171}, language = {en}, number = {27}, urldate = {2022-01-07}, journal = {Statistics in Medicine}, author = {Syriopoulou, Elisavet and Rutherford, Mark J. and Lambert, Paul C.}, year = {2021}, keywords = {regression standardization, relative survival, inverse probability weighting, doubly robust standardization, Monte Carlo simulation study}, pages = {6069--6092} } @article{rutherford_nice_2020, title = {{NICE} {DSU} {Technical} {Support} {Document} 21: {Flexible} methods for survival analysis}, language = {en}, author = {Rutherford, Mark J and Lambert, Paul C and Sweeting, Michael J and Pennington, Becky and Crowther, Michael J and Abrams, Keith R and Latimer, Nicholas R.}, year = {2020}, } @article{ederer_relative_1961, title = {The relative survival rate: a statistical methodology}, volume = {6}, issn = {0083-1921}, shorttitle = {The relative survival rate}, language = {eng}, journal = {National Cancer Institute Monograph}, author = {Ederer, F. and Axtell, L. M. and Cutler, S. J.}, month = sep, year = {1961}, OPTpmid = {13889176}, keywords = {Biometry, Humans, Neomycin, NEOMYCIN/statistics, Survival Rate}, pages = {101--121}, } flexsurv/vignettes/distributions.Rnw0000644000176200001440000002177214500354432017543 0ustar liggesusers%\VignetteIndexEntry{Distributions reference} \documentclass[nojss,nofooter]{jss} \usepackage{bm} \usepackage{tabularx} \usepackage{graphics} \usepackage{listings} \newcommand{\bbeta}{{\bm\beta}} \newcommand{\x}{{\mathbf{x}}} \newcommand{\z}{{\mathbf{z}}} \newcommand{\btheta}{{\bm{\theta}}} %\newcommand{\code}[1]{\texttt{\detokenize{#1}}} %\newcommand{\code}[1]{\texttt\lstinline|#1|} \author{Christopher H. Jackson \\ MRC Biostatistics Unit, Cambridge, UK \\ \email{chris.jackson@mrc-bsu.cam.ac.uk}} \title{flexsurv: Distributions reference} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Abstract{ A reference guide for the distributions built into flexsurv } \Keywords{survival} \begin{document} This document lists the following information for each of the built-in distributions in \code{flexsurvreg}. \begin{itemize} \item How the distribution is identified in the \code{dist} argument to \code{flexsurvreg}. \item Name of the \code{d} function in R for the probability density, showing how names of the arguments in the R function correspond to the symbols in the formula for the survivor function. In each case, there are corresponding R functions with names beginning with \code{p},\code{q} and \code{r} instead of \code{d}, for the cumulative distribution, quantiles and random number generation. The R \code{help} page for the function named here will contain more information about the distribution, e.g. the probability density function, and how particular distributions are defined as special cases of other distributions. \item The survivor function $S(t|\btheta)$ as a function of time $t$ and the parameters of the distribution $\btheta$. Any restrictions on the allowed values of the parameters are noted. \item The location parameter of the distribution, now indexed by $j$, and a function describing how the location parameter depends on covariate values $\z_j$ and covariate effects $\bbeta$. $\bbeta$ are the covariate effects indicated when printing a \code{flexsurvreg} object, which can take any real value. \item A more interpretable covariate effect measure, defined as a function of $\bbeta$. \end{itemize} In a \emph{proportional hazards} model, the ``more interpretable'' effect measure presented is the hazard ratio (HR) for one unit of the covariate. In an \emph{accelerated failure time model}, the time acceleration factor (TAF) for one unit of the covariate is presented. The survivor function is of the form $S(t) = S^*(ct)$ where $c$ is some constant that depends on the parameters. Multiplying $c$ by 2 has the same effect on survival as multiplying $t$ by 2, doubling the speed of time and halving the expected survival time. An alternative way of presenting effects from an accelerated failure time model is the ratio of expected times to the event between covariate values of 1 and 0. This equals 1/TAF, and may be easier to interpret if the time to the event is of direct interest. A HR below 1 and a TAF above 1 both indicate that higher covariate values are associated with a higher risk of the event, or shorter times to the event. % So the comparable parameters are exp(-beta) for the lognormal and gengamma 1/exp(beta) = exp(-beta) for the weibull exp(beta) for the gamma and exponential \subsection*{Weibull (accelerated failure time)} \verb+flexsurvreg(..., dist="weibull")+\\ \code{dweibull(..., shape=a, scale=mu)} \[ S(t | \mu, a) = \exp(- (t/\mu)^ a), \qquad \mu>0, a>0 \] \[ \mu_j = \exp(\z_j \bbeta), \quad TAF = \exp(-\bbeta) \] \subsection*{Weibull (proportional hazards)} \verb+flexsurvreg(..., dist="weibullPH")+\\ \code{dweibullPH(..., shape=a, scale=lambda)} \[ S(t | \lambda, a) = \exp(- \lambda t^ a), \qquad \lambda>0, a>0 \] \[ \lambda_j = \exp(\z_j \bbeta), \quad HR = \exp(\bbeta) \] (Note the argument ``scale'' to \code{dweibullPH} would perhaps better have been called ``rate'', given the analogy with the rate of the exponential model). \subsection*{Gamma} \verb+flexsurvreg(..., dist="gamma")+\\ \code{dgamma(..., shape=a, scale=mu)} \[ S(t | a, \mu) = 1 - \int_{0}^t \frac{x^{a-1} \exp{-(x/\mu)}}{\mu^a \Gamma(a)} dx, \qquad \mu>0, a>0 \] \[ \mu_j = \exp(\z_j \bbeta), \quad TAF = \exp(\bbeta) \] \subsection*{Exponential} \verb+flexsurvreg(..., dist="exp")+\\ \code{dexp(..., rate=lambda)} \[ S(t | \lambda) = \exp(-\lambda t), \qquad \lambda > 0 \] \[ \lambda_j = \exp(\z_j \bbeta), \quad HR = \exp(\bbeta), \quad TAF = \exp(\bbeta) \] \subsection*{Log-logistic} \verb+flexsurvreg(..., dist="llogis")+\\ \code{dllogis(..., shape=a, scale=b)} \[ S(t | a, b) = 1/ (1 + (t/b)^a), \qquad a>0, b>0 \] \[ b_j = \exp(\z_j \bbeta), \quad TAF = \exp(-\bbeta) \] \subsection*{Log-normal} \verb+flexsurvreg(..., dist="lnorm")+\\ \code{dlnorm(..., meanlog=mu, sdlog=sigma)} \[ S(t | \mu, \sigma) = 1 - \int_0^t \frac{1}{x\sigma\sqrt{2 \pi}} \exp{\left\{-\frac{(\log x - \mu)^2}{2 \sigma^2}\right\}} dx, \qquad \sigma > 0 \] \[ \mu_j = z_j \bbeta , \quad TAF = \exp(-\bbeta) \] \subsection*{Gompertz} \verb+flexsurvreg(..., dist="gompertz")+\\ \code{dgompertz(..., shape=a, rate=b)} \[ S(t | a, b) = \exp(-(b/a) (\exp(at) - 1)), b > 0 \] Note that $a<0$ is permitted, in which case $S(t|)$ tends to a non-zero probability as $t$ increases, i.e. a probability of living forever. \[ b_j = \exp(\z_j \bbeta), \quad HR = \exp(\bbeta) \] \subsection*{Generalised gamma (Prentice)} \verb+flexsurvreg(..., dist="gengamma")+\\ \code{dgengamma(..., mu, sigma, Q)} \[ S(t|\mu,\sigma,Q) = \begin{array}{ll} S_G(\frac{\exp(Qw)}{Q^2} ~ | ~ \frac{1}{Q^2}, 1) & (Q > 0 )\\ 1 - S_G(\frac{\exp(Qw)}{Q^2} ~ | ~ \frac{1}{Q^2}, 1) & (Q < 0)\\ S_L(t ~ | ~ \mu, \sigma) & (Q = 0)\\ \end{array} \] where $w = (\log(t) - \mu)/\sigma$, $S_G(t | a,1)$ is the survivor function of the gamma distribution with shape $a$ and scale $1$, $S_L(t |\mu,\sigma)$ is the survivor function of the log-normal distribution with log-scale mean $\mu$ and standard deviation $\sigma$, $\mu,Q$ are unrestricted, and $\sigma$ is positive. \[ \mu_j = z_j \bbeta, \quad TAF = \exp(-\bbeta) \] \subsection*{Generalised gamma (Stacy)} \verb+flexsurvreg(..., dist="gengamma.orig")+\\ \code{dgengamma.orig(..., shape=b, scale=a, k=k)} \[ S(t|a, b, k) = 1 - \int_0^t \frac{ b x^{bk -1}}{ \Gamma(k) a^{bk} }\exp(-(x/a)^b) dx \] \[ a_j = \exp(z_j \bbeta), \quad TAF = \exp(-\bbeta) \] \subsection*{Generalised F (Prentice)} \verb+flexsurvreg(..., dist="genf")+\\ \code{dgenf(..., mu, sigma, Q, P)} \[ S(t | \mu, \sigma, Q, P) = 1 - \int_0^t \frac{\delta (s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 + s_2)} B(s_1, s_2)}, \qquad \sigma>0, P>0 \] where $s_1 = 2(Q^2 + 2P + Q\delta)^{-1}$, $s_2 = 2(Q^2 + 2P -Q\delta)^{-1}$, ${\delta = (Q^2 + 2P)^{1/2}}$ and $w = (\log(x) - \mu)\delta /\sigma$ \[ \mu_j = x_j \bbeta, \quad TAF = \exp(-\bbeta) \] \subsection*{Generalised F (original)} \verb+flexsurvreg(..., dist="genf.orig")+\\ \code{dgenf.orig(..., mu, sigma, s1, s2)} \[ S(t | \mu, \sigma, s_1, s_2) = 1 - \int_0^t \frac{(s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {s_1 + s_2} B(s_1, s_2)} dx, \qquad \sigma>0, s_1>0, s_2>0 \] where $w = (\log(x) - \mu)/\sigma$, and $B(s_1,s_2) =\frac{\Gamma(s_1)\Gamma(s_2)}{\Gamma(s_1+s_2)}$ is the beta function. \[ \mu_j = z_j \bbeta , \quad TAF = \exp(-\bbeta) \] \subsection*{Spline (Royston/Parmar)} \verb+flexsurvspline(...,scale="hazard")+\\ \verb+flexsurvspline(...,scale="odds")+\\ \verb+flexsurvspline(...,scale="normal")+\\ \code{dsurvspline(..., gamma)} where the argument \texttt{gamma} collects together all parameters,\\ ~\\ or the alternative forms for the density/distribution functions (flexsurv versions 2.0 and later) where different parameters are in separate arguments:\\ \code{dsurvspline0(..., gamma0, gamma1)} (no internal knots)\\ \code{dsurvspline1(..., gamma0, gamma1, gamma2)} (1 internal knot)\\ \code{dsurvspline2(..., gamma0, gamma1, gamma2, gamma3)} (2 internal knots)\\ etc., all the way up to \code{dsurvspline7}. \[ g(S(t)) = s(x, \bm{\gamma}) \] where $x=\log(t)$ and $s()$ is a natural cubic spline function with $m$ internal knots: \[ s(x,\bm{\gamma}) = \gamma_0 + \gamma_1 x + \gamma_2 v_1(x) + \ldots + \gamma_{m+1} v_m(x) \] where $v_j(x)$ is the $j$th \emph{basis} function, \[v_j(x) = (x - k_j)^3_+ - \lambda_j(x - k_{min})^3_+ - (1 - \lambda_j) (x - k_{max})^3_+, \qquad \lambda_j = \frac{k_{max} - k_j}{k_{max} - k_{min}} \] and $(x - a)_+ = max(0, x - a)$. The link function relating the survivor function to the spline is: \[ g(S(t)) = \begin{array}{ll} \log(-\log(S(t))) &\verb+(scale="hazard")+ \\ \log(S(t)^{-1} - 1) & \verb+(scale="odds")+ \\ \Phi^{-1}(S(t)) & \verb+(scale="normal")+ \\ \end{array} \] For more details, see the main \code{flexsurv} vignette. 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Jackson \\ MRC Biostatistics Unit, Cambridge, UK \\ \email{chris.jackson@mrc-bsu.cam.ac.uk}} \title{flexsurv: flexible parametric survival modelling in R. Supplementary examples} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Abstract{ This vignette of examples supplements the main \pkg{flexsurv} user guide. } \Keywords{survival} \begin{document} \section{Examples of custom distributions} \subsection{Proportional hazards generalized gamma model} \citet{stgenreg} discuss using the \pkg{stgenreg} Stata package to construct a proportional hazards parameterisation of the three-parameter generalised gamma distribution. A similar trick can be used in \pkg{flexsurv}. A four-parameter custom distribution is created by defining its hazard (and cumulative hazard) functions. These are obtained by multiplying the built-in functions \code{hgengamma} and \code{Hgengamma} by an extra dummy parameter, which is used as the location parameter of the new distribution. The intercept of this parameter is fixed at 1 when calling \code{flexsurvreg}, so that the new model is no more complex than the generalized gamma AFT model \code{fs3}, but covariate effects on the dummy parameter are now interpreted as hazard ratios. <<>>= library(flexsurv) hgengammaPH <- function(x, dummy, mu=0, sigma=1, Q){ dummy * hgengamma(x=x, mu=mu, sigma=sigma, Q=Q) } HgengammaPH <- function(x, dummy, mu=0, sigma=1, Q){ dummy * Hgengamma(x=x, mu=mu, sigma=sigma, Q=Q) } custom.gengammaPH <- list(name="gengammaPH", pars=c("dummy","mu","sigma","Q"), location="dummy", transforms=c(log, identity, log, identity), inv.transforms=c(exp, identity, exp, identity), inits=function(t){ lt <- log(t[t>0]) c(1, mean(lt), sd(lt), 0) }) fs7 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist=custom.gengammaPH, fixedpars=1) @ \section{Examples of custom model summaries} \subsection{Plotting a hazard ratio against time} The following code plots the hazard ratio (Medium versus Good prognostic group) against time for both the proportional hazards model \code{fs7} and the better-fitting accelerated failure time model \code{fs2}. It illustrates the use of the following functions. \begin{description} \item[\code{summary.flexsurvreg}] for generating the estimated hazard at a series of times, for particular covariate categories. \item[\code{normboot.flexsurvreg}] for generating a bootstrap-style sample from the sampling distribution of the parameter estimates, for particular covariate categories. \item[\code{do.call}] for constructing a function call by supplying a list containing the function's arguments. This is used throughout the source of \pkg{flexsurv}. \end{description} <>= fs2 <- flexsurvreg(Surv(recyrs, censrec) ~ group + sigma(group), data=bc, dist="gengamma") B <- 5000 t <- seq(0.1, 8, by=0.1) hrAFT.est <- summary(fs2, t=t, type="hazard", newdata=data.frame(group="Medium"),ci=FALSE)[[1]][,"est"] / summary(fs2, t=t, type="hazard", newdata=data.frame(group="Good"),ci=FALSE)[[1]][,"est"] pars <- normboot.flexsurvreg(fs2, B=B, newdata=data.frame(group=c("Good","Medium"))) hrAFT <- matrix(nrow=B, ncol=length(t)) for (i in seq_along(t)){ haz.medium.rep <- do.call(hgengamma, c(list(t[i]), as.data.frame(pars[[2]]))) haz.good.rep <- do.call(hgengamma, c(list(t[i]), as.data.frame(pars[[1]]))) hrAFT[,i] <- haz.medium.rep / haz.good.rep } hrAFT <- apply(hrAFT, 2, quantile, c(0.025, 0.975)) hrPH.est <- summary(fs7, t=t, type="hazard", newdata=data.frame(group="Medium"),ci=FALSE)[[1]][,"est"] / summary(fs7, t=t, type="hazard", newdata=data.frame(group="Good"),ci=FALSE)[[1]][,"est"] pars <- normboot.flexsurvreg(fs7, B=B, newdata=data.frame(group=c("Good","Medium"))) hrPH <- matrix(nrow=B, ncol=length(t)) for (i in seq_along(t)){ haz.medium.rep <- do.call(hgengammaPH, c(list(t[i]), as.data.frame(pars[[2]]))) haz.good.rep <- do.call(hgengammaPH, c(list(t[i]), as.data.frame(pars[[1]]))) hrPH[,i] <- haz.medium.rep / haz.good.rep } hrPH <- apply(hrPH, 2, quantile, c(0.025, 0.975)) plot(t, hrAFT[1,], type="l", ylim=c(0, 10), col="red", xlab="Years", ylab="Hazard ratio (Medium / Good)", lwd=1, lty=2) lines(t, hrAFT[2,], col="red", lwd=1, lty=2) lines(t, hrPH[1,], col="darkgray", lwd=1, lty=2) lines(t, hrPH[2,], col="darkgray", lwd=1, lty=2) lines(t, hrAFT.est, col="red", lwd=2) lines(t, hrPH.est, col="darkgray", lwd=2) legend("topright", lwd=c(2,2), col=c("red","darkgray"), bty="n", c("Generalized gamma: standard AFT", "Generalized gamma: proportional hazards")) @ Since version 2.2 of \pkg{flexsurv}, however, the code above is obsolete, since the function \code{hr_flexsurvreg} can simply be used to calculate hazard ratios and their confidence intervals against time. <>= nd <- data.frame(group=c("Good","Medium")) hr_aft <- hr_flexsurvreg(fs2, t=t, newdata=nd) hr_ph <- hr_flexsurvreg(fs7, t=t, newdata=nd) plot(t, hr_aft$lcl, type="l", ylim=c(0, 10), col="red", xlab="Years", ylab="Hazard ratio (Medium / Good)", lwd=1, lty=2) lines(t, hr_aft$ucl, col="red", lwd=1, lty=2) lines(t, hr_aft$est, col="red", lwd=2) lines(t, hr_ph$lcl, col="darkgray", lwd=1, lty=2) lines(t, hr_ph$ucl, col="darkgray", lwd=1, lty=2) lines(t, hr_ph$est, col="darkgray", lwd=2) legend("topright", lwd=c(2,2), col=c("red","darkgray"), bty="n", c("Generalized gamma: standard AFT", "Generalized gamma: proportional hazards")) @ \subsection{Restricted mean survival} The expected survival up to time $t$, from a model with cumulative distribution $F(t|\alpha)$, is \[ E(T|T>= summary(fs2, type="rmst", t=100, tidy=TRUE) summary(fs2, fn=rmst_gengamma, t=100, tidy=TRUE) @ Or for the baseline category of "Good": <<>>= est <- fs2$res[,"est"] rmst_gengamma(t=100, mu=est[1], sigma=est[2], Q=est[3]) @ Note that the (unrestricted) median is more stable, and less than the restricted mean due to the skewness of this distribution. <<>>= summary(fs2, type="median") @ Note also that the custom function \code{fn} supplied to \code{summary.flexsurvreg} must be vectorised - previous versions of this example used an unvectorised custom function called \code{mean.gengamma} which will not work in version 2.2 or later. %\subsection{Custom summary functions with spline models} \section{Spline models} \subsection{Prognostic model for the German breast cancer data} The regression model III in \citet{sauerbrei1999building} used to create the prognostic group from the breast cancer data (supplied as \code{bc} in \pkg{flexsurv} and \code{GBSG2} in \pkg{TH.data}) can be reproduced as follows. Firstly, the required fractional polynomial transformations of the covariates are constructed. \code{progc} implements the Cox model used by \citet{sauerbrei1999building}, and \code{prog3} is a flexible fully-parametric alternative, implemented as a spline with three internal knots. The number of knots was chosen to minimise AIC. The covariate effects are very similar. After fitting the model, the prognostic index can then be derived from categorising observations in three groups according to the tertiles of the linear predictor in each model. The indices produced by the Cox model (\code{progc}) and the spline-based model (\code{progf}) agree exactly. <<>>= if (require("TH.data")){ GBSG2 <- transform(GBSG2, X1a=(age/50)^-2, X1b=(age/50)^-0.5, X4=tgrade %in% c("II","III"), X5=exp(-0.12*pnodes), X6=(progrec+1)^0.5 ) (progc <- coxph(Surv(time, cens) ~ horTh + X1a + X1b + X4 + X5 + X6, data=GBSG2)) (prog3 <- flexsurvspline(Surv(time, cens) ~ horTh + X1a + X1b + X4 + X5 + X6, k=3, data=GBSG2)) predc <- predict(progc, type="lp") progc <- cut(predc, quantile(predc, 0:3/3)) predf <- model.matrix(prog3) %*% prog3$res[-(1:5),"est"] progf <- cut(predf, quantile(predf, 0:3/3)) table(progc, progf) } @ \section{Right truncation: retrospective ascertainment} Suppose we want to estimate the distribution of the time from onset of a disease to death, but have only observed cases known to have died by the current date. In this case, times from onset to death for individuals in the data are \emph{right-truncated} by the current date minus the onset date. Predicted survival times for new cases can then be described by an un-truncated version of the fitted distribution. Denote the time from onset to death as the \emph{delay} time. This is illustrated in the following simulated example. Suppose individual onset times are uniformly distributed between 0 and 30 days. Their delay times are generated from a Gamma distribution. <<>>= set.seed(1) nsim <- 10000 onsetday <- runif(nsim, 0, 30) deathday <- onsetday + rgamma(nsim, shape=1.5, rate=1/10) @ The data are examined at 40 days. Therefore we do not observe people who have died after this time. For each individual in the observed data, their delay time is right-truncated by 40 days minus their onset day, since their delay times cannot be greater than this if they are included in the data. The right-truncation point is specified by the variable \code{rtrunc} in the data. <<>>= datt <- data.frame(delay = deathday - onsetday, event = rep(1, nsim), rtrunc = 40 - onsetday) datt <- datt[datt$delay < datt$rtrunc, ] @ The truncated Gamma model is fitted with \code{flexsurvreg} by specifying individual-specific truncation points in the argument \code{rtrunc}. The fitted model reproduces the gamma parameters that were used to simulate the data. 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J.}, journal={Journal of the American Statistical Association}, volume={94}, number={446}, pages={496--509}, year={1999}, publisher={Taylor \& Francis} } @article{nicolaie2010vertical, title={Vertical modeling: a pattern mixture approach for competing risks modeling}, author={Nicolaie, M. A. and van Houwelingen, H. C. and Putter, H.}, journal={Statistics in Medicine}, volume={29}, number={11}, pages={1190--1205}, year={2010}, publisher={Wiley Online Library} }flexsurv/vignettes/flexsurv.Rnw0000644000176200001440000020161214607502156016516 0ustar liggesusers%\VignetteIndexEntry{flexsurv user guide} %\VignetteEngine{knitr::knitr} % \documentclass[article,shortnames]{jss} \documentclass[article,shortnames,nojss,nofooter]{jss} \usepackage{bm} \usepackage{tabularx} \usepackage{graphics} \usepackage{alltt} <>= options(width=60) options(prompt="R> ") library(knitr) opts_chunk$set(fig.path="flexsurv-") render_sweave() @ %% need no \usepackage{Sweave.sty} \author{Christopher H. Jackson \\ MRC Biostatistics Unit, Cambridge, UK} \title{flexsurv: A Platform for Parametric Survival Modelling in R} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Address{ Christopher Jackson\\ MRC Biostatistics Unit\\ Cambridge Institute of Public Health\\ Robinson Way\\ Cambridge, CB2 0SR, U.K.\\ E-mail: \email{chris.jackson@mrc-bsu.cam.ac.uk} } \Abstract{ \pkg{flexsurv} is an \proglang{R} package for fully-parametric modelling of survival data. Any parametric time-to-event distribution may be fitted if the user supplies a probability density or hazard function, and ideally also their cumulative versions. Standard survival distributions are built in, including the three and four-parameter generalized gamma and F distributions. Any parameter of any distribution can be modelled as a linear or log-linear function of covariates. The package also includes the spline model of \citet{royston:parmar}, in which both baseline survival and covariate effects can be arbitrarily flexible parametric functions of time. The main model-fitting function, \code{flexsurvreg}, uses the familiar syntax of \code{survreg} from the standard \pkg{survival} package \citep{therneau:survival}. Censoring or left-truncation are specified in \code{Surv} objects. The models are fitted by maximising the full log-likelihood, and estimates and confidence intervals for any function of the model parameters can be printed or plotted. \pkg{flexsurv} also provides functions for fitting and predicting from fully-parametric multi-state models, and connects with the \pkg{mstate} package \citep{mstate:jss}. This article explains the methods and design principles of the package, giving several worked examples of its use. \emph{[Note: A version of this vignette is published as \citet{flexsurv} in Journal of Statistical Software. All content there is included here. There have been no substantial changes in the survival modelling parts since then. Version 2.0 of \pkg{flexsurv} added new features for multi-state modelling, and since that version, multi-state modelling with \pkg{flexsurv} has been described in a separate vignette.]}} \Keywords{survival, multi-state models, multistate models} \begin{document} %\SweaveOpts{concordance=TRUE} \section{Motivation and design} The Cox model for survival data is ubiquitous in medical research, since the effects of predictors can be estimated without needing to supply a baseline survival distribution that might be inaccurate. However, fully-parametric models have many advantages, and even the originator of the Cox model has expressed a preference for parametric modelling \citep[see][]{reid:cox:conversation}. Fully-specified models can be more convenient for representing complex data structures and processes \citep{aalen:process}, e.g. hazards that vary predictably, interval censoring, frailties, multiple responses, datasets or time scales, and can help with out-of-sample prediction. For example, the mean survival $\E(T) = \int_0^{\infty}S(t)dt$, used in health economic evaluations \citep{latimer2013survival}, needs the survivor function $S(t)$ to be fully-specified for all times $t$, and parametric models that combine data from multiple time periods can facilitate this \citep{survextrap:tatiana}. %% Cox "That's right, but since then various people have shown that %% the answers are very insensitive to the parametric %% formulation of the underlying distribution. And if you want %% to do things like predict the outcome for a particular patient, %% it's much more convenient to do that parametrically." \pkg{flexsurv} for \proglang{R} \citep{R} allows parametric distributions of arbitrary complexity to be fitted to survival data, gaining the convenience of parametric modelling, while avoiding the risk of model misspecification. Built-in choices include spline-based models with any number of knots \citep{royston:parmar} and 3--4 parameter generalized gamma and F distribution families. Any user-defined model may be employed by supplying at minimum an \proglang{R} function to compute the probability density or hazard, and ideally also its cumulative form. Any parameters may be modelled in terms of covariates, and any function of the parameters may be printed or plotted in model summaries. \pkg{flexsurv} is intended as a general platform for survival modelling in \proglang{R}. The \code{survreg} function in the \proglang{R} package \pkg{survival} \citep{therneau:survival} only supports two-parameter (location/scale) distributions, though users can supply their own distributions if they can be parameterised in this form. Some other contributed \proglang{R} packages can fit survival models, e.g., \pkg{eha} \citep{eha} and \pkg{VGAM} \citep{yee:wild}, though these are either limited to specific distribution families, or not specifically designed for survival analysis. Others, e.g. \pkg{ActuDistns} \citep{actudistns}, contain only the definitions of distribution functions. \pkg{flexsurv} enables such functions to be used in survival models. It is similar in spirit to the \proglang{Stata} packages \pkg{stpm2} \citep{stpm2} for spline-based survival modelling, and \pkg{stgenreg} \citep{stgenreg} for fitting survival models with user-defined hazard functions using numerical integration. Though in \pkg{flexsurv}, slow numerical integration can be avoided if the analytic cumulative distribution or hazard can be supplied, and optimisation can also be speeded by supplying analytic derivatives. \pkg{flexsurv} also has features for multi-state modelling and interval censoring, and general output reporting. It employs functional programming to work with user-defined or existing \proglang{R} functions. \S\ref{sec:general} explains the general model that \pkg{flexsurv} is based on. \S\ref{sec:models} gives examples of its use for fitting built-in survival distributions with a fixed number of parameters, and \S\ref{sec:custom} explains how users can define new distributions. \S\ref{sec:adim} concentrates on classes of models where the number of parameters can be chosen arbitrarily, such as splines. \S\ref{sec:multistate} mentions the use of \pkg{flexsurv} for fitting and predicting from fully-parametric multi-state models, which is described more fully in a separate vignette. Finally \S\ref{sec:extensions} suggests some potential future extensions. \section{General parametric survival model} \label{sec:general} The general model that \pkg{flexsurv} fits has probability density for death at time $t$: \begin{equation} \label{eq:model} f(t | \mu(\mathbf{z}), \bm{\alpha}(\mathbf{z})), \quad t \geq 0 \end{equation} The cumulative distribution function $F(t)$, survivor function $S(t) = 1 - F(t)$, cumulative hazard $H(t) = -\log S(t)$ and hazard $h(t) = f(t)/S(t)$ are also defined (suppressing the conditioning for clarity). $\mu=\alpha_0$ is the parameter of primary interest, which usually governs the mean or \emph{location} of the distribution. Other parameters $\bm{\alpha} = (\alpha_1, \ldots, \alpha_R)$ are called ``ancillary'' and determine the shape, variance or higher moments. %%% Covariates may be time-dependent, but this notation generalizes to left-truncation, ref msm section \paragraph{Covariates} All parameters may depend on a vector of covariates $\mathbf{z}$ through link-transformed linear models $g_0(\mu(\mathbf{z})) = \gamma_0 + \bm{\beta}_0^{\top} \mathbf{z}$ and $g_r(\alpha_r(\mathbf{z})) = \gamma_r + \bm{\beta}_r^{\top} \mathbf{z}$. $g()$ will typically be $\log()$ if the parameter is defined to be positive, or the identity function if the parameter is unrestricted. Suppose that the location parameter, but not the ancillary parameters, depends on covariates. If the hazard function factorises as $h(t | \bm{\alpha}, \mu(\mathbf{z})) = \mu(\mathbf{z}) h_0(t | \bm{\alpha})$, then this is a \emph{proportional hazards} (PH) model, so that the hazard ratio between two groups (defined by two different values of $\mathbf{z}$) is constant over time $t$. Alternatively, if $S(t | \mu(\mathbf{z}), \bm{\alpha}) = S_0(\mu(\mathbf{z}) t | \bm{\alpha})$ then it is an \emph{accelerated failure time} (AFT) model, so that the effect of covariates is to speed or slow the passage of time. For example, doubling the value of a covariate with coefficient $\beta=\log(2)$ would give half the expected survival time. \paragraph{Data and likelihood} Let $t_i: i=1,\ldots, n$ be a sample of times from individuals $i$. Let $c_i=1$ if $t_i$ is an observed death time, or $c_i=0$ if this is censored. Most commonly, $t_i$ may be right-censored, thus the true death time is known only to be greater than $t_i$. More generally, the survival time may be interval-censored on $(t^{min}_i, t^{max}_i)$. Also let $s_i$ be corresponding left-truncation (or delayed-entry) times, meaning that the $i$th survival time is only observed conditionally on the individual having survived up to $s_i$, thus $s_i=0$ if there is no left-truncation. With at most right-censoring, the likelihood for the parameters $\bm{\theta} = \{\bm{\gamma},\bm{\beta}\}$ in Equation \ref{eq:model}, given the corresponding data vectors, is \begin{equation} \label{eq:lik} l(\bm{\theta} | \mathbf{t},\mathbf{c},\mathbf{s}) = \left\{ \prod_{i:\ c_i=1} f_i(t_i) \prod_{i:\ c_i=0} S_i(t_i)\right\} / \prod_i S_i(s_i) \end{equation} where $f_i(t_i)$ is shorthand for $f(t_i | \mu(\mathbf{z}_i), \bm{\alpha}(\mathbf{z}_i))$, $S_i(t_i)$ is $S(t_i | \mu(\mathbf{z}_i), \bm{\alpha}(\mathbf{z}_i))$, and $\mu, \bm{\alpha}$ are related to $\bm{\gamma}$, $\bm{\beta}$ and $\mathbf{z}_i$ via the link functions defined above. The log-likelihood also has a concise form in terms of hazards and cumulative hazards, as \[ \log l(\bm{\theta}|\mathbf{t},\mathbf{c},\mathbf{s}) = \sum_{i:\ c_i=1} \left\{\log(h_i(t_i)) - H_i(t_i)\right\} - \sum_{i:\ c_i=0} H_i(t_i) + \sum_i H_i(s_i) \] With interval-censoring, the likelihood is \begin{equation} \label{eq:lik:interval} l(\bm{\theta} | \mathbf{t}^{min},\mathbf{t}^{max},\mathbf{c},\mathbf{s}) = \left\{ \prod_{i:\ c_i=1} f_i(t_i) \prod_{i:\ c_i=0} \left(S_i(t_i^{min}) - S_i(t^{max}_i)\right)\right\} / \prod_i S_i(s_i) \end{equation} %% with hazards: %% log lik is sum log(f) sum log(S) - sum log(S) %% sum(log(h) + H) - sum(H) + sum(H(si)) %% h = f/S, H=-log(S) h S S These likelihoods assume that the times of censoring are fixed or otherwise distributed independently of the parameters $\bm{\theta}$ that govern the survival times (see, e.g. \citet{aalen:process}). The individual survival times are also independent, so that \pkg{flexsurv} does not currently support shared frailty, clustered or random effects models (see \S\ref{sec:extensions}). The parameters are estimated by maximising the full log-likelihood with respect to $\bm{\theta}$, as detailed further in \S\ref{sec:comp}. \section{Fitting standard parametric survival models} \label{sec:models} An example dataset used throughout this paper is from 686 patients with primary node positive breast cancer, available in the package as \code{bc}. This was originally provided with \pkg{stpm} \citep{stpm:orig}, and analysed in much more detail by \citet{sauerbrei1999building} and \citet{royston:parmar} \footnote{A version of this dataset, including more covariates but excluding the prognostic group, is also provided as \code{GBSG2} in the package \pkg{TH.data} \citep{TH.data}.} . The first two records are shown by: <>= library("flexsurv") @ <<>>= head(bc, 2) @ The main model-fitting function is called \code{flexsurvreg}. Its first argument is an \proglang{R} \emph{formula} object. The left hand side of the formula gives the response as a survival object, using the \code{Surv} function from the \pkg{survival} package. <<>>= fs1 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") @ Here, this indicates that the response variable is \code{recyrs}. This represents the time (in years) of death or cancer recurrence when \code{censrec} is 1, or (right-)censoring when \code{censrec} is 0. The covariate \code{group} is a factor representing a prognostic score, with three levels \code{"Good"} (the baseline), \code{"Medium"} and \code{"Poor"}. All of these variables are in the data frame \code{bc}. If the argument \code{dist} is a string, this denotes a built-in survival distribution. In this case we fit a Weibull survival model. Printing the fitted model object gives estimates and confidence intervals for the model parameters and other useful information. Note that these are the \emph{same parameters} as represented by the \proglang{R} distribution function \code{dweibull}: the \code{shape} $\alpha$ and the \code{scale} $\mu$ of the survivor function $S(t) = \exp(-(t/\mu)^\alpha)$, and \code{group} has a linear effect on $\log(\mu)$. <<>>= fs1 @ For the Weibull (and exponential, log-normal and log-logistic) distribution, \code{flexsurvreg} simply acts as a wrapper for \code{survreg}: the maximum likelihood estimates are obtained by \code{survreg}, checked by \code{flexsurvreg} for optimisation convergence, and converted to \code{flexsurvreg}'s preferred parameterisation. Therefore the same model can be fitted more directly as <<>>= survreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") @ \begin{sloppypar} The maximised log-likelihoods are the same, however the parameterisation is different: the first coefficient \code{(Intercept)} reported by \code{survreg} is $\log(\mu)$, and \code{survreg}'s \code{"scale"} is \code{dweibull}'s (thus \code{flexsurvreg})'s 1 / \code{shape}. The covariate effects $\bm{\beta}$, however, have the same ``accelerated failure time'' interpretation, as linear effects on $\log(\mu)$. The multiplicative effects $\exp(\bm{\beta})$ are printed in the output as \code{exp(est)}. \end{sloppypar} The same model can be fitted in \pkg{eha}, also by maximum likelihood, as <>= library(eha) aftreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") @ The results are presented in the same parameterisation as \code{flexsurvreg}, except that the shape and scale parameters are log-transformed, and (unless the argument \code{param="lifeExp"} is supplied) the covariate effects have the opposite sign. \subsection{Additional modelling features} \label{sec:censtrunc} \subsubsection{Truncation and time-dependent covariates} \begin{sloppypar} If we also had left-truncation times in a variable called \code{start}, the response would be \code{Surv(start, recyrs, censrec)}. Or if all responses were interval-censored between lower and upper bounds \code{tmin} and \code{tmax}, then we would write \code{Surv(tmin, tmax, type = "interval2")}. \end{sloppypar} Time-dependent covariates are not supported in \pkg{flexsurv}. In other packages, they are represented in ``counting process'' form --- as a series of left-truncated survival times, which may also be right-censored. For each individual there would be multiple records, each corresponding to an interval where the covariate is assumed to be constant. The response would be of the form \code{Surv(start, stop, censrec)}, where \code{start} and \code{stop} are the limits of each interval, and \code{censrec} indicates whether a death was observed at \code{stop}. However, using this approach would require the probability of survival up to the left-truncation time to be represented by a term of the form $S_i(s_i) = \exp(-H_i(s_i))$ in the likelihood (equation 2). The cumulative hazard $H$ over the interval from time 0 to time $s_i$ depends on how the covariates change for an individual on this time interval, and \pkg{flexsurv} cannot keep track of different observations for an individual. Furthermore, prediction from models with time-dependent covariates is a difficult problem, as it requires knowledge of when the covariates are expected to change. Joint models for longitudinal and survival data are a more flexible approach for modelling the association of a survival time with a time-dependent predictor. In versions of \pkg{flexsurv} since April 2020, models with individual-specific right-truncation times are also supported. These are used for situations with ``retrospective ascertainment'', where cases are only included in the data if they have died by a specific time. These models are specified through an argument \code{rtrunc} to \code{flexsurvreg} that names the variable with the truncation times. See the Supplementary Examples vignette for a worked example. \subsubsection{Relative survival} In relative survival models \citep{nelson:relative:survival}, the survivor function is expressed as $S(t) = S^*(t)R(t)$, where $S^*(t)$ is the ``expected" or ``baseline" survival, and $R(t)$ is the \emph{relative} survival. Equivalently, the hazard is defined as $h(t) = h^*(t) + \lambda(t)$, where $h^*()$ is the baseline hazard function, and $\lambda(t)$ is the excess mortality rate associated with the disease of interest. The baseline represents a reference population, and is typically obtained from national routinely-collected mortality statistics, adjusted (e.g. by age/sex) to represent the population under study. The parametric model is defined and estimated for $R(t)$. These models are implemented in \pkg{flexsurv} by supplying the variable in the data that represents the expected mortality rate $h^*(t)$ in the \code{bhazard} argument to \code{flexsurvreg}. This is only used for the individuals in the data who die, and \code{bhazard} describes the expected hazard at the death time. The values of \code{bhazard} for censored individuals are ignored. Note that the parameters returned in the model fitted by \code{flexsurvreg} refer to the relative survival $R(t)$, rather than the absolute survival. The likelihood returned by \code{flexsurvreg} here is a \emph{partial} likelihood defined \citep[as in][equations 4--5]{nelson:relative:survival} by omitting the term $\sum_i \log(S^*(t_i))$ (summed over all individuals $i$ in the data, including both censored and uncensored times $t_i$) from the full likelihood. This term is equivalent to minus the sum of the cumulative hazards. It can be omitted from the likelihood for the purpose of estimating the parameters of the relative survival model, since it does not depend on these parameters. Hence if a full likelihood is required, (e.g. for model comparison) then this term should be added to the partial likelihood. Similarly, the predicted survival or hazard (e.g. as returned by \code{summary.flexsurvreg}, see Section~\ref{sec:plots}) from a relative survival model refers to $R(t)$ or $h(t)$. Hence if the overall survival or hazard is required, the predictions of relative survival should be converted to the ``absolute" scale by combining with the baseline, though no specific tools for doing this are provided by \pkg{flexsurv}. \subsubsection{Weighting and subsetting} Case weights and data subsets can also be specified, as in standard \proglang{R} modelling functions, using \code{weights} or \code{subset} arguments. \subsection{Built-in models} \label{sec:builtin} \code{flexsurvreg}'s currently built-in distributions are listed in Table \ref{tab:dists}. In each case, the probability density $f()$ and parameters of the fitted model are taken from an existing \proglang{R} function of the same name but beginning with the letter \code{d}. For the Weibull, exponential (\code{dexp}), gamma (\code{dgamma}) and log-normal (\code{dlnorm}), the density functions are provided with standard installations of \proglang{R}. These density functions, and the corresponding cumulative distribution functions (with first letter \code{p} instead of \code{d}) are used internally in \code{flexsurvreg} to compute the likelihood. \pkg{flexsurv} provides some additional survival distributions, including a Gompertz distribution with unrestricted shape parameter, Weibull with proportional hazards parameterisation, log-logistic, and the three- and four-parameter families described below. For all built-in distributions, \pkg{flexsurv} also defines functions beginning with \code{h} giving the hazard, and \code{H} for the cumulative hazard. A package vignette ``Distributions reference'' lists the survivor function and parameterisation of covariate effects used by each built-in distribution. \paragraph{Generalized gamma} This three-parameter distribution includes the Weibull, gamma and log-normal as special cases. The original parameterisation from \citet{stacy:gengamma} is available as\\ \code{dist = "gengamma.orig"}, however the newer parameterisation \citep{prentice:loggamma} is preferred: \code{dist = "gengamma"}. This has parameters ($\mu$,$\sigma$,$q$), and survivor function \[ \begin{array}{ll} 1 - I(\gamma,u) & (q > 0)\\ 1 - \Phi(z) & (q = 0)\\ \end{array} \] where $I(\gamma,u) = \int_0^u x^{\gamma-1}\exp(-x)/\Gamma(\gamma)$ is the incomplete gamma function (the cumulative gamma distribution with shape $\gamma$ and scale 1), $\Phi$ is the standard normal cumulative distribution, $u = \gamma \exp(|q|z)$, $z=(\log(t) - \mu)/\sigma$, and $\gamma=q^{-2}$. The \citet{prentice:loggamma} parameterisation extends the original one to include a further class of models with negative $q$, and survivor function $I(\gamma,u)$, where $z$ is replaced by $-z$. This stabilises estimation when the distribution is close to log-normal, since $q=0$ is no longer near the boundary of the parameter space. In \proglang{R} notation, \footnote{The parameter called $q$ here and in previous literature is called $Q$ in \code{dgengamma} and related functions, since the first argument of a cumulative distribution function is conventionally named \code{q}, for quantile, in \proglang{R}.} the parameter values corresponding to the three special cases are \begin{Code} dgengamma(x, mu, sigma, Q=0) == dlnorm(x, mu, sigma) dgengamma(x, mu, sigma, Q=1) == dweibull(x, shape = 1 / sigma, scale = exp(mu)) dgengamma(x, mu, sigma, Q=sigma) == dgamma(x, shape = 1 / sigma^2, rate = exp(-mu) / sigma^2) \end{Code} \paragraph{Generalized F} This four-parameter distribution includes the generalized gamma, and also the log-logistic, as special cases. The variety of hazard shapes that can be represented is discussed by \citet{ccox:genf}. It is provided here in alternative ``original'' (\code{dist = "genf.orig"}) and ``stable'' parameterisations (\code{dist = "genf"}) as presented by \citet{prentice:genf}. See \code{help(GenF)} and \code{help(GenF.orig)} in the package documentation for the exact definitions. \subsection{Covariates on ancillary parameters} The generalized gamma model is fitted to the breast cancer survival data. \code{fs2} is an AFT model, where only the parameter $\mu$ depends on the prognostic covariate \code{group}. In a second model \code{fs3}, the first ancillary parameter \code{sigma} ($\alpha_1$) also depends on this covariate, giving a model with a time-dependent effect that is neither PH nor AFT. The second ancillary parameter \code{Q} is still common between prognostic groups. <<>>= fs2 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "gengamma") fs3 <- flexsurvreg(Surv(recyrs, censrec) ~ group + sigma(group), data = bc, dist = "gengamma") @ Ancillary covariates can alternatively be supplied using the \code{anc} argument to \code{flexsurvreg}. This syntax is required if any parameter names clash with the names of functions used in model formulae (e.g., \code{factor()} or \code{I()}). <>= fs3 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, anc = list(sigma = ~ group), dist = "gengamma") @ Table \ref{tab:aic} compares all the models fitted to the breast cancer data, showing absolute fit to the data as measured by the maximised -2$\times$log likelihood $-2LL$, number of parameters $p$, and Akaike's information criterion $-2LL + 2p$ (AIC). The model \code{fs2} has the lowest AIC, indicating the best estimated predictive ability. \begin{table} \begin{tabular}{p{1.8in}lll} \hline & Parameters & Density \proglang{R} function & \code{dist}\\ & {\footnotesize{(location in \code{\color{red}{red}})}} & & \\ \hline Exponential & \code{\color{red}{rate}} & \code{dexp} & \code{"exp"} \\ Weibull (accelerated failure time) & \code{shape, {\color{red}{scale}}} & \code{dweibull} & \code{"weibull"} \\ Weibull (proportional hazards) & \code{shape, {\color{red}{scale}}} & \code{dweibullPH} & \code{"weibullPH"} \\ Gamma & \code{shape, \color{red}{rate}} & \code{dgamma} & \code{"gamma"}\\ Log-normal & \code{{\color{red}{meanlog}}, sdlog} & \code{dlnorm} & \code{"lnorm"}\\ Gompertz & \code{shape, {\color{red}{rate}}} & \code{dgompertz} & \code{"gompertz"} \\ Log-logistic & \code{shape, {\color{red}{scale}}} & \code{dllogis} & \code{"llogis"}\\ Generalized gamma (Prentice 1975) & \code{{\color{red}{mu}}, sigma, Q} & \code{dgengamma} & \code{"gengamma"} \\ Generalized gamma (Stacy 1962)& \code{shape, {\color{red}{scale}}, k} & \code{dgengamma.orig} & \code{"gengamma.orig"} \\ Generalized F (stable) & \code{{\color{red}{mu}}, sigma, Q, P} & \code{dgenf} & \code{"genf"} \\ Generalized F (original) & \code{{\color{red}{mu}}, sigma, s1, s2} & \code{dgenf.orig} & \code{"genf.orig"} \\ \hline \end{tabular} \caption{Built-in parametric survival distributions in \pkg{flexsurv}.} \label{tab:dists} \end{table} \subsection{Plotting outputs} \label{sec:plots} The \code{plot()} method for \code{flexsurvreg} objects is used as a quick check of model fit. By default, this draws a Kaplan-Meier estimate of the survivor function $S(t)$, one for each combination of categorical covariates, or just a single ``population average'' curve if there are no categorical covariates (Figure \ref{fig:surv}). The corresponding estimates from the fitted model are overlaid. Fitted values from further models can be added with the \code{lines()} method. <>= cols <- c("#E495A5", "#86B875", "#7DB0DD") # from colorspace::rainbow_hcl(3) plot(fs1, col = cols[2], lwd.obs = 2, xlab = "Years", ylab = "Recurrence-free survival") lines(fs2, col = cols[3], lty = 2) lines(fs3, col = cols[3]) text(x=c(2,3.5,4), y=c(0.4, 0.55, 0.7), c("Poor","Medium","Good")) legend("bottomleft", col = c("black", cols[2], cols[3], cols[3]), lty = c(1, 1, 2, 1), bty = "n", lwd = rep(2, 4), c("Kaplan-Meier", "Weibull", "Generalized gamma (AFT)", "Generalized gamma (time-varying)")) @ \begin{figure}[h] \centering \includegraphics{flexsurv-surv-1} \caption{Survival by prognostic group from the breast cancer data: fitted from alternative parametric models and Kaplan-Meier estimates.} \label{fig:surv} \end{figure} The argument \code{type = "hazard"} can be set to plot hazards from parametric models against kernel density estimates obtained from \pkg{muhaz} \citep{muhaz,mueller:wang}. Figure \ref{fig:haz} shows more clearly that the Weibull model is inadequate for the breast cancer data: the hazard must be increasing or decreasing --- while the generalized gamma can represent the increase and subsequent decline in hazard seen in the data. Similarly, \code{type = "cumhaz"} plots cumulative hazards. <>= plot(fs1, type = "hazard", col = cols[2], lwd.obs = 2, max.time=6, xlab = "Years", ylab = "Hazard") lines(fs2, type = "hazard", col = cols[3], lty = 2) lines(fs3, type = "hazard", col = cols[3]) text(x=c(2,2,2), y=c(0.3, 0.13, 0.05), c("Poor","Medium","Good")) legend("topright", col = c("black", cols[2], cols[3], cols[3]), lty = c(1, 1, 2, 1), bty = "n", lwd = rep(2, 4), c("Kernel density estimate", "Weibull", "Gen. gamma (AFT)", "Gen. gamma (time-varying)")) @ \begin{figure}[h] \centering \includegraphics{flexsurv-haz-1} \caption{Hazards by prognostic group from the breast cancer data: fitted from alternative parametric models and kernel density estimates.} \label{fig:haz} \end{figure} The numbers plotted are available from the \code{summary.flexsurvreg()} method. Confidence intervals are produced by simulating a large sample from the asymptotic normal distribution of the maximum likelihood estimates of $\{\bm{\beta}_r: r=0,\ldots,R\}$ \citep{mandel:simci}, via the function \code{normboot.flexsurvreg}. This very general method allows confidence intervals to be obtained for arbitrary functions of the parameters, as described in the next section. In this example, there is only a single categorical covariate, and the \code{plot} and \code{summary} methods return one observed and fitted trajectory for each level of that covariate. For more complicated models, users should specify what covariate values they want summaries for, rather than relying on the default \footnote{If there are only factor covariates, all combinations are plotted. If there are any continuous covariates, these methods by default return a ``population average'' curve, with the linear model design matrix set to its average values, including the 0/1 contrasts defining factors, which doesn't represent any specific covariate combination.}. This is done by supplying the \code{newdata} argument, a data frame or list containing covariate values, just as in standard \proglang{R} functions like \code{predict.lm}. Time-dependent covariates are not understood by these functions. This \code{plot()} method is only for casual exploratory use. For publication-standard figures, it is preferable to set up the axes beforehand (\code{plot(..., type = "n")}), and use the \code{lines()} methods for \code{flexsurvreg} objects, or construct plots by hand using the data available from \code{summary.flexsurvreg()}. \subsection{Custom model summaries} Any function of the parameters of a fitted model can be summarised or plotted by supplying the argument \code{fn} to \code{summary.flexsurvreg} or \code{plot.flexsurvreg}. This should be an \proglang{R} function, with optional first two arguments \code{t} representing time, and \code{start} representing a left-truncation point (if the result is conditional on survival up to that time). Any remaining arguments must be the parameters of the survival distribution. For example, median survival under the Weibull model \code{fs1} can be summarised as follows <<>>= median.weibull <- function(shape, scale) { qweibull(0.5, shape = shape, scale = scale) } summary(fs1, fn = median.weibull, t = 1, B = 10000) @ Although the median of the Weibull has an analytic form as $\mu \log(2)^{1/\alpha}$, the form of the code given here generalises to other distributions. The argument \code{t} (or \code{start}) can be omitted from \code{median.weibull}, because the median is a time-constant function of the parameters, unlike the survival or hazard. \code{10000} random samples are drawn to produce a slightly more precise confidence interval than the default --- users should adjust this until the desired level of precision is obtained. A useful future extension of the package would be to employ user-supplied (or built-in) derivatives of summary functions if possible, so that the delta method can be used to obtain approximate confidence intervals without simulation. \subsection{Computation} \label{sec:comp} The likelihood is maximised in \code{flexsurvreg} using the optimisation methods available through the standard \proglang{R} \code{optim} function. By default, this is the \code{"BFGS"} method \citep{nash} using the analytic derivatives of the likelihood with respect to the model parameters, if these are available, to improve the speed of convergence to the maximum. These derivatives are built-in for the exponential, Weibull, Gompertz, log-logistic, and hazard- and odds-based spline models (see \S\ref{sec:spline}). For custom distributions (see \S\ref{sec:custom}), the user can optionally supply functions with names beginning \code{"DLd"} and \code{"DLS"} respectively (e.g., \code{DLdweibull, DLSweibull}) to calculate the derivatives of the log density and log survivor functions with respect to the transformed baseline parameters $\bm{\gamma}$ (then the derivatives with respect to $\bm{\beta}$ are obtained automatically). Arguments to \code{optim} can be passed to \code{flexsurvreg} --- in particular, \code{control} options, such as convergence tolerance, iteration limit or function or parameter scaling, may need to be adjusted to achieve convergence. \section{Custom survival distributions} \label{sec:custom} \pkg{flexsurv} is not limited to its built-in distributions. Any survival model of the form (\ref{eq:model}--\ref{eq:lik:interval}) can be fitted if the user can provide either the density function $f()$ or the hazard $h()$. Many contributed \proglang{R} packages provide probability density and cumulative distribution functions for positive distributions. Though survival models may be more naturally characterised by their hazard function, representing the changing risk of death through time. For example, for survival following major surgery we may want a ``U-shaped'' hazard curve, representing a high risk soon after the operation, which then decreases, but increases naturally as survivors grow older. To supply a custom distribution, the \code{dist} argument to \code{flexsurvreg} is defined to be an \proglang{R} list object, rather than a character string. The list has the following elements. \begin{description} \item[\code{name}] Name of the distribution. In the first example below, we use a log-logistic distribution, and the name is \code{"llogis"} \footnote{though since version 0.5.1, this distribution is built into \pkg{flexsurv} as \code{dist="llogis"} }. Then there is assumed to be at least either \begin{itemize} \item a function to compute the probability density, which would be called \code{dllogis} here, or \item a function to compute the hazard, called \code{hllogis}. \end{itemize} There should also be a function called \code{pllogis} for the cumulative distribution (if \code{d} is given), or \code{H} for the cumulative hazard (to complement \code{h}), if analytic forms for these are available. If not, then \pkg{flexsurv} can compute them internally by numerical integration, as in \pkg{stgenreg} \citep{stgenreg}. The default options of the built-in \proglang{R} routine \code{integrate} for adaptive quadrature are used, though these may be changed using the \code{integ.opts} argument to \code{flexsurvreg}. Models specified this way will take an order of magnitude more time to fit, and the fitting procedure may be unstable. An example is given in \S\ref{sec:gdim}. These functions must be \emph{vectorised}, and the density function must also accept an argument \code{log}, which when \code{TRUE}, returns the log density. See the examples below. In some cases, \proglang{R}'s scoping rules may not find the functions in the working environment. They may then be supplied through the \code{dfns} argument to \code{flexsurvreg}. \item[\code{pars}] Character vector naming the parameters of the distribution $\mu,\alpha_1,...,\alpha_R$. These must match the arguments of the \proglang{R} distribution function or functions, in the same order. \item[\code{location}] Character: quoted name of the location parameter $\mu$. The location parameter will not necessarily be the first one, e.g., in \code{dweibull} the \code{scale} comes after the \code{shape}. \item[\code{transforms}] A list of functions $g()$ which transform the parameters from their natural ranges to the real line, for example, \code{c(log, identity)} if the first is positive and the second unrestricted. \footnote{This is a \emph{list}, not an \emph{atomic vector} of functions, so if the distribution only has one parameter, we should write \code{transforms = c(log)} or \code{transforms = list(log)}, not \code{transforms = log}.} \item[\code{inv.transforms}] List of corresponding inverse functions. \item[\code{inits}] A function which provides plausible initial values of the parameters for maximum likelihood estimation. This is optional, but if not provided, then each call to \code{flexsurvreg} must have an \code{inits} argument containing a vector of initial values, which is inconvenient. Implausible initial values may produce a likelihood of zero, and a fatal error message (\code{initial value in `vmmin' is not finite}) from the optimiser. Each distribution will ideally have a heuristic for initialising parameters from summaries of the data. For example, since the median of the Weibull is $\mu \log(2)^{1/\alpha}$, a sensible estimate of $\mu$ might be the median log survival time divided by $\log(2)$, with $\alpha=1$, assuming that in practice the true value of $\alpha$ is not far from 1. Then we would define the function, of one argument \code{t} giving the survival or censoring times, returning the initial values for the Weibull \code{shape} and \code{scale} respectively \footnote{though Weibull models in \code{flexsurvreg} are ``initialised'' by fitting the model with \code{survreg}, unless there is left-truncation.}. \code{inits = function(t){ c(1, median(t[t > 0]) / log(2)) } } More complicated initial value functions may use other data such as the covariate values and censoring indicators: for an example, see the function \code{flexsurv.splineinits} in the package source that computes initial values for spline models (\S\ref{sec:spline}). \end{description} \paragraph{Example: Using functions from a contributed package} The following custom model uses the log-logistic distribution functions (\code{dllogis} and \code{pllogis}) available in the package \pkg{eha}. The survivor function is $S(t|\mu,\alpha) = 1/(1 + (t/\mu)^\alpha)$, so that the log odds $\log((1-S(t))/S(t))$ of having died are a linear function of log time. <>= custom.llogis <- list(name = "llogis", pars = c("shape", "scale"), location = "scale", transforms = c(log, log), inv.transforms = c(exp, exp), inits = function(t){ c(1, median(t)) }) fs4 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = custom.llogis) @ This fits the breast cancer data better than the Weibull, since it can represent a peaked hazard, but less well than the generalized gamma (Table \ref{tab:aic}). \paragraph{Example: Wrapping functions from a contributed package} Sometimes there may be probability density and similar functions in a contributed package, but in a different format. For example, \pkg{eha} also provides a three-parameter Gompertz-Makeham distribution with hazard $h(t|\mu,\alpha_1,\alpha_2)= \alpha_2 + \alpha_1 \exp(t/\mu)$. The shape parameters $\alpha_1,\alpha_2$ are provided to \code{dmakeham} as a vector argument of length two. However, \code{flexsurvreg} expects distribution functions to have one argument for each parameter. Therefore we write our own functions that wrap around the third-party functions. <>= dmakeham3 <- function(x, shape1, shape2, scale, ...) { dmakeham(x, shape = c(shape1, shape2), scale = scale, ...) } pmakeham3 <- function(q, shape1, shape2, scale, ...) { pmakeham(q, shape = c(shape1, shape2), scale = scale, ...) } @ \code{flexsurvreg} also requires these functions to be \emph{vectorized}, as the standard distribution functions in \proglang{R} are. That is, we can supply a vector of alternative values for one or more arguments, and expect a vector of the same length to be returned. The \proglang{R} base function \code{Vectorize} can be used to do this here. <>= dmakeham3 <- Vectorize(dmakeham3) pmakeham3 <- Vectorize(pmakeham3) @ and this allows us to write, for example, <>= pmakeham3(c(0, 1, 1, Inf), 1, c(1, 1, 2, 1), 1) @ We could then use \code{dist = list(name = "makeham3", pars = c("shape1", "shape2", \\ "scale"), ...)} in a \code{flexsurvreg} model, though in the breast cancer example, the second shape parameter is poorly identifiable. \paragraph{Example: Changing the parameterisation of a distribution} We may want to fit a Weibull model like \code{fs1}, but with the proportional hazards (PH) parameterisation $S(t) = \exp(-\mu t^\alpha)$, so that the covariate effects reported in the printed \code{flexsurvreg} object can be interpreted as hazard ratios or log hazard ratios without any further transformation. Here instead of the density and cumulative distribution functions, we provide the hazard and cumulative hazard. (Note that since version 0.7, the \code{"weibullPH"} distribution is built in to \code{flexsurvreg} --- but this example has been kept here for illustrative purposes.) \footnote{The \pkg{eha} package may need to be detached first so that \pkg{flexsurv}'s built-in \code{hweibull} is used, which returns \code{NaN} if the parameter values are zero, rather than failing as \pkg{eha}'s currently does.} <>= options(warn=-1) @ <<>>= hweibullPH <- function(x, shape, scale = 1, log = FALSE){ hweibull(x, shape = shape, scale = scale ^ {-1 / shape}, log = log) } HweibullPH <- function(x, shape, scale = 1, log = FALSE){ Hweibull(x, shape = shape, scale = scale ^ {-1 / shape}, log = log) } custom.weibullPH <- list(name = "weibullPH", pars = c("shape", "scale"), location = "scale", transforms = c(log, log), inv.transforms = c(exp, exp), inits = function(t){ c(1, median(t[t > 0]) / log(2)) }) fs6 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = custom.weibullPH) fs6$res["scale", "est"] ^ {-1 / fs6$res["shape", "est"]} - fs6$res["groupMedium", "est"] / fs6$res["shape", "est"] - fs6$res["groupPoor", "est"] / fs6$res["shape", "est"] @ <>= options(warn=0) @ The fitted model is the same as \code{fs1}, therefore the maximised likelihood is the same. The parameter estimates of \code{fs6} can be transformed to those of \code{fs1} as shown. The shape $\alpha$ is common to both models, the scale $\mu^\prime$ in the AFT model is related to the PH scale $\mu$ as $\mu^\prime$ = $\mu^{-1/\alpha}$. The effects $\beta^\prime$ on life expectancy in the AFT model are related to the log hazard ratios $\beta$ as $\beta^\prime = -\beta/\alpha$. A slightly more complicated example is given in the package vignette \code{flexsurv-examples} of constructing a proportional hazards generalized gamma model. Note that \code{phreg} in \pkg{eha} also fits the Weibull and other proportional hazards models, though again the parameterisation is slightly different. \section{Arbitrary-dimension models} \label{sec:adim} \pkg{flexsurv} also supports models where the number of parameters is arbitrary. In the models discussed previously, the number of parameters in the model family is fixed (e.g., three for the generalized gamma). In this section, the model complexity can be chosen by the user, given the model family. We may want to represent more irregular hazard curves by more flexible functions, or use bigger models if a bigger sample size makes it feasible to estimate more parameters. \subsection{Royston and Parmar spline model} \label{sec:spline} \begin{sloppypar} In the spline-based survival model of \citet{royston:parmar}, a transformation $g(S(t,z))$ of the survival function is modelled as a natural cubic spline function of log time: $g(S(t,z)) = s(x, \bm{\gamma})$ where $x = \log(t)$. This model can be fitted in \pkg{flexsurv} using the function \code{flexsurvspline}, and is also available in the \proglang{Stata} package \pkg{stpm2} \citep{stpm2} (historically \pkg{stpm}, \citet{stpm:orig,stpm:update}). \end{sloppypar} Typically we use $g(S(t,\mathbf{z})) = \log(-\log(S(t,\mathbf{z}))) = \log(H(t,\mathbf{z}))$, the log cumulative hazard, giving a proportional hazards model. \paragraph{Spline parameterisation} The complexity of the model, thus the dimension of $\bm{\gamma}$, is governed by the number of \emph{knots} in the spline function $s()$. Natural cubic splines are piecewise cubic polynomials defined to be continuous, with continuous first and second derivatives at the knots, and also constrained to be linear beyond boundary knots $k_{min},k_{max}$. As well as the boundary knots there may be up to $m\geq 0$ \emph{internal} knots $k_1,\ldots, k_m$. Various spline parameterisations exist --- the one used here is from \citet{royston:parmar}. \begin{equation} \label{eq:spline} s(x,\bm{\gamma}) = \gamma_0 + \gamma_1 x + \gamma_2 v_1(x) + \ldots + \gamma_{m+1} v_m(x) \end{equation} where $v_j(x)$ is the $j$th \emph{basis} function \[v_j(x) = (x - k_j)^3_+ - \lambda_j(x - k_{min})^3_+ - (1 - \lambda_j) (x - k_{max})^3_+, \qquad \lambda_j = \frac{k_{max} - k_j}{k_{max} - k_{min}} \] and $(x - a)_+ = max(0, x - a)$. If $m=0$ then there are only two parameters $\gamma_0,\gamma_1$, and this is a Weibull model if $g()$ is the log cumulative hazard. Table \ref{tab:spline} explains two further choices of $g()$, and the parameter values and distributions they simplify to for $m=0$. The probability density and cumulative distribution functions for all these models are available as \code{dsurvspline} and \code{psurvspline}. A model with an absolute time scale ($x = t$) is also available through \code{timescale="identity"}. \begin{table} \begin{tabularx}{\textwidth}{lXlp{1.4in}} \hline Model & $g(S(t,\mathbf{z}))$ & In \code{flexsurvspline} & With $m=0$ \\ \hline Proportional hazards & $\log(-\log(S(t,\mathbf{z})))$ \newline {\footnotesize (log cumulative hazard)} & \code{scale = "hazard"} & Weibull {\footnotesize \code{shape} $\gamma_1$, \code{scale} $\exp(-\gamma_0/\gamma_1)$}\\ Proportional odds & $\log(S(t,\mathbf{z})^{-1} - 1)$ \newline {\footnotesize (log cumulative odds)} & \code{scale = "odds"} & Log-logistic {\footnotesize \code{shape} $\gamma_1$, \code{scale} $\exp(-\gamma_0/\gamma_1)$}\\ Normal / probit & $\Phi^{-1}(S(t,\mathbf{z}))$ \newline {\footnotesize (inverse normal CDF, \code{qnorm})} & \code{scale = "normal"} & Log-normal {\footnotesize \code{meanlog} $-\gamma_0/\gamma_1$, \code{sdlog} $1/\gamma_1$ }\\ \hline \end{tabularx} \caption{Alternative modelling scales for \code{flexsurvspline}, and equivalent distributions for $m=0$ (with parameter definitions as in the \proglang{R} \code{d} functions referred to elsewhere in the paper).} \label{tab:spline} \end{table} \paragraph{Covariates on spline parameters} Covariates can be placed on any parameter $\gamma$ through a linear model (with identity link function). Most straightforwardly, we can let the intercept $\gamma_0$ vary with covariates $\mathbf{z}$, giving a proportional hazards or odds model (depending on $g()$). \[g(S(t,z)) = s(\log(t), \bm{\gamma}) + \bm{\beta}^\top \mathbf{z} \] The spline coefficients $\gamma_j: j=1, 2 \ldots$, the ``ancillary'' parameters, may also be modelled as linear functions of covariates $\mathbf{z}$, as \[\gamma_j(\mathbf{z}) = \gamma_{j0} + \gamma_{j1}z_1 + \gamma_{j2}z_2 + \ldots\] giving a model where the effects of covariates are arbitrarily flexible functions of time: a non-proportional hazards or odds model. \paragraph{Spline models in \pkg{flexsurv}} The argument \code{k} to \code{flexsurvspline} defines the number of internal knots $m$. Knot locations are chosen by default from quantiles of the log uncensored death times, or users can supply their own locations in the \code{knots} argument. Initial values for numerical likelihood maximisation are chosen using the method described by \citet{royston:parmar} of Cox regression combined with transforming an empirical survival estimate. For example, the best-fitting model for the breast cancer dataset identified in \citet{royston:parmar}, a proportional odds model with one internal spline knot, is <<>>= sp1 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data = bc, k = 1, scale = "odds") @ A further model where the first ancillary parameter also depends on the prognostic group, giving a time-varying odds ratio, is fitted as <<>>= sp2 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group), data = bc, k = 1, scale = "odds") @ These models give qualitatively similar results to the generalized gamma in this dataset (Figure \ref{fig:spline:haz}), and have similar predictive ability as measured by AIC (Table \ref{tab:aic}). Though in general, an advantage of spline models is that extra flexibility is available where necessary. <>= plot(sp1, type = "hazard", col=cols[3], ylim = c(0, 0.5), xlab = "Years", ylab = "Hazard") lines(sp2, type = "hazard", col = cols[3], lty = 2) lines(fs2, type = "hazard", col = cols[2]) text(x=c(2,2,2), y=c(0.3, 0.15, 0.05), c("Poor","Medium","Good")) legend("topright", col = c("black",cols[c(3,3,2)]), lty = c(1,1,2,1), lwd = rep(2,4), c("Kernel density estimate","Spline (proportional odds)", "Spline (time-varying)","Generalized gamma (time-varying)")) @ \begin{figure}[h] \centering \includegraphics{flexsurv-splinehaz-1} \caption{Comparison of spline and generalized gamma fitted hazards for the breast cancer survival data by prognostic group.} \label{fig:spline:haz} \end{figure} In this example, proportional odds models (\code{scale = "odds"}) are better-fitting than proportional hazards models (\code{scale = "hazard"}) (Table \ref{tab:aic}). Note also that under a proportional hazards spline model with one internal knot (\code{sp3}), the log hazard ratios, and their standard errors, are substantively the same as under a standard Cox model (\code{cox3}). This illustrates that this class of flexible fully-parametric models may be a reasonable alternative to the (semi-parametric) Cox model. See \citet{royston:parmar} for more discussion of these issues. <<>>= sp3 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data = bc, k = 1, scale = "hazard") sp3$res[c("groupMedium", "groupPoor"), c("est", "se")] cox3 <- coxph(Surv(recyrs, censrec) ~ group, data = bc) coef(summary(cox3))[ , c("coef", "se(coef)")] @ An equivalent of a ``stratified" Cox model may be obtained by allowing \emph{all} the spline parameters to vary with the categorical covariate that defines the strata. In this case, this covariate might be \code{group}. With \code{k=}$m$ internal knots, the formula should then include \code{group}, representing $\gamma_0$, and $m+1$ further terms representing the parameters $\gamma_1,\ldots,\gamma_{m+1}$, named as follows. <<>>= sp4 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + gamma2(group), data = bc, k = 1, scale = "hazard") @ Other covariates might be added to this formula --- if placed on the intercept, these will be modelled through proportional hazards, as in \code{sp1}. If placed on higher-order parameters, these will represent time-varying hazard ratios. For example, if there were a covariate \code{treat} representing treatment, then <>= flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + gamma2(group) + treat + gamma1(treat), data = bc, k = 1, scale = "hazard") @ would represent a model stratified by group, where the hazard ratio for treatment is time-varying, but the model is not fully stratified by treatment. <<>>= res <- t(sapply(list(fs1, fs2, fs3, sp1, sp2, sp3, sp4), function(x)rbind(-2 * round(x$loglik,1), x$npars, round(x$AIC,1)))) rownames(res) <- c("Weibull (fs1)", "Generalized gamma (fs2)", "Generalized gamma (fs3)", "Spline (sp1)", "Spline (sp2)", "Spline (sp3)", "Spline (sp4)") colnames(res) <- c("-2 log likelihood", "Parameters", "AIC") @ \begin{table}[h] <>= res @ \caption{Comparison of parametric survival models fitted to the breast cancer data.} \label{tab:aic} \end{table} \subsection{Implementing new general-dimension models} \label{sec:gdim} The spline model above is an example of the general parametric form (Equation \ref{eq:model}), but the number of parameters, $R+1$ in Equation \ref{eq:model}, $m+2$ in Equation \ref{eq:spline}, is arbitrary. \pkg{flexsurv} has the tools to deal with any model of this form. \code{flexsurvspline} works internally by building a custom distribution and then calling \code{flexsurvreg}. Similar models may in principle be built by users using the same method. This relies on a functional programming trick. \paragraph{Creating distribution functions dynamically} The \proglang{R} distribution functions supplied to custom models are expected to have a fixed number of arguments, including one for each scalar parameter. However, the distribution functions for the spline model (e.g., \code{dsurvspline}) have an argument \code{gamma} representing the \emph{vector} of parameters $\gamma$, whose length is determined by choosing the number of knots. Just as the \emph{scalar parameters} of conventional distribution functions can be supplied as \emph{vector arguments} (as explained in \S\ref{sec:custom}), similarly, the vector parameters of spline-like distribution functions can be supplied as \emph{matrix arguments}, representing alternative parameter values. To convert a spline-like distribution function into the correct form, \pkg{flexsurv} provides the utility \code{unroll.function}. This converts a function with one (or more) vector parameters (matrix arguments) to a function with an arbitrary number of scalar parameters (vector arguments). For example, the 5-year survival probability for the baseline group under the model \code{sp1} is <<>>= gamma <- sp1$res[c("gamma0", "gamma1", "gamma2"), "est"] 1 - psurvspline(5, gamma = gamma, knots = sp1$knots) @ An alternative function to compute this can be built by \code{unroll.function}. We tell it that the vector parameter \code{gamma} should be provided instead as three scalar parameters named \code{gamma0}, \code{gamma1}, \code{gamma2}. The resulting function \code{pfn} is in the correct form for a custom \code{flexsurvreg} distribution. <<>>= pfn <- unroll.function(psurvspline, gamma = 0:2) 1 - pfn(5, gamma0 = gamma[1], gamma1 = gamma[2], gamma2 = gamma[3], knots = sp1$knots) @ Users wishing to fit a new spline-like model with a known number of parameters could just as easily write distribution functions specific to that number of parameters, and use the methods in \S\ref{sec:custom}. However the \code{unroll.function} method is intended to simplify the process of extending the \pkg{flexsurv} package to implement new model families, through wrappers similar to \code{flexsurvspline}. \paragraph{Example: splines on alternative scales} An alternative to the Royston-Parmar spline model is to model the log \emph{hazard} as a spline function of (log) time instead of the log cumulative hazard. \citet{stgenreg} demonstrate this model using the \proglang{Stata} \pkg{stgenreg} package. An advantage explained by \citet{royston:lambert:book} is that when there are multiple time-dependent effects, time-dependent hazard ratios can be interpreted independently of the values of other covariates. This can also be implemented in \code{flexsurvreg} using \code{unroll.function}. A disadvantage of this model is that the cumulative hazard (hence the survivor function) has no analytic form, therefore to compute the likelihood, the hazard function needs to be integrated numerically. This is done automatically in \code{flexsurvreg} (just as in \pkg{stgenreg}) if the cumulative hazard is not supplied. Firstly, a function must be written to compute the hazard as a function of time \code{x}, the vector of parameters \code{gamma} (which can be supplied as a matrix argument so the function can give a vector of results), and a vector of knot locations. This uses \pkg{flexsurv}'s function \code{basis} to compute the natural cubic spline basis (Equation \ref{eq:spline}), and replicates \code{x} and \code{gamma} to the length of the longest one. <<>>= hsurvspline.lh <- function(x, gamma, knots){ if(!is.matrix(gamma)) gamma <- matrix(gamma, nrow = 1) lg <- nrow(gamma) nret <- max(length(x), lg) gamma <- apply(gamma, 2, function(x)rep(x, length = nret)) x <- rep(x, length = nret) loghaz <- rowSums(basis(knots, log(x)) * gamma) exp(loghaz) } @ The equivalent function is then created for a three-knot example of this model (one internal and two boundary knots) that has arguments \code{gamma0}, \code{gamma1} and \code{gamma2} corresponding to the three columns of \code{gamma}, <<>>= hsurvspline.lh3 <- unroll.function(hsurvspline.lh, gamma = 0:2) @ To complete the model, the custom distribution list is formed, the internal knot is placed at the median uncensored log survival time, and the boundary knots are placed at the minimum and maximum. These are passed to \code{hsurvspline.lh} through the \code{aux} argument of \code{flexsurvreg}. <<>>= custom.hsurvspline.lh3 <- list( name = "survspline.lh3", pars = c("gamma0", "gamma1", "gamma2"), location = c("gamma0"), transforms = rep(c(identity), 3), inv.transforms = rep(c(identity), 3) ) dtime <- log(bc$recyrs)[bc$censrec == 1] ak <- list(knots = quantile(dtime, c(0, 0.5, 1))) @ Initial values must be provided in the call to \code{flexsurvreg}, since the custom distribution list did not include an \code{inits} component. For this example, ``default'' initial values of zero suffice, but the permitted values of $\gamma_2$ are fairly tightly constrained (from -0.5 to 0.5 here) using the \code{"L-BFGS-B"} bounded optimiser from \proglang{R}'s \code{optim} \citep{nash}. Without the constraint, extreme values of $\gamma_2$, visited by the optimiser, cause the numerical integration of the hazard function to fail. <>= sp5 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, aux = ak, inits = c(0, 0, 0, 0, 0), dist = custom.hsurvspline.lh3, method = "L-BFGS-B", lower = c(-Inf, -Inf, -0.5), upper = c(Inf, Inf, 0.5), control = list(trace = 1, REPORT = 1)) @ This takes around ten minutes to converge, so is not presented here, though the fit is poorer than the equivalent spline model for the cumulative hazard. The 95\% confidence interval for $\gamma_2$ of (0.16, 0.37) is firmly within the constraint. \citet{crowther:general} present a combined analytic / numerical integration method for this model that may make fitting it more stable. \paragraph{Other arbitrary-dimension models} Another potential application is to fractional polynomials \citep{royston1994regression}. These are of the form $\sum_{m=1}^M \alpha_m x^{p_m} \log(x)^n$ where the power $p_m$ is in the standard set $\{2,-1,-0.5,0,0.5,1,2,3\}$ (except that $\log(x)$ is used instead of $x^0$), and $n$ is a non-negative integer. They are similar to splines in that they can give arbitrarily close approximations to a nonlinear function, such as a hazard curve, and are particularly useful for expressing the effects of continuous predictors in regression models. See e.g., \citet{sauerbrei2007selection}, and several other publications by the same authors, for applications and discussion of their advantages over splines. The \proglang{R} package \pkg{gamlss} \citep{gamlss} has a function to construct a fractional polynomial basis that might be employed in \pkg{flexsurv} models. Polyhazard models \citep{polyhazard} are another potential use of this technique. These express an overall hazard as a sum of latent cause-specific hazards, each one typically from the same class of distribution, e.g., a \emph{poly-Weibull} model if they are all Weibull. For example, a U-shaped hazard curve following surgery may be the sum of early hazards from surgical mortality and later deaths from natural causes. However, such models may not always be identifiable without external information to fix or constrain the parameters of particular hazards \citep{demiris2011survival}. \section{Multi-state models} \label{sec:multistate} A \emph{multi-state model} represents how an individual moves between multiple states in continuous time. Survival analysis is a special case with two states, ``alive'' and ``dead''. \emph{Competing risks} are a further special case, where there are multiple causes of death, that is, one starting state and multiple possible destination states. Multi-state modelling with \pkg{flexsurv} was previously described in this section of the current vignette. Version 2.0 of \pkg{flexsurv} added several new features for multi-state modelling, including multi-state modelling using mixtures, and transition-specific distribution families in cause-specific hazards models. These models are now fully described in a separate \pkg{flexsurv} vignette, ``Flexible parametric multi-state modelling with the flexsurv package''. \section{Potential extensions} \label{sec:extensions} Multi-state modelling is still an area of ongoing work, and while version 2.0 extended \pkg{flexsurv} in this area, more tools and documentation in this area would still be useful. The \pkg{msm} package arguably has a more accessible interface for fitting and summarising multi-state models, but it was designed mainly for panel data rather than event time data, and therefore the event time distributions it fits are relatively inflexible. Models where multiple survival times are assumed to be correlated within groups, sometimes called (shared) frailty models \citep{hougaard1995frailty}, would also be a useful development. See, e.g., \citet{crowther2014multilevel} for a recent application based on parametric models. These might be implemented by exploiting tractability for specific distributions, such as gamma frailties, or by adjusting standard errors to account for clustering, as implemented in \code{survreg}. More complex random effects models would require numerical integration, for example, \citet{crowther2014multilevel} provide \proglang{Stata} software based on Gauss-Hermite quadrature. Alternatively, a probabilistic modelling language such as \proglang{Stan} \citep{stan-manual:2014} or \proglang{BUGS} \citep{bugs:book} would be naturally suited to complex extensions such as random effects on multiple parameters or multiple hierarchical levels. \pkg{flexsurv} is intended as a platform for parametric survival modelling. Extensions of the software to deal with different models may be written by users themselves, through the facilities described in \S\ref{sec:custom} and \S\ref{sec:gdim}. These might then be included in the package as built-in distributions, or at least demonstrated in the package's other vignette \code{flexsurv-examples}. Each new class of models would ideally come with \begin{itemize} \item guidance on what situations the model is useful for, e.g., what shape of hazards it can represent \item some intuitive interpretation of the model parameters, their plausible values in typical situations, and potential identifiability problems. This would also help with choosing initial values for numerical maximum likelihood estimation, ideally through an \code{inits} function in the custom distribution list (\S\ref{sec:custom}). \end{itemize} \pkg{flexsurv} is available from \url{http://CRAN.R-project.org/package=flexsurv}. Development versions are available on \url{https://github.com/chjackson/flexsurv-dev}, and contributions are welcome. \section*{Acknowledgements} Thanks to Milan Bouchet-Valat for help with implementing covariates on ancillary parameters, Andrea Manca for motivating the development of the package, the reviewers of the paper, and all users who have reported bugs and given suggestions. \bibliography{flexsurv} \end{document} flexsurv/data/0000755000176200001440000000000014045250755013050 5ustar liggesusersflexsurv/data/bc.txt0000644000176200001440000003266313231112051014165 0ustar liggesusers"censrec" "rectime" "group" "1" 0 1342 "Good" "2" 0 1578 "Good" "3" 0 1760 "Good" "4" 0 1152 "Good" "5" 0 967 "Good" "6" 0 629 "Good" "7" 0 461 "Good" "8" 1 991 "Good" "9" 0 758 "Good" "10" 0 1617 "Good" "11" 0 1767 "Good" "12" 0 432 "Good" "13" 0 892 "Good" "14" 0 1933 "Good" "15" 0 2456 "Good" "16" 0 553 "Good" "17" 0 1833 "Good" "18" 0 1624 "Good" "19" 0 1222 "Good" "20" 0 1499 "Good" "21" 1 755 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liggesusersflexsurv/src/RcppExports.cpp0000644000176200001440000003077114501417340015723 0ustar liggesusers// Generated by using Rcpp::compileAttributes() -> do not edit by hand // Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393 #include using namespace Rcpp; #ifdef RCPP_USE_GLOBAL_ROSTREAM Rcpp::Rostream& Rcpp::Rcout = Rcpp::Rcpp_cout_get(); Rcpp::Rostream& Rcpp::Rcerr = Rcpp::Rcpp_cerr_get(); #endif // dgenf_work Rcpp::NumericVector dgenf_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const Rcpp::NumericVector& P, const bool log); RcppExport SEXP _flexsurv_dgenf_work(SEXP xSEXP, SEXP muSEXP, SEXP sigmaSEXP, SEXP QSEXP, SEXP PSEXP, SEXP logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type mu(muSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type Q(QSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type P(PSEXP); Rcpp::traits::input_parameter< const bool >::type log(logSEXP); rcpp_result_gen = Rcpp::wrap(dgenf_work(x, mu, sigma, Q, P, log)); return rcpp_result_gen; END_RCPP } // pgenf_work Rcpp::NumericVector pgenf_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const Rcpp::NumericVector& P, const bool lower_tail, const bool give_log); RcppExport SEXP _flexsurv_pgenf_work(SEXP qSEXP, SEXP muSEXP, SEXP sigmaSEXP, SEXP QSEXP, SEXP PSEXP, SEXP lower_tailSEXP, SEXP give_logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type q(qSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type mu(muSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type Q(QSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type P(PSEXP); Rcpp::traits::input_parameter< const bool >::type lower_tail(lower_tailSEXP); Rcpp::traits::input_parameter< const bool >::type give_log(give_logSEXP); rcpp_result_gen = Rcpp::wrap(pgenf_work(q, mu, sigma, Q, P, lower_tail, give_log)); return rcpp_result_gen; END_RCPP } // check_genf Rcpp::LogicalVector check_genf(const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const Rcpp::NumericVector& P); RcppExport SEXP _flexsurv_check_genf(SEXP muSEXP, SEXP sigmaSEXP, SEXP QSEXP, SEXP PSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type mu(muSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type Q(QSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type P(PSEXP); rcpp_result_gen = Rcpp::wrap(check_genf(mu, sigma, Q, P)); return rcpp_result_gen; END_RCPP } // dgengamma_work Rcpp::NumericVector dgengamma_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const bool log); RcppExport SEXP _flexsurv_dgengamma_work(SEXP xSEXP, SEXP muSEXP, SEXP sigmaSEXP, SEXP QSEXP, SEXP logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type mu(muSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type Q(QSEXP); Rcpp::traits::input_parameter< const bool >::type log(logSEXP); rcpp_result_gen = Rcpp::wrap(dgengamma_work(x, mu, sigma, Q, log)); return rcpp_result_gen; END_RCPP } // pgengamma_work Rcpp::NumericVector pgengamma_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const bool lower_tail, const bool give_log); RcppExport SEXP _flexsurv_pgengamma_work(SEXP qSEXP, SEXP muSEXP, SEXP sigmaSEXP, SEXP QSEXP, SEXP lower_tailSEXP, SEXP give_logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type q(qSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type mu(muSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type Q(QSEXP); Rcpp::traits::input_parameter< const bool >::type lower_tail(lower_tailSEXP); Rcpp::traits::input_parameter< const bool >::type give_log(give_logSEXP); rcpp_result_gen = Rcpp::wrap(pgengamma_work(q, mu, sigma, Q, lower_tail, give_log)); return rcpp_result_gen; END_RCPP } // check_gengamma Rcpp::LogicalVector check_gengamma(const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q); RcppExport SEXP _flexsurv_check_gengamma(SEXP muSEXP, SEXP sigmaSEXP, SEXP QSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type mu(muSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type Q(QSEXP); rcpp_result_gen = Rcpp::wrap(check_gengamma(mu, sigma, Q)); return rcpp_result_gen; END_RCPP } // dgompertz_work Rcpp::NumericVector dgompertz_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& rate, const bool log); RcppExport SEXP _flexsurv_dgompertz_work(SEXP xSEXP, SEXP shapeSEXP, SEXP rateSEXP, SEXP logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type shape(shapeSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type rate(rateSEXP); Rcpp::traits::input_parameter< const bool >::type log(logSEXP); rcpp_result_gen = Rcpp::wrap(dgompertz_work(x, shape, rate, log)); return rcpp_result_gen; END_RCPP } // pgompertz_work Rcpp::NumericVector pgompertz_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& rate, const bool lower_tail, const bool give_log); RcppExport SEXP _flexsurv_pgompertz_work(SEXP qSEXP, SEXP shapeSEXP, SEXP rateSEXP, SEXP lower_tailSEXP, SEXP give_logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type q(qSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type shape(shapeSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type rate(rateSEXP); Rcpp::traits::input_parameter< const bool >::type lower_tail(lower_tailSEXP); Rcpp::traits::input_parameter< const bool >::type give_log(give_logSEXP); rcpp_result_gen = Rcpp::wrap(pgompertz_work(q, shape, rate, lower_tail, give_log)); return rcpp_result_gen; END_RCPP } // check_gompertz Rcpp::LogicalVector check_gompertz(const Rcpp::NumericVector& shape, const Rcpp::NumericVector& rate); RcppExport SEXP _flexsurv_check_gompertz(SEXP shapeSEXP, SEXP rateSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type shape(shapeSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type rate(rateSEXP); rcpp_result_gen = Rcpp::wrap(check_gompertz(shape, rate)); return rcpp_result_gen; END_RCPP } // dllogis_work Rcpp::NumericVector dllogis_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& scale, const bool log); RcppExport SEXP _flexsurv_dllogis_work(SEXP xSEXP, SEXP shapeSEXP, SEXP scaleSEXP, SEXP logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type shape(shapeSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type scale(scaleSEXP); Rcpp::traits::input_parameter< const bool >::type log(logSEXP); rcpp_result_gen = Rcpp::wrap(dllogis_work(x, shape, scale, log)); return rcpp_result_gen; END_RCPP } // pllogis_work Rcpp::NumericVector pllogis_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& scale, const bool lower_tail, const bool give_log); RcppExport SEXP _flexsurv_pllogis_work(SEXP qSEXP, SEXP shapeSEXP, SEXP scaleSEXP, SEXP lower_tailSEXP, SEXP give_logSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type q(qSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type shape(shapeSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type scale(scaleSEXP); Rcpp::traits::input_parameter< const bool >::type lower_tail(lower_tailSEXP); Rcpp::traits::input_parameter< const bool >::type give_log(give_logSEXP); rcpp_result_gen = Rcpp::wrap(pllogis_work(q, shape, scale, lower_tail, give_log)); return rcpp_result_gen; END_RCPP } // check_llogis Rcpp::LogicalVector check_llogis(const Rcpp::NumericVector& shape, const Rcpp::NumericVector& scale); RcppExport SEXP _flexsurv_check_llogis(SEXP shapeSEXP, SEXP scaleSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type shape(shapeSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type scale(scaleSEXP); rcpp_result_gen = Rcpp::wrap(check_llogis(shape, scale)); return rcpp_result_gen; END_RCPP } // exph Rcpp::NumericVector exph(const Rcpp::NumericVector& y); RcppExport SEXP _flexsurv_exph(SEXP ySEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type y(ySEXP); rcpp_result_gen = Rcpp::wrap(exph(y)); return rcpp_result_gen; END_RCPP } // dexph Rcpp::NumericVector dexph(const Rcpp::NumericVector& y); RcppExport SEXP _flexsurv_dexph(SEXP ySEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type y(ySEXP); rcpp_result_gen = Rcpp::wrap(dexph(y)); return rcpp_result_gen; END_RCPP } // basis_vector Rcpp::NumericVector basis_vector(const Rcpp::NumericVector& knots, const Rcpp::NumericVector& x); RcppExport SEXP _flexsurv_basis_vector(SEXP knotsSEXP, SEXP xSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type knots(knotsSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); rcpp_result_gen = Rcpp::wrap(basis_vector(knots, x)); return rcpp_result_gen; END_RCPP } // basis_matrix Rcpp::NumericMatrix basis_matrix(const Rcpp::NumericMatrix& knots, const Rcpp::NumericVector& x); RcppExport SEXP _flexsurv_basis_matrix(SEXP knotsSEXP, SEXP xSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< const Rcpp::NumericMatrix& >::type knots(knotsSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); rcpp_result_gen = Rcpp::wrap(basis_matrix(knots, x)); return rcpp_result_gen; END_RCPP } // dbasis_vector Rcpp::NumericVector dbasis_vector(const Rcpp::NumericVector& knots, const Rcpp::NumericVector& x); RcppExport SEXP _flexsurv_dbasis_vector(SEXP knotsSEXP, SEXP xSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type knots(knotsSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); rcpp_result_gen = Rcpp::wrap(dbasis_vector(knots, x)); return rcpp_result_gen; END_RCPP } // dbasis_matrix Rcpp::NumericMatrix dbasis_matrix(const Rcpp::NumericMatrix& knots, const Rcpp::NumericVector& x); RcppExport SEXP _flexsurv_dbasis_matrix(SEXP knotsSEXP, SEXP xSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< const Rcpp::NumericMatrix& >::type knots(knotsSEXP); Rcpp::traits::input_parameter< const Rcpp::NumericVector& >::type x(xSEXP); rcpp_result_gen = Rcpp::wrap(dbasis_matrix(knots, x)); return rcpp_result_gen; END_RCPP } flexsurv/src/splines.cpp0000644000176200001440000000705113231112051015070 0ustar liggesusers#include #include namespace { inline double cuber(const double x) { if (x <= 0) { return 0; } else { return x * x * x; } } inline double dCuber(const double x) { if (x <= 0) { return 0; } else { return 3 * x * x; } } } // [[Rcpp::export]] Rcpp::NumericVector basis_vector(const Rcpp::NumericVector& knots, const Rcpp::NumericVector& x) { if (knots.size() < 2) { throw std::runtime_error("Bad knots."); } Rcpp::NumericMatrix result(x.size(), knots.size()); result(Rcpp::_, 0) = Rcpp::rep(1, x.size()); result(Rcpp::_, 1) = x; for (R_xlen_t ind=0; ind < knots.size() - 2; ++ind) { const double last = *(knots.end() - 1); const double first = *(knots.begin()); const double lam = (last - knots[ind + 1]) / (last - first); result(Rcpp::_, ind + 2) = Rcpp::sapply(x - knots[ind + 1], cuber) - lam * Rcpp::sapply(x - first, cuber) - (1 - lam) * Rcpp::sapply(x - last, cuber); } return result; } // [[Rcpp::export]] Rcpp::NumericMatrix basis_matrix(const Rcpp::NumericMatrix& knots, const Rcpp::NumericVector& x) { if (knots.ncol() < 2) { throw std::runtime_error("Bad knots."); } if (knots.nrow() != x.size()) { throw std::runtime_error("Mismatch between knots and points"); } Rcpp::NumericMatrix result(x.size(), knots.ncol()); result(Rcpp::_, 0) = Rcpp::rep(1, x.size()); result(Rcpp::_, 1) = x; for (R_xlen_t ind_r=0; ind_r < result.nrow(); ++ind_r) { for (R_xlen_t ind=0; ind < knots.ncol() - 2;++ind) { const double last = knots(ind_r, knots.ncol() - 1); const double first = knots(ind_r, 0); const double lam = (last - knots(ind_r, ind + 1)) / (last - first); result(ind_r, ind + 2) = cuber(x[ind_r] - knots(ind_r, ind + 1)) - lam * cuber(x[ind_r] - first) - (1 - lam) * cuber(x[ind_r] - last); } } return result; } // [[Rcpp::export]] Rcpp::NumericVector dbasis_vector(const Rcpp::NumericVector& knots, const Rcpp::NumericVector& x) { if (knots.size() < 2) { throw std::runtime_error("Bad knots."); } Rcpp::NumericMatrix result(x.size(), knots.size()); result(Rcpp::_, 0) = Rcpp::rep(0, x.size()); result(Rcpp::_, 1) = Rcpp::rep(1, x.size()); for (R_xlen_t ind=0; ind < knots.size() - 2; ++ind) { const double last = *(knots.end() - 1); const double first = *(knots.begin()); const double lam = (last - knots[ind + 1]) / (last - first); result(Rcpp::_, ind + 2) = Rcpp::sapply(x - knots[ind + 1], dCuber) - lam * Rcpp::sapply(x - first, dCuber) - (1 - lam) * Rcpp::sapply(x - last, dCuber); } return result; } // [[Rcpp::export]] Rcpp::NumericMatrix dbasis_matrix(const Rcpp::NumericMatrix& knots, const Rcpp::NumericVector& x) { if (knots.ncol() < 2) { throw std::runtime_error("Bad knots."); } if (knots.nrow() != x.size()) { throw std::runtime_error("Mismatch between knots and points"); } Rcpp::NumericMatrix result(x.size(), knots.ncol()); result(Rcpp::_, 0) = Rcpp::rep(0, x.size()); result(Rcpp::_, 1) = Rcpp::rep(1, x.size()); for (R_xlen_t ind_r=0; ind_r < result.nrow(); ++ind_r) { for (R_xlen_t ind=0; ind < knots.ncol() - 2;++ind) { const double last = knots(ind_r, knots.ncol() - 1); const double first = knots(ind_r, 0); const double lam = (last - knots(ind_r, ind + 1)) / (last - first); result(ind_r, ind + 2) = dCuber(x[ind_r] - knots(ind_r, ind + 1)) - lam * dCuber(x[ind_r] - first) - (1 - lam) * dCuber(x[ind_r] - last); } } return result; } flexsurv/src/genf.cpp0000644000176200001440000001114213560603030014335 0ustar liggesusers#include #include #include "distribution.h" #include "rep_len.h" #include "gengamma.h" #include "mapply.h" namespace { namespace genf { inline bool bad(const double mu, const double sigma, const double Q, const double P) { bool res = false; if (sigma < 0) { Rcpp::warning("Negative scale parameter ""sigma"""); res = true; } if (P < 0) { Rcpp::warning("Negative shape parameter ""P"""); res = true; } return res; } class density { public: typedef double result_type; inline double operator()(const double x, const double mu, const double sigma, const double Q, const double P) const { /* check the parameters */ if (bad(mu, sigma, Q, P)) { return NA_REAL; }; if (x < 0) { return R_NegInf; } if (P==0) { return gengamma::density()(x, mu, sigma, Q); } const double tmp = Q * Q + 2 * P; const double delta = std::sqrt(tmp); const double s1 = 2 / (tmp + Q*delta); const double s2 = 2 / (tmp - Q*delta); const double expw = std::pow(x, delta/sigma) * std::exp(-mu*delta/sigma); return std::log(delta) + s1/sigma*delta*(std::log(x) - mu) + s1*(std::log(s1) - std::log(s2)) - std::log(sigma*x) - (s1+s2)*std::log(1 + s1*expw/s2) - R::lbeta(s1, s2); } }; class cdf { public: typedef double result_type; cdf(bool lower_tail_, bool give_log_) : lower_tail(lower_tail_), give_log(give_log_) {} inline double operator()(const double q, const double mu, const double sigma, const double Q, const double P) const { if (bad(mu, sigma, Q, P)) { return NA_REAL; } if ( q < 0 ) { return below_distribution(lower_tail, give_log); } if (P==0) { return gengamma::cdf(lower_tail, give_log)(q, mu, sigma, Q); } const double tmp = Q * Q + 2*P; const double delta = std::sqrt(tmp); const double s1 = 2 / (tmp + Q*delta); const double s2 = 2 / (tmp - Q*delta); const double expw = std::pow(q, delta/sigma) * std::exp(-mu*delta/sigma); const double qb = s2/(s2 + s1*expw); // two alternative constructions to avoid underflow if (qb > 0.99){ const double qb2 = s1*expw/(s2 + s1*expw); return R::pbeta(qb2, s1, s2, lower_tail, give_log); } else { return R::pbeta(qb, s2, s1, !lower_tail, give_log); } } private: bool lower_tail; bool give_log; }; } } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector dgenf_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const Rcpp::NumericVector& P, const bool log) { if (x.size() == 0) { return x; } const R_xlen_t size = std::max(P.size(), std::max(std::max(sigma.size(), Q.size()), std::max(x.size(), mu.size()))); return perhaps_exp(mapply(flexsurv::rep_len(x, size), flexsurv::rep_len(mu, size), flexsurv::rep_len(sigma, size), flexsurv::rep_len(Q, size), flexsurv::rep_len(P, size), genf::density()), log); } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector pgenf_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const Rcpp::NumericVector& P, const bool lower_tail, const bool give_log) { if (q.size() == 0) { return q; } const R_xlen_t size = std::max(P.size(), std::max(std::max(sigma.size(), Q.size()), std::max(q.size(), mu.size()))); return mapply(flexsurv::rep_len(q, size), flexsurv::rep_len(mu, size), flexsurv::rep_len(sigma, size), flexsurv::rep_len(Q, size), flexsurv::rep_len(P, size), genf::cdf(lower_tail, give_log)); } namespace Rcpp { namespace traits { template struct result_of< RESULT_TYPE (*)(U1, U2, U3, U4) >{ typedef RESULT_TYPE type ; } ; } } // [[Rcpp::export(name="check.genf", rng=false)]] Rcpp::LogicalVector check_genf(const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const Rcpp::NumericVector& P) { if ( (0==mu.size()) && (0==sigma.size()) && (0==Q.size()) && (0==P.size()) ) { Rcpp::LogicalVector null_result(0); return null_result; } const R_xlen_t size = mu.size(); return !mapply(mu, flexsurv::rep_len(sigma, size), flexsurv::rep_len(Q, size), flexsurv::rep_len(P, size), genf::bad); } flexsurv/src/llogis.cpp0000644000176200001440000000573713231112051014715 0ustar liggesusers#include #include #include "distribution.h" #include "rep_len.h" namespace { namespace llogis { inline bool bad(const double shape, const double scale) { const bool bad = (shape<=0) || (scale <= 0); if (shape < 0) { Rcpp::warning("Non-positive shape parameter"); } if (scale < 0) { Rcpp::warning("Non-positive scale parameter"); } return bad; } class density { public: typedef double result_type; inline double operator()(const double x, const double shape, const double scale) const { /* check the parameters */ if (bad(shape, scale)) { return NA_REAL; }; if (x < 0) { return R_NegInf; } const double log_shape = std::log(shape); const double log_scale = std::log(scale); return log_shape - log_scale + (shape - 1) * (std::log(x) - log_scale) - 2 * std::log(1 + std::pow(x/scale, shape)); } }; class cdf { public: typedef double result_type; cdf(bool lower_tail_, bool give_log_) : lower_tail(lower_tail_), give_log(give_log_) {} inline double operator()(const double q, const double shape, const double scale) const { /* check the arguments */ if (bad(shape, scale)) { return NA_REAL; } if ( q < 0 ) { return below_distribution(lower_tail, give_log); } return R::plogis(std::log(q), std::log(scale), 1/shape, lower_tail, give_log); } private: bool lower_tail; bool give_log; }; } } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector dllogis_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& scale, const bool log) { if (x.size() == 0) { return x; } const R_xlen_t size = std::max(x.size(), std::max(shape.size(), scale.size())); return perhaps_exp(Rcpp::mapply(flexsurv::rep_len(x, size), flexsurv::rep_len(shape, size), flexsurv::rep_len(scale, size), llogis::density()), log); } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector pllogis_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& scale, const bool lower_tail, const bool give_log) { if (q.size() == 0) { return q; } const R_xlen_t size = std::max(q.size(), std::max(shape.size(), scale.size())); return mapply(flexsurv::rep_len(q, size), flexsurv::rep_len(shape, size), flexsurv::rep_len(scale, size), llogis::cdf(lower_tail, give_log)); } // [[Rcpp::export(name="check.llogis", rng=false)]] Rcpp::LogicalVector check_llogis(const Rcpp::NumericVector& shape, const Rcpp::NumericVector& scale) { if ( (0==shape.size()) && (0==scale.size()) ) { Rcpp::LogicalVector null_result(0); return null_result; } const R_xlen_t size = shape.size(); return !Rcpp::mapply(shape, flexsurv::rep_len(scale, size), llogis::bad); } flexsurv/src/mapply.h0000644000176200001440000000012713231112051014357 0ustar liggesusers#ifndef MAPPLY_H #define MAPPLY_H #include "mapply_4.h" #include "mapply_5.h" #endif flexsurv/src/rep_len.h0000644000176200001440000000062613231112051014505 0ustar liggesusers#ifndef REPLEN_H #define REPLEN_H #include namespace { namespace flexsurv { template inline Rcpp::sugar::Rep_len rep_len(const Rcpp::VectorBase& t, R_xlen_t len ){ if (t.size() == 0) { Rcpp::stop("zero length vector provided"); } else { return Rcpp::rep_len(t, len); } } } } #endif flexsurv/src/gengamma.cpp0000644000176200001440000000344313231112051015170 0ustar liggesusers#include #include "distribution.h" #include "rep_len.h" #include "gengamma.h" #include "mapply.h" // [[Rcpp::export(rng=false)]] Rcpp::NumericVector dgengamma_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const bool log) { if (x.size() == 0) { return x; } const R_xlen_t size = std::max(std::max(sigma.size(), Q.size()), std::max(x.size(), mu.size())); return perhaps_exp(mapply(flexsurv::rep_len(x, size), flexsurv::rep_len(mu, size), flexsurv::rep_len(sigma, size), flexsurv::rep_len(Q, size), gengamma::density()), log); } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector pgengamma_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q, const bool lower_tail, const bool give_log) { if (q.size() == 0) { return q; } const R_xlen_t size = std::max(std::max(sigma.size(), Q.size()), std::max(q.size(), mu.size())); return mapply(flexsurv::rep_len(q, size), flexsurv::rep_len(mu, size), flexsurv::rep_len(sigma, size), flexsurv::rep_len(Q, size), gengamma::cdf(lower_tail, give_log)); } // [[Rcpp::export(name="check.gengamma", rng=false)]] Rcpp::LogicalVector check_gengamma(const Rcpp::NumericVector& mu, const Rcpp::NumericVector& sigma, const Rcpp::NumericVector& Q) { if ( (0==mu.size()) && (0==sigma.size()) && (0==Q.size()) ) { Rcpp::LogicalVector null_result(0); return null_result; } const R_xlen_t size = mu.size(); return !Rcpp::mapply(mu, flexsurv::rep_len(sigma, size), flexsurv::rep_len(Q, size), gengamma::bad); } flexsurv/src/distribution.h0000644000176200001440000000075114260613663015621 0ustar liggesusers#ifndef DISTRIBUTION_H #define DISTRIBUTION_H #include namespace { inline double below_distribution(bool lower_tail, bool give_log) { if (lower_tail) { if (give_log) {return R_NegInf;} else {return 0;} } else { if (give_log) {return 0;} else {return 1;} } } template inline Rcpp::NumericVector perhaps_exp(const T1& y, bool log) { if (log) { return y; } else { return Rcpp::exp(y); } } } #endif flexsurv/src/special.cpp0000644000176200001440000000164013231112051015031 0ustar liggesusers#include #include namespace { inline double restrict_hypot(double x) { if (std::isnan(x)) { return x; } x = std::abs(x); if (x > 1) { const double inv = 1/x; return std::sqrt(1 + inv * inv) * x; } else { return std::sqrt(1 + x * x); } } inline double dexph_work(const double x) { if (std::isnan(x)) { return x; } if (x >= 0) { return 1 + x/restrict_hypot(x); } else { const double h = restrict_hypot(x); return -1 / h / (x - h); } } } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector exph(const Rcpp::NumericVector& y) { // exp(asinh(x)) return Rcpp::ifelse(y >= 0, y + Rcpp::sapply(y, restrict_hypot), -1/(y - Rcpp::sapply(y, restrict_hypot))); } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector dexph(const Rcpp::NumericVector& y) { return Rcpp::sapply(y, dexph_work); } flexsurv/src/mapply_5.h0000644000176200001440000000561713231112051014614 0ustar liggesusers#ifndef MAPPLY_5 #define MAPPLY_5 #include namespace { namespace flexsurv { template < int RTYPE_1, bool NA_1, typename T_1, int RTYPE_2, bool NA_2, typename T_2, int RTYPE_3, bool NA_3, typename T_3, int RTYPE_4, bool NA_4, typename T_4, int RTYPE_5, bool NA_5, typename T_5, typename Function > class Mapply_5 : public Rcpp::VectorBase< Rcpp::traits::r_sexptype_traits< typename ::Rcpp::traits::result_of::type >::rtype , true , Mapply_5 > { public: typedef typename ::Rcpp::traits::result_of::type result_type ; typedef Rcpp::VectorBase VEC_1 ; typedef Rcpp::VectorBase VEC_2 ; typedef Rcpp::VectorBase VEC_3 ; typedef Rcpp::VectorBase VEC_4 ; typedef Rcpp::VectorBase VEC_5 ; typedef typename Rcpp::traits::Extractor::type EXT_1 ; typedef typename Rcpp::traits::Extractor::type EXT_2 ; typedef typename Rcpp::traits::Extractor::type EXT_3 ; typedef typename Rcpp::traits::Extractor::type EXT_4 ; typedef typename Rcpp::traits::Extractor::type EXT_5 ; Mapply_5(const VEC_1& vec_1_, const VEC_2& vec_2_, const VEC_3& vec_3_, const VEC_4& vec_4_, const VEC_5& vec_5_, Function fun_ ) : vec_1(vec_1_.get_ref()), vec_2(vec_2_.get_ref()), vec_3(vec_3_.get_ref()), vec_4(vec_4_.get_ref()), vec_5(vec_5_.get_ref()), fun(fun_){} inline result_type operator[]( R_xlen_t i ) const { return fun(vec_1[i], vec_2[i], vec_3[i], vec_4[i], vec_5[i]); } inline R_xlen_t size() const { return vec_1.size() ; } private: const EXT_1& vec_1 ; const EXT_2& vec_2 ; const EXT_3& vec_3 ; const EXT_4& vec_4 ; const EXT_5& vec_5 ; Function fun ; } ; } template < int RTYPE_1, bool NA_1, typename T_1, int RTYPE_2, bool NA_2, typename T_2, int RTYPE_3, bool NA_3, typename T_3, int RTYPE_4, bool NA_4, typename T_4, int RTYPE_5, bool NA_5, typename T_5, typename Function> inline flexsurv::Mapply_5 mapply( const Rcpp::VectorBase& t1, const Rcpp::VectorBase& t2, const Rcpp::VectorBase& t3, const Rcpp::VectorBase& t4, const Rcpp::VectorBase& t5, Function fun ){ return flexsurv::Mapply_5( t1, t2, t3, t4, t5, fun ) ; } } #endif flexsurv/src/gengamma.h0000644000176200001440000000412313231112051014631 0ustar liggesusers#ifndef GENGAMMA_H #define GENGAMMA_H #include #include #include "distribution.h" namespace { namespace gengamma { inline bool bad(const double mu, const double sigma, const double Q) { if (sigma < 0) { Rcpp::warning("Negative scale parameter \"sigma\""); return true; } return false; } class density { public: typedef double result_type; inline double operator()(const double x, const double mu, const double sigma, const double Q) const { /* check the parameters */ if (bad(mu, sigma, Q)) { return NA_REAL; }; if (x < 0) { return R_NegInf; } /* this function relies on interesting levels of cancellation if Q is small or x is small */ if (Q!=0) { const double y = std::log(x); const double w = (y - mu) / sigma; const double abs_q = std::abs(Q); const double qi = 1/(Q * Q); const double qw = Q * w; return -std::log(sigma*x) + std::log(abs_q) * (1 - 2 * qi) + qi * (qw - std::exp(qw)) - R::lgammafn(qi); } else { return R::dlnorm(x, mu, sigma, 1); } } }; class cdf { public: typedef double result_type; cdf(bool lower_tail_, bool give_log_) : lower_tail(lower_tail_), give_log(give_log_) {} inline double operator()(const double q, const double mu, const double sigma, const double big_q) const { /* check the arguments */ if (bad(mu, sigma, big_q)) { return NA_REAL; } if ( q < 0 ) { return below_distribution(lower_tail, give_log); } if (big_q!=0) { const double y = std::log(q); const double w = (y - mu) / sigma; const double qq = 1/(big_q * big_q); const double expnu = std::exp(big_q * w) * qq; if (big_q > 0) { return R::pgamma(expnu, qq, 1, lower_tail, give_log); } else { return R::pgamma(expnu, qq, 1, !lower_tail, give_log); } } else { return R::plnorm(q, mu, sigma, lower_tail, give_log); } } private: bool lower_tail; bool give_log; }; } } #endif flexsurv/src/mapply_4.h0000644000176200001440000000476513231112051014616 0ustar liggesusers #ifndef MAPPLY_4 #define MAPPLY_4 #include namespace { namespace flexsurv { template < int RTYPE_1, bool NA_1, typename T_1, int RTYPE_2, bool NA_2, typename T_2, int RTYPE_3, bool NA_3, typename T_3, int RTYPE_4, bool NA_4, typename T_4, typename Function > class Mapply_4 : public Rcpp::VectorBase< Rcpp::traits::r_sexptype_traits< typename ::Rcpp::traits::result_of::type >::rtype , true , Mapply_4 > { public: typedef typename ::Rcpp::traits::result_of::type result_type ; typedef Rcpp::VectorBase VEC_1 ; typedef Rcpp::VectorBase VEC_2 ; typedef Rcpp::VectorBase VEC_3 ; typedef Rcpp::VectorBase VEC_4 ; typedef typename Rcpp::traits::Extractor::type EXT_1 ; typedef typename Rcpp::traits::Extractor::type EXT_2 ; typedef typename Rcpp::traits::Extractor::type EXT_3 ; typedef typename Rcpp::traits::Extractor::type EXT_4 ; Mapply_4(const VEC_1& vec_1_, const VEC_2& vec_2_, const VEC_3& vec_3_, const VEC_4& vec_4_, Function fun_ ) : vec_1(vec_1_.get_ref()), vec_2(vec_2_.get_ref()), vec_3(vec_3_.get_ref()), vec_4(vec_4_.get_ref()), fun(fun_){} inline result_type operator[]( R_xlen_t i ) const { return fun( vec_1[i], vec_2[i], vec_3[i], vec_4[i] ); } inline R_xlen_t size() const { return vec_1.size() ; } private: const EXT_1& vec_1 ; const EXT_2& vec_2 ; const EXT_3& vec_3 ; const EXT_4& vec_4 ; Function fun ; } ; } template < int RTYPE_1, bool NA_1, typename T_1, int RTYPE_2, bool NA_2, typename T_2, int RTYPE_3, bool NA_3, typename T_3, int RTYPE_4, bool NA_4, typename T_4, typename Function> inline flexsurv::Mapply_4 mapply( const Rcpp::VectorBase& t1, const Rcpp::VectorBase& t2, const Rcpp::VectorBase& t3, const Rcpp::VectorBase& t4, Function fun ){ return flexsurv::Mapply_4( t1, t2, t3, t4, fun ) ; } } #endif flexsurv/src/flexsurv-init.c0000644000176200001440000000550713231112051015676 0ustar liggesusers/* Automatically generated by * tools::package_native_routine_registration_skeleton in r-devel from * 2017-03-27 */ /* Future versions of Rcpp may generate this, so this may not be * needed in the future */ #include #include #include // for NULL #include /* .Call calls */ extern SEXP _flexsurv_basis_matrix(SEXP, SEXP); extern SEXP _flexsurv_basis_vector(SEXP, SEXP); extern SEXP _flexsurv_check_genf(SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_check_gengamma(SEXP, SEXP, SEXP); extern SEXP _flexsurv_check_gompertz(SEXP, SEXP); extern SEXP _flexsurv_check_llogis(SEXP, SEXP); extern SEXP _flexsurv_dbasis_matrix(SEXP, SEXP); extern SEXP _flexsurv_dbasis_vector(SEXP, SEXP); extern SEXP _flexsurv_dexph(SEXP); extern SEXP _flexsurv_dgenf_work(SEXP, SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_dgengamma_work(SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_dgompertz_work(SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_dllogis_work(SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_exph(SEXP); extern SEXP _flexsurv_pgenf_work(SEXP, SEXP, SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_pgengamma_work(SEXP, SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_pgompertz_work(SEXP, SEXP, SEXP, SEXP, SEXP); extern SEXP _flexsurv_pllogis_work(SEXP, SEXP, SEXP, SEXP, SEXP); static const R_CallMethodDef CallEntries[] = { {"_flexsurv_basis_matrix", (DL_FUNC) &_flexsurv_basis_matrix, 2}, {"_flexsurv_basis_vector", (DL_FUNC) &_flexsurv_basis_vector, 2}, {"_flexsurv_check_genf", (DL_FUNC) &_flexsurv_check_genf, 4}, {"_flexsurv_check_gengamma", (DL_FUNC) &_flexsurv_check_gengamma, 3}, {"_flexsurv_check_gompertz", (DL_FUNC) &_flexsurv_check_gompertz, 2}, {"_flexsurv_check_llogis", (DL_FUNC) &_flexsurv_check_llogis, 2}, {"_flexsurv_dbasis_matrix", (DL_FUNC) &_flexsurv_dbasis_matrix, 2}, {"_flexsurv_dbasis_vector", (DL_FUNC) &_flexsurv_dbasis_vector, 2}, {"_flexsurv_dexph", (DL_FUNC) &_flexsurv_dexph, 1}, {"_flexsurv_dgenf_work", (DL_FUNC) &_flexsurv_dgenf_work, 6}, {"_flexsurv_dgengamma_work", (DL_FUNC) &_flexsurv_dgengamma_work, 5}, {"_flexsurv_dgompertz_work", (DL_FUNC) &_flexsurv_dgompertz_work, 4}, {"_flexsurv_dllogis_work", (DL_FUNC) &_flexsurv_dllogis_work, 4}, {"_flexsurv_exph", (DL_FUNC) &_flexsurv_exph, 1}, {"_flexsurv_pgenf_work", (DL_FUNC) &_flexsurv_pgenf_work, 7}, {"_flexsurv_pgengamma_work", (DL_FUNC) &_flexsurv_pgengamma_work, 6}, {"_flexsurv_pgompertz_work", (DL_FUNC) &_flexsurv_pgompertz_work, 5}, {"_flexsurv_pllogis_work", (DL_FUNC) &_flexsurv_pllogis_work, 5}, {NULL, NULL, 0} }; void R_init_flexsurv(DllInfo *dll) { R_registerRoutines(dll, NULL, CallEntries, NULL, NULL); R_useDynamicSymbols(dll, TRUE); } flexsurv/src/gompertz.cpp0000644000176200001440000000714013231112051015261 0ustar liggesusers#include #include #include "distribution.h" #include "rep_len.h" namespace { namespace gompertz { inline double exprel(const double x) { if (x!=0) { return expm1(x) / x; } else { return 1; } } inline double safe_coeff(const double q, const double shape, const double rate) { if (! std::isinf(q)) { const double scale_q = shape * q; return - rate * q * exprel(scale_q); } else { // If shape is negative, Gompertz reaches asymptote > 0 if (shape < 0) { return rate / shape; } else { return R_NegInf; } } } inline bool bad(const double shape, const double rate) { if (rate < 0) { Rcpp::warning("Negative rate parameter"); return true; } else { return false; } } class density { public: typedef double result_type; inline double operator()(const double x, const double shape, const double rate) const { if (bad(shape, rate)) { return NA_REAL; } if (x < 0) { return R_NegInf; } const double scale_x = shape * x; const double shift = x * exprel(scale_x); return std::log(rate) + scale_x - rate * shift; } }; class cdf { public: typedef double result_type; cdf(bool lower_tail_, bool give_log_) : lower_tail(lower_tail_), give_log(give_log_) {} inline double operator()(const double q, const double shape, const double rate) const { if (bad(shape, rate)) { return NA_REAL; } if (q < 0) { return below_distribution(lower_tail, give_log); } if (shape != 0) { const double coeff = safe_coeff(q, shape, rate); /* my, there's a lot of cases here */ if ((!give_log) & (lower_tail)) { return -expm1(coeff); } if ( (!give_log) & (!lower_tail)) { return std::exp(coeff); } if (give_log & lower_tail) { return log1p(-std::exp(coeff)); } // fall off the end here return coeff; } else { return R::pexp(q * rate, 1, lower_tail, give_log); } } private: bool lower_tail; bool give_log; }; } } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector dgompertz_work(const Rcpp::NumericVector& x, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& rate, const bool log) { if (x.size() == 0) { return x; } const R_xlen_t size = std::max(x.size(), std::max(shape.size(), rate.size())); return perhaps_exp(Rcpp::mapply(flexsurv::rep_len(x, size), flexsurv::rep_len(shape, size), flexsurv::rep_len(rate, size), gompertz::density()), log); } // [[Rcpp::export(rng=false)]] Rcpp::NumericVector pgompertz_work(const Rcpp::NumericVector& q, const Rcpp::NumericVector& shape, const Rcpp::NumericVector& rate, const bool lower_tail, const bool give_log) { if (q.size() == 0) { return q; } const R_xlen_t size = std::max(q.size(), std::max(shape.size(), rate.size())); return Rcpp::mapply(flexsurv::rep_len(q, size), flexsurv::rep_len(shape, size), flexsurv::rep_len(rate, size), gompertz::cdf(lower_tail, give_log)); } // [[Rcpp::export(name="check.gompertz", rng=false)]] Rcpp::LogicalVector check_gompertz(const Rcpp::NumericVector& shape, const Rcpp::NumericVector& rate) { if ( (0==shape.size()) && (0==rate.size()) ) { Rcpp::LogicalVector null_result(0); return null_result; } const R_xlen_t size = shape.size(); return !Rcpp::mapply(shape, flexsurv::rep_len(rate, size), gompertz::bad); } flexsurv/NAMESPACE0000644000176200001440000001463714554254215013371 0ustar liggesusers# Generated by roxygen2: do not edit by hand S3method(AIC,fmsm) S3method(AICC,flexsurvreg) S3method(AICc,flexsurvreg) S3method(BIC,flexsurvreg) S3method(augment,flexsurvreg) S3method(coef,flexsurvreg) S3method(glance,flexsurvreg) S3method(lines,flexsurvreg) S3method(lines,survrtrunc) S3method(logLik,flexsurvreg) S3method(model.frame,flexsurvmix) S3method(model.frame,flexsurvreg) S3method(model.matrix,flexsurvreg) S3method(nobs,flexsurvreg) S3method(plot,flexsurvreg) S3method(plot,standsurv) S3method(plot,survrtrunc) S3method(predict,flexsurvreg) S3method(print,flexsurvmix) S3method(print,flexsurvreg) S3method(print,flexsurvrtrunc) S3method(print,fmsm) S3method(print,summary.flexsurvreg) S3method(print,totlos.fs) S3method(residuals,flexsurvreg) S3method(simulate,flexsurvreg) S3method(summary,flexsurvreg) S3method(summary,flexsurvrtrunc) S3method(tidy,flexsurvreg) S3method(tidy,standsurv) S3method(vcov,flexsurvreg) export(AICC) export(AICc) export(Hexp) export(Hgamma) export(Hgenf) export(Hgenf.orig) export(Hgengamma) export(Hgengamma.orig) export(Hgompertz) export(Hllogis) export(Hlnorm) export(Hsurvspline) export(Hsurvspline0) export(Hsurvspline1) export(Hsurvspline2) export(Hsurvspline3) export(Hsurvspline4) export(Hsurvspline5) export(Hsurvspline6) export(Hsurvspline7) export(Hweibull) export(HweibullPH) export(ajfit) export(ajfit_flexsurvmix) export(ajfit_fmsm) export(augment) export(basis) export(bootci.fmsm) export(coxsnell_flexsurvreg) export(dbasis) export(dfss) export(dgenf) export(dgenf.orig) export(dgengamma) export(dgengamma.orig) export(dgompertz) export(dllogis) export(dsurvspline) export(dsurvspline0) export(dsurvspline1) export(dsurvspline2) export(dsurvspline3) export(dsurvspline4) export(dsurvspline5) export(dsurvspline6) export(dsurvspline7) export(dweibullPH) export(flexsurv.dists) export(flexsurvmix) export(flexsurvreg) export(flexsurvrtrunc) export(flexsurvspline) export(fmixmsm) export(fmsm) export(fss) export(glance) export(hexp) export(hgamma) export(hgenf) export(hgenf.orig) export(hgengamma) export(hgengamma.orig) export(hgompertz) export(hllogis) export(hlnorm) export(hr_flexsurvreg) export(hsurvspline) export(hsurvspline0) export(hsurvspline1) export(hsurvspline2) export(hsurvspline3) export(hsurvspline4) export(hsurvspline5) export(hsurvspline6) export(hsurvspline7) export(hweibull) export(hweibullPH) export(mean_exp) export(mean_flexsurvmix) export(mean_gamma) export(mean_genf) export(mean_genf.orig) export(mean_gengamma) export(mean_gengamma.orig) export(mean_gompertz) export(mean_llogis) export(mean_lnorm) export(mean_survspline) export(mean_survspline0) export(mean_survspline1) export(mean_survspline2) export(mean_survspline3) export(mean_survspline4) export(mean_survspline5) export(mean_survspline6) export(mean_survspline7) export(mean_weibull) export(mean_weibullPH) export(meanfinal_fmixmsm) export(msfit.flexsurvreg) export(normboot.flexsurvreg) export(p_flexsurvmix) export(pars.fmsm) export(pdf_flexsurvmix) export(pfinal_fmsm) export(pgenf) export(pgenf.orig) export(pgengamma) export(pgengamma.orig) export(pgompertz) export(pllogis) export(pmatrix.fs) export(pmatrix.simfs) export(ppath_fmixmsm) export(probs_flexsurvmix) export(psurvspline) export(psurvspline0) export(psurvspline1) export(psurvspline2) export(psurvspline3) export(psurvspline4) export(psurvspline5) export(psurvspline6) export(psurvspline7) export(pweibullPH) export(qfinal_fmixmsm) export(qgeneric) export(qgenf) export(qgenf.orig) export(qgengamma) export(qgengamma.orig) export(qgompertz) export(qllogis) export(qsurvspline) export(qsurvspline0) export(qsurvspline1) export(qsurvspline2) export(qsurvspline3) export(qsurvspline4) export(qsurvspline5) export(qsurvspline6) export(qsurvspline7) export(quantile_flexsurvmix) export(qweibullPH) export(rgenf) export(rgenf.orig) export(rgengamma) export(rgengamma.orig) export(rgompertz) export(rllogis) export(rmst_exp) export(rmst_flexsurvmix) export(rmst_gamma) export(rmst_generic) export(rmst_genf) export(rmst_genf.orig) export(rmst_gengamma) export(rmst_gengamma.orig) export(rmst_gompertz) export(rmst_llogis) export(rmst_lnorm) export(rmst_survspline) export(rmst_survspline0) export(rmst_survspline1) export(rmst_survspline2) export(rmst_survspline3) export(rmst_survspline4) export(rmst_survspline5) export(rmst_survspline6) export(rmst_survspline7) export(rmst_weibull) export(rmst_weibullPH) export(rsurvspline) export(rsurvspline0) export(rsurvspline1) export(rsurvspline2) export(rsurvspline3) export(rsurvspline4) export(rsurvspline5) export(rsurvspline6) export(rsurvspline7) export(rweibullPH) export(sim.fmsm) export(simfinal_fmsm) export(simfs_bytrans) export(standsurv) export(survrtrunc) export(tidy) export(totlos.fs) export(totlos.simfs) export(unroll.function) import(ggplot2) import(rlang) import(stats) importFrom(Matrix,nearPD) importFrom(Rcpp,sourceCpp) importFrom(deSolve,ode) importFrom(dplyr,bind_cols) importFrom(dplyr,bind_rows) importFrom(dplyr,distinct) importFrom(dplyr,full_join) importFrom(dplyr,group_by) importFrom(dplyr,inner_join) importFrom(dplyr,left_join) importFrom(dplyr,mutate) importFrom(dplyr,n) importFrom(dplyr,pull) importFrom(dplyr,rename) importFrom(dplyr,select) importFrom(dplyr,slice) importFrom(dplyr,summarise) importFrom(dplyr,ungroup) importFrom(generics,augment) importFrom(generics,glance) importFrom(generics,tidy) importFrom(graphics,lines) importFrom(graphics,plot) importFrom(magrittr,"%>%") importFrom(mstate,msfit) importFrom(mstate,probtrans) importFrom(muhaz,muhaz) importFrom(mvtnorm,rmvnorm) importFrom(numDeriv,grad) importFrom(numDeriv,hessian) importFrom(purrr,map2_dbl) importFrom(quadprog,solve.QP) importFrom(rlang,":=") importFrom(rlang,.data) importFrom(statmod,gauss.quad) importFrom(stats,predict) importFrom(stats,residuals) importFrom(survival,Surv) importFrom(survival,coxph) importFrom(survival,survfit) importFrom(survival,survreg) importFrom(survival,survreg.control) importFrom(tibble,as_tibble) importFrom(tibble,tibble) importFrom(tidyr,pivot_longer) importFrom(tidyr,pivot_wider) importFrom(tidyr,unnest) importFrom(tidyselect,all_of) importFrom(tidyselect,matches) importFrom(tidyselect,num_range) importFrom(utils,globalVariables) useDynLib(flexsurv, .registration = TRUE) flexsurv/NEWS.md0000644000176200001440000005230114657632123013240 0ustar liggesusers# Version 2.3.2 (2024-08-16) * Vignette source included to satisfy CRAN checks. * Fix of prediction with `spline="splines2ns"`. # Version 2.3.1 (2024-07-14) * Fix for simulating from semi-Markov models with `tcovs` option, which was not completing for some model configurations. * Fix for `simulate.flexsurvreg()` with vector `start` argument (#192). # Version 2.3 (2024-04-21) * Analytic Hessian calculation for models where this is possible, that is, Weibull, Gompertz, exponential, and spline models in hazard and odds scales. * Analytic gradient calculation for Weibull proportional hazards models. * Vignette now firmly warns against using flexsurv with time-dependent covariates (#176). * New argument `spline="splines2ns"` can now be specified to use an orthogonal spline basis in `flexsurvspline()`. * Weighted likelihood for relative survival models now implemented consistently with other models, as a weighted sum of individual log-likelihoods. * `standsurv` now returns results in the same order of times `t` as given by the user, for consistency with `summary.flexsurvreg`. * Quantiles of standardised survival now available in `standsurv`. * Non-default factor contrasts now handled. * `pmatrix.simfs` can now accept a vector of times `t` and has a `tidy` output option. * `BIC` and `AICc` functions added. * Column name of `predict()` output changed from `"time"` to `"eval_time"`, for consistency with tidymodels update. * Default value for `t` now chosen in `hr_flexsurvreg`. * `coxsnell.flexsurvreg` now handles delayed entry. * Warning given if the name of a location parameter is included in the ancillary part of the model specification. * Fix for computing quantiles for custom distributions (#187). Thank you to all who have contributed code for this version: @mikesweeting @stephematician @ndunnewind @mattwarkentin @hfrick @kkmann; or reported issues: @anddis @irtimmins @sbihorel @zou-ims @aghaynes @huftis @mafed @hezht3 @sebffischer (and anyone else who reported issues via email). # Version 2.2.2 (2023-01-31) * Allow unicode characters in vignette, to satisfy R CMD check on r-devel. # Version 2.2.1 (2022-12-22) * New `simulate.flexsurvreg` method to simulate data from a fitted `flexsurvreg()` or `flexsurvspline()` model. Thanks to Mark Clements for help with this. * Fix of bug for `summary()` method with type = `"quantile"` or `"median"` and left-truncation in the prediction (`start` > 0). * Correction to the examples and interpretation of Cox-Snell residuals. # Version 2.2 (2022-06-16) * New function `standsurv` for survival and hazards standardised over an observed distribution for covariates. Contributed by Michael Sweeting . See the new vignette about it. * New function `hr_flexsurvreg` to compute the hazard ratio from a fitted `flexsurvreg()` or `flexsurvspline()` model as a function of time, with confidence intervals. * `summary.flexsurvreg` has been rewritten to make it cleaner and faster. User-visible changes: - Custom summary functions in `summary.flexsurvreg` must now be vectorised. - A new argument `cross` specifies whether to compute summaries for all combinations of times t and covariate values, or for covariate values matched with corresponding times t, in custom summary functions. - Covariate names when `tidy=FALSE` now consistently don't include spaces. * Better handling of NAs in summary and prediction functions. Thanks to Matthew Warkentin. * New functions for Cox-Snell residuals: `coxsnell_flexsurvreg` or residuals(..., type="coxsnell"). * `rmst_generic`, `mean_survspline`, `rmst_survspline` and related functions (e.g. `mean_survspline1`) handle alternative parameter values in a vectorised way. * Allow output functions to work on models that have been stripped of data with `x$data <- NULL`, if possible. # Version 2.1 (2021-09-13) * Fix of a bug that affected models with baseline hazard offsets and exponential, Weibull, Gompertz and hazard/odds-based spline models, where convergence may have been falsely reported due to incorrect likelihood derivatives. * New vignette section and better help page documentation about relative survival models. * `start` parameter added to `predict.flexsurvreg`. * New function `pdf_flexsurmix` for the fitted density function in a `flexsurvmix` model. * Fix for tidy method with one-parameter exponential models. * Fixes for `h/Hgamma` and `h/Hlnorm` with `log = TRUE`. * Minor numerical improvements to `h/H` functions for some distributions. * Bug fix for `simfs_bytrans` when some transitions don't happen. * `NaNs produced` warnings should occur less often during fitting. # Version 2.0 (2021-02-22) * A new class of multi-state models based on mixtures (Larson and Dinse 1985). A new vignette on multi-state modelling describes this model class and contrasts it with standard (cause-specific hazards) multi-state models. * Different parametric families are now supported for different transitions in multi-state models. * New function `fmsm` allows a list of flexsurvreg objects to be associated with a particular transition structure matrix, to create a multi-state model. * New function `simfinal_fmsm` to summarise times and probabilities of final absorbing events in multi-state models, using simulation. * More features for right-truncated data. Individual-level right-truncation times supported with new "rtrunc" argument to flexsurvreg and flexsurvspline. A comparable non-parametric estimator for right-truncated data is provided in a new function, `survrtrunc`. Alternative parametric estimators, which make use of the time of an initiating event, are provided in a new function, `flexsurvrtrunc`. * A new vignette describes properties of the different built-in parametric distributions in more detail. * `qgeneric` is now vectorised, thanks to the `vuniroot` function imported from the `rstpm2` package by Mark Clements. This massively boosts the speed of `rsurvspline`, hence speeding up simulations from spline-based multi-state models. * `pmatrix.fs` can now calculate transition probabilities conditionally on the the transition being to one of a subset of the states. * "tidy" argument to `pmatrix.fs` for tidy data frame output. * "tidy" argument to `sim.fmsm` for returning simulations in tidy data frame format with one row per transition, and associated function `simfs_bytrans`. * Bootstrapping function `bootci.fmsm` made available for users to get confidence intervals / distributions for their own flexsurv model output functions. * Parallel processing capability for bootstrap confidence intervals. * Distribution and mean functions for the Royston-Parmar model named like `dsurvspline2`, `psurvspline4` and so on, with one argument per parameter, rather than all parameters collected in a single argument, going up to 7 knots / 9 parameters. * Return value from `pars.fmsm` is now a list rather than a matrix, even if the model family is the same for each transition. * `summary.flexsurvreg` given a new argument "na.action" to control whether missing values in "newdata" are dropped. Defaults to producing summaries of `NA` when there are missing values, while previously missing values were dropped. * S3 methods have been added for the generics defined in the broom package. These functions create tidy data frames containing the results of fitted models. The new functions are `tidy.flexsurvreg`, `glance.flexsurvreg`, and `augment.flexsurvreg`. * S3 methods have been added for the predict and residuals generics. `predict.flexsurvreg` has full support for all model outcomes supported by `summary.flexsurvreg`. `residuals.flexsurvreg` currently only supports a naive difference between observed survival and predicted mean, neglecting censoring. * Case weights accounted for in nonparametric survival and cumulative hazard estimates in `plot.flexsurvreg`. Thanks to https://github.com/andbe. # Version 1.1.1 (2019-03-18) * New type="quantiles" and type="link" for summary.flexsurvreg. Thanks to Leonardo Marques for the contribution. * Allow different covariates per transition in multi-state models supplied as a list of flexsurvreg objects. Thanks to David McAllister for the contribution. * Bug fix for qllogis with lower.tail=FALSE. * Bug fix for likelihood when all events are observed. * Bug fix for "ylim" argument in plot method for survival or cumulative hazard. * Allow dynamic symbols in C code. * Various other minor code and doc fixes, see github commit history. # Version 1.1 (2017-03-27) * Substantial speed improvements in fitting most of the built-in models, from implementing their PDFs and CDFs in C++. Thanks to Paul Metcalfe for contributing this. Results may therefore differ from previous versions in edge cases. * As a result the package now depends on Rcpp. * Mean, median and restricted mean included as built-in functions in summary.flexsurvreg. Thanks to Jordan Amdahl for the contribution. * Documentation migrated to roxygen. Thanks to Paul Metcalfe for the contribution. * Various minor bug fixes, see github commits. # Version 1.0.2 (2016-09-26) * Bug fix: "start" was being ignored by plot.flexsurvreg. Thanks to Ruth Keogh. * Built-in distribution names are now case-insensitive. Thanks to Jordan Amdahl. * Fix for Weibull hazard function to avoid numeric instability. Thanks to Jordan Amdahl. * Fix to hsurvspline when t includes 0. Thanks to Jordan Amdahl. * Vectorised parameters supported in qgeneric. # Version 1.0.1 (2016-05-31) * Bug fix: covariates were labelled wrongly in summary.flexsurvreg tidy output. Thanks to Owain Saunders. # Version 1.0.0 (2016-05-10) * Version number bumped to 1.0.0 to accompany the publication of the vignette in Journal of Statistical Software. # Version 0.7.1 (2016-03-24) * Slightly more efficient likelihood calculations, and removed spurious warning from likelihood with interval censoring. * Tests modified to work with the latest (and current) testthat. # Version 0.7 (2015-11-13) * flexsurvspline now allows the log cumulative hazard (or its alternatives) to be modelled as a spline function of time instead of log time. * The routine for generating initial values in flexsurvspline has been improved. This now obeys the constraint that the log cumulative hazard is increasing, thus avoiding errors from optim() when this wasn't satisfied. Cox regression is used as a fallback to initialise covariate effects if this fails. * As a result, flexsurv now depends on the "quadprog" package. * dweibullPH and related functions give the Weibull distribution in proportional hazards parameterisation, and "weibullPH" is supported as a built-in model for flexsurvreg. * Option to summary.flexsurvreg to return a tidy data frame. * New "logliki" component in model objects, containing vector of log-likelihoods for each observation at the estimated or fixed parameters. * Fix of various bugs with supplying "newdata" to summary functions (github issue #7). The behaviour here should now be like predict.lm, e.g. variables in newdata that were originally factors should be supplied as factor or character, not numeric. * Fix of bug that prevented plots being drawn by categorical covariates by default. * Fix of bugs with spline models and no data censored, or all data interval censored (github issue #3). * Fix of bugs with subsetting in flexsurvspline (github issue #6). # Version 0.6 (2015-04-13) * CRAN release. Also includes the changes from Version 0.5.1. * Full support for multi-state models fitted as a list of independent transition-specific models. * New function pars.fmsm to return transition-specific parameters in multi-state models. * Bug fix for empirical hazard plots with categorical covariates. Thanks to Milan Bouchet-Valat. # Version 0.5.1 (2015-02-24) * github-only release. * Log-logistic distribution built in to flexsurvreg, and distribution functions provided. * Bug fix in tcovs option in semi-Markov model simulation. * "digits" argument supported by default model print function. This is passed to "format" to format the parameter estimates, and defaults to 3. * Bug fix in "events" printed output for interval censored data. Thanks to Sabrina Russo. * pgompertz returns Inf for q=Inf, even for parameters denoting "living forever", since the CDF is P(X <= q) not P(X < q). This affected some fits of the Gompertz distribution. # Version 0.5 (2014-09-22) * Major new release, so version number bumped from 0.3 to 0.5. * New package vignettes: a user guide and a vignette of examples. * Development moved from r-forge to https://github.com/chjackson/flexsurv-dev. Spline models and ancillary covariates: * Major rewrite of flexsurvspline. This now works by calling flexsurvreg with a custom distribution written dynamically. Models can now include covariate effects that vary as spline functions of time, by including covariates on "gamma1" or on any further parameters. * New argument "anc" to flexsurvreg, as an alternative and preferred way of modelling covariates on ancillary parameters. * New general utility "unroll.function" which converts a function with matrix arguments to the equivalent function with vector arguments. The new flexsurvspline works by unrolling "dsurvspline". * Quantile, random number, hazard and cumulative hazard functions for spline distribution. * Autogeneration of initial values for flexsurvspline now accounts for left-truncation. Thanks to Ana Borges for the report. Other new modelling features: * Several utilities for parametric multi-state modelling, including transition probabilities and simulation ("pmatrix.fs", "totlos.fs", "sim.fmsm","pmatrix.simfs", "totlos.simfs"). An "msfit.flexsurvreg" method also gives cumulative transition-specific hazards in the format of the "mstate" package. * Interval censoring supported in the Surv() response. * Relative survival models, using the "bhazard" argument to flexsurvreg to specify the expected mortality rate. * flexsurvreg now uses survreg internally to fit Weibull, exponential and log-normal models, unless there is left-truncation. Custom distributions: * Custom distributions can be defined through the hazard function. This can be optionally supplemented with the cumulative hazard function, otherwise this is obtained by numerical integration. * In custom distributions specified by the density, the cumulative distribution can now be omitted, and it will be calculated by numerical integration. * New arguments "dfns" and "aux" to flexsurvreg, which can be used to supply custom distribution functions and arguments to pass to them. * Document that density functions for custom distributions need "log" argument. * Documented how to supply derivatives of custom distributions for use in optimisation. Output functions: * New "newdata" argument to summary.flexsurvreg and plot.flexsurvreg for an easier way of supplying covariate values. * User-defined summary functions can be used in summary.flexsurvreg and plot.flexsurvreg as an alternative to survival, hazard or cumulative hazard. * New function "normboot.flexsurvreg" to simulate parameters from the asymptotic normal distribution of their estimates. Used for representing uncertainty in any function of the parameters. * summary.flexsurvreg can be called with ci=FALSE to omit confidence intervals. * "start" argument defaults to 0 for all prediction times in summary.flexsurvreg. * Bug fix in summary.flexsurvreg for left-truncated models, which was returning probabilities > 1 before the truncation time. * New model.frame and model.matrix methods to extract the data from fitted flexsurvreg objects. * Accept vector X in summary.flexsurvreg, and give informative error if X in wrong format. Thanks to Mark Danese. * Extra arguments can be passed to both muhaz and plot.muhaz in plot.flexsurvreg(...,type="hazard",...) Printed output: * Use format() not signif() for printing flexsurvreg objects, to avoid spurious zero significant figures. Thanks to Kenneth Chen. * Standard errors included in printed output of flexsurvreg, but only for parameters optimised on natural or log scales (which includes all built-in distributions). Distribution functions: * Bug fix in rgengamma for Q=0 (log-normal) and sigma not equal to 1. * Don't warn for shape parameters being exactly zero in generalized gamma and F, just give NaN. * basis() and fss() functions for the natural cubic spline basis made available to users. # Version 0.3.1 (2014-02-14) * R-forge only release. * Distribution functions tidied up, making special value handling and vectorisation consistent. Hazard and cumulative hazard functions for all supported distributions. * Vectors of different col, lwd and lty can be passed to plot.flexsurvreg for multiple fitted lines. Thanks to Julia Sandberg for the report. # Version 0.3 (2014-01-19) * CRAN release. Includes changes from 0.2.1 to 0.2.3. # Version 0.2.3 (2013-10-09) * R-forge only release. * Parameters other than the location parameter can now have covariates on them in flexsurvreg. Thanks to Milan Bouchet-Valat for help with this. * subset and na.action arguments in flexsurvreg and flexsurvspline. * coef, vcov and confint methods for all fitted model objects. * Distribution functions for generalized gamma, generalized F, and Gompertz, now allow all parameters to be vectorised. * Bug fix in analytic derivatives for Weibull. * Restored print output introduced in 0.1.2 which had been accidentally removed in 0.1.5. # Version 0.2.2 (2013-07-26) * R-forge only release. * Case weights supported in flexsurvreg and flexsurvspline. # Version 0.2.1 (2013-07-03) * R-forge only release. * Default left truncation times were being set wrongly for user-supplied times in summary.flexsurvreg, giving wrong confidence intervals. These now default to 0. * Confidence intervals set to 1 for t=0 under spline models. Thanks to Paul Pynsent. * dgompertz,dgengamma,dgengamma.orig,dgenf,dgenf.orig fixed to return -Inf instead of 0 when density is zero and log=TRUE. Thanks to Gao Zheng. # Version 0.2 (2013-05-13) * New summary() method for fitted flexsurvreg and flexsurvspline model objects gives fitted survival, cumulative hazard or hazard curves, with confidence intervals mosly computed by a simulation method. * This allows plot.flexsurvreg to plot confidence intervals for the fitted survival, hazard or cumulative hazard. * Left-truncated survival observations are supported in flexsurvreg and flexsurvspline. * New psurvspline and dsurvspline functions giving distribution and density function for the spline model. * Analytic derivatives used in optimisation for spline (odds and hazard scale, not normal), exponential, Weibull and Gompertz models. * Default to BFGS optimisation method, which uses derivatives where available and should be much faster, instead of Nelder-Mead. * Work around NaN warnings from spline models presumably due to parameters violating implicit constraints. * If "knots" specified, boundary knots set to min/max of uncensored times, not all times, to match results when "k" is specified. Thanks to Paul Pynsent. # Version 0.1.5 (2012-08-29) * Data are now stored in fitted flexsurvreg and flexsurvspline model objects, avoiding environment search errors and allowing package functions to be called within other functions. Thanks to Hanna Daniel for the report. * Gompertz documentation clarified for the case when there is a chance of living forever. qgompertz and rgompertz now return Inf in these cases, with no warning, instead of NaN. Thanks to Michael Sweeting. # Version 0.1.4 (2012-03-22) * maxt argument in plot.flexsurvreg. * Plots no longer complain if data named "dat". * Corrected wrong bug fix from Version 0.1.3 for transforming parameter estimates in output when fixedpars=TRUE. * AIC penalty corrected for models with some fixed parameters. * qgengamma corrected for parameter Q<0. Thanks to Benn Ackley. # Version 0.1.3 (2012-01-17) * No longer complains about invalid initial values when there are zero survival times. * Don't transform parameter estimates in output when fixedpars=TRUE. * Checking functions for distribution utilities don't complain about vectorised parameter values. # Version 0.1.2 (2011-11-08) * Initial CRAN release. * More features in print output for flexsurvreg and flexsurvspline models. # Version 0.1.1 (2011-04-19) * Fix of drop=FALSE bug in flexsurvspline.inits which caused flexsurvspline to fail with single covariates. # Version 0.1 (2011-03-14) Initial release flexsurv/inst/0000755000176200001440000000000014657665216013127 5ustar liggesusersflexsurv/inst/CITATION0000644000176200001440000000135113231112051014227 0ustar liggesusersbibentry(bibtype = "Article", title = "{flexsurv}: A Platform for Parametric Survival Modeling in {R}", author = person(given = "Christopher", family = "Jackson", email = "chris.jackson@mrc-bsu.cam.ac.uk"), journal = "Journal of Statistical Software", year = "2016", volume = "70", number = "8", pages = "1--33", doi = "10.18637/jss.v070.i08", header = "To cite flexsurv in publications use:", textVersion = paste("Christopher Jackson (2016).", "flexsurv: A Platform for Parametric Survival Modeling in R.", "Journal of Statistical Software, 70(8), 1-33.", "doi:10.18637/jss.v070.i08") ) flexsurv/inst/doc/0000755000176200001440000000000014657665171013674 5ustar liggesusersflexsurv/inst/doc/standsurv.Rmd0000644000176200001440000010446014417276462016371 0ustar liggesusers--- title: "Calculating standardized survival measures in flexsurv" author: "Michael Sweeting^[mikesweeting79@gmail.com]" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Calculating standardized survival measures in flexsurv} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} bibliography: "standsurv.bib" --- ```{r, include = FALSE} knitr::opts_chunk$set( fig.dim = c(8, 6), collapse = TRUE, comment = "#>" ) ``` # Background ## Standardized survival measures `standsurv` is a post-estimation command that takes a `flexsurvreg` object and calculates standardized survival measures. After fitting a parametric survival model in `flexsurv` it is often useful to compute and visualise the marginal (or standardized) survival. For example, suppose a survival model is fitted adjusted for treatment group, age, and sex. A separate predicted survival curve can be obtained for each individual based on their covariate pattern or a prediction can be obtained by setting covariates to their mean values (both can be obtained using `summary.flexsurvreg`), but it may be more useful to obtain the marginal survival for each treatment group. Regression standardization achieves this by fitting a regression model including the treatment group $Z$, covariates $X$ and possible interactions between $X$ and $Z$. The standardized survival can be estimated by obtaining predictions for every individual in the study under each fixed treatment arm and averaging these individual-specific estimates. The marginal survival over the distribution of covariates in the study assuming all participants were assigned to arm $Z=z$ is: \begin{equation} S_s(t|Z=z) = E[S(t | Z=z, X)] = \frac{1}{N} \sum_{i=1}^{N} S(t | Z=z, X=x_i) \end{equation} for covariate values (vectors) $x_1,...,x_{N}$. Here standarization is done over all $N$ patients in the study and provides a counterfactual marginal estimate when setting $Z=z$. The standardized survival is therefore an estimate of the marginal survival if all study patients had been assigned to group $z$. Under certain assumptions, differences in marginal survival provide estimates of causal effects (@syriopoulou_inverse_2021) and certain estimands such as the average treatment effect (ATE) can be targeted: $$ ATE = S_s(t|Z=z_1) - S_s(t|Z=z_0)]$$ Alternatively, an average treatment effect in the treated (ATET) estimand can be targeted by averaging over only patients who were in the intervention treatment arm $Z=z_1$. Standardization estimates can also be obtained for other target populations of interest. For example it may be important to predict survival in an external population with different characteristics to the study population. The hazard function for the standardized survival can be obtained to understand how the shape of the hazard changes over time. This provides an estimate of the marginal hazard. It can be shown (@rutherford_nice_2020, Appendix I) that the hazard of the standardized survival can be calculated as \begin{equation} h_s(t|Z=z) = \frac{\sum_{i=1}^{N} S(t|Z=z,X=x_i)h(t|Z=z,X=x_i)}{\sum_{i=1}^{N} S(t | Z=z, X=x_i)} \end{equation} This is a weighted average of the $N$ individual hazard functions, weighted by the probability of survival at time $t$. Patients who are unlikely to have survived to $t$ will contribute less weight to this hazard function. ## Calculating marginal expected survival and hazard In economic evaluations parametric survival models are used to extrapolate clinical trial data to estimate lifetime benefits. In this context it is often useful to plot marginal 'expected' (general population) survival alongside parametric models fitted and extrapolated from trial data in order to aid interpretation and for a visual comparison between the trial subjects and the population at large. Displaying expected survival and hazard functions can aid understanding of whether the assumed hazard and survival functions are credible (@rutherford_nice_2020). Expected survival is defined as the all-cause survival in a general population with the same key characteristics as the study subjects. General population mortality rates are often taken from national lifetables that are stratified by age, sex, calendar year and occasionally other prognostic factors (e.g. deprivation indices). The Ederer or "exact" method for estimating expected survival assumes subjects in the trial population are not censored before the end of a stated follow-up time [@ederer_relative_1961]. The expected survival is then the survival we would expect to see in an age-sex matched general population if all patients are continuously followed-up. This is the approach used by `standsurv` to calculate expected survival and is the "most appropriate when doing forcasting, sample size calculations or other predictions of the 'future' where censoring is not an issue" [@therneau_1999]. Based on the exact method, the marginal expected survival using background mortality rates is calculated using all $N$ patients in the trial at any time point $t$: \begin{equation} S^*(t) = \frac{1}{N} \sum_{i=1}^N S_i^*(t) \end{equation} where $S_i^*(t)$ is the expected survival for the $i$th subject at time $t$. It follows that the marginal expected hazard is a weighted average of the expected hazard rates: \begin{equation} h^*(t) = \frac{ \sum_{i=1}^N S_i^*(t) h_i^*(t)}{\sum_{i=1}^N S_i^*(t)} \end{equation} The expected survival for the $i$th subject at follow-up time $t$ is calculated based on matching to the general population hazard rates. If lifetables are utilised these often provide mortality rates by sex ($s$), age ($a$) and calendar year ($y$), in yearly or 5-yearly categories. In practice the expected survival at time $t$ for a given subject is calculated from the cumulative hazard. At a given follow-up time $t$ this is the sum of $h^*_{asy} \times \textrm{Number of days in state } (a,s,y)$ in the follow-up where $h^*_{asy}$ is the expected hazard for age $a$, sex $s$, year $y$. This requires follow-up time for each individual in the study dataset to be split by multiple timescales (e.g. age and year) into time epochs, which can be visualised as a Lexis diagram. Each epoch can then be matched to a corresponding expected mortality rate. ## Incorporation of background mortality into survival models Incorporating background mortality into survival models directly is recommended as it helps avoid extremely implausible projections (@rutherford_nice_2020). This can be done using an excess mortality / relative survival model where population based 'expected' rates, often from life tables, are introduced to explain background mortality. The concept behind these models is to partition the all-cause mortality into excess mortality caused by the disease of interest and that due to other causes. A parametric model can then be applied to the isolated excess mortality. This may be particularly useful when making long-term extrapolations as the pattern of disease-specific mortality and other cause mortality are likely to be very different over time. Alternatively, if cause of death information is available and reliable, a separate cause-specific model can be fitted to the disease-specific mortality and other cause mortality. The all-cause mortality rate at time $t$ for individual $i$ can be partitioned into two constituent parts: \begin{equation} h_i(t) = h^*_i(t) + \lambda_i(t) \end{equation} where $h_i(t)$ is the all-cause mortality rate (hazard), $h^*_i(t)$ is the expected or background mortality rate and $\lambda_i(t)$ is the excess mortality rate. Equivalently, the hazard rates can be transformed to the survival scale which gives the all-cause survival at time $t$ as the product of the expected survival and the relative survival: \begin{equation} S_i(t) = S^*_i(t) R_i(t) \end{equation} The relative survival, $R_i(t)$, is therefore the ratio of all-cause survival and the expected survival in the background population. Typically, $h_i^*(t)$ (and hence $S_i^*(t)$) are obtained from population lifetables. The expected mortality rates are assumed to be fixed and known and a parametric model is then used to estimate the relative survival (or equivalently excess hazard). # `standsurv` `standsurv` is a post-estimation command that takes a `flexsurv` regression and calculates standardized survival measures and contrasts. Expected mortality rates and survival can also be obtained. The main features of the command are that it enables the calculation and plotting over any specified follow-up times of 1. Marginal survival, hazard and restricted mean survival time (RMST) metrics 2. Marginal expected (population) survival and hazard functions matched to the study population 3. Marginal all-cause survival and all-cause hazard after fitting relative survival models 4. Contrasts in survival, hazard and RMST metrics (e.g. marginal hazard ratio, differences in marginal RMST) 5. Confidence intervals and standard errors for all measures and contrasts using either the delta method or bootstrapping Through a simple syntax the user can specify the groups that they wish to calculate the marginal metrics. These groups can be formed by any combination of covariate values. ## A worked example: the pbc dataset For this example we will use data from the German Breast Cancer Study Group 1984-1989, which is the R dataset `bc` found in the `flexsurv` package. This dataset has death, or censoring times for 686 primary node positive breast cancer patients together with a 3-level prognostic group variable with levels "Good", "Medium" and "Poor". For this demonstration we collapse the prognostic variable into 2 levels: "Good" and "Medium/Poor". We also create some artificial ages and diagnosis dates for the patients, along with assuming all patients are female. We allow a correlation between the age at diagnosis for a patient and their survival time so that age is a prognostic variable. The mean age is 65 with a standard deviation of 5. We load this dataset and create these additional variables. ```{r, message = FALSE, warning = FALSE} library(flexsurv) library(flexsurvcure) library(ggplot2) library(dplyr) library(survminer) ``` ```{r} data(bc) set.seed(236236) ## Age at diagnosis is correlated with survival time. A longer survival time ## gives a younger mean age bc$age <- rnorm(dim(bc)[1], mean = 65 - scale(bc$recyrs, scale=F), sd = 5) ## Create age at diagnosis in days - used later for matching to expected rates bc$agedays <- floor(bc$age * 365.25) ## Create some random diagnosis dates between 01/01/1984 and 31/12/1989 bc$diag <- as.Date(floor(runif(dim(bc)[1], as.Date("01/01/1984", "%d/%m/%Y"), as.Date("31/12/1989", "%d/%m/%Y"))), origin="1970-01-01") ## Create sex (assume all are female) bc$sex <- factor("female") ## 2-level prognostic variable bc$group2 <- ifelse(bc$group=="Good", "Good", "Medium/Poor") head(bc) ``` A plot of the Kaplan-Meier shows a clear separation in the survival curves between the two prognostic groups. ```{r} km <- survfit(Surv(recyrs, censrec)~group2, data=bc) kmsurvplot <- ggsurvplot(km) kmsurvplot + xlab("Time from diagnosis (years)") ``` ## A stratified Weibull model We start by fitting a Weibull model to each group separately. One way to do this is to fit a single saturated model whereby group affects both the scale and shape parameters of the Weibull distribution. This effectively means we have a separate scale and shape parameter for each group, which is equivalent to fitting two separate models. Such a model does not make a proportional hazards assumption and hence the hazard ratio will change over time. The saturated model approach has advantages as we can use the model to easily investigate treatment effects using `standsurv` as we shall see later. Including group in the main formula of `flexsurvreg` allows group to affect the scale parameter of the Weibull distribution whilst we use the `anc` argument in `flexsurvreg` to additionally allow group to affect the shape parameter. ```{r} model.weibull.sep <- flexsurvreg(Surv(recyrs, censrec)~group2, anc = list(shape = ~ group2), data=bc, dist="weibullPH") model.weibull.sep ``` Given that the model only contains `group2` and no other covariates we can obtain the predicted (fitted) survival for each of the two groups using the `summary` function and storing these predictions in a tidy data.frame with the argument `tidy=T`. ```{r} predictions <- summary(model.weibull.sep, type = "survival", tidy=T) ggplot() + geom_line(aes(x=time, y=est, color = group2), data=predictions) + geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot) ``` The Weibull model does not appear to fit the data very well and so we should try other parametric distributions. However, for illustration purposes we shall continue using the Weibull model. We will now show that the same predictions can be obtained from `standsurv` but with the benefit of addition flexibility. ## Using `standsurv` to calculate marginal survival `standsurv` works similarly to the `margins` command in `R` and `standsurv` in Stata by allowing the user to specify a list of scenarios in which specific covariates are fixed to certain values. This is done using the `at` argument of `standsurv` to provide the list of scenarios where each scenario is itself a list containing covariates that are to be fixed. In our worked example the two scenarios are `list(group2 = "Good")` and `list(group2 = "Medium/Poor")`. Any covariates not specified in the `at` scenarios are averaged over, hence creating marginal, or standardized, estimates of the metric of interest. In the example above, there are no other covariates in the model so we will get the same answer as obtained from `summary`. But the later worked example extends this to models containing other covariates. The default is to calculate survival probabilities at the event times in the data but this can be changed with the `type` and `t` arguments, respectively. The returned object is a tidy data.frame with columns named `at1` up to `atn` for the n scenarios specified in the `at` argument. ```{r} ss.weibull.sep.surv <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) ss.weibull.sep.surv ``` Further details such as labels for the `at` scenarios are stored in attributes of the `standsurv` object. These are utilised by the `plot` function. A plot of the marginal estimates can be easily produced using the `plot` function, which produces a `ggplot` object. ```{r} plot(ss.weibull.sep.surv) ``` The plot can be easily further manipulated, for example by changing axis labels and adding further plots. ```{r} plot(ss.weibull.sep.surv) + xlab("Time since diagnosis (years)") + geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot) ``` ## Other metrics: marginal hazards and marginal RMST We can use the `type` argument to calculate marginal hazards or restricted mean survival time (RMST). For example a plot of the hazard functions for the two groups is obtained as follows: ```{r} ss.weibull.sep.haz <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) plot(ss.weibull.sep.haz) + xlab("Time since diagnosis (years)") ``` Whilst a plot of RMST is given by ```{r} ss.weibull.sep.rmst <- standsurv(model.weibull.sep, type = "rmst", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) plot(ss.weibull.sep.rmst) + xlab("Time since diagnosis (years)") ``` ## Calculating contrasts The advantage of fitting a saturated model now becomes clear as we can calculate contrasts between our `at` scenarios. Suppose we are interested in the difference in the survival functions between the two groups. This is easily calculated using the `contrast = "difference"` argument, and a plot of the contrast can be obtained using `contrast = TRUE` argument in the `plot` function. ```{r} ss.weibull.sep.3 <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), contrast = "difference") plot(ss.weibull.sep.3, contrast=TRUE) + xlab("Time since diagnosis (years)") + ylab("Difference in survival probabilities") + geom_hline(yintercept = 0) ``` Alternatively, we may wish to visualise the implied hazard ratio from fitting separate Weibull models to the two groups. In the breast cancer example we see that the hazard ratio (treatment effect) starts very high before decreasing, suggesting that those with Medium/Poor prognosis start with a high elevated risk but have a continued excess risk up to the end of follow-up, compared to those with Good prognosis. ```{r} ss.weibull.sep.4 <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), contrast = "ratio") plot(ss.weibull.sep.4, contrast=TRUE) + xlab("Time since diagnosis (years)") + ylab("Hazard ratio") + geom_hline(yintercept = 1) ``` ## Confidence intervals and standard errors Confidence intervals and standard errors for both the metric of interest and contrasts can be obtained either through bootstrapping or using the delta method. Bootstrap confidence intervals are calculated by specifying `ci = TRUE`, `boot = TRUE`, and providing the number of bootstrap samples using `B`. We can also set the seed using the `seed` argument to allow reproducibility. If instead the delta method is to be used to obtain confidence intervals then we specify `ci = TRUE`, `boot = FALSE`. The delta method obtains confidence intervals by calculating standard errors for a given transformation of the metric of interest and then assuming normality. The default is to use a log transformation; hence if `type = "survival"` the confidence intervals are symmetric for the log survival probabilities. Alternative transformations can be specified using the `trans` argument. The code below shows confidence intervals for marginal survival calculated through a bootstrap method (with `B = 100`) compared to a delta method. For computational efficiency here we only predict for 10 time points. ```{r} ss.weibull.sep.boot <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=10), ci = TRUE, boot = TRUE, B = 100, seed = 2367) ss.weibull.sep.deltam <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=10), ci = TRUE, boot = FALSE) plot(ss.weibull.sep.boot, ci = TRUE) + geom_ribbon(aes(x=time, ymin=survival_lci, ymax=survival_uci, color=at, linetype = "Delta method"), fill=NA, data=attr(ss.weibull.sep.deltam,"standpred_at")) + scale_linetype_manual(values = c("Bootstrap" = "solid", "Delta method"= "dashed")) + ggtitle("Comparison of bootstrap and delta method confidence intervals") ``` ## Adding age as a covariate Suppose age has been added as a covariate to the survival model. If age is not included in our `at` scenarios `standsurv` will by default produce standardized estimates of survival averaged over the age distribution in our study population. Alternatively we could pass a new prediction dataset to `standsurv` and obtain standardized estimates for this population. As an example, we obtain marginal survival estimates after fitting a stratified Weibull model, firstly standardized to the age-distribution of our study population and secondly standardized to an older population with mean age of 75 and standard deviation 5. ```{r} model.weibull.age.sep <- flexsurvreg(Surv(recyrs, censrec)~group2 + age, anc = list(shape = ~ group2 + age), data=bc, dist="weibullPH") ## Marginal survival standardized to age distribution of study population ss.weibull.age.sep.surv <- standsurv(model.weibull.age.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50) ) ## Marginal survival standardized to an older population # create a new prediction dataset as a copy of the bc data but whose ages are drawn from # a normal distribution with mean age 75, sd 5. newpred.data <- bc set.seed(247) newpred.data$age = rnorm(dim(bc)[1], 75, 5) ss.weibull.age2.sep.surv <- standsurv(model.weibull.age.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), newdata=newpred.data) ## Overlay both marginal survival curves plot(ss.weibull.age.sep.surv) + geom_line(aes(x=time, y=survival, color=at, linetype = "Older population"), data = attr(ss.weibull.age2.sep.surv, "standpred_at") ) + scale_linetype_manual(values = c("Study" = "solid", "Older population"= "dashed")) ``` ## Calculating expected survival and hazard in `standsurv` To overlay marginal expected survival or hazard curves we require a lifetable of population hazard rates. To demonstrate we use the US lifetable that comes with the `survival` package, called `survexp.us`. Other lifetables can be obtained directly from the Human Mortality Database (HMD) using the `HMDHFDplus` package. The `survexp.us` lifetable is a `ratetable` object with stratification factors age, sex and year. It gives rates of mortality per person-day for combinations of the stratification factors. A summary of the `survexp.us` object shows that the time-scale is in days. ```{r} summary(survexp.us) ``` To use the lifetable to get expected rates for our trial population we need to match age, sex and year variables in our dataset to those in the ratetable. We can use the `rmap` argument to do this. `standsurv` utilises the `survexp` function in the `survival` package to calculate expected survival over the times specified in `t` using the 'exact' method of Ederer. We note that sex in our data is coded the same as in the `ratetable` ("male" and "female") and importantly that we have variables that record both age at diagnosis and diagnosis date in days. It is important that the user ensures that the study data are correctly coded and have variables on the same timescale as in the `ratetable` so that matching is successful. The code below demonstrates that for our data we therefore need to match the `year` variable in the `ratetable` to the `diag` variable in our study data, and the `age` variable in the `ratetable` to the `agedays` variable in our study data. We need to specify three more arguments in `standsurv`. First, the lifetable, which must be a `ratetable` object and is specified using the `ratetable` argument. Second, we may need to pass our trial dataset to `standsurv` if the stratifying factors do not appear as covariates in the `flexsurv` model. Finally, we need to be careful to tell `standsurv` what the time scale transformation is between the fitted `flexsurv` model and the time scale in `ratetable`. We can use the `scale.ratetable` argument to do this. Typically ratetable objects are expressed in days (e.g. rates per person-day). The default is therefore `scale.ratetable = 365.25`, which indicates that the survival model was fitted in years but the ratetable is in days. After running `standsurv` we can plot the expected survival (or hazard) by using the argument `expected = TRUE` in the `plot()` function. ```{r} ss.weibull.sep.expected <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.expected, expected = T) ``` We can see that the marginal expected survival is much higher than the marginal (predicted) survival for our breast cancer population. We can also obtain the expected hazards: ```{r} ss.weibull.sep.expectedh <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.expectedh, expected = T) ``` The hazard plot shows that our model is predicting an increasing hazard over time for the cancer population, which remains significantly higher than the expected hazard in the general population. The monotonically increasing hazard imposed by the Weibull distribution may be implausible and this may make us question the suitability of a Weibull model if we wish to extrapolate. ## Incorporation of background mortality A relative survival model can be fitted using `flexsurv` by incorporating background mortality rates. The model then estimates excess hazard rates and relative survival measures. For prediction purposes, following the fitting of a relative survival model, `standsurv` allows the user to either obtain marginal predictions of relative survival / excess hazard or of all-cause survival / all-cause hazard. The latter are calculated by multiplying relative survival estimates with expected survival to get all-cause survival, or by adding excess hazard rates to expected hazard to get all-cause hazard. We demonstrate this by fitting a relative survival cure model to the breast cancer data and obtaining predicted all-cause survival and all-cause hazard up to 30-years after diagnosis. A mixture cure model makes the assumption that a proportion of the study population will never experience the event. In a relative survival framework the cure model assumes that the excess mortality rate approaches zero (or equivalently the relative survival reaches an asymptote determined by the cure fraction). We fit a relative survival cure model with a Weibull distribution assumed for the uncured. The relative survival mixture-cure model is fitted below. We must pass to `flexsurvcure` the expected hazard rates at the event / censoring time for each individual, as it is the expected rates at the event times that are used in the likelihood function for a parametric relative survival model. For this we need to initally do some data wrangling. Firstly, we calculate attained age and attained year (in whole years) at the event time for all study subjects. Secondly, we join the data with the expected rates using the matching variables attained age, attained year and sex. In the example, we express the expected rate as per person-year as this is the timescale used in the flexsurv regression model. ```{r} ## reshape US lifetable to be a tidy data.frame, and convert rates to per person-year as flexsurv regression is in years survexp.us.df <- as.data.frame.table(survexp.us, responseName = "exprate") %>% mutate(exprate = 365.25 * exprate) survexp.us.df$age <- as.numeric(as.character(survexp.us.df$age)) survexp.us.df$year <- as.numeric(as.character(survexp.us.df$year)) ## Obtain attained age and attained calendar year in (whole) years bc <- bc %>% mutate(attained.age.yr = floor(age + recyrs), attained.year = lubridate::year(diag + rectime)) ## merge in (left join) expected rates at event time bc <- bc %>% left_join(survexp.us.df, by = c("attained.age.yr"="age", "attained.year"="year", "sex"="sex")) # A stratified relative survival mixture-cure model model.weibull.sep.rs <- flexsurvcure(Surv(recyrs, censrec)~group2, anc = list(shape = ~ group2, scale = ~ group2), data=bc, dist="weibullPH", bhazard=exprate) model.weibull.sep.rs ``` We can now use `standsurv` to obtain all-cause survival and hazard predictions using `type = "survival"` and `type = "hazard"`. If instead we had wanted predictions of relative survival or excess hazards we would use `type = "relsurvival"` and `type = "excesshazard"`, respectively. ```{r} ## All-cause survival ss.weibull.sep.rs.surv <- standsurv(model.weibull.sep.rs, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.surv, expected = T) # All-cause hazard ss.weibull.sep.rs.haz <- standsurv(model.weibull.sep.rs, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.haz, expected = T) ``` The marginal excess hazard is now unimodal since the cure model is forcing the initially increasing excess hazard to tend to zero in the long-term where only 'cured' subjects remain. The marginal all-cause hazard tends to the expected hazard and follows it thereafter. A plot of the excess hazard confirms this. ```{r} # Excess hazard ss.weibull.sep.rs.excesshaz <- standsurv(model.weibull.sep.rs, type = "excesshazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.excesshaz) ``` # Conclusions `standsurv` is a powerful post-estimation command that allows easy calculation of a number of useful prediction metrics. Contrasts can be made between any counterfactual populations of interest and, through regression standardisation, allows the targeting of marginal estimands. Confidence intervals, via the delta method or bootstrapping, are available and benchmarking against or incorporating background mortality rates is also supported. # References flexsurv/inst/doc/flexsurv.R0000644000176200001440000002136014657664736015705 0ustar liggesusers## ----echo=FALSE------------------------------------------- options(width=60) options(prompt="R> ") library(knitr) opts_chunk$set(fig.path="flexsurv-") render_sweave() ## ----results='hide'--------------------------------------- library("flexsurv") ## --------------------------------------------------------- head(bc, 2) ## --------------------------------------------------------- fs1 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") ## --------------------------------------------------------- fs1 ## --------------------------------------------------------- survreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") ## ----results='hide',eval=FALSE---------------------------- # library(eha) # aftreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") ## --------------------------------------------------------- fs2 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "gengamma") fs3 <- flexsurvreg(Surv(recyrs, censrec) ~ group + sigma(group), data = bc, dist = "gengamma") ## ----eval=FALSE------------------------------------------- # fs3 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, # anc = list(sigma = ~ group), dist = "gengamma") ## ----surv,include=FALSE----------------------------------- cols <- c("#E495A5", "#86B875", "#7DB0DD") # from colorspace::rainbow_hcl(3) plot(fs1, col = cols[2], lwd.obs = 2, xlab = "Years", ylab = "Recurrence-free survival") lines(fs2, col = cols[3], lty = 2) lines(fs3, col = cols[3]) text(x=c(2,3.5,4), y=c(0.4, 0.55, 0.7), c("Poor","Medium","Good")) legend("bottomleft", col = c("black", cols[2], cols[3], cols[3]), lty = c(1, 1, 2, 1), bty = "n", lwd = rep(2, 4), c("Kaplan-Meier", "Weibull", "Generalized gamma (AFT)", "Generalized gamma (time-varying)")) ## ----haz,include=FALSE------------------------------------ plot(fs1, type = "hazard", col = cols[2], lwd.obs = 2, max.time=6, xlab = "Years", ylab = "Hazard") lines(fs2, type = "hazard", col = cols[3], lty = 2) lines(fs3, type = "hazard", col = cols[3]) text(x=c(2,2,2), y=c(0.3, 0.13, 0.05), c("Poor","Medium","Good")) legend("topright", col = c("black", cols[2], cols[3], cols[3]), lty = c(1, 1, 2, 1), bty = "n", lwd = rep(2, 4), c("Kernel density estimate", "Weibull", "Gen. gamma (AFT)", "Gen. gamma (time-varying)")) ## --------------------------------------------------------- median.weibull <- function(shape, scale) { qweibull(0.5, shape = shape, scale = scale) } summary(fs1, fn = median.weibull, t = 1, B = 10000) ## ----eval=FALSE------------------------------------------- # custom.llogis <- list(name = "llogis", pars = c("shape", "scale"), # location = "scale", # transforms = c(log, log), # inv.transforms = c(exp, exp), # inits = function(t){ c(1, median(t)) }) # fs4 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, # dist = custom.llogis) ## ----eval=FALSE------------------------------------------- # dmakeham3 <- function(x, shape1, shape2, scale, ...) { # dmakeham(x, shape = c(shape1, shape2), scale = scale, ...) # } # pmakeham3 <- function(q, shape1, shape2, scale, ...) { # pmakeham(q, shape = c(shape1, shape2), scale = scale, ...) # } ## ----eval=FALSE------------------------------------------- # dmakeham3 <- Vectorize(dmakeham3) # pmakeham3 <- Vectorize(pmakeham3) ## ----eval=FALSE------------------------------------------- # pmakeham3(c(0, 1, 1, Inf), 1, c(1, 1, 2, 1), 1) ## ----echo=FALSE------------------------------------------- options(warn=-1) ## --------------------------------------------------------- hweibullPH <- function(x, shape, scale = 1, log = FALSE){ hweibull(x, shape = shape, scale = scale ^ {-1 / shape}, log = log) } HweibullPH <- function(x, shape, scale = 1, log = FALSE){ Hweibull(x, shape = shape, scale = scale ^ {-1 / shape}, log = log) } custom.weibullPH <- list(name = "weibullPH", pars = c("shape", "scale"), location = "scale", transforms = c(log, log), inv.transforms = c(exp, exp), inits = function(t){ c(1, median(t[t > 0]) / log(2)) }) fs6 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = custom.weibullPH) fs6$res["scale", "est"] ^ {-1 / fs6$res["shape", "est"]} - fs6$res["groupMedium", "est"] / fs6$res["shape", "est"] - fs6$res["groupPoor", "est"] / fs6$res["shape", "est"] ## ----echo=FALSE------------------------------------------- options(warn=0) ## --------------------------------------------------------- sp1 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data = bc, k = 1, scale = "odds") ## --------------------------------------------------------- sp2 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group), data = bc, k = 1, scale = "odds") ## ----splinehaz,include=FALSE------------------------------ plot(sp1, type = "hazard", col=cols[3], ylim = c(0, 0.5), xlab = "Years", ylab = "Hazard") lines(sp2, type = "hazard", col = cols[3], lty = 2) lines(fs2, type = "hazard", col = cols[2]) text(x=c(2,2,2), y=c(0.3, 0.15, 0.05), c("Poor","Medium","Good")) legend("topright", col = c("black",cols[c(3,3,2)]), lty = c(1,1,2,1), lwd = rep(2,4), c("Kernel density estimate","Spline (proportional odds)", "Spline (time-varying)","Generalized gamma (time-varying)")) ## --------------------------------------------------------- sp3 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data = bc, k = 1, scale = "hazard") sp3$res[c("groupMedium", "groupPoor"), c("est", "se")] cox3 <- coxph(Surv(recyrs, censrec) ~ group, data = bc) coef(summary(cox3))[ , c("coef", "se(coef)")] ## --------------------------------------------------------- sp4 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + gamma2(group), data = bc, k = 1, scale = "hazard") ## ----eval=FALSE------------------------------------------- # flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + # gamma2(group) + treat + gamma1(treat), # data = bc, k = 1, scale = "hazard") ## --------------------------------------------------------- res <- t(sapply(list(fs1, fs2, fs3, sp1, sp2, sp3, sp4), function(x)rbind(-2 * round(x$loglik,1), x$npars, round(x$AIC,1)))) rownames(res) <- c("Weibull (fs1)", "Generalized gamma (fs2)", "Generalized gamma (fs3)", "Spline (sp1)", "Spline (sp2)", "Spline (sp3)", "Spline (sp4)") colnames(res) <- c("-2 log likelihood", "Parameters", "AIC") ## ----size="scriptsize"------------------------------------ res ## --------------------------------------------------------- gamma <- sp1$res[c("gamma0", "gamma1", "gamma2"), "est"] 1 - psurvspline(5, gamma = gamma, knots = sp1$knots) ## --------------------------------------------------------- pfn <- unroll.function(psurvspline, gamma = 0:2) 1 - pfn(5, gamma0 = gamma[1], gamma1 = gamma[2], gamma2 = gamma[3], knots = sp1$knots) ## --------------------------------------------------------- hsurvspline.lh <- function(x, gamma, knots){ if(!is.matrix(gamma)) gamma <- matrix(gamma, nrow = 1) lg <- nrow(gamma) nret <- max(length(x), lg) gamma <- apply(gamma, 2, function(x)rep(x, length = nret)) x <- rep(x, length = nret) loghaz <- rowSums(basis(knots, log(x)) * gamma) exp(loghaz) } ## --------------------------------------------------------- hsurvspline.lh3 <- unroll.function(hsurvspline.lh, gamma = 0:2) ## --------------------------------------------------------- custom.hsurvspline.lh3 <- list( name = "survspline.lh3", pars = c("gamma0", "gamma1", "gamma2"), location = c("gamma0"), transforms = rep(c(identity), 3), inv.transforms = rep(c(identity), 3) ) dtime <- log(bc$recyrs)[bc$censrec == 1] ak <- list(knots = quantile(dtime, c(0, 0.5, 1))) ## ----eval=FALSE------------------------------------------- # sp5 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, aux = ak, # inits = c(0, 0, 0, 0, 0), # dist = custom.hsurvspline.lh3, # method = "L-BFGS-B", lower = c(-Inf, -Inf, -0.5), # upper = c(Inf, Inf, 0.5), # control = list(trace = 1, REPORT = 1)) flexsurv/inst/doc/distributions.pdf0000644000176200001440000066471314657665141017307 0ustar liggesusers%PDF-1.5 %ÐÔÅØ 1 0 obj << /S /GoTo /D [2 0 R /Fit] >> endobj 5 0 obj << /Length 2976 /Filter /FlateDecode >> stream xڽɎÇõ>_AäDb¹»ªz3 ²â%2 òødùÐ${f(q¤¯ÏÛjkG‚ãä@²»¶·¯Åbr?)&?Þ£ßïno¾ù¡®&e£tYÙÉí<¶ªª&.Ui»ÉíròÛôMQVÏÊéð¾Žð9àë|¾}6³ÖLÿ¾’‰N¬æ¸ßpx·=>›£§85Üá|øµ…Ïbxöûí+F¢T]UiD¢Öª®ëÉÌtÊ5#ñò÷áùi·‡ï:‹ÏÿIñï+êÏt3}‡Xí¶ À˜IY¨®èJ03•*L;™•FUŽÌÂú׸ñ%žd¦ßþ­?!`G%>/è…Öýº•ÉÓsFá%¢°Á“æ™ZÂç~ù_Fœn UŠÉ„!¯4MŒ*ˆÃT)¢ÛsCRðy‹p‘©ðy'ã;aôß೑=8?ƒÏÜÉSö/dÿFÞÝYJÖ¼c´Ey¾¿½ySÚå¤-Ah­jÛÉbsóÛïÅd ï€.Óµ“GZ´™X‹Ëד_nþ}U;ÕÕºFÂu«•©›I]Ôª‚"ý¢íU­_œ”Ü/‰;œ4+«N•ÈÄNiݸ“HxA-éIt’Ätv’x-.Ûøù$2©¥Å)’Ëüì´%6Å‘õ‰V$"ÝÒÒŸ‡&‡Êý1²7Òã¶JôØj°Üf2Ó•j Ôý,Fö >€o¥§ËcÎ l­l…"¡mß26dzPðaEP«zÚ¯I Óc¡ƒÁª¢ì¾Vê$å Ã7 fÓyªzÄöþ¼‰P!è§]ð¼,ìÿ]|¦ª”!?aTYþ!éý«ß îkR|ü}’©u­ŠÎžf€Ç*P€¼8“ûMáˆññ5ÿÜ¡E¦(Ðë¶CÍéçÎ )0£\>ñš%¥Çt¦5SˆÍ¶±$‚‡ OamCpœãAÛžd~Ì0…82™5µªÁ½%±;£.¢Ò6(¬MÍÃ"ÝøxÒ+Vð¹/Ò—ã|H=%w² §í²?Q¼<æäcÉSŽÑ1ÞÇQdO‰œ8 {A/ Ž²œãÉá÷Ë?s¦zBþvÐ÷Lÿˆè‚]0Ê‚Þ(a9¢@1³Ò‘„DXÔ†°zw`Áמ ÞŠq¢6º$vÆ»³ËRÓ S+qM‚É–R¾Afç$á~%û·îAÎvgL§H5fŸ³J5eíLçy6R¨Bk·â}îŒR¿¢g>d‚J \dÝá‹'­œ}!C*vö‘9»‚ÇR?é%Ò&P:3­ ‰Xcƒ®Á3Jøœjæ)(^3•e_HÖ(eHïñÄ>„ç°|R¿%ò dþí6‘Wÿ(þÏœ³3º®[0ɶí8Á)“A;ÇÓ{†žÏý‰$§7 _8‡|“uºm•†²3Ñ鸞I“v-ªD Oãí55 Uü AÂåÕ#­]HVJB·?9 ë*ó3q^º žé³¬1à1º¦vVM ”ªÚ4Op½Uç&Ѫy g&‚g%x:ÅcAª!TšÁÙè1çÐ×™"r·[¯¸Û´”ÖN†Á!¼v\©!÷OX ]R/ÃkL'Ê#&Ò-%fp1ðȃ¤[βz ¯Á©Ç.kéeï ,Éž·÷ ºÏ–¶…äõOênAÔõ–䈕¾õ´`µªïš®ªDÄý–ÍÆhàuY]†‚þyXÉŽ¶>µÓ|±Á©‘‰š§¤ÑÿûìFzÚ!}–>™—¥ã{Ç7"e¾kŸÒ‡Dé™Dñ†(æ*ßUâ˜ïÉZ»:r½8ƒ>ôÓ/[>¡ré „”"¤@_oM¬Ñ°[ÆíK¹Qž‚­ §Šig]WÊv^öÔEßíŸUÒ(Œ’Æ®ÑCÿ™½âÕ^{YÕ„‚|ÃÞ•æZô±+#\Mß”ÆzI"ž"I.—Èëî°$¹ü¨/¤…gPß©÷™¯œì5âzRdÓõÈIØ©Ëú2ªôŸÉç,à K"îz’àrúÓkJ@IäÒ<Ò‚EáήyrŠ3—4÷Y\ÑX¹² "§94Aê¦m¦ý6+öNuUp (} ‘/: 8»;WÄ®™»´ fjV–¼lˆ •¤묮Ø2Æu£î»T­mâ ›‰Y,œ&›¼à®wqŠØ #"‚[ì}¾øT…D‹£e»­€HDÑrÃÓ¡âÊí²ÄÇqñ“  ½>‡±®C¶9«­|Eò]w¥µHSù"eŽHèFQ±ò7Ù|®³7è?§ÚÓã¨U{6)ÓÕbú×,V¥ÒfŒ”­£¤qêðÈÊ_é&ÕªNš%+¿‚‚E–„VÕuù¥R¾|ŒzF˜FPŸ,ò­È¢µq+RdMwáÑS[TøÙ±žn]]Øû‹œè>±—w²Û½ïêm]’«µ´¤ÒÂJ§3jä j~¤*° ?œ×‘®â†õ§q!v¼jžfGKiî@U3jý1¥RP> ¶ôrö=©×®‹¹êoP‚Ú¥÷(mÓû¢{//ŸB3>C4ÄqÛé'»­ —yŽd©ŸóEÝ(#èù:a1,Jڸǵ¼(+èšGK‹cÖQ#ØC×QG‰²]*P|¦l6ê¤ù`«m®%Å @ÉëKVÓB¢?n%¿pñÍ1–Ìi7Â[FQ½kA ·§žK=8QPØ ŽèƇ×둉òA 42Ï>‡‰ö"¾¥éÅŸÕ1Š?aç(Û¸¼gâ¢ã3eÄ€sx¦Îá­‹²Ž˜$w >bÁDÜ÷§Ö/±zÜ•Zw%,Ê©£ÊáÈ£õ’1 k7-ЕԆã¿%ôÞËýZFÊo ä[ùÏOÔÜL/xÓG)¹Ï E@\E½Ýè+Oæ¨þV>ßJ„žç{kp|×¾5¶\uJp¹¿Ù I³MeÿEôýíÍrý07 endstream endobj 2 0 obj << /Type /Page /Contents 5 0 R /Resources 4 0 R /MediaBox [0 0 595.276 841.89] /Parent 20 0 R /Annots [ 3 0 R ] >> endobj 3 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 1] /Rect [213.717 649.684 392.916 665.225] /Subtype/Link/A<> >> endobj 6 0 obj << /D [2 0 R /XYZ 80 770.89 null] >> endobj 7 0 obj << /D [2 0 R /XYZ 81 733.028 null] >> endobj 4 0 obj << /Font << /F65 8 0 R /F33 9 0 R /F77 10 0 R /F85 11 0 R /F64 12 0 R /F42 13 0 R /F39 14 0 R /F45 15 0 R /F52 16 0 R /F49 17 0 R /F43 18 0 R /F46 19 0 R >> /ProcSet [ /PDF /Text ] >> endobj 23 0 obj << /Length 1592 /Filter /FlateDecode >> stream xÚÍYÝoÛ6÷_!ôI&–ß7t@‡õ{(¶ÖÀ€5}Pm9ÉfÇ™í4^ÿúÝ‘”E9”í¶N“Åu<Þ÷»ŸB³óŒf¯¿ŒO_ ‘1J,µ,M³’eFb…ÊF“ì}·F¿=}YêXˆIK¤6 ÃÉœQ¦†,¯7ðgu–p}úqXH)ò_áþ_¬Ã |øˆRëð°¸Z !x¾¬áiZ¹ú þŒk\@ƒÁ»Ö%…P¤ÔÚÛóÔ©2ýmþqXp×3\jÈM~ë_3ÿS]MÂÿ K‘?‰&¯p®ñÓ> y™×¹á-:ráGд{‚7c¸ªu˜â…pÀ«¾@‰s©—^bÜøi¨T^5±ªpfPot^¡'7¦U°|^W+\8«ÆÑ\°Ã!,˜ JZ§ÛË° >þ!v-Ãq×?^b1õãOµ®Cˆ0`¾ýÁ .‚¢J/–UK?¯I„yãS[´·ñ*˜\¨¿³ñyªUƱJqLðWP“¼¿âÖÖq ÎÜåL;£ŠbÄÆã:¼h·#èVŸâÀe¸Y6fA,¶€&æ­1&NV°†Sb¬ñÖL£e6!¾ÛÃÓœÜ ¯’:'Û "«¸³Âñ [ù ®'p݆ÙÎÕ y®'‘‘»9190·ß’U“àp] ÏÂs$2C³Hdi#'y§Þ0K ³àpÚmé-}ç%…% ¬lëØšP' ‡ ´*–ÄÊFàï” A¨h—áú§aÁ4Ô‹”MÌVÆF1< %xî~êÍudh× K´fRšÒ_Yª/óùÚœ´Uöí~­5t«KÀ_E¥—Kº-‰µ:+"±¾íõúšIŽ¡tB€LþsR»!¦õ:é²"RÉH­ß ~•\¦Ù^•3†H&Á-Jhs’Û`v¤‰2 Ɉ¦“J»)+,ÒJ%ó¢3Ep"ùÖùωµ¬­Rk«È‹RÄk”Ë´‘J—‰´èÏ1 8F|¿Â"¢¦vQ {üVý~·ç¡ëÔÎyø"‡ºøõ”Qî¶[s}<Œ\cõ^\»ÎÃãïtª æ åg‡ñXqW3~‡ëõ7bG£ã^0dÆæaáIxîÅn…ã~BL‡0¥Íõc@Eí gÝöƒ &¤Ë÷b‹¹{–ä¾³ÄÕ:Ql@^Ðïj? 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%%EOF flexsurv/inst/doc/flexsurv-examples.R0000644000176200001440000001466514657665170017524 0ustar liggesusers### R code from vignette source 'flexsurv-examples.Rnw' ################################################### ### code chunk number 1: flexsurv-examples.Rnw:39-59 ################################################### library(flexsurv) hgengammaPH <- function(x, dummy, mu=0, sigma=1, Q){ dummy * hgengamma(x=x, mu=mu, sigma=sigma, Q=Q) } HgengammaPH <- function(x, dummy, mu=0, sigma=1, Q){ dummy * Hgengamma(x=x, mu=mu, sigma=sigma, Q=Q) } custom.gengammaPH <- list(name="gengammaPH", pars=c("dummy","mu","sigma","Q"), location="dummy", transforms=c(log, identity, log, identity), inv.transforms=c(exp, identity, exp, identity), inits=function(t){ lt <- log(t[t>0]) c(1, mean(lt), sd(lt), 0) }) fs7 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist=custom.gengammaPH, fixedpars=1) ################################################### ### code chunk number 2: flexsurv-examples.Rnw:84-127 ################################################### fs2 <- flexsurvreg(Surv(recyrs, censrec) ~ group + sigma(group), data=bc, dist="gengamma") B <- 5000 t <- seq(0.1, 8, by=0.1) hrAFT.est <- summary(fs2, t=t, type="hazard", newdata=data.frame(group="Medium"),ci=FALSE)[[1]][,"est"] / summary(fs2, t=t, type="hazard", newdata=data.frame(group="Good"),ci=FALSE)[[1]][,"est"] pars <- normboot.flexsurvreg(fs2, B=B, newdata=data.frame(group=c("Good","Medium"))) hrAFT <- matrix(nrow=B, ncol=length(t)) for (i in seq_along(t)){ haz.medium.rep <- do.call(hgengamma, c(list(t[i]), as.data.frame(pars[[2]]))) haz.good.rep <- do.call(hgengamma, c(list(t[i]), as.data.frame(pars[[1]]))) hrAFT[,i] <- haz.medium.rep / haz.good.rep } hrAFT <- apply(hrAFT, 2, quantile, c(0.025, 0.975)) hrPH.est <- summary(fs7, t=t, type="hazard", newdata=data.frame(group="Medium"),ci=FALSE)[[1]][,"est"] / summary(fs7, t=t, type="hazard", newdata=data.frame(group="Good"),ci=FALSE)[[1]][,"est"] pars <- normboot.flexsurvreg(fs7, B=B, newdata=data.frame(group=c("Good","Medium"))) hrPH <- matrix(nrow=B, ncol=length(t)) for (i in seq_along(t)){ haz.medium.rep <- do.call(hgengammaPH, c(list(t[i]), as.data.frame(pars[[2]]))) haz.good.rep <- do.call(hgengammaPH, c(list(t[i]), as.data.frame(pars[[1]]))) hrPH[,i] <- haz.medium.rep / haz.good.rep } hrPH <- apply(hrPH, 2, quantile, c(0.025, 0.975)) plot(t, hrAFT[1,], type="l", ylim=c(0, 10), col="red", xlab="Years", ylab="Hazard ratio (Medium / Good)", lwd=1, lty=2) lines(t, hrAFT[2,], col="red", lwd=1, lty=2) lines(t, hrPH[1,], col="darkgray", lwd=1, lty=2) lines(t, hrPH[2,], col="darkgray", lwd=1, lty=2) lines(t, hrAFT.est, col="red", lwd=2) lines(t, hrPH.est, col="darkgray", lwd=2) legend("topright", lwd=c(2,2), col=c("red","darkgray"), bty="n", c("Generalized gamma: standard AFT", "Generalized gamma: proportional hazards")) ################################################### ### code chunk number 3: flexsurv-examples.Rnw:132-146 (eval = FALSE) ################################################### ## nd <- data.frame(group=c("Good","Medium")) ## hr_aft <- hr_flexsurvreg(fs2, t=t, newdata=nd) ## hr_ph <- hr_flexsurvreg(fs7, t=t, newdata=nd) ## ## plot(t, hr_aft$lcl, type="l", ylim=c(0, 10), col="red", xlab="Years", ## ylab="Hazard ratio (Medium / Good)", lwd=1, lty=2) ## lines(t, hr_aft$ucl, col="red", lwd=1, lty=2) ## lines(t, hr_aft$est, col="red", lwd=2) ## ## lines(t, hr_ph$lcl, col="darkgray", lwd=1, lty=2) ## lines(t, hr_ph$ucl, col="darkgray", lwd=1, lty=2) ## lines(t, hr_ph$est, col="darkgray", lwd=2) ## legend("topright", lwd=c(2,2), col=c("red","darkgray"), bty="n", ## c("Generalized gamma: standard AFT", "Generalized gamma: proportional hazards")) ################################################### ### code chunk number 4: flexsurv-examples.Rnw:168-170 ################################################### summary(fs2, type="rmst", t=100, tidy=TRUE) summary(fs2, fn=rmst_gengamma, t=100, tidy=TRUE) ################################################### ### code chunk number 5: flexsurv-examples.Rnw:174-176 ################################################### est <- fs2$res[,"est"] rmst_gengamma(t=100, mu=est[1], sigma=est[2], Q=est[3]) ################################################### ### code chunk number 6: flexsurv-examples.Rnw:180-181 ################################################### summary(fs2, type="median") ################################################### ### code chunk number 7: flexsurv-examples.Rnw:211-231 ################################################### if (require("TH.data")){ GBSG2 <- transform(GBSG2, X1a=(age/50)^-2, X1b=(age/50)^-0.5, X4=tgrade %in% c("II","III"), X5=exp(-0.12*pnodes), X6=(progrec+1)^0.5 ) (progc <- coxph(Surv(time, cens) ~ horTh + X1a + X1b + X4 + X5 + X6, data=GBSG2)) (prog3 <- flexsurvspline(Surv(time, cens) ~ horTh + X1a + X1b + X4 + X5 + X6, k=3, data=GBSG2)) predc <- predict(progc, type="lp") progc <- cut(predc, quantile(predc, 0:3/3)) predf <- model.matrix(prog3) %*% prog3$res[-(1:5),"est"] progf <- cut(predf, quantile(predf, 0:3/3)) table(progc, progf) } ################################################### ### code chunk number 8: flexsurv-examples.Rnw:251-255 ################################################### set.seed(1) nsim <- 10000 onsetday <- runif(nsim, 0, 30) deathday <- onsetday + rgamma(nsim, shape=1.5, rate=1/10) ################################################### ### code chunk number 9: flexsurv-examples.Rnw:265-269 ################################################### datt <- data.frame(delay = deathday - onsetday, event = rep(1, nsim), rtrunc = 40 - onsetday) datt <- datt[datt$delay < datt$rtrunc, ] ################################################### ### code chunk number 10: flexsurv-examples.Rnw:279-282 ################################################### fitt <- flexsurvreg(Surv(delay, event) ~ 1, data=datt, rtrunc = rtrunc, dist="gamma") fitt summary(fitt, t=1, fn = mean_gamma) flexsurv/inst/doc/multistate.R0000644000176200001440000002140314657665122016206 0ustar liggesusers## ----echo=FALSE------------------------------------------- options(width=60) options(prompt="R> ") library(knitr) opts_chunk$set(fig.path="flexsurv-") render_sweave() ## --------------------------------------------------------- library(flexsurv) bosms3[18:22, ] ## --------------------------------------------------------- crexp <- flexsurvreg(Surv(years, status) ~ trans, data = bosms3, dist = "exp") crwei <- flexsurvreg(Surv(years, status) ~ trans + shape(trans), data = bosms3, dist = "weibull") cfwei <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans + shape(trans), data = bosms3, dist = "weibull") ## --------------------------------------------------------- crcox <- coxph(Surv(years, status) ~ strata(trans), data = bosms3) cfcox <- coxph(Surv(Tstart, Tstop, status) ~ strata(trans), data = bosms3) ## --------------------------------------------------------- mod_nobos_bos <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data = bosms3, dist = "weibull") mod_nobos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "weibull") mod_bos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==3), data = bosms3, dist = "weibull") ## --------------------------------------------------------- tmat <- rbind(c(NA, 1, 2), c(NA, NA, 3), c(NA, NA, NA)) crfs <- fmsm(mod_nobos_bos, mod_nobos_death, mod_bos_death, trans = tmat) ## --------------------------------------------------------- require("mstate") mrcox <- msfit(crcox, trans = tmat) mfcox <- msfit(cfcox, trans = tmat) ## --------------------------------------------------------- tgrid <- seq(0, 14, by = 0.1) mrwei <- msfit.flexsurvreg(crwei, t = tgrid, trans = tmat) mrexp <- msfit.flexsurvreg(crexp, t = tgrid, trans = tmat) mfwei <- msfit.flexsurvreg(cfwei, t = tgrid, trans = tmat) ## ----cumhaz,include=FALSE--------------------------------- cols <- c("black", "#E495A5", "#86B875", "#7DB0DD") # colorspace::rainbow_hcl(3) plot(mrcox, xlab = "Years after baseline", lwd = 3, xlim = c(0, 14), cols = cols[1:3]) for (i in 1:3){ lines(tgrid, mrexp$Haz$Haz[mrexp$Haz$trans == i], col = cols[i], lty = 2, lwd = 2) lines(tgrid, mrwei$Haz$Haz[mrwei$Haz$trans == i], col = cols[i], lty = 3, lwd = 2) } lines(mfcox$Haz$time[mfcox$Haz$trans == 3], mfcox$Haz$Haz[mfcox$Haz$trans == 3], type = "s", col = cols[4], lty = 1, lwd = 2) lines(tgrid, mfwei$Haz$Haz[mfwei$Haz$trans == 3], col = cols[4], lty = 3, lwd = 2) legend("topleft", inset = c(0, 0.2), lwd = 2, col = cols[4], c("2 -> 3 (clock-forward)"), bty = "n") legend("topleft", inset = c(0, 0.3), c("Non-parametric", "Exponential", "Weibull"), lty = c(1, 2, 3), lwd = c(3, 2, 2), bty = "n") ## --------------------------------------------------------- pmatrix.fs(cfwei, t = c(5, 10), trans = tmat) ## ----eval=FALSE------------------------------------------- # pmatrix.simfs(crwei, trans = tmat, t = 5) # pmatrix.simfs(crwei, trans = tmat, t = 10) ## --------------------------------------------------------- ptc <- probtrans(mfcox, predt = 0, direction = "forward")[[1]] round(ptc[c(165, 193),], 3) ## --------------------------------------------------------- ptw <- probtrans(mfwei, predt = 0, direction = "forward")[[1]] round(ptw[ptw$time %in% c(5, 10),], 3) ## ----eval=FALSE------------------------------------------- # mssample(mrcox$Haz, trans = tmat, clock = "reset", M = 1000, # tvec = c(5, 10)) # mssample(mrwei$Haz, trans = tmat, clock = "reset", M = 1000, # tvec = c(5, 10)) ## --------------------------------------------------------- tmat_nobos <- rbind("No BOS"=c(NA,1,2), "BOS"=c(NA,NA,NA),"Death"=c(NA,NA,NA)) crfs_nobos <- fmsm(mod_nobos_bos, mod_nobos_death, trans = tmat_nobos) pmatrix.fs(crfs_nobos, from=1, t=100000)["No BOS",c("BOS","Death")] ## --------------------------------------------------------- modexp_nobos_bos <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data = bosms3, dist = "exponential") modexp_nobos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "exponential") crfs_nobos <- fmsm(modexp_nobos_bos, modexp_nobos_death, trans=tmat_nobos) pmatrix.fs(crfs_nobos, from=1, t=100000)["No BOS",c("BOS","Death")] rate12 <- modexp_nobos_bos$res["rate","est"] rate13 <- modexp_nobos_death$res["rate","est"] rate12 / (rate12 + rate13) ## --------------------------------------------------------- crfs_nobos <- fmsm(mod_nobos_bos, mod_nobos_death, trans = tmat_nobos) simfinal_fmsm(crfs_nobos, probs = c(0.25, 0.5, 0.75), M=10000) ## --------------------------------------------------------- simfinal_fmsm(crfs, probs = c(0.25, 0.5, 0.75), M=10000) ## --------------------------------------------------------- bosms3[bosms3$id %in% c(4,5),] bosmx3 <- bosms3 bosmx3$Tstart <- bosmx3$Tstop <- bosmx3$trans <- NULL bosmx3 <- bosmx3[!(bosmx3$status==0 & duplicated(paste(bosmx3$id, bosmx3$from))),] bosmx3$event <- ifelse(bosmx3$status==0, NA, bosmx3$to) bosmx3$event <- factor(bosmx3$event, labels=c("BOS","Death")) bosmx3$to <- NULL bosmx3[bosmx3$id %in% c(4,5),] ## --------------------------------------------------------- bosfs <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) bosfs ## --------------------------------------------------------- set.seed(1) bosmx3$x <- rnorm(nrow(bosmx3),0,1) bosfsp <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential"), pformula = ~ x) bosfsp ## --------------------------------------------------------- bosfst <- flexsurvmix(Surv(years, status) ~ x, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) ## --------------------------------------------------------- flexsurvmix(list(Surv(years, status) ~ x, Surv(years, status) ~ 1), event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) ## --------------------------------------------------------- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential"), anc = list(BOS=list(shape=~x), Death=list(rate=~1))) ## --------------------------------------------------------- nd <- data.frame(x=c(0,1)) probs_flexsurvmix(bosfsp, newdata=nd, B=50) ## --------------------------------------------------------- mean_flexsurvmix(bosfst, newdata=nd) quantile_flexsurvmix(bosfst, B=50, newdata=nd, probs=c(0.25, 0.5, 0.75)) ## --------------------------------------------------------- p_flexsurvmix(bosfst, t=c(5, 10), B=10, startname="No BOS") ## --------------------------------------------------------- bdat <- bosmx3[bosmx3$from==2,] bdat$event <- factor(bdat$event) bosfst_bos <- flexsurvmix(Surv(years, status) ~ x, event=event, data=bdat, dists = c(Death="exponential")) bosfmix <- fmixmsm("No BOS"=bosfst, "BOS"=bosfst_bos) ## --------------------------------------------------------- ppath_fmixmsm(bosfmix, B=20) ppath_fmixmsm(bosfmix, B=20, final=TRUE) ## --------------------------------------------------------- meanfinal_fmixmsm(bosfmix, B=10) qfinal_fmixmsm(bosfmix, B=10) meanfinal_fmixmsm(bosfmix, B=10, final=TRUE) ## ----fig.height=3----------------------------------------- aj <- ajfit_flexsurvmix(bosfs, start="No BOS") bosfs_bos <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bdat, dists = c(Death="exponential")) aj2 <- ajfit_flexsurvmix(bosfs_bos, start="BOS") library(ggplot2) ggplot(aj, aes(x=time, y=val, lty=model, col=state)) + geom_line() + xlab("Years after transplant") + ylab("Probability of having moved to state") ggplot(aj2, aes(x=time, y=val, lty=model, col=state)) + xlab("Years after transplant") + ylab("Probability of having moved to state") + geom_line() ## ----message=FALSE---------------------------------------- library(dplyr) aj3 <- ajfit_fmsm(crfs_nobos) %>% filter(model=="Parametric") %>% mutate(model = "Cause specific hazards") %>% mutate(state = factor(state, labels=c("No BOS","BOS","Death"))) %>% full_join(aj) ggplot(aj3, aes(x=time, y=val, lty=model, col=state)) + xlab("Years after transplant") + ylab("Probability of having moved to state") + geom_line() flexsurv/inst/doc/multistate.Rnw0000644000176200001440000014302114471114027016537 0ustar liggesusers%\VignetteIndexEntry{Multi-state modelling with flexsurv} %\VignetteEngine{knitr::knitr} % \documentclass[article,shortnames]{jss} \documentclass[article,shortnames,nojss,nofooter]{jss} \usepackage{bm} \usepackage{tabularx} \usepackage{graphics} \usepackage{alltt} \usepackage[utf8]{inputenc} <>= options(width=60) options(prompt="R> ") library(knitr) opts_chunk$set(fig.path="flexsurv-") render_sweave() @ %% need no \usepackage{Sweave.sty} \author{Christopher H. Jackson \\ MRC Biostatistics Unit, Cambridge, UK} \title{Flexible parametric multi-state modelling with flexsurv} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Address{ Christopher Jackson\\ MRC Biostatistics Unit\\ Cambridge Institute of Public Health\\ Robinson Way\\ Cambridge, CB2 0SR, U.K.\\ E-mail: \email{chris.jackson@mrc-bsu.cam.ac.uk} } \Abstract{ A \emph{multi-state model} represents how an individual moves between multiple states in continuous time. Survival analysis is a special case with two states, ``alive'' and ``dead''. \emph{Competing risks} are a further special case, where there are multiple causes of death, that is, one starting state and multiple possible destination states. This vignette describes the two forms of multi-state or competing risks models that can be implemented in \pkg{flexsurv}. Section~\ref{sec:causespec} describes models based on \emph{cause-specific hazards}. Section~\ref{sec:mixture} describes a less commonly-used approach based on \emph{mixture models}. Cause-specific hazards models tend to be faster to fit, whereas the parameters of the mixture models are easier to interpret. } \Keywords{multi-state models, multistate models, competing risks} \begin{document} \section{Overview} \label{sec:multistate} This vignette describes multi-state models for data where there are a series of event times $t_{1},\dots, t_{n}$ for an individual, corresponding to changes of state. The last of these may be an observed or right-censored event time. Note \emph{panel data} are not considered here --- that is, observations of the state of the process at an arbitrary set of times \citep{kalbfleisch:lawless}. In panel data, we do not necessarily know the time of each transition, or even whether transitions of a certain type have occurred at all between a pair of observations. Multi-state models for that type of data (and also exact event times) can be fitted with the \pkg{msm} package for \proglang{R} \citep{msmjss}, but are restricted to (piecewise) exponential event time distributions. Knowing the exact event times enables much more flexible models, which \pkg{flexsurv} can fit. The \pkg{flexsurv} package provides two general frameworks for multi-state modelling. \begin{enumerate} \item The most common framework is based on \emph{cause-specific hazards} of competing risks. This is an extension of standard survival modelling, and is explained in Section~\ref{sec:causespec}. \item An alternative approach is based on \emph{mixture models}. For example, suppose there are three competing states that an individual in state $r$ may move to next. People are then classified into three \emph{mixture components}, defined by the state the person moves to. The probabilities of each next state, and the distribution of the time of moving to each state, are estimated jointly. These quantities are easier to interpret than cause specific hazards. This approach was originally described by \citet{larson1985mixture}. In Section~\ref{sec:mixture} we explain how to implement it using the \code{flexsurvmix} function. \end{enumerate} \section{Multi-state modelling using cause-specific hazards} \label{sec:causespec} Given that an individual is in state $X(t)$ at time $t$, their next state, and the time of the change, are governed by a set of \emph{transition intensities} or \emph{transition hazards} \[q_{rs}(t,\mathbf{z}(t),\mathcal{F}_t) = \lim_{\delta t \rightarrow 0} \Prob(X(t+\delta t) = s | X(t) = r, \mathbf{z}(t), \mathcal{F}_t) / \delta t \] for states $r, s = 1,\dots,R$, which for a survival model are equivalent to the hazard $h(t)$. The intensity represents the instantaneous risk of moving from state $r$ to state $s$, and is zero if the transition is impossible. It may depend on covariates $\mathbf{z}(t)$, the time $t$ itself, and possibly also the ``history'' of the process up to that time, $\mathcal{F}_t$: the states previously visited or the length of time spent in them. \paragraph{Alternative time scales} In semi-Markov (``clock-reset'') models, $q_{rs}(t)$ is defined as a function of the time $t$ since entry into the current state. Any software to fit survival models can also fit this kind of multi-state model, as the following sections will explain. In an inhomogeneous Markov model, $t$ represents the time since the beginning of the process (that is, a ``clock-forward'' scale is used), but the intensity $q_{rs}(t)$ does not depend further on $\mathcal{F}_t$. Again, standard survival modelling software can be used, with the additional requirement that it can deal with left-truncation or \emph{counting process} data, which \code{survreg}, for example, does not currently support. These approaches are equivalent for competing risks models, since there is at most one transition for each individual, so that the time since the beginning of the process equals the time spent in the current state. Therefore no left-truncation is necessary. Note also that in a clock-reset model, the time since the beginning of the process may enter the model as a covariate. Likewise, in a clock-forward model, the time spent in the current state may enter as a covariate, in which case the model is no longer Markov. \paragraph{Example} For illustration, consider a simple three-state example, previously studied by \citet{heng:paper}. Recipients of lung transplants are are risk of bronchiolitis obliterans syndrome (BOS). This was defined as a decrease in lung function to below 80\% of a baseline value defined in the six months following transplant. A three-state ``illness-death'' model represents the risk of developing BOS, the risk of dying before developing BOS, and the risk of death after BOS. BOS is assumed to be irreversible, so there are only three allowed transitions (Figure \ref{fig:bosmsm}), each with an intensity function $q_{rs}(t)$. \begin{figure}[h] \centering \scalebox{0.6}{\includegraphics{bosmsm.pdf}} \caption{Three-state multi-state model for bronchiolitis obliterans syndrome (BOS).} \label{fig:bosmsm} \end{figure} \subsection{Representing multi-state data as survival data} \label{sec:multistate:data} \citet{andersen:keiding} and \citet{putter:mstate} explain how to implement multi-state models by manipulating the data into a suitable form for survival modelling software --- an overview is given here. For each permitted $r \rightarrow s$ transition in the multi-state model, there is a corresponding ``survival'' (time-to-event) model, with hazard rates defined by $q_{rs}(t)$. For a patient who enters state $r$ at time $t_{j}$, their next event at $t_{j+1}$ is defined by the model structure to be one of a set of competing events $s_1,\ldots,s_{n_r}$. This implies there are $n_r$ corresponding survival models for this state $r$, and $\sum_r n_r$ models over all states $r$. In the BOS example, there are $n_1=2,n_2=1$ and $n_3=0$ possible transitions from states 1, 2 and 3 respectively. The data to inform the $n_r$ models from state $r$ consists firstly of an indicator for whether the transition to the corresponding state $s_1,\ldots,s_{n_r}$ is observed or censored at $t_{j+1}$. If the individual moves to state $s_k$, the transitions to all other states in this set are censored at this time. This indicator is coupled with: \begin{itemize} \item (for a semi-Markov model) the time elapsed $dt_{j} = t_{j+1} - t_{j}$ from state $r$ entry to state $s$ entry. The ``survival'' model for the $r \rightarrow s$ transition is fitted to this time. \item (for an inhomogeneous Markov model) the start and stop time $(t_j,t_{j+1})$, as in \S\ref{sec:censtrunc}. The $r \rightarrow s$ model is fitted to the right-censored time $t_{j+1}$ from the \emph{start of the process}, but is conditional on not experiencing the $r \rightarrow s$ transition until after the state $r$ entry time. In other words, the $r \rightarrow s$ transition model is \emph{left-truncated} at the state $r$ entry time. \end{itemize} In this form, the outcomes of two patients in the BOS data are <<>>= library(flexsurv) bosms3[18:22, ] @ Each row represents an observed (\code{status = 1}) or censored (\code{status = 0}) transition time for one of three time-to-event models indicated by the categorical variable \code{trans} (defined as a factor). Times are expressed in years, with the baseline time 0 representing six months after transplant. Values of \code{trans} of 1, 2, 3 correspond to no BOS$\rightarrow$BOS, no BOS$\rightarrow$death and BOS$\rightarrow$death respectively. The first row indicates that the patient (\code{id} 7) moved from state 1 (no BOS) to state 2 (BOS) at 0.17 years, but (second row) this is also interpreted as a censored time of moving from state 1 to state 3, potential death before BOS onset. This patient then died, given by the third row with \code{status} 1 for \code{trans} 3. Patient 8 died before BOS onset, therefore at 8.2 years their potential BOS onset is censored (fourth row), but their death before BOS is observed (fifth row). The \pkg{mstate} \proglang{R} package \citep{mstate:cmpb,mstate:jss} has a utility \code{msprep} to produce data of this form from ``wide-format'' datasets where rows represent individuals, and times of different events appear in different columns. \pkg{msm} has a similar utility \code{msm2Surv} for producing the required form given longitudinal data where rows represent state observations. \subsection{Multi-state model likelihood with cause-specific hazards} \label{sec:multistate:lik} After forming survival data as described above, a multi-state model can be fitted by maximising the standard survival model likelihood~(given at the start of the main \pkg{flexsurv} vignette), $l(\bm{\theta} | \mathbf{x}) = \prod_i l_i(\bm{\theta}|x_i)$, where $\mathbf{x}$ is the data, and $i$ now indexes multiple observations for multiple individuals. This can also be written as a product over the $K=\sum_r n_r$ transitions $k$, and the $m_k$ observations $j$ pertaining to the $k$th transition. The transition type will typically enter this model as a categorical covariate --- see the examples in the next section. \begin{equation} \label{eq:lik:multistate} l(\bm{\theta} | \mathbf{x}) = \prod_{k=1}^K \prod_{j=1}^{m_k} l_{jk}(\bm{\theta}|\mathbf{x}_{jk}) \end{equation} Therefore if the parameter vector $\bm{\theta}$ can be partitioned as $(\bm{\theta}_1|\ldots|\bm{\theta}_K)$, independent components for each transition $k$, the likelihood becomes the product of $K$ independent transition-specific likelihoods \citep{andersen:keiding}. The full multi-state model can then be fitted by maximising each of these independently, using $K$ separate calls to a survival modelling function such as \code{flexsurvreg}. This can give vast computational savings over maximising the joint likelihood for $\bm{\theta}$ with a single fit. For example, \citet{francesca:smmr} used \pkg{flexsurv} to fit a parametric multi-state model with 21 transitions and 84 parameters for over 30,000 observations, which was computationally impractical via the joint likelihood, whereas it only took about a minute to perform 21 transition-specific fits. On the other hand, if any parameters are constrained between transitions (e.g. if hazards are proportional between transitions, or the effects of covariates on different transitions are the same) then it is necessary to maximise the joint likelihood~(\ref{eq:lik:multistate}) with a single call. \subsection{Fitting parametric multi-state models with cause-specific hazards} \label{sec:multistate:fitting} \paragraph{Joint likelihood} Three multi-state models are fitted to the BOS data using \code{flexsurvreg}, firstly using a single likelihood maximisation for each model. The first two use the ``clock-reset'' time scale. \code{crexp} is a simple time-homogeneous Markov model where all transition intensities are constant through time, so that the clock-forward and clock-reset scales are identical. The time to the next event is exponentially-distributed, but with a different rate $q_{rs}$ for each transition type \code{trans}. \code{crwei} is a semi-Markov model where the times to BOS onset, death without BOS and the time from BOS onset to death all have Weibull distributions, with a different shape and scale for each transition type. \code{cfwei} is a clock-forward, inhomogeneous Markov version of the Weibull model: the 1$\rightarrow$2 and 1$\rightarrow$3 transition models are the same, but the third has a different interpretation, now the time \emph{from baseline} to death with BOS has a Weibull distribution. <<>>= crexp <- flexsurvreg(Surv(years, status) ~ trans, data = bosms3, dist = "exp") crwei <- flexsurvreg(Surv(years, status) ~ trans + shape(trans), data = bosms3, dist = "weibull") cfwei <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans + shape(trans), data = bosms3, dist = "weibull") @ \paragraph{Semi-parametric equivalents} The equivalent Cox models are also fitted using \code{coxph} from the \pkg{survival} package. These specify a different baseline hazard for each transition type through a function \code{strata} in the formula, so since there are no other covariates, they are essentially non-parametric. Note that the \code{strata} function is not currently understood by \code{flexsurvreg} --- the user must say explicitly what parameters, if any, vary with the transition type, as in \code{crwei}. <<>>= crcox <- coxph(Surv(years, status) ~ strata(trans), data = bosms3) cfcox <- coxph(Surv(Tstart, Tstop, status) ~ strata(trans), data = bosms3) @ In all cases, if there were other covariates, they could simply be included in the model formula. Typically, covariate effects will vary with the transition type, so that an interaction term with \code{trans} would be included. Some post-processing might then be needed to combine the main covariate effects and interaction terms into an easily-interpretable quantity (such as the hazard ratio for the $r,s$ transition). Alternatively, \pkg{mstate} has a utility \code{expand.covs} to expand a single covariate in the data into a set of transition-specific covariates, to aid interpretation \citep[see][]{mstate:jss}. \paragraph{Transition-specific models} In this small example, the joint likelihood can be maximised easily with a single function call, but for larger models and datasets, this may be unfeasible. A more computationally-efficient approach is to fit a list of transition-specific models, as follows. <<>>= mod_nobos_bos <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data = bosms3, dist = "weibull") mod_nobos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "weibull") mod_bos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==3), data = bosms3, dist = "weibull") @ We then define a matrix \code{tmat} describes the transition structure of the multi-state model , as a matrix of integers whose $r,s$ entry is $i$ if the $i$th transition type is $r,s$, and has \code{NA}s on the diagonal and where the $r,s$ transition is disallowed. <<>>= tmat <- rbind(c(NA, 1, 2), c(NA, NA, 3), c(NA, NA, NA)) crfs <- fmsm(mod_nobos_bos, mod_nobos_death, mod_bos_death, trans = tmat) @ The three transition models are then grouped together, and the transition matrix is attached, using the \code{fmsm} function. This constructs an R object, \code{crfs}, that fully describes the multistate model. The \code{fmsm} object can be supplied to the output and prediction functions described in the subsequent sections, instead of a single \code{flexsurvreg} object. However, this approach is not possible if there are constraints in the parameters across transitions, such as common covariate effects. \begin{sloppypar} Any parametric distribution can be employed in a multi-state model, just as for standard survival models, with \code{flexsurvreg}. Spline models may also be fitted with \code{flexsurvspline}, and if hazards are assumed proportional, they are expected to give similar results to the Cox model. Since \pkg{flexsurv} version 2.0, different parametric families can be used for different transitions, though in earlier versions, the same family had to be used. \end{sloppypar} \subsection{Obtaining cumulative transition-specific hazards} Multi-state models can be characterised by their cumulative $r \rightarrow s$ transition-specific hazard functions $H_{rs}(t) = \int_0^t q_{rs}(u)du$. For \emph{semi-parametric} multi-state models fitted with \code{coxph}, the function \code{msfit} in \pkg{mstate} \citep{mstate:cmpb,mstate:jss} provides piecewise-constant estimates and covariances for $H_{rs}(t)$. For the Cox models for the BOS data, <<>>= require("mstate") mrcox <- msfit(crcox, trans = tmat) mfcox <- msfit(cfcox, trans = tmat) @ \pkg{flexsurv} provides an analogous function \code{msfit.flexsurvreg} to produce cumulative hazards from \emph{fully-parametric} multi-state models in the same format. This is a short wrapper around \code{summary.flexsurvreg(..., type = "cumhaz")}, previously mentioned in \S\ref{sec:plots}. The difference from \pkg{mstate}'s method is that hazard estimates can be produced for any grid of times \code{t}, at any level of detail and even beyond the range of the data, since the model is fully parametric. The argument \code{newdata} can be used in the same way to specify a desired covariate category, though in this example there are no covariates in addition to the transition type. The name of the (factor) covariate indicating the transition type can also be supplied through the \code{tvar} argument, in this case it is the default, \code{"trans"}. <<>>= tgrid <- seq(0, 14, by = 0.1) mrwei <- msfit.flexsurvreg(crwei, t = tgrid, trans = tmat) mrexp <- msfit.flexsurvreg(crexp, t = tgrid, trans = tmat) mfwei <- msfit.flexsurvreg(cfwei, t = tgrid, trans = tmat) @ These can be plotted (Figure \ref{fig:bos:cumhaz}) to show the fit of the parametric models compared to the non-parametric estimates. Both models appear to fit adequately, though give diverging extrapolations after around 6 years when the data become sparse. The Weibull clock-reset model has an improved AIC of \Sexpr{round(crwei$AIC)}, compared to \Sexpr{round(crexp$AIC)} for the exponential model. For the $2\rightarrow 3$ transition, the clock-forward and clock-reset models give slightly different hazard trajectories. <>= cols <- c("black", "#E495A5", "#86B875", "#7DB0DD") # colorspace::rainbow_hcl(3) plot(mrcox, xlab = "Years after baseline", lwd = 3, xlim = c(0, 14), cols = cols[1:3]) for (i in 1:3){ lines(tgrid, mrexp$Haz$Haz[mrexp$Haz$trans == i], col = cols[i], lty = 2, lwd = 2) lines(tgrid, mrwei$Haz$Haz[mrwei$Haz$trans == i], col = cols[i], lty = 3, lwd = 2) } lines(mfcox$Haz$time[mfcox$Haz$trans == 3], mfcox$Haz$Haz[mfcox$Haz$trans == 3], type = "s", col = cols[4], lty = 1, lwd = 2) lines(tgrid, mfwei$Haz$Haz[mfwei$Haz$trans == 3], col = cols[4], lty = 3, lwd = 2) legend("topleft", inset = c(0, 0.2), lwd = 2, col = cols[4], c("2 -> 3 (clock-forward)"), bty = "n") legend("topleft", inset = c(0, 0.3), c("Non-parametric", "Exponential", "Weibull"), lty = c(1, 2, 3), lwd = c(3, 2, 2), bty = "n") @ \begin{figure}[h] \includegraphics{flexsurv-cumhaz-1} \caption{Cumulative hazards for three transitions in the BOS multi-state model (clock-reset), under non-parametric, exponential and Weibull models. For the $2\rightarrow 3$ transition, an alternative clock-forward scale is shown for the non-parametric and Weibull models.} \label{fig:bos:cumhaz} \end{figure} \subsection{Prediction from parametric multi-state models with cause-specific hazards} The \emph{transition probabilities} of the multi-state model are the probabilities of occupying each state $s$ at time $t > t_0$, given that the individual is in state $r$ at time $t_0$. \[ P(t_0, t) = \Prob(X(t) = s | X(t_0) = r) \] \paragraph{Markov models} For a time-inhomogeneous Markov model, these are related to the transition intensities via the Kolmogorov forward equation \[ \frac{d P(t_0,t)}{dt} = P(t_0,t) Q(t) \] with initial condition $P(t_0,t_0) = I$ \citep{cox:miller}. This can be solved numerically, as in \citet{titman:nonhomog}. This is implemented in the function \code{pmatrix.fs}, using the \pkg{deSolve} package \citep{deSolve}. This returns the full transition probability matrix $P(t_0,t)$ from time $t_0=0$ to a time or set of times $t$ specified in the call. Under the Weibull model, the probability of remaining alive and free of BOS is estimated at 0.3 at 5 years and 0.09 at 10 years: <<>>= pmatrix.fs(cfwei, t = c(5, 10), trans = tmat) @ Confidence intervals can be obtained by simulation from the asymptotic distribution of the maximum likelihood estimates --- see \code{help(pmatrix.fs)} for full details. A similar function \code{totlos.fs} is provided to estimate the expected total amount of time spent in state $s$ up to time $t$ for a process that starts in state $r$, defined as $\int_{u=0}^tP(0,u)_{rs}du$. \paragraph{Semi-Markov models} For semi-Markov models, the Kolmogorov equation does not apply, since the transition intensity matrix $Q(t)$ is no longer a deterministic function of $t$, but depends on when the transitions occur between time $t_0$ and $t$. Predictions can then be made by simulation. The function \code{sim.fmsm} simulates trajectories from parametric semi-Markov models by repeatedly generating the time to the next transition until the individual reaches an absorbing state or a specified censoring time. This requires the presence of a function to generate random numbers from the underlying parametric distribution --- and is fast for built-in distributions which use vectorised functions such as \code{rweibull}. \code{pmatrix.simfs} calculates the transition probability matrix by using \code{sim.fmsm} to simulate state histories for a large number of individuals, by default 100000. Simulation-based confidence-intervals are also available in \code{pmatrix.simfs}, at an extra computational cost, and the expected total length of stay in each state is available from \code{totlos.simfs}. <>= pmatrix.simfs(crwei, trans = tmat, t = 5) pmatrix.simfs(crwei, trans = tmat, t = 10) @ \paragraph{Prediction via mstate} Alternatively, predictions can be made by supplying the cumulative transition-specific hazards, calculated with \code{msfit.flexsurvreg}, to functions in the \pkg{mstate} package. For Markov models, the solution to the Kolmogorov equation \citep[e.g.,][]{aalen:process} is given by a product integral, which can be approximated as \[ P(t_0, t) = \prod_{i=0}^{m-1} \left\{ I + Q(t_i)dt \right\} \] where a fine grid of times $t_0,t_1,\ldots,t_m=t$ is chosen to span the prediction interval, and $Q(t_i)dt$ is the increment in the cumulative hazard matrix between times $t_i$ and $t_{i+1}$. $Q$ may also depend on other covariates, as long as these are known in advance. In \pkg{mstate}, these can be calculated with the \code{probtrans} function, applied to the cumulative hazards returned by \code{msfit}. For Cox models, the time grid is naturally defined by the observed survival times, giving the Aalen-Johansen estimator \citep{andersen}. Here, the probability of remaining alive and free of BOS is estimated at 0.27 at 5 years and 0.17 at 10 years. <<>>= ptc <- probtrans(mfcox, predt = 0, direction = "forward")[[1]] round(ptc[c(165, 193),], 3) @ For parametric models, using a similar discrete-time approximation was suggested by \citet{cook:lawless}. This is achieved by passing the object returned by \code{msfit.flexsurvreg} to \code{probtrans} in \pkg{mstate}. It can be made arbitrarily accurate by choosing a finer resolution for the grid of times when calling \code{msfit.flexsurvreg}. <<>>= ptw <- probtrans(mfwei, predt = 0, direction = "forward")[[1]] round(ptw[ptw$time %in% c(5, 10),], 3) @ \code{pstate1}--\code{pstate3} are close to the first rows of the matrices returned by \code{pmatrix.fs}. The discrepancy from the Cox model is more marked at 10 years when the data are more sparse (Figure \ref{fig:bos:cumhaz}). A finer time grid would be required to achieve a similar level of accuracy to \code{pmatrix.fs} for the point estimates, at the cost of a slower run time than \code{pmatrix.fs}. However, an advantage of \code{probtrans} is that standard errors are available more cheaply. For semi-Markov models, \pkg{mstate} provides the function \code{mssample} to produce both simulated trajectories and transition probability matrices from semi-Markov models, given the estimated piecewise-constant cumulative hazards \citep{fiocco:mstatepred}, produced by \code{msfit} or \code{msfit.flexsurvreg}, though this is generally less efficient than \code{pmatrix.simfs}. In this example, 1000 samples from \code{mssample} give estimates of transition probabilities that are accurate to within around 0.02. However with \code{pmatrix.simfs}, greater precision is achieved by simulating 100 times as many trajectories in a shorter time. <>= mssample(mrcox$Haz, trans = tmat, clock = "reset", M = 1000, tvec = c(5, 10)) mssample(mrwei$Haz, trans = tmat, clock = "reset", M = 1000, tvec = c(5, 10)) @ \subsection{Next-state probabilities} \label{sec:nextstate} In a multi-state situation we are usually interested in the probability that a person in one state will move to a specific state next, rather than to the other competing states. In the BOS example we might want to estimate the probability that a patient will die before getting BOS, or get BOS before dying. In a mixture multi-state model (Section~\ref{sec:mixture}), these are explicit parameters of the model. In a multi-state model parameterised by cause-specific hazards, these probabilities are related to the hazards through the Kolmogorov forward equation. To obtain these, we consider the full multi-state model as a set of \emph{competing risks submodels}. There is one submodel for each state a person can transition from (the "transient" states of the model). In the BOS example, there is one submodel for the transitions from no BOS (with two competing risks: BOS and death), and a second submodel for the single transition from BOS to death. The probability that the the next state after $r$ is $s$ can then be obtained in practice as the transition probability $P(X(t)=s | X(t_0)=r)$, under the submodel for transient state $r$, for a very large time $t$. \code{pmatrix.fs} can be used for this. <<>>= tmat_nobos <- rbind("No BOS"=c(NA,1,2), "BOS"=c(NA,NA,NA),"Death"=c(NA,NA,NA)) crfs_nobos <- fmsm(mod_nobos_bos, mod_nobos_death, trans = tmat_nobos) pmatrix.fs(crfs_nobos, from=1, t=100000)["No BOS",c("BOS","Death")] @ In a time-homogeneous Markov model, i.e. where the times from state $r$ to state $s$ are all exponentially distributed with a constant rate $\lambda_{rs}$, the probability that the next state after $r$ is $s$ is simply $\lambda_{rs} / \sum_u \lambda_{ru}$, where the sum is taken over all possible next states after $r$. We can check the result from \code{pmatrix.fs} agrees with this: <<>>= modexp_nobos_bos <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==1), data = bosms3, dist = "exponential") modexp_nobos_death <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==2), data = bosms3, dist = "exponential") crfs_nobos <- fmsm(modexp_nobos_bos, modexp_nobos_death, trans=tmat_nobos) pmatrix.fs(crfs_nobos, from=1, t=100000)["No BOS",c("BOS","Death")] rate12 <- modexp_nobos_bos$res["rate","est"] rate13 <- modexp_nobos_death$res["rate","est"] rate12 / (rate12 + rate13) @ \subsection{Distribution of the time to the next state} \label{sec:nexttime} Under the cause-specific hazards model, the time until the next observed transition can be considered to equal the \emph{minimum} of a set of latent times --- one latent time for each potential transition whose cause-specific hazard defines the multi-state model. The distribution of this time is not generally known analytically, given a set of parametric distributions defining the cause-specific hazards. For example, if there were two competing latent event times $T_1$, $T_2$ with cause-specific hazards distributed as Gamma$(a_1,b_1)$ and Weibull$(a_2,b_2)$ respectively, then the equivalent mixture model would be specified by the conditional distributions of $T_1|T_1 T_2$, which wouldn't have a standard form. Instead this time can be computed using simulation, via \code{sim.fmsm}. The function \code{simfinal_fmsm} wraps \code{sim.fmsm} to summarise the distribution of the time to each absorbing state in a multi-state model, conditionally on that state occurring. If this is applied to a \emph{competing-risks submodel} for state $r$ of a multi-state model, this simply produces the time to the \emph{next} state in the full model, since the absorbing states of the submodel define the potential next states after state $r$. This is done here to calculate the mean, median and interquartile range for the time to BOS (given survival) and the time to death (given no BOS before death). The function also produces estimates of the probability of each of these states, though as we saw in Section~\ref{sec:nextstate}, this is available more efficiently via \code{pmatrix.fs}. Note the number of simulated individuals $M$ can be increased for more accuracy, and optionally the $B$ argument can be supplied to obtain simulation-based confidence intervals around the estimates. <<>>= crfs_nobos <- fmsm(mod_nobos_bos, mod_nobos_death, trans = tmat_nobos) simfinal_fmsm(crfs_nobos, probs = c(0.25, 0.5, 0.75), M=10000) @ \subsection{Obtaining probabilities of, and times to, a final absorbing state} \label{sec:ultimate} As the previous section mentioned, \code{simfinal_fmsm} can be applied to any multi-state model with an absorbing state, to estimate the distribution of the time from the start of the process to the absorbing state. If there are multiple absorbing states, it can also estimate the probability that the individual ends up in each one. For the BOS model, there is only one absorbing state, death, so the function returns a probability of 1 that the patient will eventually die, and summaries of the distribution of the time from transplant to death. <<>>= simfinal_fmsm(crfs, probs = c(0.25, 0.5, 0.75), M=10000) @ \code{simfinal_fmsm} requires a semi-Markov multi-state model, or a simple competing risks model, constructed through \code{fmsm}. Though for a simple competing risks model, \code{pmatrix.fs} can be used to get the probability of each competing state, as in~\ref{sec:nextstate}. \section{Multi-state modelling using mixtures} \label{sec:mixture} \subsection{Definitions} A ``mixture'' multi-state model, first described for competing risks models by \citet{larson1985mixture} is described in terms of: \begin{itemize} \item the probability $\pi_{rs}$ that the next state after state $r$ is state $s$ \item the distribution of the time $T_{rs}$ from state $r$ entry to state $s$ entry, given that the next state after $r$ is state $s$. \end{itemize} In other words, the transition intensity is defined by \[ q_{rs}(t) = \left\{ \begin{array}{ll} q^*_{rs}(t) & \mbox{if } I_{r} = s \\ 0 & \mbox{if } I_{r} \neq s\\ \end{array} \right. \] where $I_{r}$ is a latent categorical variable that determines which transition will happen next for an individual in state $r$, governed by probabilities $\pi_{r,s} = P(I_{r} = s)$, with $\sum_{s \in \mathcal{S}_r} \pi_{r,s} = 1$ over the potential next state $\mathcal{S}_r$ after state $r$. The transition intensity $q^*_{rs}(t) $ is defined by the hazard function of a parametric distribution that governs the time $S_{rs}$ from state $r$ entry until the transition to state $s$, \emph{given that this is the transition that occurs}. The mixture model describes a mechanism where the transition that happens is determined ``in advance" at time zero, whereas in the cause-specific hazards model, the risks of different events ``compete" with each other as time proceeds. However, in practice, both models can represent situations where individuals can experience any of the competing events. In the mixture model, we only specify a distribution for the time to the event \emph{that happens first} among the competing risks, and do not model events that don't occur. As discussed by \citet{cox1959analysis}, if the time-to-event distributions are specified correctly in both frameworks, then they can both represent the same process. In practice however, they will differ. As discussed in Section~\ref{sec:nexttime}, given a particular parametric form for a set of cause-specific hazards, the form of the distribution for the \emph{minimum} of the potential event times, the one that actually happens, won't be available. The main advantage of the mixture model is that it is parameterised in terms of quantities that have an easy, direct interpretation. In the mixture model, we specify a parametric distribution with density $f_{r,s}(|\theta_{r,s})$ (and CDF $F_{r,s}()$) for the time of transition to state $s$ for a person in state $r$, conditionally on this transition being the one that occurs. We have data consisting of state transitions, indexed by $j$, experienced by individuals $i$. This can either be \begin{itemize} \item \emph{an exact transition time:} $\{y_{i,j}, r_{i,j}, s_{i,j}, \delta_{i,j}=1\}$, where a transition to state $s_{i,j}$ is known to occur at a time $y_{i,j}$ after entry to state $r_{i,j}$. \item \emph{right censoring} $\{y_{i,j},r_{i,j},\delta_{i,j}=2\}$, where an individual's follow-up ends while they are in state $r_{i,j}$, at time $y_{i,j}$ after entering this state, thus the next state and the time of transition to it are unknown. \end{itemize} Therefore, for an exact time of transition to a known state $s_{i,j}$, i.e. $\delta_{i,j}=1$, the likelihood contribution is simply \[ l_{i,j} = \pi_{r_{i,j}s_{i,j}} f_{r_{i,j},s_{i,j}}(y_{i,j} | \theta_{r_{i,j},s_{i,j}}) \] For observations $j$ of right-censoring at $y_{i,j}$, the state that the person will move to, and the time of that transition, is unknown. Thus it is unknown which of the distributions $f_{r,s}$ the transition time will obey, and the likelihood contribution is of the form of a mixture model, that sums over the set $\mathcal{S}_r$ of potential next states after $r$: \[ l_{i,j} = \sum_{s \in \mathcal{S}_r} \pi_{r_{i,j}s} (1 - F_{r_{i,j},s}(y_{i,j} | \theta_{r_{i,j},s})) \] \subsection{Data for mixture competing risks models} The required data format for the mixture model is shown for the BOS data in the object \code{bosmx3}. This has \begin{itemize} \item one row for each observed event time \item one row for each ``end of follow-up" time where we know an individual was still at risk of making a transition, but we don't know which transition will occur. \end{itemize} Recall that in the data \code{bosms3} used to implement the cause-specific hazards model, a individual ``censored" at time $t$ contributed a row in the data \emph{for each} of the events that might have occurred after $t$. The difference from \code{bosmx3} is that for these individuals, \code{bosmx3} only has \emph{one} row per ``censored" individual. For example, patient 5 is censored at 11 years, when they were still at risk of either BOS or death. Also we do not include censoring times for events competing with events that were observed, e.g. when patient 4 below got BOS (state 2) at year 2, thus were ``censored" at the same time for the transition from state 1 (no BOS) to state 3 (death). The process of transforming the cause-specific dataset to the mixture dataset is shown below. Multiple censoring records, for different destination states, are condensed to a single censoring record. Each row of \code{bosmx3} then corresponds to a transition. A new column called \code{event} is created, which should be a factor that identifies the terminal event of the transition, which takes the value \code{NA} in cases of censoring where the transition that will happen is unknown. Columns not needed for the mixture model are removed. Informative labels for the factor levels of \code{event} are added to identify the states. <<>>= bosms3[bosms3$id %in% c(4,5),] bosmx3 <- bosms3 bosmx3$Tstart <- bosmx3$Tstop <- bosmx3$trans <- NULL bosmx3 <- bosmx3[!(bosmx3$status==0 & duplicated(paste(bosmx3$id, bosmx3$from))),] bosmx3$event <- ifelse(bosmx3$status==0, NA, bosmx3$to) bosmx3$event <- factor(bosmx3$event, labels=c("BOS","Death")) bosmx3$to <- NULL bosmx3[bosmx3$id %in% c(4,5),] @ \subsection{Fitting mixture competing risks models} The \code{flexsurvmix} function fits a mixture model to competing risks data. To fit a full multi-state mixture model, we fit one mixture competing risks model for each transient state in the multi-state structure. The models are then grouped together (Section~\ref{sec:fmixmsm}) to form the full multi-state model. The mixture model for the event following transplant (BOS or death before BOS, the 1-2 and 1-3 transitions in the multi-state structure) is fitted as follows. A Weibull distribution is fitted for the time to BOS given BOS onset, and an exponential distribution is fitted for the time to death given death before BOS onset. These distributions are specified in the \code{dists} argument. The same distributions as in \code{flexsurvreg} are supported (including custom distributions, in the same way). <<>>= bosfs <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) bosfs @ The printed results object shows the two event probabilities $\pi_{rs}$ in the first two rows, and the parameters of the time-to-event distributions in the remaining rows. The maximum likelihood estimates are in column \code{est}, and estimates on a (multinomial) logit or log transformed scale are in column \code{est.t}, with standard errors on the transformed scale in \code{se}. Covariates can be included on the event probabilities through multinomial logistic regression. For illustration, we just simulate some fake covariate data in the variable \code{x}. The log odds ratio for this covariate on the odds of death (with the first category, BOS here, always taken as the baseline) is shown in the row with \code{terms} labelled \code{prob2(x)}. <<>>= set.seed(1) bosmx3$x <- rnorm(nrow(bosmx3),0,1) bosfsp <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential"), pformula = ~ x) bosfsp @ Covariates may also be included on any parameter of any time-to-event distribution, as in \code{flexsurvreg}. If the covariate is named on the right hand side of the \code{Surv} formula in the first argument, then it is included on the location parameter of all distributions. <<>>= bosfst <- flexsurvmix(Surv(years, status) ~ x, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) @ The first argument may be a list of formulae, to indicate that different covariates are included on the location parameter for different events. <<>>= flexsurvmix(list(Surv(years, status) ~ x, Surv(years, status) ~ 1), event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential")) @ An argument \code{anc} is used to supply covariates on ancillary parameters (e.g. shape parameters). This must be a list of length matching the number of competing events, each component being a named list in the format used for the \code{anc} argument in \code{flexsurvreg}. If there are no covariates for a particular component, just specify a null formula on the location parameter (as below, \code{rate=~1}). <<>>= flexsurvmix(Surv(years, status) ~ 1, event=event, data=bosmx3[bosmx3$from==1,], dists = c(BOS="weibull", Death="exponential"), anc = list(BOS=list(shape=~x), Death=list(rate=~1))) @ \subsection{Predictions from mixture competing risks models} A few functions have been supplied to extract estimates and confidence intervals for interpretable quantities, for given covariate values. Here we extract estimates of various quantities for covariate values of \code{x=0} and \code{x=1}. These values are provided in a data frame \code{nd} that will be supplied as the \code{newdata} argument to various extractor functions. The first extractor function \code{probs_flexsurvmix} gives the fitted event probabilities, by event and covariate value. This is applied here to the fitted model \code{bosfsp} that included a covariate on the event probabilities. All these functions take an argument \code{B} which specifies the number of samples to use for calculating bootstrap-like confidence limits --- increase this for more accurate limits. <<>>= nd <- data.frame(x=c(0,1)) probs_flexsurvmix(bosfsp, newdata=nd, B=50) @ \code{mean_flexsurvmix} extracts the mean time to each event conditionally on that event occurring, from the mean of the fitted time-to-event distribution. \code{quantile_flexsurvmix} extracts the quantiles of these distributions, e.g. the interquartile range in this example summarises the variability between individuals for this time. <<>>= mean_flexsurvmix(bosfst, newdata=nd) quantile_flexsurvmix(bosfst, B=50, newdata=nd, probs=c(0.25, 0.5, 0.75)) @ \code{p_flexsurvmix} extracts the probability of being in each of the states at a time $t$ in the future, shown for $t=5,10$ here. The \code{startname} argument supplies an informative name to the ``starting" state that the model \code{bosfst} describes transitions from. <<>>= p_flexsurvmix(bosfst, t=c(5, 10), B=10, startname="No BOS") @ \subsection{Forming a mixture multi-state model} \label{sec:fmixmsm} We supplement the mixture model for the event following state 1 (no BOS) with a second model \code{bosfst_bos} for the events following BOS (the other transient state in the multi-state model). Although this is fitted with \code{flexsurvmix}, there is only one potential next state after BOS, which is death, so internally this just fits a standard survival model using \code{flexsurvreg}. The two mixture models are then coupled together using the \code{fmixmsm} function, which returns an object containing the entire multi-state model, here named \code{bosfmix}. This object contains attributes listing the potential pathways that an individual can take through the states. These pathways are identified automatically by naming the arguments to \code{fmixmsm} with the label of the state that each model describes transitions from --- here the first model \code{bosfst} describes transitions from ``No BOS" and the second describes transitions from BOS. (Note we redefine the \code{event} factor so that empty levels are dropped) <<>>= bdat <- bosmx3[bosmx3$from==2,] bdat$event <- factor(bdat$event) bosfst_bos <- flexsurvmix(Surv(years, status) ~ x, event=event, data=bdat, dists = c(Death="exponential")) bosfmix <- fmixmsm("No BOS"=bosfst, "BOS"=bosfst_bos) @ Now we can predict outcomes from the full multi-state model. All these functions work by simulating a large population of individuals from the model, by default \code{M=10000}, so increase this for more accuracy. A cut-off time \code{t=1000} is also applied to the simulated data that assumes people have all reached the absorbing state by this time -- increase this if necessary. These functions currently require models to have at least one absorbing state, and no ``cycles" in their transition structure. The function \code{ppath_fmixmsm} returns the probability of following each of the potential pathways through the model. For this example, they are the same for both covariate values \code{x=0} and \code{x=1}. Setting \code{final=TRUE} aggregates the pathway probabilities by the final (absorbing) state, returning the probability of ending in each of the potential final states, which is trivially 1 in this case for the single absorbing state of death. <<>>= ppath_fmixmsm(bosfmix, B=20) ppath_fmixmsm(bosfmix, B=20, final=TRUE) @ To estimate the mean time to the final state for individuals following each pathway, use \code{meanfinal_fmixmsm}, and for the quantiles of the distribution of this time over individuals (by default the median and a 95\% interval), use \code{qfinal_fmixmsm}. Supplying \code{final=TRUE} in these functions summarises the mean time to the final state, averaged over all potential pathways (according to the probability of following those pathways). Again, covariate values can be supplied in the \code{newdata} argument if needed. <<>>= meanfinal_fmixmsm(bosfmix, B=10) qfinal_fmixmsm(bosfmix, B=10) meanfinal_fmixmsm(bosfmix, B=10, final=TRUE) @ \subsection{Goodness of fit checking} The fit of mixture competing risks models can be checked by comparing predictions of the state occupancy probabilities (as returned by \code{p_flexsurvmix}) with nonparametric estimates of these quantities \citep{aalen:johansen}. This is only supported for models with no covariates or only factor covariates (where subgroup-specific predictions are compared with stratified nonparametric estimates). The function \code{ajfit_flexsurvmix} derives these estimates from both the mixture model and the Aalen-Johansen method, and collects them in a tidy data frame ready for plotting, e.g. with the \pkg{ggplot2} package. The mixture models fit nicely here. A \code{start} argument is supplied to give an informative label to the starting state in the plots. Note we are plotting not probability of \emph{being in} a state at time $t$, but the probability of \emph{having made} the respective transition --- here we are checking the competing risks submodels one at time. <>= aj <- ajfit_flexsurvmix(bosfs, start="No BOS") bosfs_bos <- flexsurvmix(Surv(years, status) ~ 1, event=event, data=bdat, dists = c(Death="exponential")) aj2 <- ajfit_flexsurvmix(bosfs_bos, start="BOS") library(ggplot2) ggplot(aj, aes(x=time, y=val, lty=model, col=state)) + geom_line() + xlab("Years after transplant") + ylab("Probability of having moved to state") ggplot(aj2, aes(x=time, y=val, lty=model, col=state)) + xlab("Years after transplant") + ylab("Probability of having moved to state") + geom_line() @ Checking against Aalen-Johansen estimates is also supported for cause-specific hazards models that are grouped together using \code{fmsm}. Thus we can compare cause-specific hazards and mixture models that have been fitted to the same data. We do this here for the \code{fmsm} object \code{crfs_nobos} created in Section~\ref{sec:nextstate}. <>= library(dplyr) aj3 <- ajfit_fmsm(crfs_nobos) %>% filter(model=="Parametric") %>% mutate(model = "Cause specific hazards") %>% mutate(state = factor(state, labels=c("No BOS","BOS","Death"))) %>% full_join(aj) ggplot(aj3, aes(x=time, y=val, lty=model, col=state)) + xlab("Years after transplant") + ylab("Probability of having moved to state") + geom_line() @ \section{Comparison of frameworks for parametric multi-state modelling} As the mixture model is described by the probabilities of observable events and the times to those events, it is somewhat easier to interpret then the cause-specific hazards model. While those quantities can be computed under the cause-specific hazards model, they require potentially-expensive simulation. An advantage of the cause-specific hazards model is that it tends to be faster to \emph{fit}, if the transition-specific models are fitted independently. Another competing-risks modelling framework not implemented here is typically referred to as \emph{subdistribution} hazard modelling --- essentially covariate effects are applied to the probabilities of occupying different states at time $t$, rather than to the cause-specific hazards. This leads to covariate effects that are easier to interpret compared to, e.g. cause-specific hazard ratios. The method has been implemented semiparametrically~\citep{fine1999proportional} and parametrically~\citep{lambert2017flexible}. A further framework referred to as ``vertical" modelling \citep{nicolaie2010vertical} involves factorising the joint distribution of events and event times as $P(time)P(event|time)$, whereas the mixture modelling framework uses $P(event)P(time|event)$. \bibliography{flexsurv} \end{document} flexsurv/inst/doc/flexsurv.pdf0000644000176200001440000222270214660035012016227 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type /ObjStm /Length 5371 /Filter /FlateDecode /N 93 /First 759 >> stream xœí\Ys7¶~¿¿ocWÊÆŽv¥ReËVìx‰cˉ“?´©–Ô E*\;¿~¾s’ÍM¦HÍøÞªë²Ðh4úà; –¦¥0B#¬0±N8k…¡4"ˆèµˆB•ÊŠJ(åòB…«ÊÒ½ÊkÔ1B…Š …ª¬¨¢ñ ­AE¡­Æ5 í"Ê+¡ƒUB—BǨQY˜R[TFEaŒÁË€e®NG/ya<èé¸%Ê£0•CýJزÂÃRXíñP ‹Âha=Þ#ø3VØñ--êyá4è˜ Q€è@|ØR¸€{@u• .|Yáj„×HHX¦B£Nx‡ÊxÅ{ºÂGnLø üØJf5hâJ€}€Ð"8âwˆxnE,AÌ9U…« C Dt¢‹PJèJĈė¢*Á HTªB£ZT@‰ÊCú( ¤Ãº3%PNé ? †“±ø'쿯aÿ”:N=§ÓÈiÅ)à‹J.é}•¨DA%*ÑP‰ˆJTt¢ò^È£á`Ò ¢JoÉÍi[?~*ªä*Whˆ5ZU€Q¼ñªá2g®ÿº§£^3&Å¥¢“ÏW Õ;oÄwß%F¥Ä^;iŠÑðóx2Ü¿ªG—õè®o„ü~x2Dm!G§Í(·^2D¾Qéæ‰O©ÑÞ¥¶4EE¦«|¡ag`4ët(`jTÿÍôÄá»>ÞåxROšû¿Ç· T«K(Ó‘(‰Ñ¨¢ÂñÕpÅPÐØ6å˪ 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Jackson \\ MRC Biostatistics Unit, Cambridge, UK \\ \email{chris.jackson@mrc-bsu.cam.ac.uk}} \title{flexsurv: Distributions reference} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Abstract{ A reference guide for the distributions built into flexsurv } \Keywords{survival} \begin{document} This document lists the following information for each of the built-in distributions in \code{flexsurvreg}. \begin{itemize} \item How the distribution is identified in the \code{dist} argument to \code{flexsurvreg}. \item Name of the \code{d} function in R for the probability density, showing how names of the arguments in the R function correspond to the symbols in the formula for the survivor function. In each case, there are corresponding R functions with names beginning with \code{p},\code{q} and \code{r} instead of \code{d}, for the cumulative distribution, quantiles and random number generation. The R \code{help} page for the function named here will contain more information about the distribution, e.g. the probability density function, and how particular distributions are defined as special cases of other distributions. \item The survivor function $S(t|\btheta)$ as a function of time $t$ and the parameters of the distribution $\btheta$. Any restrictions on the allowed values of the parameters are noted. \item The location parameter of the distribution, now indexed by $j$, and a function describing how the location parameter depends on covariate values $\z_j$ and covariate effects $\bbeta$. $\bbeta$ are the covariate effects indicated when printing a \code{flexsurvreg} object, which can take any real value. \item A more interpretable covariate effect measure, defined as a function of $\bbeta$. \end{itemize} In a \emph{proportional hazards} model, the ``more interpretable'' effect measure presented is the hazard ratio (HR) for one unit of the covariate. In an \emph{accelerated failure time model}, the time acceleration factor (TAF) for one unit of the covariate is presented. The survivor function is of the form $S(t) = S^*(ct)$ where $c$ is some constant that depends on the parameters. Multiplying $c$ by 2 has the same effect on survival as multiplying $t$ by 2, doubling the speed of time and halving the expected survival time. An alternative way of presenting effects from an accelerated failure time model is the ratio of expected times to the event between covariate values of 1 and 0. This equals 1/TAF, and may be easier to interpret if the time to the event is of direct interest. A HR below 1 and a TAF above 1 both indicate that higher covariate values are associated with a higher risk of the event, or shorter times to the event. % So the comparable parameters are exp(-beta) for the lognormal and gengamma 1/exp(beta) = exp(-beta) for the weibull exp(beta) for the gamma and exponential \subsection*{Weibull (accelerated failure time)} \verb+flexsurvreg(..., dist="weibull")+\\ \code{dweibull(..., shape=a, scale=mu)} \[ S(t | \mu, a) = \exp(- (t/\mu)^ a), \qquad \mu>0, a>0 \] \[ \mu_j = \exp(\z_j \bbeta), \quad TAF = \exp(-\bbeta) \] \subsection*{Weibull (proportional hazards)} \verb+flexsurvreg(..., dist="weibullPH")+\\ \code{dweibullPH(..., shape=a, scale=lambda)} \[ S(t | \lambda, a) = \exp(- \lambda t^ a), \qquad \lambda>0, a>0 \] \[ \lambda_j = \exp(\z_j \bbeta), \quad HR = \exp(\bbeta) \] (Note the argument ``scale'' to \code{dweibullPH} would perhaps better have been called ``rate'', given the analogy with the rate of the exponential model). \subsection*{Gamma} \verb+flexsurvreg(..., dist="gamma")+\\ \code{dgamma(..., shape=a, scale=mu)} \[ S(t | a, \mu) = 1 - \int_{0}^t \frac{x^{a-1} \exp{-(x/\mu)}}{\mu^a \Gamma(a)} dx, \qquad \mu>0, a>0 \] \[ \mu_j = \exp(\z_j \bbeta), \quad TAF = \exp(\bbeta) \] \subsection*{Exponential} \verb+flexsurvreg(..., dist="exp")+\\ \code{dexp(..., rate=lambda)} \[ S(t | \lambda) = \exp(-\lambda t), \qquad \lambda > 0 \] \[ \lambda_j = \exp(\z_j \bbeta), \quad HR = \exp(\bbeta), \quad TAF = \exp(\bbeta) \] \subsection*{Log-logistic} \verb+flexsurvreg(..., dist="llogis")+\\ \code{dllogis(..., shape=a, scale=b)} \[ S(t | a, b) = 1/ (1 + (t/b)^a), \qquad a>0, b>0 \] \[ b_j = \exp(\z_j \bbeta), \quad TAF = \exp(-\bbeta) \] \subsection*{Log-normal} \verb+flexsurvreg(..., dist="lnorm")+\\ \code{dlnorm(..., meanlog=mu, sdlog=sigma)} \[ S(t | \mu, \sigma) = 1 - \int_0^t \frac{1}{x\sigma\sqrt{2 \pi}} \exp{\left\{-\frac{(\log x - \mu)^2}{2 \sigma^2}\right\}} dx, \qquad \sigma > 0 \] \[ \mu_j = z_j \bbeta , \quad TAF = \exp(-\bbeta) \] \subsection*{Gompertz} \verb+flexsurvreg(..., dist="gompertz")+\\ \code{dgompertz(..., shape=a, rate=b)} \[ S(t | a, b) = \exp(-(b/a) (\exp(at) - 1)), b > 0 \] Note that $a<0$ is permitted, in which case $S(t|)$ tends to a non-zero probability as $t$ increases, i.e. a probability of living forever. \[ b_j = \exp(\z_j \bbeta), \quad HR = \exp(\bbeta) \] \subsection*{Generalised gamma (Prentice)} \verb+flexsurvreg(..., dist="gengamma")+\\ \code{dgengamma(..., mu, sigma, Q)} \[ S(t|\mu,\sigma,Q) = \begin{array}{ll} S_G(\frac{\exp(Qw)}{Q^2} ~ | ~ \frac{1}{Q^2}, 1) & (Q > 0 )\\ 1 - S_G(\frac{\exp(Qw)}{Q^2} ~ | ~ \frac{1}{Q^2}, 1) & (Q < 0)\\ S_L(t ~ | ~ \mu, \sigma) & (Q = 0)\\ \end{array} \] where $w = (\log(t) - \mu)/\sigma$, $S_G(t | a,1)$ is the survivor function of the gamma distribution with shape $a$ and scale $1$, $S_L(t |\mu,\sigma)$ is the survivor function of the log-normal distribution with log-scale mean $\mu$ and standard deviation $\sigma$, $\mu,Q$ are unrestricted, and $\sigma$ is positive. \[ \mu_j = z_j \bbeta, \quad TAF = \exp(-\bbeta) \] \subsection*{Generalised gamma (Stacy)} \verb+flexsurvreg(..., dist="gengamma.orig")+\\ \code{dgengamma.orig(..., shape=b, scale=a, k=k)} \[ S(t|a, b, k) = 1 - \int_0^t \frac{ b x^{bk -1}}{ \Gamma(k) a^{bk} }\exp(-(x/a)^b) dx \] \[ a_j = \exp(z_j \bbeta), \quad TAF = \exp(-\bbeta) \] \subsection*{Generalised F (Prentice)} \verb+flexsurvreg(..., dist="genf")+\\ \code{dgenf(..., mu, sigma, Q, P)} \[ S(t | \mu, \sigma, Q, P) = 1 - \int_0^t \frac{\delta (s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 + s_2)} B(s_1, s_2)}, \qquad \sigma>0, P>0 \] where $s_1 = 2(Q^2 + 2P + Q\delta)^{-1}$, $s_2 = 2(Q^2 + 2P -Q\delta)^{-1}$, ${\delta = (Q^2 + 2P)^{1/2}}$ and $w = (\log(x) - \mu)\delta /\sigma$ \[ \mu_j = x_j \bbeta, \quad TAF = \exp(-\bbeta) \] \subsection*{Generalised F (original)} \verb+flexsurvreg(..., dist="genf.orig")+\\ \code{dgenf.orig(..., mu, sigma, s1, s2)} \[ S(t | \mu, \sigma, s_1, s_2) = 1 - \int_0^t \frac{(s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {s_1 + s_2} B(s_1, s_2)} dx, \qquad \sigma>0, s_1>0, s_2>0 \] where $w = (\log(x) - \mu)/\sigma$, and $B(s_1,s_2) =\frac{\Gamma(s_1)\Gamma(s_2)}{\Gamma(s_1+s_2)}$ is the beta function. \[ \mu_j = z_j \bbeta , \quad TAF = \exp(-\bbeta) \] \subsection*{Spline (Royston/Parmar)} \verb+flexsurvspline(...,scale="hazard")+\\ \verb+flexsurvspline(...,scale="odds")+\\ \verb+flexsurvspline(...,scale="normal")+\\ \code{dsurvspline(..., gamma)} where the argument \texttt{gamma} collects together all parameters,\\ ~\\ or the alternative forms for the density/distribution functions (flexsurv versions 2.0 and later) where different parameters are in separate arguments:\\ \code{dsurvspline0(..., gamma0, gamma1)} (no internal knots)\\ \code{dsurvspline1(..., gamma0, gamma1, gamma2)} (1 internal knot)\\ \code{dsurvspline2(..., gamma0, gamma1, gamma2, gamma3)} (2 internal knots)\\ etc., all the way up to \code{dsurvspline7}. \[ g(S(t)) = s(x, \bm{\gamma}) \] where $x=\log(t)$ and $s()$ is a natural cubic spline function with $m$ internal knots: \[ s(x,\bm{\gamma}) = \gamma_0 + \gamma_1 x + \gamma_2 v_1(x) + \ldots + \gamma_{m+1} v_m(x) \] where $v_j(x)$ is the $j$th \emph{basis} function, \[v_j(x) = (x - k_j)^3_+ - \lambda_j(x - k_{min})^3_+ - (1 - \lambda_j) (x - k_{max})^3_+, \qquad \lambda_j = \frac{k_{max} - k_j}{k_{max} - k_{min}} \] and $(x - a)_+ = max(0, x - a)$. The link function relating the survivor function to the spline is: \[ g(S(t)) = \begin{array}{ll} \log(-\log(S(t))) &\verb+(scale="hazard")+ \\ \log(S(t)^{-1} - 1) & \verb+(scale="odds")+ \\ \Phi^{-1}(S(t)) & \verb+(scale="normal")+ \\ \end{array} \] For more details, see the main \code{flexsurv} vignette. The location parameter is \[ \gamma_{0j} = z_j \bbeta \] For \verb+scale="hazard"+, the hazard ratio is $\exp(\bbeta)$. \end{document} flexsurv/inst/doc/standsurv.R0000644000176200001440000003405314657635411016047 0ustar liggesusers## ----include = FALSE---------------------------------------------------------- knitr::opts_chunk$set( fig.dim = c(8, 6), collapse = TRUE, comment = "#>" ) ## ----message = FALSE, warning = FALSE----------------------------------------- library(flexsurv) library(flexsurvcure) library(ggplot2) library(dplyr) library(survminer) ## ----------------------------------------------------------------------------- data(bc) set.seed(236236) ## Age at diagnosis is correlated with survival time. A longer survival time ## gives a younger mean age bc$age <- rnorm(dim(bc)[1], mean = 65 - scale(bc$recyrs, scale=F), sd = 5) ## Create age at diagnosis in days - used later for matching to expected rates bc$agedays <- floor(bc$age * 365.25) ## Create some random diagnosis dates between 01/01/1984 and 31/12/1989 bc$diag <- as.Date(floor(runif(dim(bc)[1], as.Date("01/01/1984", "%d/%m/%Y"), as.Date("31/12/1989", "%d/%m/%Y"))), origin="1970-01-01") ## Create sex (assume all are female) bc$sex <- factor("female") ## 2-level prognostic variable bc$group2 <- ifelse(bc$group=="Good", "Good", "Medium/Poor") head(bc) ## ----------------------------------------------------------------------------- km <- survfit(Surv(recyrs, censrec)~group2, data=bc) kmsurvplot <- ggsurvplot(km) kmsurvplot + xlab("Time from diagnosis (years)") ## ----------------------------------------------------------------------------- model.weibull.sep <- flexsurvreg(Surv(recyrs, censrec)~group2, anc = list(shape = ~ group2), data=bc, dist="weibullPH") model.weibull.sep ## ----------------------------------------------------------------------------- predictions <- summary(model.weibull.sep, type = "survival", tidy=T) ggplot() + geom_line(aes(x=time, y=est, color = group2), data=predictions) + geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot) ## ----------------------------------------------------------------------------- ss.weibull.sep.surv <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) ss.weibull.sep.surv ## ----------------------------------------------------------------------------- plot(ss.weibull.sep.surv) ## ----------------------------------------------------------------------------- plot(ss.weibull.sep.surv) + xlab("Time since diagnosis (years)") + geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot) ## ----------------------------------------------------------------------------- ss.weibull.sep.haz <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) plot(ss.weibull.sep.haz) + xlab("Time since diagnosis (years)") ## ----------------------------------------------------------------------------- ss.weibull.sep.rmst <- standsurv(model.weibull.sep, type = "rmst", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor"))) plot(ss.weibull.sep.rmst) + xlab("Time since diagnosis (years)") ## ----------------------------------------------------------------------------- ss.weibull.sep.3 <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), contrast = "difference") plot(ss.weibull.sep.3, contrast=TRUE) + xlab("Time since diagnosis (years)") + ylab("Difference in survival probabilities") + geom_hline(yintercept = 0) ## ----------------------------------------------------------------------------- ss.weibull.sep.4 <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), contrast = "ratio") plot(ss.weibull.sep.4, contrast=TRUE) + xlab("Time since diagnosis (years)") + ylab("Hazard ratio") + geom_hline(yintercept = 1) ## ----------------------------------------------------------------------------- ss.weibull.sep.boot <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=10), ci = TRUE, boot = TRUE, B = 100, seed = 2367) ss.weibull.sep.deltam <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=10), ci = TRUE, boot = FALSE) plot(ss.weibull.sep.boot, ci = TRUE) + geom_ribbon(aes(x=time, ymin=survival_lci, ymax=survival_uci, color=at, linetype = "Delta method"), fill=NA, data=attr(ss.weibull.sep.deltam,"standpred_at")) + scale_linetype_manual(values = c("Bootstrap" = "solid", "Delta method"= "dashed")) + ggtitle("Comparison of bootstrap and delta method confidence intervals") ## ----------------------------------------------------------------------------- model.weibull.age.sep <- flexsurvreg(Surv(recyrs, censrec)~group2 + age, anc = list(shape = ~ group2 + age), data=bc, dist="weibullPH") ## Marginal survival standardized to age distribution of study population ss.weibull.age.sep.surv <- standsurv(model.weibull.age.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50) ) ## Marginal survival standardized to an older population # create a new prediction dataset as a copy of the bc data but whose ages are drawn from # a normal distribution with mean age 75, sd 5. newpred.data <- bc set.seed(247) newpred.data$age = rnorm(dim(bc)[1], 75, 5) ss.weibull.age2.sep.surv <- standsurv(model.weibull.age.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), newdata=newpred.data) ## Overlay both marginal survival curves plot(ss.weibull.age.sep.surv) + geom_line(aes(x=time, y=survival, color=at, linetype = "Older population"), data = attr(ss.weibull.age2.sep.surv, "standpred_at") ) + scale_linetype_manual(values = c("Study" = "solid", "Older population"= "dashed")) ## ----------------------------------------------------------------------------- summary(survexp.us) ## ----------------------------------------------------------------------------- ss.weibull.sep.expected <- standsurv(model.weibull.sep, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.expected, expected = T) ## ----------------------------------------------------------------------------- ss.weibull.sep.expectedh <- standsurv(model.weibull.sep, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,7,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.expectedh, expected = T) ## ----------------------------------------------------------------------------- ## reshape US lifetable to be a tidy data.frame, and convert rates to per person-year as flexsurv regression is in years survexp.us.df <- as.data.frame.table(survexp.us, responseName = "exprate") %>% mutate(exprate = 365.25 * exprate) survexp.us.df$age <- as.numeric(as.character(survexp.us.df$age)) survexp.us.df$year <- as.numeric(as.character(survexp.us.df$year)) ## Obtain attained age and attained calendar year in (whole) years bc <- bc %>% mutate(attained.age.yr = floor(age + recyrs), attained.year = lubridate::year(diag + rectime)) ## merge in (left join) expected rates at event time bc <- bc %>% left_join(survexp.us.df, by = c("attained.age.yr"="age", "attained.year"="year", "sex"="sex")) # A stratified relative survival mixture-cure model model.weibull.sep.rs <- flexsurvcure(Surv(recyrs, censrec)~group2, anc = list(shape = ~ group2, scale = ~ group2), data=bc, dist="weibullPH", bhazard=exprate) model.weibull.sep.rs ## ----------------------------------------------------------------------------- ## All-cause survival ss.weibull.sep.rs.surv <- standsurv(model.weibull.sep.rs, type = "survival", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.surv, expected = T) # All-cause hazard ss.weibull.sep.rs.haz <- standsurv(model.weibull.sep.rs, type = "hazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.haz, expected = T) ## ----------------------------------------------------------------------------- # Excess hazard ss.weibull.sep.rs.excesshaz <- standsurv(model.weibull.sep.rs, type = "excesshazard", at = list(list(group2 = "Good"), list(group2 = "Medium/Poor")), t = seq(0,30,length=50), rmap=list(sex = sex, year = diag, age = agedays ), ratetable = survexp.us, scale.ratetable = 365.25, newdata = bc ) plot(ss.weibull.sep.rs.excesshaz) flexsurv/inst/doc/standsurv.html0000644000176200001440000106505314657635413016621 0ustar liggesusers Calculating standardized survival measures in flexsurv

Calculating standardized survival measures in flexsurv

Michael Sweeting1

Background

Standardized survival measures

standsurv is a post-estimation command that takes a flexsurvreg object and calculates standardized survival measures. After fitting a parametric survival model in flexsurv it is often useful to compute and visualise the marginal (or standardized) survival. For example, suppose a survival model is fitted adjusted for treatment group, age, and sex. A separate predicted survival curve can be obtained for each individual based on their covariate pattern or a prediction can be obtained by setting covariates to their mean values (both can be obtained using summary.flexsurvreg), but it may be more useful to obtain the marginal survival for each treatment group. Regression standardization achieves this by fitting a regression model including the treatment group \(Z\), covariates \(X\) and possible interactions between \(X\) and \(Z\). The standardized survival can be estimated by obtaining predictions for every individual in the study under each fixed treatment arm and averaging these individual-specific estimates. The marginal survival over the distribution of covariates in the study assuming all participants were assigned to arm \(Z=z\) is: \[\begin{equation} S_s(t|Z=z) = E[S(t | Z=z, X)] = \frac{1}{N} \sum_{i=1}^{N} S(t | Z=z, X=x_i) \end{equation}\] for covariate values (vectors) \(x_1,...,x_{N}\). Here standarization is done over all \(N\) patients in the study and provides a counterfactual marginal estimate when setting \(Z=z\). The standardized survival is therefore an estimate of the marginal survival if all study patients had been assigned to group \(z\). Under certain assumptions, differences in marginal survival provide estimates of causal effects (Syriopoulou, Rutherford, and Lambert (2021)) and certain estimands such as the average treatment effect (ATE) can be targeted: \[ ATE = S_s(t|Z=z_1) - S_s(t|Z=z_0)]\] Alternatively, an average treatment effect in the treated (ATET) estimand can be targeted by averaging over only patients who were in the intervention treatment arm \(Z=z_1\). Standardization estimates can also be obtained for other target populations of interest. For example it may be important to predict survival in an external population with different characteristics to the study population.

The hazard function for the standardized survival can be obtained to understand how the shape of the hazard changes over time. This provides an estimate of the marginal hazard. It can be shown (Rutherford et al. (2020), Appendix I) that the hazard of the standardized survival can be calculated as \[\begin{equation} h_s(t|Z=z) = \frac{\sum_{i=1}^{N} S(t|Z=z,X=x_i)h(t|Z=z,X=x_i)}{\sum_{i=1}^{N} S(t | Z=z, X=x_i)} \end{equation}\] This is a weighted average of the \(N\) individual hazard functions, weighted by the probability of survival at time \(t\). Patients who are unlikely to have survived to \(t\) will contribute less weight to this hazard function.

Calculating marginal expected survival and hazard

In economic evaluations parametric survival models are used to extrapolate clinical trial data to estimate lifetime benefits. In this context it is often useful to plot marginal ‘expected’ (general population) survival alongside parametric models fitted and extrapolated from trial data in order to aid interpretation and for a visual comparison between the trial subjects and the population at large. Displaying expected survival and hazard functions can aid understanding of whether the assumed hazard and survival functions are credible (Rutherford et al. (2020)). Expected survival is defined as the all-cause survival in a general population with the same key characteristics as the study subjects. General population mortality rates are often taken from national lifetables that are stratified by age, sex, calendar year and occasionally other prognostic factors (e.g. deprivation indices).

The Ederer or “exact†method for estimating expected survival assumes subjects in the trial population are not censored before the end of a stated follow-up time (Ederer, Axtell, and Cutler 1961). The expected survival is then the survival we would expect to see in an age-sex matched general population if all patients are continuously followed-up. This is the approach used by standsurv to calculate expected survival and is the “most appropriate when doing forcasting, sample size calculations or other predictions of the ‘future’ where censoring is not an issue†(Therneau 1999).

Based on the exact method, the marginal expected survival using background mortality rates is calculated using all \(N\) patients in the trial at any time point \(t\):

\[\begin{equation} S^*(t) = \frac{1}{N} \sum_{i=1}^N S_i^*(t) \end{equation}\] where \(S_i^*(t)\) is the expected survival for the \(i\)th subject at time \(t\). It follows that the marginal expected hazard is a weighted average of the expected hazard rates: \[\begin{equation} h^*(t) = \frac{ \sum_{i=1}^N S_i^*(t) h_i^*(t)}{\sum_{i=1}^N S_i^*(t)} \end{equation}\]

The expected survival for the \(i\)th subject at follow-up time \(t\) is calculated based on matching to the general population hazard rates. If lifetables are utilised these often provide mortality rates by sex (\(s\)), age (\(a\)) and calendar year (\(y\)), in yearly or 5-yearly categories. In practice the expected survival at time \(t\) for a given subject is calculated from the cumulative hazard. At a given follow-up time \(t\) this is the sum of \(h^*_{asy} \times \textrm{Number of days in state } (a,s,y)\) in the follow-up where \(h^*_{asy}\) is the expected hazard for age \(a\), sex \(s\), year \(y\). This requires follow-up time for each individual in the study dataset to be split by multiple timescales (e.g. age and year) into time epochs, which can be visualised as a Lexis diagram. Each epoch can then be matched to a corresponding expected mortality rate.

Incorporation of background mortality into survival models

Incorporating background mortality into survival models directly is recommended as it helps avoid extremely implausible projections (Rutherford et al. (2020)). This can be done using an excess mortality / relative survival model where population based ‘expected’ rates, often from life tables, are introduced to explain background mortality. The concept behind these models is to partition the all-cause mortality into excess mortality caused by the disease of interest and that due to other causes. A parametric model can then be applied to the isolated excess mortality. This may be particularly useful when making long-term extrapolations as the pattern of disease-specific mortality and other cause mortality are likely to be very different over time. Alternatively, if cause of death information is available and reliable, a separate cause-specific model can be fitted to the disease-specific mortality and other cause mortality.

The all-cause mortality rate at time \(t\) for individual \(i\) can be partitioned into two constituent parts: \[\begin{equation} h_i(t) = h^*_i(t) + \lambda_i(t) \end{equation}\] where \(h_i(t)\) is the all-cause mortality rate (hazard), \(h^*_i(t)\) is the expected or background mortality rate and \(\lambda_i(t)\) is the excess mortality rate. Equivalently, the hazard rates can be transformed to the survival scale which gives the all-cause survival at time \(t\) as the product of the expected survival and the relative survival: \[\begin{equation} S_i(t) = S^*_i(t) R_i(t) \end{equation}\] The relative survival, \(R_i(t)\), is therefore the ratio of all-cause survival and the expected survival in the background population. Typically, \(h_i^*(t)\) (and hence \(S_i^*(t)\)) are obtained from population lifetables. The expected mortality rates are assumed to be fixed and known and a parametric model is then used to estimate the relative survival (or equivalently excess hazard).

standsurv

standsurv is a post-estimation command that takes a flexsurv regression and calculates standardized survival measures and contrasts. Expected mortality rates and survival can also be obtained. The main features of the command are that it enables the calculation and plotting over any specified follow-up times of

  1. Marginal survival, hazard and restricted mean survival time (RMST) metrics
  2. Marginal expected (population) survival and hazard functions matched to the study population
  3. Marginal all-cause survival and all-cause hazard after fitting relative survival models
  4. Contrasts in survival, hazard and RMST metrics (e.g. marginal hazard ratio, differences in marginal RMST)
  5. Confidence intervals and standard errors for all measures and contrasts using either the delta method or bootstrapping

Through a simple syntax the user can specify the groups that they wish to calculate the marginal metrics. These groups can be formed by any combination of covariate values.

A worked example: the pbc dataset

For this example we will use data from the German Breast Cancer Study Group 1984-1989, which is the R dataset bc found in the flexsurv package. This dataset has death, or censoring times for 686 primary node positive breast cancer patients together with a 3-level prognostic group variable with levels “Goodâ€, “Medium†and “Poorâ€. For this demonstration we collapse the prognostic variable into 2 levels: “Good†and “Medium/Poorâ€. We also create some artificial ages and diagnosis dates for the patients, along with assuming all patients are female. We allow a correlation between the age at diagnosis for a patient and their survival time so that age is a prognostic variable. The mean age is 65 with a standard deviation of 5. We load this dataset and create these additional variables.

library(flexsurv)
library(flexsurvcure)
library(ggplot2)
library(dplyr)
library(survminer)
data(bc)
set.seed(236236)
## Age at diagnosis is correlated with survival time. A longer survival time 
## gives a younger mean age
bc$age <- rnorm(dim(bc)[1], mean = 65 - scale(bc$recyrs, scale=F), sd = 5)
## Create age at diagnosis in days - used later for matching to expected rates
bc$agedays <- floor(bc$age * 365.25)
## Create some random diagnosis dates between 01/01/1984 and 31/12/1989
bc$diag <- as.Date(floor(runif(dim(bc)[1], as.Date("01/01/1984", "%d/%m/%Y"), 
                               as.Date("31/12/1989", "%d/%m/%Y"))), 
                   origin="1970-01-01")
## Create sex (assume all are female)
bc$sex <- factor("female")
## 2-level prognostic variable
bc$group2 <- ifelse(bc$group=="Good", "Good", "Medium/Poor")
head(bc)
#>   censrec rectime group   recyrs      age agedays       diag    sex group2
#> 1       0    1342  Good 3.676712 64.38839   23517 1986-09-15 female   Good
#> 2       0    1578  Good 4.323288 67.31488   24586 1986-08-12 female   Good
#> 3       0    1760  Good 4.821918 61.77993   22565 1985-11-10 female   Good
#> 4       0    1152  Good 3.156164 65.20415   23815 1987-02-28 female   Good
#> 5       0     967  Good 2.649315 68.74975   25110 1986-05-18 female   Good
#> 6       0     629  Good 1.723288 64.53328   23570 1987-03-07 female   Good

A plot of the Kaplan-Meier shows a clear separation in the survival curves between the two prognostic groups.

km <- survfit(Surv(recyrs, censrec)~group2, data=bc)
kmsurvplot <- ggsurvplot(km) 
kmsurvplot + xlab("Time from diagnosis (years)")

A stratified Weibull model

We start by fitting a Weibull model to each group separately. One way to do this is to fit a single saturated model whereby group affects both the scale and shape parameters of the Weibull distribution. This effectively means we have a separate scale and shape parameter for each group, which is equivalent to fitting two separate models. Such a model does not make a proportional hazards assumption and hence the hazard ratio will change over time. The saturated model approach has advantages as we can use the model to easily investigate treatment effects using standsurv as we shall see later. Including group in the main formula of flexsurvreg allows group to affect the scale parameter of the Weibull distribution whilst we use the anc argument in flexsurvreg to additionally allow group to affect the shape parameter.

model.weibull.sep <- flexsurvreg(Surv(recyrs, censrec)~group2, 
                                 anc = list(shape = ~ group2), 
                                 data=bc, dist="weibullPH")
model.weibull.sep
#> Call:
#> flexsurvreg(formula = Surv(recyrs, censrec) ~ group2, anc = list(shape = ~group2), 
#>     data = bc, dist = "weibullPH")
#> 
#> Estimates: 
#>                           data mean  est       L95%      U95%      se      
#> shape                           NA    1.68681   1.32989   2.13952   0.20461
#> scale                           NA    0.02187   0.01119   0.04274   0.00748
#> group2Medium/Poor          0.66618    1.84846   1.14534   2.55157   0.35874
#> shape(group2Medium/Poor)   0.66618   -0.28237  -0.54219  -0.02254   0.13257
#>                           exp(est)  L95%      U95%    
#> shape                           NA        NA        NA
#> scale                           NA        NA        NA
#> group2Medium/Poor          6.35001   3.14351  12.82725
#> shape(group2Medium/Poor)   0.75400   0.58147   0.97771
#> 
#> N = 686,  Events: 299,  Censored: 387
#> Total time at risk: 2113.425
#> Log-likelihood = -830.4043, df = 4
#> AIC = 1668.809

Given that the model only contains group2 and no other covariates we can obtain the predicted (fitted) survival for each of the two groups using the summary function and storing these predictions in a tidy data.frame with the argument tidy=T.

predictions <- summary(model.weibull.sep, type = "survival", tidy=T)
ggplot() + geom_line(aes(x=time, y=est, color = group2), data=predictions) + 
  geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot)

The Weibull model does not appear to fit the data very well and so we should try other parametric distributions. However, for illustration purposes we shall continue using the Weibull model. We will now show that the same predictions can be obtained from standsurv but with the benefit of addition flexibility.

Using standsurv to calculate marginal survival

standsurv works similarly to the margins command in R and standsurv in Stata by allowing the user to specify a list of scenarios in which specific covariates are fixed to certain values. This is done using the at argument of standsurv to provide the list of scenarios where each scenario is itself a list containing covariates that are to be fixed. In our worked example the two scenarios are list(group2 = "Good") and list(group2 = "Medium/Poor"). Any covariates not specified in the at scenarios are averaged over, hence creating marginal, or standardized, estimates of the metric of interest. In the example above, there are no other covariates in the model so we will get the same answer as obtained from summary. But the later worked example extends this to models containing other covariates. The default is to calculate survival probabilities at the event times in the data but this can be changed with the type and t arguments, respectively. The returned object is a tidy data.frame with columns named at1 up to atn for the n scenarios specified in the at argument.

ss.weibull.sep.surv <- standsurv(model.weibull.sep,
                                             type = "survival",
                                             at = list(list(group2 = "Good"),
                                                       list(group2 = "Medium/Poor")))
ss.weibull.sep.surv
#> # A tibble: 574 × 3
#>      time   at1   at2
#>     <dbl> <dbl> <dbl>
#>  1 0.0219 1.00  0.999
#>  2 0.0411 1.00  0.998
#>  3 0.0438 1.00  0.997
#>  4 0.0466 1.00  0.997
#>  5 0.0493 1.00  0.997
#>  6 0.0795 1.00  0.994
#>  7 0.115  0.999 0.991
#>  8 0.126  0.999 0.990
#>  9 0.156  0.999 0.987
#> 10 0.173  0.999 0.985
#> # ℹ 564 more rows

Further details such as labels for the at scenarios are stored in attributes of the standsurv object. These are utilised by the plot function. A plot of the marginal estimates can be easily produced using the plot function, which produces a ggplot object.

plot(ss.weibull.sep.surv)

The plot can be easily further manipulated, for example by changing axis labels and adding further plots.

plot(ss.weibull.sep.surv) + xlab("Time since diagnosis (years)") +
  geom_step(aes(x=time, y=surv, group=strata), data=kmsurvplot$data.survplot)

Other metrics: marginal hazards and marginal RMST

We can use the type argument to calculate marginal hazards or restricted mean survival time (RMST). For example a plot of the hazard functions for the two groups is obtained as follows:

ss.weibull.sep.haz <- standsurv(model.weibull.sep,
                                            type = "hazard",
                                            at = list(list(group2 = "Good"),
                                                      list(group2 = "Medium/Poor")))
plot(ss.weibull.sep.haz) + xlab("Time since diagnosis (years)")

Whilst a plot of RMST is given by

ss.weibull.sep.rmst <- standsurv(model.weibull.sep,
                                             type = "rmst",
                                             at = list(list(group2 = "Good"),
                                                       list(group2 = "Medium/Poor")))
plot(ss.weibull.sep.rmst) + xlab("Time since diagnosis (years)")

Calculating contrasts

The advantage of fitting a saturated model now becomes clear as we can calculate contrasts between our at scenarios. Suppose we are interested in the difference in the survival functions between the two groups. This is easily calculated using the contrast = "difference" argument, and a plot of the contrast can be obtained using contrast = TRUE argument in the plot function.

ss.weibull.sep.3 <- standsurv(model.weibull.sep,
                                          type = "survival",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                          contrast = "difference")
plot(ss.weibull.sep.3, contrast=TRUE) + xlab("Time since diagnosis (years)") +
  ylab("Difference in survival probabilities")  + geom_hline(yintercept = 0)

Alternatively, we may wish to visualise the implied hazard ratio from fitting separate Weibull models to the two groups. In the breast cancer example we see that the hazard ratio (treatment effect) starts very high before decreasing, suggesting that those with Medium/Poor prognosis start with a high elevated risk but have a continued excess risk up to the end of follow-up, compared to those with Good prognosis.

ss.weibull.sep.4 <- standsurv(model.weibull.sep,
                                          type = "hazard",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                          contrast = "ratio")
plot(ss.weibull.sep.4, contrast=TRUE) + xlab("Time since diagnosis (years)") +
  ylab("Hazard ratio") + geom_hline(yintercept = 1)

Confidence intervals and standard errors

Confidence intervals and standard errors for both the metric of interest and contrasts can be obtained either through bootstrapping or using the delta method. Bootstrap confidence intervals are calculated by specifying ci = TRUE, boot = TRUE, and providing the number of bootstrap samples using B. We can also set the seed using the seed argument to allow reproducibility.

If instead the delta method is to be used to obtain confidence intervals then we specify ci = TRUE, boot = FALSE. The delta method obtains confidence intervals by calculating standard errors for a given transformation of the metric of interest and then assuming normality. The default is to use a log transformation; hence if type = "survival" the confidence intervals are symmetric for the log survival probabilities. Alternative transformations can be specified using the trans argument.

The code below shows confidence intervals for marginal survival calculated through a bootstrap method (with B = 100) compared to a delta method. For computational efficiency here we only predict for 10 time points.

ss.weibull.sep.boot <- standsurv(model.weibull.sep,
                                          type = "survival",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                          t = seq(0,7,length=10),
                                          ci = TRUE,
                                          boot = TRUE,
                                          B = 100,
                                          seed = 2367)
#> Calculating bootstrap standard errors / confidence intervals

ss.weibull.sep.deltam <- standsurv(model.weibull.sep,
                                          type = "survival",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                          t = seq(0,7,length=10),
                                          ci = TRUE,
                                          boot = FALSE)
#> Calculating standard errors / confidence intervals using delta method

plot(ss.weibull.sep.boot, ci = TRUE) +  
  geom_ribbon(aes(x=time, ymin=survival_lci, ymax=survival_uci, color=at, linetype = "Delta method"), fill=NA,
              data=attr(ss.weibull.sep.deltam,"standpred_at")) +
  scale_linetype_manual(values = c("Bootstrap" = "solid", "Delta method"= "dashed")) +
  ggtitle("Comparison of bootstrap and delta method confidence intervals")
#> Scale for linetype is already present.
#> Adding another scale for linetype, which will replace the existing scale.

Adding age as a covariate

Suppose age has been added as a covariate to the survival model. If age is not included in our at scenarios standsurv will by default produce standardized estimates of survival averaged over the age distribution in our study population. Alternatively we could pass a new prediction dataset to standsurv and obtain standardized estimates for this population. As an example, we obtain marginal survival estimates after fitting a stratified Weibull model, firstly standardized to the age-distribution of our study population and secondly standardized to an older population with mean age of 75 and standard deviation 5.

model.weibull.age.sep <- flexsurvreg(Surv(recyrs, censrec)~group2 + age, 
                                 anc = list(shape = ~ group2 + age), 
                                 data=bc, dist="weibullPH")

## Marginal survival standardized to age distribution of study population
ss.weibull.age.sep.surv <- standsurv(model.weibull.age.sep,
                                             type = "survival",
                                             at = list(list(group2 = "Good"),
                                                       list(group2 = "Medium/Poor")),
                                             t = seq(0,7,length=50)
)

## Marginal survival standardized to an older population
# create a new prediction dataset as a copy of the bc data but whose ages are drawn from
# a normal distribution with mean age 75, sd 5.
newpred.data <- bc
set.seed(247)
newpred.data$age = rnorm(dim(bc)[1], 75, 5)
ss.weibull.age2.sep.surv <- standsurv(model.weibull.age.sep,
                                             type = "survival",
                                             at = list(list(group2 = "Good"),
                                                       list(group2 = "Medium/Poor")),
                                             t = seq(0,7,length=50),
                                             newdata=newpred.data)

## Overlay both marginal survival curves
plot(ss.weibull.age.sep.surv) + 
  geom_line(aes(x=time, y=survival, color=at, linetype = "Older population"),
            data = attr(ss.weibull.age2.sep.surv, "standpred_at") ) +
  scale_linetype_manual(values = c("Study" = "solid", "Older population"= "dashed"))
#> Scale for linetype is already present.
#> Adding another scale for linetype, which will replace the existing scale.

Calculating expected survival and hazard in standsurv

To overlay marginal expected survival or hazard curves we require a lifetable of population hazard rates. To demonstrate we use the US lifetable that comes with the survival package, called survexp.us. Other lifetables can be obtained directly from the Human Mortality Database (HMD) using the HMDHFDplus package.

The survexp.us lifetable is a ratetable object with stratification factors age, sex and year. It gives rates of mortality per person-day for combinations of the stratification factors. A summary of the survexp.us object shows that the time-scale is in days.

summary(survexp.us)
#>  Rate table with 3 dimensions:
#>  age ranges from 0 to 39812.25; with 110 categories
#>  sex has levels of: male female
#>  year ranges from 1940-01-01 to 2020-01-01; with 81 categories

To use the lifetable to get expected rates for our trial population we need to match age, sex and year variables in our dataset to those in the ratetable. We can use the rmap argument to do this. standsurv utilises the survexp function in the survival package to calculate expected survival over the times specified in t using the ‘exact’ method of Ederer. We note that sex in our data is coded the same as in the ratetable (“male†and “femaleâ€) and importantly that we have variables that record both age at diagnosis and diagnosis date in days. It is important that the user ensures that the study data are correctly coded and have variables on the same timescale as in the ratetable so that matching is successful. The code below demonstrates that for our data we therefore need to match the year variable in the ratetable to the diag variable in our study data, and the age variable in the ratetable to the agedays variable in our study data.

We need to specify three more arguments in standsurv. First, the lifetable, which must be a ratetable object and is specified using the ratetable argument. Second, we may need to pass our trial dataset to standsurv if the stratifying factors do not appear as covariates in the flexsurv model. Finally, we need to be careful to tell standsurv what the time scale transformation is between the fitted flexsurv model and the time scale in ratetable. We can use the scale.ratetable argument to do this. Typically ratetable objects are expressed in days (e.g. rates per person-day). The default is therefore scale.ratetable = 365.25, which indicates that the survival model was fitted in years but the ratetable is in days.

After running standsurv we can plot the expected survival (or hazard) by using the argument expected = TRUE in the plot() function.

ss.weibull.sep.expected <- standsurv(model.weibull.sep,
                                                 type = "survival",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                                 t = seq(0,7,length=50),
                                                 rmap=list(sex = sex,
                                                           year = diag,
                                                           age = agedays
                                                 ),
                                                 ratetable = survexp.us,
                                                 scale.ratetable = 365.25,
                                                 newdata = bc
)
#> Calculating marginal expected survival and hazard
plot(ss.weibull.sep.expected, expected = T)

We can see that the marginal expected survival is much higher than the marginal (predicted) survival for our breast cancer population. We can also obtain the expected hazards:

ss.weibull.sep.expectedh <- standsurv(model.weibull.sep,
                                                 type = "hazard",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                                 t = seq(0,7,length=50),
                                                 rmap=list(sex = sex,
                                                           year = diag,
                                                           age = agedays
                                                 ),
                                                 ratetable = survexp.us,
                                                 scale.ratetable = 365.25,
                                                 newdata = bc
)
#> Calculating marginal expected survival and hazard
plot(ss.weibull.sep.expectedh, expected = T)

The hazard plot shows that our model is predicting an increasing hazard over time for the cancer population, which remains significantly higher than the expected hazard in the general population. The monotonically increasing hazard imposed by the Weibull distribution may be implausible and this may make us question the suitability of a Weibull model if we wish to extrapolate.

Incorporation of background mortality

A relative survival model can be fitted using flexsurv by incorporating background mortality rates. The model then estimates excess hazard rates and relative survival measures. For prediction purposes, following the fitting of a relative survival model, standsurv allows the user to either obtain marginal predictions of relative survival / excess hazard or of all-cause survival / all-cause hazard. The latter are calculated by multiplying relative survival estimates with expected survival to get all-cause survival, or by adding excess hazard rates to expected hazard to get all-cause hazard.

We demonstrate this by fitting a relative survival cure model to the breast cancer data and obtaining predicted all-cause survival and all-cause hazard up to 30-years after diagnosis. A mixture cure model makes the assumption that a proportion of the study population will never experience the event. In a relative survival framework the cure model assumes that the excess mortality rate approaches zero (or equivalently the relative survival reaches an asymptote determined by the cure fraction). We fit a relative survival cure model with a Weibull distribution assumed for the uncured.

The relative survival mixture-cure model is fitted below. We must pass to flexsurvcure the expected hazard rates at the event / censoring time for each individual, as it is the expected rates at the event times that are used in the likelihood function for a parametric relative survival model. For this we need to initally do some data wrangling. Firstly, we calculate attained age and attained year (in whole years) at the event time for all study subjects. Secondly, we join the data with the expected rates using the matching variables attained age, attained year and sex. In the example, we express the expected rate as per person-year as this is the timescale used in the flexsurv regression model.

## reshape US lifetable to be a tidy data.frame, and convert rates to per person-year as flexsurv regression is in years
survexp.us.df <- as.data.frame.table(survexp.us, responseName = "exprate") %>%
  mutate(exprate = 365.25 * exprate)
survexp.us.df$age <- as.numeric(as.character(survexp.us.df$age))
survexp.us.df$year <- as.numeric(as.character(survexp.us.df$year))

## Obtain attained age and attained calendar year in (whole) years
bc <- bc %>% mutate(attained.age.yr = floor(age + recyrs),
                    attained.year = lubridate::year(diag + rectime))

## merge in (left join) expected rates at event time
bc <- bc %>% left_join(survexp.us.df, by = c("attained.age.yr"="age", 
                                        "attained.year"="year", 
                                        "sex"="sex")) 

# A stratified relative survival mixture-cure model
model.weibull.sep.rs <- flexsurvcure(Surv(recyrs, censrec)~group2, 
                                 anc = list(shape = ~ group2,
                                            scale = ~ group2), 
                                 data=bc, dist="weibullPH",
                                 bhazard=exprate)

model.weibull.sep.rs
#> Call:
#> flexsurvcure(formula = Surv(recyrs, censrec) ~ group2, data = bc, 
#>     bhazard = exprate, dist = "weibullPH", anc = list(shape = ~group2, 
#>         scale = ~group2))
#> 
#> Estimates: 
#>                           data mean  est       L95%      U95%      se      
#> theta                           NA    0.73277   0.60988   0.82787        NA
#> shape                           NA    2.62590   1.88756   3.65306   0.44231
#> scale                           NA    0.02973   0.00993   0.08896   0.01663
#> group2Medium/Poor          0.66618   -1.76733  -2.48411  -1.05055   0.36571
#> shape(group2Medium/Poor)   0.66618   -0.52951  -0.88563  -0.17340   0.18170
#> scale(group2Medium/Poor)   0.66618    1.81159   0.68352   2.93965   0.57555
#>                           exp(est)  L95%      U95%    
#> theta                           NA        NA        NA
#> shape                           NA        NA        NA
#> scale                           NA        NA        NA
#> group2Medium/Poor          0.17079   0.08340   0.34974
#> shape(group2Medium/Poor)   0.58889   0.41245   0.84080
#> scale(group2Medium/Poor)   6.12014   1.98084  18.90922
#> 
#> N = 686,  Events: 299,  Censored: 387
#> Total time at risk: 2113.425
#> Log-likelihood = -784.3236, df = 6
#> AIC = 1580.647

We can now use standsurv to obtain all-cause survival and hazard predictions using type = "survival" and type = "hazard". If instead we had wanted predictions of relative survival or excess hazards we would use type = "relsurvival" and type = "excesshazard", respectively.

## All-cause survival
ss.weibull.sep.rs.surv <- standsurv(model.weibull.sep.rs,
                                                 type = "survival",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                                 t = seq(0,30,length=50),
                                                 rmap=list(sex = sex,
                                                           year = diag,
                                                           age = agedays
                                                 ),
                                                 ratetable = survexp.us,
                                                 scale.ratetable = 365.25,
                                                 newdata = bc
)
#> Marginal all-cause survival will be calculated
#> Calculating marginal expected survival and hazard
plot(ss.weibull.sep.rs.surv, expected = T)


# All-cause hazard
ss.weibull.sep.rs.haz <- standsurv(model.weibull.sep.rs,
                                                 type = "hazard",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                                 t = seq(0,30,length=50),
                                                 rmap=list(sex = sex,
                                                           year = diag,
                                                           age = agedays
                                                 ),
                                                 ratetable = survexp.us,
                                                 scale.ratetable = 365.25,
                                                 newdata = bc
)
#> Marginal all-cause hazard will be calculated
#> Calculating marginal expected survival and hazard
plot(ss.weibull.sep.rs.haz, expected = T)

The marginal excess hazard is now unimodal since the cure model is forcing the initially increasing excess hazard to tend to zero in the long-term where only ‘cured’ subjects remain. The marginal all-cause hazard tends to the expected hazard and follows it thereafter.

A plot of the excess hazard confirms this.

# Excess hazard
ss.weibull.sep.rs.excesshaz <- standsurv(model.weibull.sep.rs,
                                                 type = "excesshazard",
                                                 at = list(list(group2 = "Good"),
                                                           list(group2 = "Medium/Poor")),
                                                 t = seq(0,30,length=50),
                                                 rmap=list(sex = sex,
                                                           year = diag,
                                                           age = agedays
                                                 ),
                                                 ratetable = survexp.us,
                                                 scale.ratetable = 365.25,
                                                 newdata = bc
)
#> Calculating marginal expected survival and hazard
plot(ss.weibull.sep.rs.excesshaz)

Conclusions

standsurv is a powerful post-estimation command that allows easy calculation of a number of useful prediction metrics. Contrasts can be made between any counterfactual populations of interest and, through regression standardisation, allows the targeting of marginal estimands. Confidence intervals, via the delta method or bootstrapping, are available and benchmarking against or incorporating background mortality rates is also supported.

References

Ederer, F., L. M. Axtell, and S. J. Cutler. 1961. “The Relative Survival Rate: A Statistical Methodology.†National Cancer Institute Monograph 6 (September): 101–21.
Rutherford, Mark J, Paul C Lambert, Michael J Sweeting, Becky Pennington, Michael J Crowther, Keith R Abrams, and Nicholas R. Latimer. 2020. “NICE DSU Technical Support Document 21: Flexible Methods for Survival Analysis.â€
Syriopoulou, Elisavet, Mark J. Rutherford, and Paul C. Lambert. 2021. “Inverse Probability Weighting and Doubly Robust Standardization in the Relative Survival Framework.†Statistics in Medicine 40 (27): 6069–92. https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9171.
Therneau, Terry M. 1999. “A Package for Survival Analysis in S.†https://www.mayo.edu/research/documents/tr53pdf/doc-10027379.

  1. ↩︎

flexsurv/inst/doc/flexsurv-examples.Rnw0000644000176200001440000002630214144502574020045 0ustar liggesusers%\VignetteIndexEntry{Supplementary examples of using flexsurv} \documentclass[nojss,nofooter]{jss} \usepackage{bm} \usepackage{tabularx} \usepackage{graphics} \author{Christopher H. Jackson \\ MRC Biostatistics Unit, Cambridge, UK \\ \email{chris.jackson@mrc-bsu.cam.ac.uk}} \title{flexsurv: flexible parametric survival modelling in R. Supplementary examples} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Abstract{ This vignette of examples supplements the main \pkg{flexsurv} user guide. } \Keywords{survival} \begin{document} \section{Examples of custom distributions} \subsection{Proportional hazards generalized gamma model} \citet{stgenreg} discuss using the \pkg{stgenreg} Stata package to construct a proportional hazards parameterisation of the three-parameter generalised gamma distribution. A similar trick can be used in \pkg{flexsurv}. A four-parameter custom distribution is created by defining its hazard (and cumulative hazard) functions. These are obtained by multiplying the built-in functions \code{hgengamma} and \code{Hgengamma} by an extra dummy parameter, which is used as the location parameter of the new distribution. The intercept of this parameter is fixed at 1 when calling \code{flexsurvreg}, so that the new model is no more complex than the generalized gamma AFT model \code{fs3}, but covariate effects on the dummy parameter are now interpreted as hazard ratios. <<>>= library(flexsurv) hgengammaPH <- function(x, dummy, mu=0, sigma=1, Q){ dummy * hgengamma(x=x, mu=mu, sigma=sigma, Q=Q) } HgengammaPH <- function(x, dummy, mu=0, sigma=1, Q){ dummy * Hgengamma(x=x, mu=mu, sigma=sigma, Q=Q) } custom.gengammaPH <- list(name="gengammaPH", pars=c("dummy","mu","sigma","Q"), location="dummy", transforms=c(log, identity, log, identity), inv.transforms=c(exp, identity, exp, identity), inits=function(t){ lt <- log(t[t>0]) c(1, mean(lt), sd(lt), 0) }) fs7 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist=custom.gengammaPH, fixedpars=1) @ \section{Examples of custom model summaries} \subsection{Plotting a hazard ratio against time} The following code plots the hazard ratio (Medium versus Good prognostic group) against time for both the proportional hazards model \code{fs7} and the better-fitting accelerated failure time model \code{fs2}. It illustrates the use of the following functions. \begin{description} \item[\code{summary.flexsurvreg}] for generating the estimated hazard at a series of times, for particular covariate categories. \item[\code{normboot.flexsurvreg}] for generating a bootstrap-style sample from the sampling distribution of the parameter estimates, for particular covariate categories. \item[\code{do.call}] for constructing a function call by supplying a list containing the function's arguments. This is used throughout the source of \pkg{flexsurv}. \end{description} <>= fs2 <- flexsurvreg(Surv(recyrs, censrec) ~ group + sigma(group), data=bc, dist="gengamma") B <- 5000 t <- seq(0.1, 8, by=0.1) hrAFT.est <- summary(fs2, t=t, type="hazard", newdata=data.frame(group="Medium"),ci=FALSE)[[1]][,"est"] / summary(fs2, t=t, type="hazard", newdata=data.frame(group="Good"),ci=FALSE)[[1]][,"est"] pars <- normboot.flexsurvreg(fs2, B=B, newdata=data.frame(group=c("Good","Medium"))) hrAFT <- matrix(nrow=B, ncol=length(t)) for (i in seq_along(t)){ haz.medium.rep <- do.call(hgengamma, c(list(t[i]), as.data.frame(pars[[2]]))) haz.good.rep <- do.call(hgengamma, c(list(t[i]), as.data.frame(pars[[1]]))) hrAFT[,i] <- haz.medium.rep / haz.good.rep } hrAFT <- apply(hrAFT, 2, quantile, c(0.025, 0.975)) hrPH.est <- summary(fs7, t=t, type="hazard", newdata=data.frame(group="Medium"),ci=FALSE)[[1]][,"est"] / summary(fs7, t=t, type="hazard", newdata=data.frame(group="Good"),ci=FALSE)[[1]][,"est"] pars <- normboot.flexsurvreg(fs7, B=B, newdata=data.frame(group=c("Good","Medium"))) hrPH <- matrix(nrow=B, ncol=length(t)) for (i in seq_along(t)){ haz.medium.rep <- do.call(hgengammaPH, c(list(t[i]), as.data.frame(pars[[2]]))) haz.good.rep <- do.call(hgengammaPH, c(list(t[i]), as.data.frame(pars[[1]]))) hrPH[,i] <- haz.medium.rep / haz.good.rep } hrPH <- apply(hrPH, 2, quantile, c(0.025, 0.975)) plot(t, hrAFT[1,], type="l", ylim=c(0, 10), col="red", xlab="Years", ylab="Hazard ratio (Medium / Good)", lwd=1, lty=2) lines(t, hrAFT[2,], col="red", lwd=1, lty=2) lines(t, hrPH[1,], col="darkgray", lwd=1, lty=2) lines(t, hrPH[2,], col="darkgray", lwd=1, lty=2) lines(t, hrAFT.est, col="red", lwd=2) lines(t, hrPH.est, col="darkgray", lwd=2) legend("topright", lwd=c(2,2), col=c("red","darkgray"), bty="n", c("Generalized gamma: standard AFT", "Generalized gamma: proportional hazards")) @ Since version 2.2 of \pkg{flexsurv}, however, the code above is obsolete, since the function \code{hr_flexsurvreg} can simply be used to calculate hazard ratios and their confidence intervals against time. <>= nd <- data.frame(group=c("Good","Medium")) hr_aft <- hr_flexsurvreg(fs2, t=t, newdata=nd) hr_ph <- hr_flexsurvreg(fs7, t=t, newdata=nd) plot(t, hr_aft$lcl, type="l", ylim=c(0, 10), col="red", xlab="Years", ylab="Hazard ratio (Medium / Good)", lwd=1, lty=2) lines(t, hr_aft$ucl, col="red", lwd=1, lty=2) lines(t, hr_aft$est, col="red", lwd=2) lines(t, hr_ph$lcl, col="darkgray", lwd=1, lty=2) lines(t, hr_ph$ucl, col="darkgray", lwd=1, lty=2) lines(t, hr_ph$est, col="darkgray", lwd=2) legend("topright", lwd=c(2,2), col=c("red","darkgray"), bty="n", c("Generalized gamma: standard AFT", "Generalized gamma: proportional hazards")) @ \subsection{Restricted mean survival} The expected survival up to time $t$, from a model with cumulative distribution $F(t|\alpha)$, is \[ E(T|T>= summary(fs2, type="rmst", t=100, tidy=TRUE) summary(fs2, fn=rmst_gengamma, t=100, tidy=TRUE) @ Or for the baseline category of "Good": <<>>= est <- fs2$res[,"est"] rmst_gengamma(t=100, mu=est[1], sigma=est[2], Q=est[3]) @ Note that the (unrestricted) median is more stable, and less than the restricted mean due to the skewness of this distribution. <<>>= summary(fs2, type="median") @ Note also that the custom function \code{fn} supplied to \code{summary.flexsurvreg} must be vectorised - previous versions of this example used an unvectorised custom function called \code{mean.gengamma} which will not work in version 2.2 or later. %\subsection{Custom summary functions with spline models} \section{Spline models} \subsection{Prognostic model for the German breast cancer data} The regression model III in \citet{sauerbrei1999building} used to create the prognostic group from the breast cancer data (supplied as \code{bc} in \pkg{flexsurv} and \code{GBSG2} in \pkg{TH.data}) can be reproduced as follows. Firstly, the required fractional polynomial transformations of the covariates are constructed. \code{progc} implements the Cox model used by \citet{sauerbrei1999building}, and \code{prog3} is a flexible fully-parametric alternative, implemented as a spline with three internal knots. The number of knots was chosen to minimise AIC. The covariate effects are very similar. After fitting the model, the prognostic index can then be derived from categorising observations in three groups according to the tertiles of the linear predictor in each model. The indices produced by the Cox model (\code{progc}) and the spline-based model (\code{progf}) agree exactly. <<>>= if (require("TH.data")){ GBSG2 <- transform(GBSG2, X1a=(age/50)^-2, X1b=(age/50)^-0.5, X4=tgrade %in% c("II","III"), X5=exp(-0.12*pnodes), X6=(progrec+1)^0.5 ) (progc <- coxph(Surv(time, cens) ~ horTh + X1a + X1b + X4 + X5 + X6, data=GBSG2)) (prog3 <- flexsurvspline(Surv(time, cens) ~ horTh + X1a + X1b + X4 + X5 + X6, k=3, data=GBSG2)) predc <- predict(progc, type="lp") progc <- cut(predc, quantile(predc, 0:3/3)) predf <- model.matrix(prog3) %*% prog3$res[-(1:5),"est"] progf <- cut(predf, quantile(predf, 0:3/3)) table(progc, progf) } @ \section{Right truncation: retrospective ascertainment} Suppose we want to estimate the distribution of the time from onset of a disease to death, but have only observed cases known to have died by the current date. In this case, times from onset to death for individuals in the data are \emph{right-truncated} by the current date minus the onset date. Predicted survival times for new cases can then be described by an un-truncated version of the fitted distribution. Denote the time from onset to death as the \emph{delay} time. This is illustrated in the following simulated example. Suppose individual onset times are uniformly distributed between 0 and 30 days. Their delay times are generated from a Gamma distribution. <<>>= set.seed(1) nsim <- 10000 onsetday <- runif(nsim, 0, 30) deathday <- onsetday + rgamma(nsim, shape=1.5, rate=1/10) @ The data are examined at 40 days. Therefore we do not observe people who have died after this time. For each individual in the observed data, their delay time is right-truncated by 40 days minus their onset day, since their delay times cannot be greater than this if they are included in the data. The right-truncation point is specified by the variable \code{rtrunc} in the data. <<>>= datt <- data.frame(delay = deathday - onsetday, event = rep(1, nsim), rtrunc = 40 - onsetday) datt <- datt[datt$delay < datt$rtrunc, ] @ The truncated Gamma model is fitted with \code{flexsurvreg} by specifying individual-specific truncation points in the argument \code{rtrunc}. The fitted model reproduces the gamma parameters that were used to simulate the data. After fitting the model, we can use the fitted model to predict the mean time to death - this is approximately the shape / rate of the untruncated gamma distribution. <<>>= fitt <- flexsurvreg(Surv(delay, event) ~ 1, data=datt, rtrunc = rtrunc, dist="gamma") fitt summary(fitt, t=1, fn = mean_gamma) @ \bibliography{flexsurv} \end{document} flexsurv/inst/doc/multistate.pdf0000644000176200001440000135752514660035012016557 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type /ObjStm /Length 6027 /Filter /FlateDecode /N 98 /First 802 >> stream xœí€¾…â6Cï«è¡Bæ3no%öÃb2À†šËêël>)ï@0|æÁ7€Í,:Eo2ƒ&*çߌ"ç±ÀΓ90f·Âî»Ø02Ø{0~²™FW¦C¹-ÚEë}ÀûãèV!ªÈ88ñÑ|8©ßN1-÷ÀóÀàûG¯_íÿðä`Ý=l…T0ÃRx~Ò Y…˜ßüÍȉ$ÓVcG!™SwÁîj>›•“‡—ÓY1»Kà#!Kn™‚à‘{û߀™’á’Bš‚ òÌ¡FÆŠ*˜Q«dÈö”ÂE¨T§… XסRêºÂE©T׸”ê´h”ê˜ÀÕuZ$Jõ€ L±ŽË)uŒæj|<-JÅ:®-ÔVÌßd<8*‘ùÛÝ=˜cùu¶ŒÜK2™Úˆ°ŒãÉ8”ŒXÉ8X²·Ò×fw±æ j;û5Ú¦{ÝU=~¿{ü󸪣W­(jÝÓ»°æªø&W¥¸ëuU6t»Î¿¾úð²J:¨Ž¨„¯»Õ5\yØŒ«ïÇÕwãúìÙëã·/¸îŒ‡§%‚µ1Õ7‹MÁõcêz0}}xôáy  Ž¾]žŒ‡ÓnÚê6Ê뇵`šoŒX”èÏ5lO®ñáàè×Ç/VîŒP·Á·aAȵÝþ\Äöä"ÇOùðë {TŒz»& ¾SÑÆt³~‰þ,Å®ýADT¯LÕ¸*éôÍ¢FÄüêøÅñîJ„o·ŠðMXW¨µ\XlL>•èÏlO„¿¿÷SóˆïÓ¯`²§Õ¸Û\™°¹2mÎo¶V¢?‰²+I@ÓåjLß".¨²zásÿÿÛô­øÆê»øÙüý›“ßQüpBû—‚)Q+ä2é©ýg=̳Éx~…oƒîèMuïþСÝòs5(Ÿí ŽÌ&ó’4ëÝìÁB|[ôöâü¦ø†ˆ .EŵEE%ñÞ‰(Hç4½*úÛAü&M&ã"f ËÚǦ@´•¿..Ë$ ‰!Rm‚ï_Âüv(´iÉ¡ê:ÓcÇï¿{¿wŒáÅq{‘¦C ÚæïºøBôǦÇR?{óáxçÅ;kÉùzÄãÛk×$çJôGfeÝèɤ,pYrÂrvo÷¡äBs/´ÐF óÿâü_÷S?ÀäÞ»ò=\ŒO¯{âí»§ï³½ùpxRŒF%>yQMü»:= ÿË~D Ff*ƒ‡MöÈ4ÏÀxAŽË~Ñثê3-쓪ývŸ}ºS7- ö9=o2µû$;§óŽG¨ÁÝ'ù¿º*!&Ú+†Óå ¯ùì¦ôãYyv>DqH\9w0œ ð ×P庀kÈ,Þ?‰íúÛòÑ5äÓëä«ÇÒi€ëÜ£îu‡ADÂÊÔÑ@jÓ_H™ˆ¤BdKø5ng ‘ïcüï‡Ç“ª¼ÛÒ˜5¹4M±„£6%³?jü7søþb1éhŽ¥¿ºŽ¿BR¬c×èS·/S é­gà€Ï“âêyY_Ìðµ•C¢Ä›$­‹s0ª+æíËö÷6@ZéâcÉÐíUÃR‚kJǦhÍÚd‹ÁÃãÑù°DÂÍÊË_(ŽZN¼AÈž×Q˜,?\^Üi™A¡K©¡wÒ©Lù,þnû£N(MZžK¡¿LµL¡ªL L‘ŒL®W&÷¸’WÖžíy¥XY‚lºÂÝêì¬D/§ôê—å§åpV`‘Ï.J¨á:ö°¸<9-0ί*tƒ9Ä¢ÕìÄ`|yY@‡r:eùtXL/X~Ž: Tâå;¸Æ™ïáJq¤¶/ñõG~@\~ËòŸ×¨o¸Ø›¿Ç9=¡÷ø9ŒHŸ1ò‚¾bùï, Y~Éò„‹àþ`9q€¨ÉœåŸ£/úÊòoHš8ñ…߆É`:ÿüýçÿ>íµÖ™¦š4)Ãÿïÿ5è"Lg]£0, À"ãpZžÅЮÀ²S2ÝUiYŠ(¹’ ®Ž‚ÐO&Å –g³êüœTk:ÝD§;Ãh<¿"×9‹4žOŠ!]¡Ö-:ŸVÓ«añmÑ¿¾îÑ"ÏMf;JY|ýã…ÈD]‚ À?ðM™»¦ôÞga«2õO°cЈ±ôJe ºÐc'cÕØ$LüÙtÅéÒkˆµ¯šº&* ¼+‚ÅMnˆ÷²f‡©a ò’^aKðwF€ÝÄVŸƒkÐ'íV^à48è@[š¦4ŽCh a:ÜÁTÂí[¯ RÌ©H-29 ÏpO"‡¸Úl†;ÈpÃC¦VJ!%!ýáºu˜þZ"®è\9G|9Þs„®Æ}N ÉkÉõ¢ªÄÙœ¼³ qÂC§Æ¡.P̆ºªŠjð]èÕp>ŃùŸådÌòñzöeŒÎnR–¸^‘Ÿa(ïDË?æÅ09)R…’ßIî…ÖþþìSŽÈØ.,ááËj¸À€‚7~ý» ¤¦˜LÆ_"Îçå Õ—èØ!!ÉGå9iitµÑ·Òò²¿aRu’Â908'uöé0ñXB@!RÝ€T¨Žú6%ŒF|¢ÇnúðV ÓOÿæØ«wV]m³%:–’`ndÝä8êf,£Uˆe Ð8"Aeìr “:•Í)Ä‘½F½¶A£Ã`¤ :Gý7Ç*Ði®QãphGÎq‚«P= íE4¼EõÃBMfÉ¢ênÑààF?2JŽÌS4R±éÒZm›¬§GnöØ@©èn­Ç[¶4:/¯›Î ³«Ä ·Ô³Ç[ÉÄ2ö ©’LeÉ8š dÁàâr4ÁΡq5’z 4ü& Ùô$>†JáX >S9ÚGÜÁâdy\Aˆ‚Å…‡Èû"Ühn eðq(kIj¥¾Öÿ6Ic¶õ²¦¾"ÅréïÀÖÓ_t äýLƒöX*òšr!xÛþÉŒ¦GËÄÜ&µ62Ë*TωAH)ç‘.ØOYÄÙì‘؉›Ÿ‰Ú'¶Ñ³ ºB® p˜>mKG1“‹áM-‹²F²1åæ$hz,ÆͺâX_öHŒ­r #"Hø(³ÍðdùŒí$«Çý| 67寗¤a µÑ-k+Üþ/•{I°k’`·—„åú$aÁF½Á?j]áêš$$ûµè{¨€NF‚Ò¸'ëÿIÿ¾´ 0-1DÐÖÑž|ꀴrêhìñÈ & Vâ¶`o+ðit ‚BpTA5…ŠBpCñv ÿc1”ÐBaÊà½\@ˆRbƒ\ ¤VbXËf\v—² ³/`54Ðú˜Ê‡}Jºsès­“~9t«U^Óœ (2´‡¨º”ZQC ¡8Ú)2¦”r_†€&]º§: 4Š#ó" égZïå*Ý´‚™Xr³†ÒM‹ƒm‰'˜ÁÉ.S$B|G3åH>0õB˜JÄäASP c™xÜøOðÉS@ª)J9KI×L nUûnœlò°ÉÉåò†™áq0GØY¢A@ûd’†äÝx h8Q,èÔrD˜'f‰ÈwlCÊÅpÜDã³4x×JzÖZº+H<{<‡2aiÞ­ˆ‘Š5 }KGÕs…Á^ô=:Ü‹²ê”'S”Ö[Z†@šj(6¥Ø?¦3ä’‚‹ rÞÅ9ipH¤ÙÎP?’@ã‘îÖcHÙ@œ@ŠÒ :ƒeÓuÇrIMnÑHŠ$Ú ­"®Ú’çÂã y.ñQÅ%ð…±x1ˆ™Qk<-à‰’^®(µ¤Û-jrrÐŽxݶ0$%‚$ƒ×1%OFÁ°÷¨->ú<Ž8+—1¢³ï.¥-rȦql*Sn¤5öäIãF=EŒì);KuŸúhîi„¼pÌw•‰Þ=BÛ„é6e‚Ù(ãXÍ>±%æŽSçl0G¡„4†Kdc?åcô€4 ?!QÁ¢.!ŃžO#HÔîÈ¡4BìI%.ƒ…•KÉL“®Mª4ç[gÄ·ÅU¢÷¢­ù ¶FÎE%ÉiÐ…àQry•¤GÕOÛh½)¬ÔDØäÐ7b±Çåhþ‰Êÿ‰Ê—Qy,—2A†x™ôÝFÄšÓ¢PjMÌhñœGr7…d±¡ÿVA‹xô Z´Ûdá’¨‘EŠ+;‘ÂÞ’‡%;(Šˆ³MQå…®Hj5gb F°ˆŽb—8ªà‘&™Q àHàœK÷ÆÉH2BÃÛèc­]«G;÷<л…ÎMùûDL wkãƵÕ*µwVè½™¿jQýçü—ü×í‡@«6ÊËÓbz‘—#ú~à¿j3[~ïaLýj¦ñf¹…³irm<+OO†Ô±¾ˆ}é*V¯gé·1Uóš© =XE9£NW„QèÒ¿Ü ­R(mŠ /ã¹mÖÒˆþCÅßѯ\O"Å­gmÈãH˜u Y·NµF÷~ߥsÒÎÞ] èr1é·[N ³<Ô,p!ŒnMl-’î=mÛ=±[,ƒlNöÀ,÷TâNÈ¥‡mì“Œ;2W·X~ÔB­ÅÄ×ïþŽ¹ÆfʬХ¹µÞti²¥›¹Æà§Np?TX¥‚^ ¯93ÞG„›Èý«ê²¢9÷vǃG³bqн£ú{qÙÁ|8«Ðñ!v9û?ÄM±ó)–é³hSüìËÇx³ )ß¹·˜a7‘vìlj ©G=$ÏÞ|.'Ÿ«ò õOŸ­ZÜ1óiù`zUª³jÀ.Š?‹Éé4j³ýÔÄâû™‰féëC!zk‘>Ì Òg£D:ó.ÒWD:­ÿ±Ø}›[Ï$xq<­Üf¸ÓùÉâKq™mÀ‘€Þaå€kd^H&÷ÍU9zL2•úåoæ3 ®S<&u€GñòŸ§åâvú¢Rë3KO ÖñâøÆõ&Ž‡#÷ð|"Þß|îRŸSÎŒ°é:Á&˜5|‘~›c¦óõ¡Mc"\ê£;jJ<¨i!oR¦ã æ½Wž?ýRÍ.d¼ådRžÁí—å·/cΚðu8Ö`‰‡<íÀ5ÓÄþ4çÔFÏ©åü»àÝVMßÓÄÓ ÒÆÅ~MþE¾ê:¨üüóîjendstream endobj 100 0 obj << /Filter /FlateDecode /Length 3311 >> stream xÚ¥ZIsÛF¾ëW r"«Ât£±tæ”xâL–Ùbådç’ȱH0eÅ©ùñó¶^B²§¦T€î×Û[¾·´òì>˳ïnòÉó›Û›?½®šL×ÊèÒf·w™Óª©uV­´uÙí6{»x½Ô‹øí~‡?{ø]cC·\…Yœà½=ãŸC/g¡Ù`w±8,M½x” .رð­½ÈøC¿\ÉçG²„ß{žã ¿/;¦—ë q/NŒ ~XþzûE+W–ûW…-³•5ª²ŸåÕN†ìi=n×QMÿWÅÏðDÜü{\¨?ò E‘é\¹Üi\aU”*/šl¥ Uzný èƯx÷ßàî{9´Ž¾ð}CD÷ËQ:/_ò^Sq¦µg*r龓þ_~Ä=Ý|{{óÛyæ™ÎU…S¹Ë6‡›·¿æÙšÈrU¸&{"¢Cf-’?donþõ¬J8å*Sá!McTQÕY¥+U×–ù5jÁàåÝn.´•édį8ÓJ—NiˆvʘÚÏDŒmª„„X5%LAX4ˆÕdz4ÈŽúûe Ü! 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00000 n 0000201811 00000 n 0000201967 00000 n 0000202162 00000 n 0000202286 00000 n 0000202396 00000 n 0000202434 00000 n 0000202561 00000 n trailer << /Size 168 /Root 166 0 R /Info 167 0 R /ID [ ] >> startxref 203535 %%EOF flexsurv/inst/doc/flexsurv.Rnw0000644000176200001440000020161214607502156016230 0ustar liggesusers%\VignetteIndexEntry{flexsurv user guide} %\VignetteEngine{knitr::knitr} % \documentclass[article,shortnames]{jss} \documentclass[article,shortnames,nojss,nofooter]{jss} \usepackage{bm} \usepackage{tabularx} \usepackage{graphics} \usepackage{alltt} <>= options(width=60) options(prompt="R> ") library(knitr) opts_chunk$set(fig.path="flexsurv-") render_sweave() @ %% need no \usepackage{Sweave.sty} \author{Christopher H. Jackson \\ MRC Biostatistics Unit, Cambridge, UK} \title{flexsurv: A Platform for Parametric Survival Modelling in R} \Plainauthor{Christopher Jackson, MRC Biostatistics Unit} \Address{ Christopher Jackson\\ MRC Biostatistics Unit\\ Cambridge Institute of Public Health\\ Robinson Way\\ Cambridge, CB2 0SR, U.K.\\ E-mail: \email{chris.jackson@mrc-bsu.cam.ac.uk} } \Abstract{ \pkg{flexsurv} is an \proglang{R} package for fully-parametric modelling of survival data. Any parametric time-to-event distribution may be fitted if the user supplies a probability density or hazard function, and ideally also their cumulative versions. Standard survival distributions are built in, including the three and four-parameter generalized gamma and F distributions. Any parameter of any distribution can be modelled as a linear or log-linear function of covariates. The package also includes the spline model of \citet{royston:parmar}, in which both baseline survival and covariate effects can be arbitrarily flexible parametric functions of time. The main model-fitting function, \code{flexsurvreg}, uses the familiar syntax of \code{survreg} from the standard \pkg{survival} package \citep{therneau:survival}. Censoring or left-truncation are specified in \code{Surv} objects. The models are fitted by maximising the full log-likelihood, and estimates and confidence intervals for any function of the model parameters can be printed or plotted. \pkg{flexsurv} also provides functions for fitting and predicting from fully-parametric multi-state models, and connects with the \pkg{mstate} package \citep{mstate:jss}. This article explains the methods and design principles of the package, giving several worked examples of its use. \emph{[Note: A version of this vignette is published as \citet{flexsurv} in Journal of Statistical Software. All content there is included here. There have been no substantial changes in the survival modelling parts since then. Version 2.0 of \pkg{flexsurv} added new features for multi-state modelling, and since that version, multi-state modelling with \pkg{flexsurv} has been described in a separate vignette.]}} \Keywords{survival, multi-state models, multistate models} \begin{document} %\SweaveOpts{concordance=TRUE} \section{Motivation and design} The Cox model for survival data is ubiquitous in medical research, since the effects of predictors can be estimated without needing to supply a baseline survival distribution that might be inaccurate. However, fully-parametric models have many advantages, and even the originator of the Cox model has expressed a preference for parametric modelling \citep[see][]{reid:cox:conversation}. Fully-specified models can be more convenient for representing complex data structures and processes \citep{aalen:process}, e.g. hazards that vary predictably, interval censoring, frailties, multiple responses, datasets or time scales, and can help with out-of-sample prediction. For example, the mean survival $\E(T) = \int_0^{\infty}S(t)dt$, used in health economic evaluations \citep{latimer2013survival}, needs the survivor function $S(t)$ to be fully-specified for all times $t$, and parametric models that combine data from multiple time periods can facilitate this \citep{survextrap:tatiana}. %% Cox "That's right, but since then various people have shown that %% the answers are very insensitive to the parametric %% formulation of the underlying distribution. And if you want %% to do things like predict the outcome for a particular patient, %% it's much more convenient to do that parametrically." \pkg{flexsurv} for \proglang{R} \citep{R} allows parametric distributions of arbitrary complexity to be fitted to survival data, gaining the convenience of parametric modelling, while avoiding the risk of model misspecification. Built-in choices include spline-based models with any number of knots \citep{royston:parmar} and 3--4 parameter generalized gamma and F distribution families. Any user-defined model may be employed by supplying at minimum an \proglang{R} function to compute the probability density or hazard, and ideally also its cumulative form. Any parameters may be modelled in terms of covariates, and any function of the parameters may be printed or plotted in model summaries. \pkg{flexsurv} is intended as a general platform for survival modelling in \proglang{R}. The \code{survreg} function in the \proglang{R} package \pkg{survival} \citep{therneau:survival} only supports two-parameter (location/scale) distributions, though users can supply their own distributions if they can be parameterised in this form. Some other contributed \proglang{R} packages can fit survival models, e.g., \pkg{eha} \citep{eha} and \pkg{VGAM} \citep{yee:wild}, though these are either limited to specific distribution families, or not specifically designed for survival analysis. Others, e.g. \pkg{ActuDistns} \citep{actudistns}, contain only the definitions of distribution functions. \pkg{flexsurv} enables such functions to be used in survival models. It is similar in spirit to the \proglang{Stata} packages \pkg{stpm2} \citep{stpm2} for spline-based survival modelling, and \pkg{stgenreg} \citep{stgenreg} for fitting survival models with user-defined hazard functions using numerical integration. Though in \pkg{flexsurv}, slow numerical integration can be avoided if the analytic cumulative distribution or hazard can be supplied, and optimisation can also be speeded by supplying analytic derivatives. \pkg{flexsurv} also has features for multi-state modelling and interval censoring, and general output reporting. It employs functional programming to work with user-defined or existing \proglang{R} functions. \S\ref{sec:general} explains the general model that \pkg{flexsurv} is based on. \S\ref{sec:models} gives examples of its use for fitting built-in survival distributions with a fixed number of parameters, and \S\ref{sec:custom} explains how users can define new distributions. \S\ref{sec:adim} concentrates on classes of models where the number of parameters can be chosen arbitrarily, such as splines. \S\ref{sec:multistate} mentions the use of \pkg{flexsurv} for fitting and predicting from fully-parametric multi-state models, which is described more fully in a separate vignette. Finally \S\ref{sec:extensions} suggests some potential future extensions. \section{General parametric survival model} \label{sec:general} The general model that \pkg{flexsurv} fits has probability density for death at time $t$: \begin{equation} \label{eq:model} f(t | \mu(\mathbf{z}), \bm{\alpha}(\mathbf{z})), \quad t \geq 0 \end{equation} The cumulative distribution function $F(t)$, survivor function $S(t) = 1 - F(t)$, cumulative hazard $H(t) = -\log S(t)$ and hazard $h(t) = f(t)/S(t)$ are also defined (suppressing the conditioning for clarity). $\mu=\alpha_0$ is the parameter of primary interest, which usually governs the mean or \emph{location} of the distribution. Other parameters $\bm{\alpha} = (\alpha_1, \ldots, \alpha_R)$ are called ``ancillary'' and determine the shape, variance or higher moments. %%% Covariates may be time-dependent, but this notation generalizes to left-truncation, ref msm section \paragraph{Covariates} All parameters may depend on a vector of covariates $\mathbf{z}$ through link-transformed linear models $g_0(\mu(\mathbf{z})) = \gamma_0 + \bm{\beta}_0^{\top} \mathbf{z}$ and $g_r(\alpha_r(\mathbf{z})) = \gamma_r + \bm{\beta}_r^{\top} \mathbf{z}$. $g()$ will typically be $\log()$ if the parameter is defined to be positive, or the identity function if the parameter is unrestricted. Suppose that the location parameter, but not the ancillary parameters, depends on covariates. If the hazard function factorises as $h(t | \bm{\alpha}, \mu(\mathbf{z})) = \mu(\mathbf{z}) h_0(t | \bm{\alpha})$, then this is a \emph{proportional hazards} (PH) model, so that the hazard ratio between two groups (defined by two different values of $\mathbf{z}$) is constant over time $t$. Alternatively, if $S(t | \mu(\mathbf{z}), \bm{\alpha}) = S_0(\mu(\mathbf{z}) t | \bm{\alpha})$ then it is an \emph{accelerated failure time} (AFT) model, so that the effect of covariates is to speed or slow the passage of time. For example, doubling the value of a covariate with coefficient $\beta=\log(2)$ would give half the expected survival time. \paragraph{Data and likelihood} Let $t_i: i=1,\ldots, n$ be a sample of times from individuals $i$. Let $c_i=1$ if $t_i$ is an observed death time, or $c_i=0$ if this is censored. Most commonly, $t_i$ may be right-censored, thus the true death time is known only to be greater than $t_i$. More generally, the survival time may be interval-censored on $(t^{min}_i, t^{max}_i)$. Also let $s_i$ be corresponding left-truncation (or delayed-entry) times, meaning that the $i$th survival time is only observed conditionally on the individual having survived up to $s_i$, thus $s_i=0$ if there is no left-truncation. With at most right-censoring, the likelihood for the parameters $\bm{\theta} = \{\bm{\gamma},\bm{\beta}\}$ in Equation \ref{eq:model}, given the corresponding data vectors, is \begin{equation} \label{eq:lik} l(\bm{\theta} | \mathbf{t},\mathbf{c},\mathbf{s}) = \left\{ \prod_{i:\ c_i=1} f_i(t_i) \prod_{i:\ c_i=0} S_i(t_i)\right\} / \prod_i S_i(s_i) \end{equation} where $f_i(t_i)$ is shorthand for $f(t_i | \mu(\mathbf{z}_i), \bm{\alpha}(\mathbf{z}_i))$, $S_i(t_i)$ is $S(t_i | \mu(\mathbf{z}_i), \bm{\alpha}(\mathbf{z}_i))$, and $\mu, \bm{\alpha}$ are related to $\bm{\gamma}$, $\bm{\beta}$ and $\mathbf{z}_i$ via the link functions defined above. The log-likelihood also has a concise form in terms of hazards and cumulative hazards, as \[ \log l(\bm{\theta}|\mathbf{t},\mathbf{c},\mathbf{s}) = \sum_{i:\ c_i=1} \left\{\log(h_i(t_i)) - H_i(t_i)\right\} - \sum_{i:\ c_i=0} H_i(t_i) + \sum_i H_i(s_i) \] With interval-censoring, the likelihood is \begin{equation} \label{eq:lik:interval} l(\bm{\theta} | \mathbf{t}^{min},\mathbf{t}^{max},\mathbf{c},\mathbf{s}) = \left\{ \prod_{i:\ c_i=1} f_i(t_i) \prod_{i:\ c_i=0} \left(S_i(t_i^{min}) - S_i(t^{max}_i)\right)\right\} / \prod_i S_i(s_i) \end{equation} %% with hazards: %% log lik is sum log(f) sum log(S) - sum log(S) %% sum(log(h) + H) - sum(H) + sum(H(si)) %% h = f/S, H=-log(S) h S S These likelihoods assume that the times of censoring are fixed or otherwise distributed independently of the parameters $\bm{\theta}$ that govern the survival times (see, e.g. \citet{aalen:process}). The individual survival times are also independent, so that \pkg{flexsurv} does not currently support shared frailty, clustered or random effects models (see \S\ref{sec:extensions}). The parameters are estimated by maximising the full log-likelihood with respect to $\bm{\theta}$, as detailed further in \S\ref{sec:comp}. \section{Fitting standard parametric survival models} \label{sec:models} An example dataset used throughout this paper is from 686 patients with primary node positive breast cancer, available in the package as \code{bc}. This was originally provided with \pkg{stpm} \citep{stpm:orig}, and analysed in much more detail by \citet{sauerbrei1999building} and \citet{royston:parmar} \footnote{A version of this dataset, including more covariates but excluding the prognostic group, is also provided as \code{GBSG2} in the package \pkg{TH.data} \citep{TH.data}.} . The first two records are shown by: <>= library("flexsurv") @ <<>>= head(bc, 2) @ The main model-fitting function is called \code{flexsurvreg}. Its first argument is an \proglang{R} \emph{formula} object. The left hand side of the formula gives the response as a survival object, using the \code{Surv} function from the \pkg{survival} package. <<>>= fs1 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") @ Here, this indicates that the response variable is \code{recyrs}. This represents the time (in years) of death or cancer recurrence when \code{censrec} is 1, or (right-)censoring when \code{censrec} is 0. The covariate \code{group} is a factor representing a prognostic score, with three levels \code{"Good"} (the baseline), \code{"Medium"} and \code{"Poor"}. All of these variables are in the data frame \code{bc}. If the argument \code{dist} is a string, this denotes a built-in survival distribution. In this case we fit a Weibull survival model. Printing the fitted model object gives estimates and confidence intervals for the model parameters and other useful information. Note that these are the \emph{same parameters} as represented by the \proglang{R} distribution function \code{dweibull}: the \code{shape} $\alpha$ and the \code{scale} $\mu$ of the survivor function $S(t) = \exp(-(t/\mu)^\alpha)$, and \code{group} has a linear effect on $\log(\mu)$. <<>>= fs1 @ For the Weibull (and exponential, log-normal and log-logistic) distribution, \code{flexsurvreg} simply acts as a wrapper for \code{survreg}: the maximum likelihood estimates are obtained by \code{survreg}, checked by \code{flexsurvreg} for optimisation convergence, and converted to \code{flexsurvreg}'s preferred parameterisation. Therefore the same model can be fitted more directly as <<>>= survreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") @ \begin{sloppypar} The maximised log-likelihoods are the same, however the parameterisation is different: the first coefficient \code{(Intercept)} reported by \code{survreg} is $\log(\mu)$, and \code{survreg}'s \code{"scale"} is \code{dweibull}'s (thus \code{flexsurvreg})'s 1 / \code{shape}. The covariate effects $\bm{\beta}$, however, have the same ``accelerated failure time'' interpretation, as linear effects on $\log(\mu)$. The multiplicative effects $\exp(\bm{\beta})$ are printed in the output as \code{exp(est)}. \end{sloppypar} The same model can be fitted in \pkg{eha}, also by maximum likelihood, as <>= library(eha) aftreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "weibull") @ The results are presented in the same parameterisation as \code{flexsurvreg}, except that the shape and scale parameters are log-transformed, and (unless the argument \code{param="lifeExp"} is supplied) the covariate effects have the opposite sign. \subsection{Additional modelling features} \label{sec:censtrunc} \subsubsection{Truncation and time-dependent covariates} \begin{sloppypar} If we also had left-truncation times in a variable called \code{start}, the response would be \code{Surv(start, recyrs, censrec)}. Or if all responses were interval-censored between lower and upper bounds \code{tmin} and \code{tmax}, then we would write \code{Surv(tmin, tmax, type = "interval2")}. \end{sloppypar} Time-dependent covariates are not supported in \pkg{flexsurv}. In other packages, they are represented in ``counting process'' form --- as a series of left-truncated survival times, which may also be right-censored. For each individual there would be multiple records, each corresponding to an interval where the covariate is assumed to be constant. The response would be of the form \code{Surv(start, stop, censrec)}, where \code{start} and \code{stop} are the limits of each interval, and \code{censrec} indicates whether a death was observed at \code{stop}. However, using this approach would require the probability of survival up to the left-truncation time to be represented by a term of the form $S_i(s_i) = \exp(-H_i(s_i))$ in the likelihood (equation 2). The cumulative hazard $H$ over the interval from time 0 to time $s_i$ depends on how the covariates change for an individual on this time interval, and \pkg{flexsurv} cannot keep track of different observations for an individual. Furthermore, prediction from models with time-dependent covariates is a difficult problem, as it requires knowledge of when the covariates are expected to change. Joint models for longitudinal and survival data are a more flexible approach for modelling the association of a survival time with a time-dependent predictor. In versions of \pkg{flexsurv} since April 2020, models with individual-specific right-truncation times are also supported. These are used for situations with ``retrospective ascertainment'', where cases are only included in the data if they have died by a specific time. These models are specified through an argument \code{rtrunc} to \code{flexsurvreg} that names the variable with the truncation times. See the Supplementary Examples vignette for a worked example. \subsubsection{Relative survival} In relative survival models \citep{nelson:relative:survival}, the survivor function is expressed as $S(t) = S^*(t)R(t)$, where $S^*(t)$ is the ``expected" or ``baseline" survival, and $R(t)$ is the \emph{relative} survival. Equivalently, the hazard is defined as $h(t) = h^*(t) + \lambda(t)$, where $h^*()$ is the baseline hazard function, and $\lambda(t)$ is the excess mortality rate associated with the disease of interest. The baseline represents a reference population, and is typically obtained from national routinely-collected mortality statistics, adjusted (e.g. by age/sex) to represent the population under study. The parametric model is defined and estimated for $R(t)$. These models are implemented in \pkg{flexsurv} by supplying the variable in the data that represents the expected mortality rate $h^*(t)$ in the \code{bhazard} argument to \code{flexsurvreg}. This is only used for the individuals in the data who die, and \code{bhazard} describes the expected hazard at the death time. The values of \code{bhazard} for censored individuals are ignored. Note that the parameters returned in the model fitted by \code{flexsurvreg} refer to the relative survival $R(t)$, rather than the absolute survival. The likelihood returned by \code{flexsurvreg} here is a \emph{partial} likelihood defined \citep[as in][equations 4--5]{nelson:relative:survival} by omitting the term $\sum_i \log(S^*(t_i))$ (summed over all individuals $i$ in the data, including both censored and uncensored times $t_i$) from the full likelihood. This term is equivalent to minus the sum of the cumulative hazards. It can be omitted from the likelihood for the purpose of estimating the parameters of the relative survival model, since it does not depend on these parameters. Hence if a full likelihood is required, (e.g. for model comparison) then this term should be added to the partial likelihood. Similarly, the predicted survival or hazard (e.g. as returned by \code{summary.flexsurvreg}, see Section~\ref{sec:plots}) from a relative survival model refers to $R(t)$ or $h(t)$. Hence if the overall survival or hazard is required, the predictions of relative survival should be converted to the ``absolute" scale by combining with the baseline, though no specific tools for doing this are provided by \pkg{flexsurv}. \subsubsection{Weighting and subsetting} Case weights and data subsets can also be specified, as in standard \proglang{R} modelling functions, using \code{weights} or \code{subset} arguments. \subsection{Built-in models} \label{sec:builtin} \code{flexsurvreg}'s currently built-in distributions are listed in Table \ref{tab:dists}. In each case, the probability density $f()$ and parameters of the fitted model are taken from an existing \proglang{R} function of the same name but beginning with the letter \code{d}. For the Weibull, exponential (\code{dexp}), gamma (\code{dgamma}) and log-normal (\code{dlnorm}), the density functions are provided with standard installations of \proglang{R}. These density functions, and the corresponding cumulative distribution functions (with first letter \code{p} instead of \code{d}) are used internally in \code{flexsurvreg} to compute the likelihood. \pkg{flexsurv} provides some additional survival distributions, including a Gompertz distribution with unrestricted shape parameter, Weibull with proportional hazards parameterisation, log-logistic, and the three- and four-parameter families described below. For all built-in distributions, \pkg{flexsurv} also defines functions beginning with \code{h} giving the hazard, and \code{H} for the cumulative hazard. A package vignette ``Distributions reference'' lists the survivor function and parameterisation of covariate effects used by each built-in distribution. \paragraph{Generalized gamma} This three-parameter distribution includes the Weibull, gamma and log-normal as special cases. The original parameterisation from \citet{stacy:gengamma} is available as\\ \code{dist = "gengamma.orig"}, however the newer parameterisation \citep{prentice:loggamma} is preferred: \code{dist = "gengamma"}. This has parameters ($\mu$,$\sigma$,$q$), and survivor function \[ \begin{array}{ll} 1 - I(\gamma,u) & (q > 0)\\ 1 - \Phi(z) & (q = 0)\\ \end{array} \] where $I(\gamma,u) = \int_0^u x^{\gamma-1}\exp(-x)/\Gamma(\gamma)$ is the incomplete gamma function (the cumulative gamma distribution with shape $\gamma$ and scale 1), $\Phi$ is the standard normal cumulative distribution, $u = \gamma \exp(|q|z)$, $z=(\log(t) - \mu)/\sigma$, and $\gamma=q^{-2}$. The \citet{prentice:loggamma} parameterisation extends the original one to include a further class of models with negative $q$, and survivor function $I(\gamma,u)$, where $z$ is replaced by $-z$. This stabilises estimation when the distribution is close to log-normal, since $q=0$ is no longer near the boundary of the parameter space. In \proglang{R} notation, \footnote{The parameter called $q$ here and in previous literature is called $Q$ in \code{dgengamma} and related functions, since the first argument of a cumulative distribution function is conventionally named \code{q}, for quantile, in \proglang{R}.} the parameter values corresponding to the three special cases are \begin{Code} dgengamma(x, mu, sigma, Q=0) == dlnorm(x, mu, sigma) dgengamma(x, mu, sigma, Q=1) == dweibull(x, shape = 1 / sigma, scale = exp(mu)) dgengamma(x, mu, sigma, Q=sigma) == dgamma(x, shape = 1 / sigma^2, rate = exp(-mu) / sigma^2) \end{Code} \paragraph{Generalized F} This four-parameter distribution includes the generalized gamma, and also the log-logistic, as special cases. The variety of hazard shapes that can be represented is discussed by \citet{ccox:genf}. It is provided here in alternative ``original'' (\code{dist = "genf.orig"}) and ``stable'' parameterisations (\code{dist = "genf"}) as presented by \citet{prentice:genf}. See \code{help(GenF)} and \code{help(GenF.orig)} in the package documentation for the exact definitions. \subsection{Covariates on ancillary parameters} The generalized gamma model is fitted to the breast cancer survival data. \code{fs2} is an AFT model, where only the parameter $\mu$ depends on the prognostic covariate \code{group}. In a second model \code{fs3}, the first ancillary parameter \code{sigma} ($\alpha_1$) also depends on this covariate, giving a model with a time-dependent effect that is neither PH nor AFT. The second ancillary parameter \code{Q} is still common between prognostic groups. <<>>= fs2 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = "gengamma") fs3 <- flexsurvreg(Surv(recyrs, censrec) ~ group + sigma(group), data = bc, dist = "gengamma") @ Ancillary covariates can alternatively be supplied using the \code{anc} argument to \code{flexsurvreg}. This syntax is required if any parameter names clash with the names of functions used in model formulae (e.g., \code{factor()} or \code{I()}). <>= fs3 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, anc = list(sigma = ~ group), dist = "gengamma") @ Table \ref{tab:aic} compares all the models fitted to the breast cancer data, showing absolute fit to the data as measured by the maximised -2$\times$log likelihood $-2LL$, number of parameters $p$, and Akaike's information criterion $-2LL + 2p$ (AIC). The model \code{fs2} has the lowest AIC, indicating the best estimated predictive ability. \begin{table} \begin{tabular}{p{1.8in}lll} \hline & Parameters & Density \proglang{R} function & \code{dist}\\ & {\footnotesize{(location in \code{\color{red}{red}})}} & & \\ \hline Exponential & \code{\color{red}{rate}} & \code{dexp} & \code{"exp"} \\ Weibull (accelerated failure time) & \code{shape, {\color{red}{scale}}} & \code{dweibull} & \code{"weibull"} \\ Weibull (proportional hazards) & \code{shape, {\color{red}{scale}}} & \code{dweibullPH} & \code{"weibullPH"} \\ Gamma & \code{shape, \color{red}{rate}} & \code{dgamma} & \code{"gamma"}\\ Log-normal & \code{{\color{red}{meanlog}}, sdlog} & \code{dlnorm} & \code{"lnorm"}\\ Gompertz & \code{shape, {\color{red}{rate}}} & \code{dgompertz} & \code{"gompertz"} \\ Log-logistic & \code{shape, {\color{red}{scale}}} & \code{dllogis} & \code{"llogis"}\\ Generalized gamma (Prentice 1975) & \code{{\color{red}{mu}}, sigma, Q} & \code{dgengamma} & \code{"gengamma"} \\ Generalized gamma (Stacy 1962)& \code{shape, {\color{red}{scale}}, k} & \code{dgengamma.orig} & \code{"gengamma.orig"} \\ Generalized F (stable) & \code{{\color{red}{mu}}, sigma, Q, P} & \code{dgenf} & \code{"genf"} \\ Generalized F (original) & \code{{\color{red}{mu}}, sigma, s1, s2} & \code{dgenf.orig} & \code{"genf.orig"} \\ \hline \end{tabular} \caption{Built-in parametric survival distributions in \pkg{flexsurv}.} \label{tab:dists} \end{table} \subsection{Plotting outputs} \label{sec:plots} The \code{plot()} method for \code{flexsurvreg} objects is used as a quick check of model fit. By default, this draws a Kaplan-Meier estimate of the survivor function $S(t)$, one for each combination of categorical covariates, or just a single ``population average'' curve if there are no categorical covariates (Figure \ref{fig:surv}). The corresponding estimates from the fitted model are overlaid. Fitted values from further models can be added with the \code{lines()} method. <>= cols <- c("#E495A5", "#86B875", "#7DB0DD") # from colorspace::rainbow_hcl(3) plot(fs1, col = cols[2], lwd.obs = 2, xlab = "Years", ylab = "Recurrence-free survival") lines(fs2, col = cols[3], lty = 2) lines(fs3, col = cols[3]) text(x=c(2,3.5,4), y=c(0.4, 0.55, 0.7), c("Poor","Medium","Good")) legend("bottomleft", col = c("black", cols[2], cols[3], cols[3]), lty = c(1, 1, 2, 1), bty = "n", lwd = rep(2, 4), c("Kaplan-Meier", "Weibull", "Generalized gamma (AFT)", "Generalized gamma (time-varying)")) @ \begin{figure}[h] \centering \includegraphics{flexsurv-surv-1} \caption{Survival by prognostic group from the breast cancer data: fitted from alternative parametric models and Kaplan-Meier estimates.} \label{fig:surv} \end{figure} The argument \code{type = "hazard"} can be set to plot hazards from parametric models against kernel density estimates obtained from \pkg{muhaz} \citep{muhaz,mueller:wang}. Figure \ref{fig:haz} shows more clearly that the Weibull model is inadequate for the breast cancer data: the hazard must be increasing or decreasing --- while the generalized gamma can represent the increase and subsequent decline in hazard seen in the data. Similarly, \code{type = "cumhaz"} plots cumulative hazards. <>= plot(fs1, type = "hazard", col = cols[2], lwd.obs = 2, max.time=6, xlab = "Years", ylab = "Hazard") lines(fs2, type = "hazard", col = cols[3], lty = 2) lines(fs3, type = "hazard", col = cols[3]) text(x=c(2,2,2), y=c(0.3, 0.13, 0.05), c("Poor","Medium","Good")) legend("topright", col = c("black", cols[2], cols[3], cols[3]), lty = c(1, 1, 2, 1), bty = "n", lwd = rep(2, 4), c("Kernel density estimate", "Weibull", "Gen. gamma (AFT)", "Gen. gamma (time-varying)")) @ \begin{figure}[h] \centering \includegraphics{flexsurv-haz-1} \caption{Hazards by prognostic group from the breast cancer data: fitted from alternative parametric models and kernel density estimates.} \label{fig:haz} \end{figure} The numbers plotted are available from the \code{summary.flexsurvreg()} method. Confidence intervals are produced by simulating a large sample from the asymptotic normal distribution of the maximum likelihood estimates of $\{\bm{\beta}_r: r=0,\ldots,R\}$ \citep{mandel:simci}, via the function \code{normboot.flexsurvreg}. This very general method allows confidence intervals to be obtained for arbitrary functions of the parameters, as described in the next section. In this example, there is only a single categorical covariate, and the \code{plot} and \code{summary} methods return one observed and fitted trajectory for each level of that covariate. For more complicated models, users should specify what covariate values they want summaries for, rather than relying on the default \footnote{If there are only factor covariates, all combinations are plotted. If there are any continuous covariates, these methods by default return a ``population average'' curve, with the linear model design matrix set to its average values, including the 0/1 contrasts defining factors, which doesn't represent any specific covariate combination.}. This is done by supplying the \code{newdata} argument, a data frame or list containing covariate values, just as in standard \proglang{R} functions like \code{predict.lm}. Time-dependent covariates are not understood by these functions. This \code{plot()} method is only for casual exploratory use. For publication-standard figures, it is preferable to set up the axes beforehand (\code{plot(..., type = "n")}), and use the \code{lines()} methods for \code{flexsurvreg} objects, or construct plots by hand using the data available from \code{summary.flexsurvreg()}. \subsection{Custom model summaries} Any function of the parameters of a fitted model can be summarised or plotted by supplying the argument \code{fn} to \code{summary.flexsurvreg} or \code{plot.flexsurvreg}. This should be an \proglang{R} function, with optional first two arguments \code{t} representing time, and \code{start} representing a left-truncation point (if the result is conditional on survival up to that time). Any remaining arguments must be the parameters of the survival distribution. For example, median survival under the Weibull model \code{fs1} can be summarised as follows <<>>= median.weibull <- function(shape, scale) { qweibull(0.5, shape = shape, scale = scale) } summary(fs1, fn = median.weibull, t = 1, B = 10000) @ Although the median of the Weibull has an analytic form as $\mu \log(2)^{1/\alpha}$, the form of the code given here generalises to other distributions. The argument \code{t} (or \code{start}) can be omitted from \code{median.weibull}, because the median is a time-constant function of the parameters, unlike the survival or hazard. \code{10000} random samples are drawn to produce a slightly more precise confidence interval than the default --- users should adjust this until the desired level of precision is obtained. A useful future extension of the package would be to employ user-supplied (or built-in) derivatives of summary functions if possible, so that the delta method can be used to obtain approximate confidence intervals without simulation. \subsection{Computation} \label{sec:comp} The likelihood is maximised in \code{flexsurvreg} using the optimisation methods available through the standard \proglang{R} \code{optim} function. By default, this is the \code{"BFGS"} method \citep{nash} using the analytic derivatives of the likelihood with respect to the model parameters, if these are available, to improve the speed of convergence to the maximum. These derivatives are built-in for the exponential, Weibull, Gompertz, log-logistic, and hazard- and odds-based spline models (see \S\ref{sec:spline}). For custom distributions (see \S\ref{sec:custom}), the user can optionally supply functions with names beginning \code{"DLd"} and \code{"DLS"} respectively (e.g., \code{DLdweibull, DLSweibull}) to calculate the derivatives of the log density and log survivor functions with respect to the transformed baseline parameters $\bm{\gamma}$ (then the derivatives with respect to $\bm{\beta}$ are obtained automatically). Arguments to \code{optim} can be passed to \code{flexsurvreg} --- in particular, \code{control} options, such as convergence tolerance, iteration limit or function or parameter scaling, may need to be adjusted to achieve convergence. \section{Custom survival distributions} \label{sec:custom} \pkg{flexsurv} is not limited to its built-in distributions. Any survival model of the form (\ref{eq:model}--\ref{eq:lik:interval}) can be fitted if the user can provide either the density function $f()$ or the hazard $h()$. Many contributed \proglang{R} packages provide probability density and cumulative distribution functions for positive distributions. Though survival models may be more naturally characterised by their hazard function, representing the changing risk of death through time. For example, for survival following major surgery we may want a ``U-shaped'' hazard curve, representing a high risk soon after the operation, which then decreases, but increases naturally as survivors grow older. To supply a custom distribution, the \code{dist} argument to \code{flexsurvreg} is defined to be an \proglang{R} list object, rather than a character string. The list has the following elements. \begin{description} \item[\code{name}] Name of the distribution. In the first example below, we use a log-logistic distribution, and the name is \code{"llogis"} \footnote{though since version 0.5.1, this distribution is built into \pkg{flexsurv} as \code{dist="llogis"} }. Then there is assumed to be at least either \begin{itemize} \item a function to compute the probability density, which would be called \code{dllogis} here, or \item a function to compute the hazard, called \code{hllogis}. \end{itemize} There should also be a function called \code{pllogis} for the cumulative distribution (if \code{d} is given), or \code{H} for the cumulative hazard (to complement \code{h}), if analytic forms for these are available. If not, then \pkg{flexsurv} can compute them internally by numerical integration, as in \pkg{stgenreg} \citep{stgenreg}. The default options of the built-in \proglang{R} routine \code{integrate} for adaptive quadrature are used, though these may be changed using the \code{integ.opts} argument to \code{flexsurvreg}. Models specified this way will take an order of magnitude more time to fit, and the fitting procedure may be unstable. An example is given in \S\ref{sec:gdim}. These functions must be \emph{vectorised}, and the density function must also accept an argument \code{log}, which when \code{TRUE}, returns the log density. See the examples below. In some cases, \proglang{R}'s scoping rules may not find the functions in the working environment. They may then be supplied through the \code{dfns} argument to \code{flexsurvreg}. \item[\code{pars}] Character vector naming the parameters of the distribution $\mu,\alpha_1,...,\alpha_R$. These must match the arguments of the \proglang{R} distribution function or functions, in the same order. \item[\code{location}] Character: quoted name of the location parameter $\mu$. The location parameter will not necessarily be the first one, e.g., in \code{dweibull} the \code{scale} comes after the \code{shape}. \item[\code{transforms}] A list of functions $g()$ which transform the parameters from their natural ranges to the real line, for example, \code{c(log, identity)} if the first is positive and the second unrestricted. \footnote{This is a \emph{list}, not an \emph{atomic vector} of functions, so if the distribution only has one parameter, we should write \code{transforms = c(log)} or \code{transforms = list(log)}, not \code{transforms = log}.} \item[\code{inv.transforms}] List of corresponding inverse functions. \item[\code{inits}] A function which provides plausible initial values of the parameters for maximum likelihood estimation. This is optional, but if not provided, then each call to \code{flexsurvreg} must have an \code{inits} argument containing a vector of initial values, which is inconvenient. Implausible initial values may produce a likelihood of zero, and a fatal error message (\code{initial value in `vmmin' is not finite}) from the optimiser. Each distribution will ideally have a heuristic for initialising parameters from summaries of the data. For example, since the median of the Weibull is $\mu \log(2)^{1/\alpha}$, a sensible estimate of $\mu$ might be the median log survival time divided by $\log(2)$, with $\alpha=1$, assuming that in practice the true value of $\alpha$ is not far from 1. Then we would define the function, of one argument \code{t} giving the survival or censoring times, returning the initial values for the Weibull \code{shape} and \code{scale} respectively \footnote{though Weibull models in \code{flexsurvreg} are ``initialised'' by fitting the model with \code{survreg}, unless there is left-truncation.}. \code{inits = function(t){ c(1, median(t[t > 0]) / log(2)) } } More complicated initial value functions may use other data such as the covariate values and censoring indicators: for an example, see the function \code{flexsurv.splineinits} in the package source that computes initial values for spline models (\S\ref{sec:spline}). \end{description} \paragraph{Example: Using functions from a contributed package} The following custom model uses the log-logistic distribution functions (\code{dllogis} and \code{pllogis}) available in the package \pkg{eha}. The survivor function is $S(t|\mu,\alpha) = 1/(1 + (t/\mu)^\alpha)$, so that the log odds $\log((1-S(t))/S(t))$ of having died are a linear function of log time. <>= custom.llogis <- list(name = "llogis", pars = c("shape", "scale"), location = "scale", transforms = c(log, log), inv.transforms = c(exp, exp), inits = function(t){ c(1, median(t)) }) fs4 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = custom.llogis) @ This fits the breast cancer data better than the Weibull, since it can represent a peaked hazard, but less well than the generalized gamma (Table \ref{tab:aic}). \paragraph{Example: Wrapping functions from a contributed package} Sometimes there may be probability density and similar functions in a contributed package, but in a different format. For example, \pkg{eha} also provides a three-parameter Gompertz-Makeham distribution with hazard $h(t|\mu,\alpha_1,\alpha_2)= \alpha_2 + \alpha_1 \exp(t/\mu)$. The shape parameters $\alpha_1,\alpha_2$ are provided to \code{dmakeham} as a vector argument of length two. However, \code{flexsurvreg} expects distribution functions to have one argument for each parameter. Therefore we write our own functions that wrap around the third-party functions. <>= dmakeham3 <- function(x, shape1, shape2, scale, ...) { dmakeham(x, shape = c(shape1, shape2), scale = scale, ...) } pmakeham3 <- function(q, shape1, shape2, scale, ...) { pmakeham(q, shape = c(shape1, shape2), scale = scale, ...) } @ \code{flexsurvreg} also requires these functions to be \emph{vectorized}, as the standard distribution functions in \proglang{R} are. That is, we can supply a vector of alternative values for one or more arguments, and expect a vector of the same length to be returned. The \proglang{R} base function \code{Vectorize} can be used to do this here. <>= dmakeham3 <- Vectorize(dmakeham3) pmakeham3 <- Vectorize(pmakeham3) @ and this allows us to write, for example, <>= pmakeham3(c(0, 1, 1, Inf), 1, c(1, 1, 2, 1), 1) @ We could then use \code{dist = list(name = "makeham3", pars = c("shape1", "shape2", \\ "scale"), ...)} in a \code{flexsurvreg} model, though in the breast cancer example, the second shape parameter is poorly identifiable. \paragraph{Example: Changing the parameterisation of a distribution} We may want to fit a Weibull model like \code{fs1}, but with the proportional hazards (PH) parameterisation $S(t) = \exp(-\mu t^\alpha)$, so that the covariate effects reported in the printed \code{flexsurvreg} object can be interpreted as hazard ratios or log hazard ratios without any further transformation. Here instead of the density and cumulative distribution functions, we provide the hazard and cumulative hazard. (Note that since version 0.7, the \code{"weibullPH"} distribution is built in to \code{flexsurvreg} --- but this example has been kept here for illustrative purposes.) \footnote{The \pkg{eha} package may need to be detached first so that \pkg{flexsurv}'s built-in \code{hweibull} is used, which returns \code{NaN} if the parameter values are zero, rather than failing as \pkg{eha}'s currently does.} <>= options(warn=-1) @ <<>>= hweibullPH <- function(x, shape, scale = 1, log = FALSE){ hweibull(x, shape = shape, scale = scale ^ {-1 / shape}, log = log) } HweibullPH <- function(x, shape, scale = 1, log = FALSE){ Hweibull(x, shape = shape, scale = scale ^ {-1 / shape}, log = log) } custom.weibullPH <- list(name = "weibullPH", pars = c("shape", "scale"), location = "scale", transforms = c(log, log), inv.transforms = c(exp, exp), inits = function(t){ c(1, median(t[t > 0]) / log(2)) }) fs6 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, dist = custom.weibullPH) fs6$res["scale", "est"] ^ {-1 / fs6$res["shape", "est"]} - fs6$res["groupMedium", "est"] / fs6$res["shape", "est"] - fs6$res["groupPoor", "est"] / fs6$res["shape", "est"] @ <>= options(warn=0) @ The fitted model is the same as \code{fs1}, therefore the maximised likelihood is the same. The parameter estimates of \code{fs6} can be transformed to those of \code{fs1} as shown. The shape $\alpha$ is common to both models, the scale $\mu^\prime$ in the AFT model is related to the PH scale $\mu$ as $\mu^\prime$ = $\mu^{-1/\alpha}$. The effects $\beta^\prime$ on life expectancy in the AFT model are related to the log hazard ratios $\beta$ as $\beta^\prime = -\beta/\alpha$. A slightly more complicated example is given in the package vignette \code{flexsurv-examples} of constructing a proportional hazards generalized gamma model. Note that \code{phreg} in \pkg{eha} also fits the Weibull and other proportional hazards models, though again the parameterisation is slightly different. \section{Arbitrary-dimension models} \label{sec:adim} \pkg{flexsurv} also supports models where the number of parameters is arbitrary. In the models discussed previously, the number of parameters in the model family is fixed (e.g., three for the generalized gamma). In this section, the model complexity can be chosen by the user, given the model family. We may want to represent more irregular hazard curves by more flexible functions, or use bigger models if a bigger sample size makes it feasible to estimate more parameters. \subsection{Royston and Parmar spline model} \label{sec:spline} \begin{sloppypar} In the spline-based survival model of \citet{royston:parmar}, a transformation $g(S(t,z))$ of the survival function is modelled as a natural cubic spline function of log time: $g(S(t,z)) = s(x, \bm{\gamma})$ where $x = \log(t)$. This model can be fitted in \pkg{flexsurv} using the function \code{flexsurvspline}, and is also available in the \proglang{Stata} package \pkg{stpm2} \citep{stpm2} (historically \pkg{stpm}, \citet{stpm:orig,stpm:update}). \end{sloppypar} Typically we use $g(S(t,\mathbf{z})) = \log(-\log(S(t,\mathbf{z}))) = \log(H(t,\mathbf{z}))$, the log cumulative hazard, giving a proportional hazards model. \paragraph{Spline parameterisation} The complexity of the model, thus the dimension of $\bm{\gamma}$, is governed by the number of \emph{knots} in the spline function $s()$. Natural cubic splines are piecewise cubic polynomials defined to be continuous, with continuous first and second derivatives at the knots, and also constrained to be linear beyond boundary knots $k_{min},k_{max}$. As well as the boundary knots there may be up to $m\geq 0$ \emph{internal} knots $k_1,\ldots, k_m$. Various spline parameterisations exist --- the one used here is from \citet{royston:parmar}. \begin{equation} \label{eq:spline} s(x,\bm{\gamma}) = \gamma_0 + \gamma_1 x + \gamma_2 v_1(x) + \ldots + \gamma_{m+1} v_m(x) \end{equation} where $v_j(x)$ is the $j$th \emph{basis} function \[v_j(x) = (x - k_j)^3_+ - \lambda_j(x - k_{min})^3_+ - (1 - \lambda_j) (x - k_{max})^3_+, \qquad \lambda_j = \frac{k_{max} - k_j}{k_{max} - k_{min}} \] and $(x - a)_+ = max(0, x - a)$. If $m=0$ then there are only two parameters $\gamma_0,\gamma_1$, and this is a Weibull model if $g()$ is the log cumulative hazard. Table \ref{tab:spline} explains two further choices of $g()$, and the parameter values and distributions they simplify to for $m=0$. The probability density and cumulative distribution functions for all these models are available as \code{dsurvspline} and \code{psurvspline}. A model with an absolute time scale ($x = t$) is also available through \code{timescale="identity"}. \begin{table} \begin{tabularx}{\textwidth}{lXlp{1.4in}} \hline Model & $g(S(t,\mathbf{z}))$ & In \code{flexsurvspline} & With $m=0$ \\ \hline Proportional hazards & $\log(-\log(S(t,\mathbf{z})))$ \newline {\footnotesize (log cumulative hazard)} & \code{scale = "hazard"} & Weibull {\footnotesize \code{shape} $\gamma_1$, \code{scale} $\exp(-\gamma_0/\gamma_1)$}\\ Proportional odds & $\log(S(t,\mathbf{z})^{-1} - 1)$ \newline {\footnotesize (log cumulative odds)} & \code{scale = "odds"} & Log-logistic {\footnotesize \code{shape} $\gamma_1$, \code{scale} $\exp(-\gamma_0/\gamma_1)$}\\ Normal / probit & $\Phi^{-1}(S(t,\mathbf{z}))$ \newline {\footnotesize (inverse normal CDF, \code{qnorm})} & \code{scale = "normal"} & Log-normal {\footnotesize \code{meanlog} $-\gamma_0/\gamma_1$, \code{sdlog} $1/\gamma_1$ }\\ \hline \end{tabularx} \caption{Alternative modelling scales for \code{flexsurvspline}, and equivalent distributions for $m=0$ (with parameter definitions as in the \proglang{R} \code{d} functions referred to elsewhere in the paper).} \label{tab:spline} \end{table} \paragraph{Covariates on spline parameters} Covariates can be placed on any parameter $\gamma$ through a linear model (with identity link function). Most straightforwardly, we can let the intercept $\gamma_0$ vary with covariates $\mathbf{z}$, giving a proportional hazards or odds model (depending on $g()$). \[g(S(t,z)) = s(\log(t), \bm{\gamma}) + \bm{\beta}^\top \mathbf{z} \] The spline coefficients $\gamma_j: j=1, 2 \ldots$, the ``ancillary'' parameters, may also be modelled as linear functions of covariates $\mathbf{z}$, as \[\gamma_j(\mathbf{z}) = \gamma_{j0} + \gamma_{j1}z_1 + \gamma_{j2}z_2 + \ldots\] giving a model where the effects of covariates are arbitrarily flexible functions of time: a non-proportional hazards or odds model. \paragraph{Spline models in \pkg{flexsurv}} The argument \code{k} to \code{flexsurvspline} defines the number of internal knots $m$. Knot locations are chosen by default from quantiles of the log uncensored death times, or users can supply their own locations in the \code{knots} argument. Initial values for numerical likelihood maximisation are chosen using the method described by \citet{royston:parmar} of Cox regression combined with transforming an empirical survival estimate. For example, the best-fitting model for the breast cancer dataset identified in \citet{royston:parmar}, a proportional odds model with one internal spline knot, is <<>>= sp1 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data = bc, k = 1, scale = "odds") @ A further model where the first ancillary parameter also depends on the prognostic group, giving a time-varying odds ratio, is fitted as <<>>= sp2 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group), data = bc, k = 1, scale = "odds") @ These models give qualitatively similar results to the generalized gamma in this dataset (Figure \ref{fig:spline:haz}), and have similar predictive ability as measured by AIC (Table \ref{tab:aic}). Though in general, an advantage of spline models is that extra flexibility is available where necessary. <>= plot(sp1, type = "hazard", col=cols[3], ylim = c(0, 0.5), xlab = "Years", ylab = "Hazard") lines(sp2, type = "hazard", col = cols[3], lty = 2) lines(fs2, type = "hazard", col = cols[2]) text(x=c(2,2,2), y=c(0.3, 0.15, 0.05), c("Poor","Medium","Good")) legend("topright", col = c("black",cols[c(3,3,2)]), lty = c(1,1,2,1), lwd = rep(2,4), c("Kernel density estimate","Spline (proportional odds)", "Spline (time-varying)","Generalized gamma (time-varying)")) @ \begin{figure}[h] \centering \includegraphics{flexsurv-splinehaz-1} \caption{Comparison of spline and generalized gamma fitted hazards for the breast cancer survival data by prognostic group.} \label{fig:spline:haz} \end{figure} In this example, proportional odds models (\code{scale = "odds"}) are better-fitting than proportional hazards models (\code{scale = "hazard"}) (Table \ref{tab:aic}). Note also that under a proportional hazards spline model with one internal knot (\code{sp3}), the log hazard ratios, and their standard errors, are substantively the same as under a standard Cox model (\code{cox3}). This illustrates that this class of flexible fully-parametric models may be a reasonable alternative to the (semi-parametric) Cox model. See \citet{royston:parmar} for more discussion of these issues. <<>>= sp3 <- flexsurvspline(Surv(recyrs, censrec) ~ group, data = bc, k = 1, scale = "hazard") sp3$res[c("groupMedium", "groupPoor"), c("est", "se")] cox3 <- coxph(Surv(recyrs, censrec) ~ group, data = bc) coef(summary(cox3))[ , c("coef", "se(coef)")] @ An equivalent of a ``stratified" Cox model may be obtained by allowing \emph{all} the spline parameters to vary with the categorical covariate that defines the strata. In this case, this covariate might be \code{group}. With \code{k=}$m$ internal knots, the formula should then include \code{group}, representing $\gamma_0$, and $m+1$ further terms representing the parameters $\gamma_1,\ldots,\gamma_{m+1}$, named as follows. <<>>= sp4 <- flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + gamma2(group), data = bc, k = 1, scale = "hazard") @ Other covariates might be added to this formula --- if placed on the intercept, these will be modelled through proportional hazards, as in \code{sp1}. If placed on higher-order parameters, these will represent time-varying hazard ratios. For example, if there were a covariate \code{treat} representing treatment, then <>= flexsurvspline(Surv(recyrs, censrec) ~ group + gamma1(group) + gamma2(group) + treat + gamma1(treat), data = bc, k = 1, scale = "hazard") @ would represent a model stratified by group, where the hazard ratio for treatment is time-varying, but the model is not fully stratified by treatment. <<>>= res <- t(sapply(list(fs1, fs2, fs3, sp1, sp2, sp3, sp4), function(x)rbind(-2 * round(x$loglik,1), x$npars, round(x$AIC,1)))) rownames(res) <- c("Weibull (fs1)", "Generalized gamma (fs2)", "Generalized gamma (fs3)", "Spline (sp1)", "Spline (sp2)", "Spline (sp3)", "Spline (sp4)") colnames(res) <- c("-2 log likelihood", "Parameters", "AIC") @ \begin{table}[h] <>= res @ \caption{Comparison of parametric survival models fitted to the breast cancer data.} \label{tab:aic} \end{table} \subsection{Implementing new general-dimension models} \label{sec:gdim} The spline model above is an example of the general parametric form (Equation \ref{eq:model}), but the number of parameters, $R+1$ in Equation \ref{eq:model}, $m+2$ in Equation \ref{eq:spline}, is arbitrary. \pkg{flexsurv} has the tools to deal with any model of this form. \code{flexsurvspline} works internally by building a custom distribution and then calling \code{flexsurvreg}. Similar models may in principle be built by users using the same method. This relies on a functional programming trick. \paragraph{Creating distribution functions dynamically} The \proglang{R} distribution functions supplied to custom models are expected to have a fixed number of arguments, including one for each scalar parameter. However, the distribution functions for the spline model (e.g., \code{dsurvspline}) have an argument \code{gamma} representing the \emph{vector} of parameters $\gamma$, whose length is determined by choosing the number of knots. Just as the \emph{scalar parameters} of conventional distribution functions can be supplied as \emph{vector arguments} (as explained in \S\ref{sec:custom}), similarly, the vector parameters of spline-like distribution functions can be supplied as \emph{matrix arguments}, representing alternative parameter values. To convert a spline-like distribution function into the correct form, \pkg{flexsurv} provides the utility \code{unroll.function}. This converts a function with one (or more) vector parameters (matrix arguments) to a function with an arbitrary number of scalar parameters (vector arguments). For example, the 5-year survival probability for the baseline group under the model \code{sp1} is <<>>= gamma <- sp1$res[c("gamma0", "gamma1", "gamma2"), "est"] 1 - psurvspline(5, gamma = gamma, knots = sp1$knots) @ An alternative function to compute this can be built by \code{unroll.function}. We tell it that the vector parameter \code{gamma} should be provided instead as three scalar parameters named \code{gamma0}, \code{gamma1}, \code{gamma2}. The resulting function \code{pfn} is in the correct form for a custom \code{flexsurvreg} distribution. <<>>= pfn <- unroll.function(psurvspline, gamma = 0:2) 1 - pfn(5, gamma0 = gamma[1], gamma1 = gamma[2], gamma2 = gamma[3], knots = sp1$knots) @ Users wishing to fit a new spline-like model with a known number of parameters could just as easily write distribution functions specific to that number of parameters, and use the methods in \S\ref{sec:custom}. However the \code{unroll.function} method is intended to simplify the process of extending the \pkg{flexsurv} package to implement new model families, through wrappers similar to \code{flexsurvspline}. \paragraph{Example: splines on alternative scales} An alternative to the Royston-Parmar spline model is to model the log \emph{hazard} as a spline function of (log) time instead of the log cumulative hazard. \citet{stgenreg} demonstrate this model using the \proglang{Stata} \pkg{stgenreg} package. An advantage explained by \citet{royston:lambert:book} is that when there are multiple time-dependent effects, time-dependent hazard ratios can be interpreted independently of the values of other covariates. This can also be implemented in \code{flexsurvreg} using \code{unroll.function}. A disadvantage of this model is that the cumulative hazard (hence the survivor function) has no analytic form, therefore to compute the likelihood, the hazard function needs to be integrated numerically. This is done automatically in \code{flexsurvreg} (just as in \pkg{stgenreg}) if the cumulative hazard is not supplied. Firstly, a function must be written to compute the hazard as a function of time \code{x}, the vector of parameters \code{gamma} (which can be supplied as a matrix argument so the function can give a vector of results), and a vector of knot locations. This uses \pkg{flexsurv}'s function \code{basis} to compute the natural cubic spline basis (Equation \ref{eq:spline}), and replicates \code{x} and \code{gamma} to the length of the longest one. <<>>= hsurvspline.lh <- function(x, gamma, knots){ if(!is.matrix(gamma)) gamma <- matrix(gamma, nrow = 1) lg <- nrow(gamma) nret <- max(length(x), lg) gamma <- apply(gamma, 2, function(x)rep(x, length = nret)) x <- rep(x, length = nret) loghaz <- rowSums(basis(knots, log(x)) * gamma) exp(loghaz) } @ The equivalent function is then created for a three-knot example of this model (one internal and two boundary knots) that has arguments \code{gamma0}, \code{gamma1} and \code{gamma2} corresponding to the three columns of \code{gamma}, <<>>= hsurvspline.lh3 <- unroll.function(hsurvspline.lh, gamma = 0:2) @ To complete the model, the custom distribution list is formed, the internal knot is placed at the median uncensored log survival time, and the boundary knots are placed at the minimum and maximum. These are passed to \code{hsurvspline.lh} through the \code{aux} argument of \code{flexsurvreg}. <<>>= custom.hsurvspline.lh3 <- list( name = "survspline.lh3", pars = c("gamma0", "gamma1", "gamma2"), location = c("gamma0"), transforms = rep(c(identity), 3), inv.transforms = rep(c(identity), 3) ) dtime <- log(bc$recyrs)[bc$censrec == 1] ak <- list(knots = quantile(dtime, c(0, 0.5, 1))) @ Initial values must be provided in the call to \code{flexsurvreg}, since the custom distribution list did not include an \code{inits} component. For this example, ``default'' initial values of zero suffice, but the permitted values of $\gamma_2$ are fairly tightly constrained (from -0.5 to 0.5 here) using the \code{"L-BFGS-B"} bounded optimiser from \proglang{R}'s \code{optim} \citep{nash}. Without the constraint, extreme values of $\gamma_2$, visited by the optimiser, cause the numerical integration of the hazard function to fail. <>= sp5 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data = bc, aux = ak, inits = c(0, 0, 0, 0, 0), dist = custom.hsurvspline.lh3, method = "L-BFGS-B", lower = c(-Inf, -Inf, -0.5), upper = c(Inf, Inf, 0.5), control = list(trace = 1, REPORT = 1)) @ This takes around ten minutes to converge, so is not presented here, though the fit is poorer than the equivalent spline model for the cumulative hazard. The 95\% confidence interval for $\gamma_2$ of (0.16, 0.37) is firmly within the constraint. \citet{crowther:general} present a combined analytic / numerical integration method for this model that may make fitting it more stable. \paragraph{Other arbitrary-dimension models} Another potential application is to fractional polynomials \citep{royston1994regression}. These are of the form $\sum_{m=1}^M \alpha_m x^{p_m} \log(x)^n$ where the power $p_m$ is in the standard set $\{2,-1,-0.5,0,0.5,1,2,3\}$ (except that $\log(x)$ is used instead of $x^0$), and $n$ is a non-negative integer. They are similar to splines in that they can give arbitrarily close approximations to a nonlinear function, such as a hazard curve, and are particularly useful for expressing the effects of continuous predictors in regression models. See e.g., \citet{sauerbrei2007selection}, and several other publications by the same authors, for applications and discussion of their advantages over splines. The \proglang{R} package \pkg{gamlss} \citep{gamlss} has a function to construct a fractional polynomial basis that might be employed in \pkg{flexsurv} models. Polyhazard models \citep{polyhazard} are another potential use of this technique. These express an overall hazard as a sum of latent cause-specific hazards, each one typically from the same class of distribution, e.g., a \emph{poly-Weibull} model if they are all Weibull. For example, a U-shaped hazard curve following surgery may be the sum of early hazards from surgical mortality and later deaths from natural causes. However, such models may not always be identifiable without external information to fix or constrain the parameters of particular hazards \citep{demiris2011survival}. \section{Multi-state models} \label{sec:multistate} A \emph{multi-state model} represents how an individual moves between multiple states in continuous time. Survival analysis is a special case with two states, ``alive'' and ``dead''. \emph{Competing risks} are a further special case, where there are multiple causes of death, that is, one starting state and multiple possible destination states. Multi-state modelling with \pkg{flexsurv} was previously described in this section of the current vignette. Version 2.0 of \pkg{flexsurv} added several new features for multi-state modelling, including multi-state modelling using mixtures, and transition-specific distribution families in cause-specific hazards models. These models are now fully described in a separate \pkg{flexsurv} vignette, ``Flexible parametric multi-state modelling with the flexsurv package''. \section{Potential extensions} \label{sec:extensions} Multi-state modelling is still an area of ongoing work, and while version 2.0 extended \pkg{flexsurv} in this area, more tools and documentation in this area would still be useful. The \pkg{msm} package arguably has a more accessible interface for fitting and summarising multi-state models, but it was designed mainly for panel data rather than event time data, and therefore the event time distributions it fits are relatively inflexible. Models where multiple survival times are assumed to be correlated within groups, sometimes called (shared) frailty models \citep{hougaard1995frailty}, would also be a useful development. See, e.g., \citet{crowther2014multilevel} for a recent application based on parametric models. These might be implemented by exploiting tractability for specific distributions, such as gamma frailties, or by adjusting standard errors to account for clustering, as implemented in \code{survreg}. More complex random effects models would require numerical integration, for example, \citet{crowther2014multilevel} provide \proglang{Stata} software based on Gauss-Hermite quadrature. Alternatively, a probabilistic modelling language such as \proglang{Stan} \citep{stan-manual:2014} or \proglang{BUGS} \citep{bugs:book} would be naturally suited to complex extensions such as random effects on multiple parameters or multiple hierarchical levels. \pkg{flexsurv} is intended as a platform for parametric survival modelling. Extensions of the software to deal with different models may be written by users themselves, through the facilities described in \S\ref{sec:custom} and \S\ref{sec:gdim}. These might then be included in the package as built-in distributions, or at least demonstrated in the package's other vignette \code{flexsurv-examples}. Each new class of models would ideally come with \begin{itemize} \item guidance on what situations the model is useful for, e.g., what shape of hazards it can represent \item some intuitive interpretation of the model parameters, their plausible values in typical situations, and potential identifiability problems. This would also help with choosing initial values for numerical maximum likelihood estimation, ideally through an \code{inits} function in the custom distribution list (\S\ref{sec:custom}). \end{itemize} \pkg{flexsurv} is available from \url{http://CRAN.R-project.org/package=flexsurv}. Development versions are available on \url{https://github.com/chjackson/flexsurv-dev}, and contributions are welcome. \section*{Acknowledgements} Thanks to Milan Bouchet-Valat for help with implementing covariates on ancillary parameters, Andrea Manca for motivating the development of the package, the reviewers of the paper, and all users who have reported bugs and given suggestions. \bibliography{flexsurv} \end{document} flexsurv/inst/NEWS0000644000176200001440000004735214610437463013627 0ustar liggesusers-*- text -*- For changes in Version 2.3 and later, see https://chjackson.github.io/flexsurv/news which is built from NEWS.md in the source root directory. Version 2.2.2 (2023-01-31) ------------------------- * Allow unicode characters in vignette, to satisfy R CMD check on r-devel. Version 2.2.1 (2022-12-22) ------------------------- * New `simulate.flexsurvreg` method to simulate data from a fitted flexsurvreg or flexsurvspline model. Thanks to Mark Clements for help with this. * Fix of bug for summary() method with type = "quantile" or "median" and left-truncation in the prediction (start > 0). * Correction to the examples and interpretation of Cox-Snell residuals. Version 2.2 (2022-06-16) ------------------------- * New function `standsurv` for survival and hazards standardised over an observed distribution for covariates. Contributed by Michael Sweeting . See the new vignette about it. * New function `hr_flexsurvreg` to compute the hazard ratio from a fitted flexsurvreg or flexsurvspline model as a function of time, with confidence intervals. * `summary.flexsurvreg` has been rewritten to make it cleaner and faster. User-visible changes: - Custom summary functions in `summary.flexsurvreg` must now be vectorised. - A new argument `cross` specifies whether to compute summaries for all combinations of times t and covariate values, or for covariate values matched with corresponding times t, in custom summary functions. - Covariate names when `tidy=FALSE` now consistently don't include spaces. * Better handling of NAs in summary and prediction functions. Thanks to Matthew Warkentin. * New functions for Cox-Snell residuals: `coxsnell_flexsurvreg` or residuals(..., type="coxsnell"). * rmst_generic, mean_survspline, rmst_survspline and related functions (e.g. mean_survspline1) handle alternative parameter values in a vectorised way. * Allow output functions to work on models that have been stripped of data with x$data <- NULL, if possible Version 2.1 (2021-09-13) ------------------------- * Fix of a bug that affected models with baseline hazard offsets and exponential, Weibull, Gompertz and hazard/odds-based spline models, where convergence may have been falsely reported due to incorrect likelihood derivatives. * New vignette section and better help page documentation about relative survival models. * `start` parameter added to `predict.flexsurvreg`. * New function `pdf_flexsurmix` for the fitted density function in a `flexsurvmix` model. * Fix for tidy method with one-parameter exponential models. * Fixes for h/Hgamma and h/Hlnorm with log = TRUE. * Minor numerical improvements to h/H functions for some distributions. * Bug fix for `simfs_bytrans` when some transitions don't happen. * `NaNs produced` warnings should occur less often during fitting. Version 2.0 (2021-02-22) -------------------- * A new class of multi-state models based on mixtures (Larson and Dinse 1985). A new vignette on multi-state modelling describes this model class and contrasts it with standard (cause-specific hazards) multi-state models. * Different parametric families are now supported for different transitions in multi-state models. * New function "fmsm" allows a list of flexsurvreg objects to be associated with a particular transition structure matrix, to create a multi-state model. * New functions simfinal_fmsm to summarise times and probabilities of final absorbing events in multi-state models, using simulation. * More features for right-truncated data. Individual-level right-truncation times supported with new "rtrunc" argument to flexsurvreg and flexsurvspline. A comparable non-parametric estimator for right-truncated data is provided in a new function, "survrtrunc". Alternative parametric estimators, which make use of the time of an initiating event, are provided in a new function, "flexsurvrtrunc". * A new vignette describes properties of the different built-in parametric distributions in more detail. * qgeneric is now vectorised, thanks to the vuniroot function imported from the rstpm2 package by Mark Clements. This massively boosts the speed of rsurvspline, hence speeding up simulations from spline-based multi-state models. * pmatrix.fs can now calculate transition probabilities conditionally on the the transition being to one of a subset of the states. * "tidy" argument to pmatrix.fs for tidy data frame output. * "tidy" argument to sim.fmsm for returning simulations in tidy data frame format with one row per transition, and associated function simfs_bytrans. * Bootstrapping function bootci.fmsm made available for users to get confidence intervals / distributions for their own flexsurv model output functions. * Parallel processing capability for bootstrap confidence intervals. * Distribution and mean functions for the Royston-Parmar model named like dsurvspline2, psurvspline4 and so on, with one argument per parameter, rather than all parameters collected in a single argument, going up to 7 knots / 9 parameters. * Return value from pars.fmsm is now a list rather than a matrix, even if the model family is the same for each transition. * summary.flexsurvreg given a new argument "na.action" to control whether missing values in "newdata" are dropped. Defaults to producing summaries of NA when there are missing values, while previously missing values were dropped. * S3 methods have been added for the generics defined in the broom package. These functions create tidy data frames containing the results of fitted models. The new functions are tidy.flexsurvreg, glance.flexsurvreg, and augment.flexsurvreg. * S3 methods have been added for the predict and residuals generics. predict.flexsurvreg has full support for all model outcomes supported by summary.flexsurvreg. residuals.flexsurvreg currently only supports a naive difference between observed survival and predicted mean, neglecting censoring. * Case weights accounted for in nonparametric survival and cumulative hazard estimates in plot.flexsurvreg. Thanks to https://github.com/andbe. Version 1.1.1 (2019-03-18) ------------- * New type="quantiles" and type="link" for summary.flexsurvreg. Thanks to Leonardo Marques for the contribution. * Allow different covariates per transition in multi-state models supplied as a list of flexsurvreg objects. Thanks to David McAllister for the contribution. * Bug fix for qllogis with lower.tail=FALSE. * Bug fix for likelihood when all events are observed. * Bug fix for "ylim" argument in plot method for survival or cumulative hazard. * Allow dynamic symbols in C code. * Various other minor code and doc fixes, see github commit history. Version 1.1 (2017-03-27) ------------- * Substantial speed improvements in fitting most of the built-in models, from implementing their PDFs and CDFs in C++. Thanks to Paul Metcalfe for contributing this. Results may therefore differ from previous versions in edge cases. * As a result the package now depends on Rcpp. * Mean, median and restricted mean included as built-in functions in summary.flexsurvreg. Thanks to Jordan Amdahl for the contribution. * Documentation migrated to roxygen. Thanks to Paul Metcalfe for the contribution. * Various minor bug fixes, see github commits. Version 1.0.2 (2016-09-26) ------------- * Bug fix: "start" was being ignored by plot.flexsurvreg. Thanks to Ruth Keogh. * Built-in distribution names are now case-insensitive. Thanks to Jordan Amdahl. * Fix for Weibull hazard function to avoid numeric instability. Thanks to Jordan Amdahl. * Fix to hsurvspline when t includes 0. Thanks to Jordan Amdahl. * Vectorised parameters supported in qgeneric. Version 1.0.1 (2016-05-31) ------------- * Bug fix: covariates were labelled wrongly in summary.flexsurvreg tidy output. Thanks to Owain Saunders. Version 1.0.0 (2016-05-10) ------------- * Version number bumped to 1.0.0 to accompany the publication of the vignette in Journal of Statistical Software. Version 0.7.1 (2016-03-24) ------------- * Slightly more efficient likelihood calculations, and removed spurious warning from likelihood with interval censoring. * Tests modified to work with the latest (and current) testthat. Version 0.7 (2015-11-13) ----------- * flexsurvspline now allows the log cumulative hazard (or its alternatives) to be modelled as a spline function of time instead of log time. * The routine for generating initial values in flexsurvspline has been improved. This now obeys the constraint that the log cumulative hazard is increasing, thus avoiding errors from optim() when this wasn't satisfied. Cox regression is used as a fallback to initialise covariate effects if this fails. * As a result, flexsurv now depends on the "quadprog" package. * dweibullPH and related functions give the Weibull distribution in proportional hazards parameterisation, and "weibullPH" is supported as a built-in model for flexsurvreg. * Option to summary.flexsurvreg to return a tidy data frame. * New "logliki" component in model objects, containing vector of log-likelihoods for each observation at the estimated or fixed parameters. * Fix of various bugs with supplying "newdata" to summary functions (github issue #7). The behaviour here should now be like predict.lm, e.g. variables in newdata that were originally factors should be supplied as factor or character, not numeric. * Fix of bug that prevented plots being drawn by categorical covariates by default. * Fix of bugs with spline models and no data censored, or all data interval censored (github issue #3). * Fix of bugs with subsetting in flexsurvspline (github issue #6). Version 0.6 (2015-04-13) ----------- * CRAN release. Also includes the changes from Version 0.5.1. * Full support for multi-state models fitted as a list of independent transition-specific models. * New function pars.fmsm to return transition-specific parameters in multi-state models. * Bug fix for empirical hazard plots with categorical covariates. Thanks to Milan Bouchet-Valat. Version 0.5.1 (2015-02-24) ------------- * github-only release. * Log-logistic distribution built in to flexsurvreg, and distribution functions provided. * Bug fix in tcovs option in semi-Markov model simulation. * "digits" argument supported by default model print function. This is passed to "format" to format the parameter estimates, and defaults to 3. * Bug fix in "events" printed output for interval censored data. Thanks to Sabrina Russo. * pgompertz returns Inf for q=Inf, even for parameters denoting "living forever", since the CDF is P(X <= q) not P(X < q). This affected some fits of the Gompertz distribution. Version 0.5 (2014-09-22) ----------- * Major new release, so version number bumped from 0.3 to 0.5. * New package vignettes: a user guide and a vignette of examples. * Development moved from r-forge to https://github.com/chjackson/flexsurv-dev. Spline models and ancillary covariates: * Major rewrite of flexsurvspline. This now works by calling flexsurvreg with a custom distribution written dynamically. Models can now include covariate effects that vary as spline functions of time, by including covariates on "gamma1" or on any further parameters. * New argument "anc" to flexsurvreg, as an alternative and preferred way of modelling covariates on ancillary parameters. * New general utility "unroll.function" which converts a function with matrix arguments to the equivalent function with vector arguments. The new flexsurvspline works by unrolling "dsurvspline". * Quantile, random number, hazard and cumulative hazard functions for spline distribution. * Autogeneration of initial values for flexsurvspline now accounts for left-truncation. Thanks to Ana Borges for the report. Other new modelling features: * Several utilities for parametric multi-state modelling, including transition probabilities and simulation ("pmatrix.fs", "totlos.fs", "sim.fmsm","pmatrix.simfs", "totlos.simfs"). An "msfit.flexsurvreg" method also gives cumulative transition-specific hazards in the format of the "mstate" package. * Interval censoring supported in the Surv() response. * Relative survival models, using the "bhazard" argument to flexsurvreg to specify the expected mortality rate. * flexsurvreg now uses survreg internally to fit Weibull, exponential and log-normal models, unless there is left-truncation. Custom distributions: * Custom distributions can be defined through the hazard function. This can be optionally supplemented with the cumulative hazard function, otherwise this is obtained by numerical integration. * In custom distributions specified by the density, the cumulative distribution can now be omitted, and it will be calculated by numerical integration. * New arguments "dfns" and "aux" to flexsurvreg, which can be used to supply custom distribution functions and arguments to pass to them. * Document that density functions for custom distributions need "log" argument. * Documented how to supply derivatives of custom distributions for use in optimisation. Output functions: * New "newdata" argument to summary.flexsurvreg and plot.flexsurvreg for an easier way of supplying covariate values. * User-defined summary functions can be used in summary.flexsurvreg and plot.flexsurvreg as an alternative to survival, hazard or cumulative hazard. * New function "normboot.flexsurvreg" to simulate parameters from the asymptotic normal distribution of their estimates. Used for representing uncertainty in any function of the parameters. * summary.flexsurvreg can be called with ci=FALSE to omit confidence intervals. * "start" argument defaults to 0 for all prediction times in summary.flexsurvreg. * Bug fix in summary.flexsurvreg for left-truncated models, which was returning probabilities > 1 before the truncation time. * New model.frame and model.matrix methods to extract the data from fitted flexsurvreg objects. * Accept vector X in summary.flexsurvreg, and give informative error if X in wrong format. Thanks to Mark Danese. * Extra arguments can be passed to both muhaz and plot.muhaz in plot.flexsurvreg(...,type="hazard",...) Printed output: * Use format() not signif() for printing flexsurvreg objects, to avoid spurious zero significant figures. Thanks to Kenneth Chen. * Standard errors included in printed output of flexsurvreg, but only for parameters optimised on natural or log scales (which includes all built-in distributions). Distribution functions: * Bug fix in rgengamma for Q=0 (log-normal) and sigma not equal to 1. * Don't warn for shape parameters being exactly zero in generalized gamma and F, just give NaN. * basis() and fss() functions for the natural cubic spline basis made available to users. Version 0.3.1 (2014-02-14) -------------------------- * R-forge only release. * Distribution functions tidied up, making special value handling and vectorisation consistent. Hazard and cumulative hazard functions for all supported distributions. * Vectors of different col, lwd and lty can be passed to plot.flexsurvreg for multiple fitted lines. Thanks to Julia Sandberg for the report. Version 0.3 (2014-01-19) ------------------------ * CRAN release. Includes changes from 0.2.1 to 0.2.3. Version 0.2.3 (2013-10-09) ------------------------- * R-forge only release. * Parameters other than the location parameter can now have covariates on them in flexsurvreg. Thanks to Milan Bouchet-Valat for help with this. * subset and na.action arguments in flexsurvreg and flexsurvspline. * coef, vcov and confint methods for all fitted model objects. * Distribution functions for generalized gamma, generalized F, and Gompertz, now allow all parameters to be vectorised. * Bug fix in analytic derivatives for Weibull. * Restored print output introduced in 0.1.2 which had been accidentally removed in 0.1.5. Version 0.2.2 (2013-07-26) ------------------------- * R-forge only release. * Case weights supported in flexsurvreg and flexsurvspline. Version 0.2.1 (2013-07-03) ------------------------- * R-forge only release. * Default left truncation times were being set wrongly for user-supplied times in summary.flexsurvreg, giving wrong confidence intervals. These now default to 0. * Confidence intervals set to 1 for t=0 under spline models. Thanks to Paul Pynsent. * dgompertz,dgengamma,dgengamma.orig,dgenf,dgenf.orig fixed to return -Inf instead of 0 when density is zero and log=TRUE. Thanks to Gao Zheng. Version 0.2 (2013-05-13) ------------------------- * New summary() method for fitted flexsurvreg and flexsurvspline model objects gives fitted survival, cumulative hazard or hazard curves, with confidence intervals mosly computed by a simulation method. * This allows plot.flexsurvreg to plot confidence intervals for the fitted survival, hazard or cumulative hazard. * Left-truncated survival observations are supported in flexsurvreg and flexsurvspline. * New psurvspline and dsurvspline functions giving distribution and density function for the spline model. * Analytic derivatives used in optimisation for spline (odds and hazard scale, not normal), exponential, Weibull and Gompertz models. * Default to BFGS optimisation method, which uses derivatives where available and should be much faster, instead of Nelder-Mead. * Work around NaN warnings from spline models presumably due to parameters violating implicit constraints. * If "knots" specified, boundary knots set to min/max of uncensored times, not all times, to match results when "k" is specified. Thanks to Paul Pynsent. Version 0.1.5 (2012-08-29) ------------------------- * Data are now stored in fitted flexsurvreg and flexsurvspline model objects, avoiding environment search errors and allowing package functions to be called within other functions. Thanks to Hanna Daniel for the report. * Gompertz documentation clarified for the case when there is a chance of living forever. qgompertz and rgompertz now return Inf in these cases, with no warning, instead of NaN. Thanks to Michael Sweeting. Version 0.1.4 (2012-03-22) -------------------------- * maxt argument in plot.flexsurvreg. * Plots no longer complain if data named "dat". * Corrected wrong bug fix from Version 0.1.3 for transforming parameter estimates in output when fixedpars=TRUE. * AIC penalty corrected for models with some fixed parameters. * qgengamma corrected for parameter Q<0. Thanks to Benn Ackley. Version 0.1.3 (2012-01-17) -------------------------- * No longer complains about invalid initial values when there are zero survival times. * Don't transform parameter estimates in output when fixedpars=TRUE. * Checking functions for distribution utilities don't complain about vectorised parameter values. Version 0.1.2 (2011-11-08) -------------------------- * Initial CRAN release. * More features in print output for flexsurvreg and flexsurvspline models. Version 0.1.1 (2011-04-19) -------------------------- * Fix of drop=FALSE bug in flexsurvspline.inits which caused flexsurvspline to fail with single covariates. Version 0.1 (2011-03-14) ------------------------ Initial release flexsurv/build/0000755000176200001440000000000014657665171013251 5ustar liggesusersflexsurv/build/vignette.rds0000644000176200001440000000056714657665171015620 0ustar liggesusers‹•SMO1-°   1^›xñGÿ€„‹11êÁk¥³Ð¤ínº]<ù¿MÄÙ¥e?ä ‡N;oÚyofÒ·!¤M‚m1š® \]>îÃÄ2Í“Ô¬§ÏŠ;ð<”°Ùc:sØH¥Ò ¼m¡‚^r„ŒxO­ˆtR \ùØ0KØëäw÷L.RɬÐKZa†‹à4)ÖLR ÏP¡©Oé^½OÓ ]¦‚ƒ Ý<æb'…Zª"Ræ™°«f–ëYµj zá3ݾ¤1ªW -3[ê‹¡Qˆ¬yÎCºzi£²¯+«ä¯ÆÆ<<ÒØm4¶ il¬³ŸU¦ê A9S/¦:Q‡‘fo+ãËá‚cÏEþ°ÿó~ÐFÓrºš)H\°çÀ`.¤M÷U؃ÓyšÍݱå‹9™A Øçž>À6‹ úu¢¾‰²©'ææÍn·ûj*ZH–xEpfÙ44ø½ïDô™Juflexsurv/build/partial.rdb0000644000176200001440000000007414657634663015401 0ustar liggesusers‹‹àb```b`a’Ì ¦0°0 FN Íš—˜›Z d@$þû$¬²7flexsurv/man/0000755000176200001440000000000014657665216012725 5ustar liggesusersflexsurv/man/GenF.orig.Rd0000644000176200001440000000710414603767323014765 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/GenF.R \name{GenF.orig} \alias{GenF.orig} \alias{dgenf.orig} \alias{pgenf.orig} \alias{qgenf.orig} \alias{rgenf.orig} \alias{Hgenf.orig} \alias{hgenf.orig} \title{Generalized F distribution (original parameterisation)} \usage{ dgenf.orig(x, mu = 0, sigma = 1, s1, s2, log = FALSE) pgenf.orig(q, mu = 0, sigma = 1, s1, s2, lower.tail = TRUE, log.p = FALSE) Hgenf.orig(x, mu = 0, sigma = 1, s1, s2) hgenf.orig(x, mu = 0, sigma = 1, s1, s2) qgenf.orig(p, mu = 0, sigma = 1, s1, s2, lower.tail = TRUE, log.p = FALSE) rgenf.orig(n, mu = 0, sigma = 1, s1, s2) } \arguments{ \item{x, q}{vector of quantiles.} \item{mu}{Vector of location parameters.} \item{sigma}{Vector of scale parameters.} \item{s1}{Vector of first F shape parameters.} \item{s2}{vector of second F shape parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dgenf.orig} gives the density, \code{pgenf.orig} gives the distribution function, \code{qgenf.orig} gives the quantile function, \code{rgenf.orig} generates random deviates, \code{Hgenf.orig} retuns the cumulative hazard and \code{hgenf.orig} the hazard. } \description{ Density, distribution function, quantile function and random generation for the generalized F distribution, using the less flexible original parameterisation described by Prentice (1975). } \details{ If \eqn{y \sim F(2s_1, 2s_2)}{y ~ F(2*s1, 2*s2)}, and \eqn{w = \log(y)}{w = log(y)} then \eqn{x = \exp(w\sigma + \mu)}{x = exp(w*sigma + mu)} has the original generalized F distribution with location parameter \eqn{\mu}{mu}, scale parameter \eqn{\sigma>0}{sigma>0} and shape parameters \eqn{s_1>0,s_2>0}{s1>0,s2>0}. The probability density function of \eqn{x} is \deqn{f(x | \mu, \sigma, s_1, s_2) = \frac{(s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 + s_2)} B(s_1, s_2)}}{ f(x | mu, sigma, s_1, s_2) = ((s1/s2)^{s1} e^{s1 w}) / (sigma x (1 + s1 e^w/s2) ^ (s1 + s2) B(s1, s2))} where \eqn{w = (\log(x) - \mu)/\sigma}{w = (log(x) - mu)/sigma}, and \eqn{B(s_1,s_2) = \Gamma(s_1)\Gamma(s_2)/\Gamma(s_1+s_2)}{B(s1,s2) = \Gamma(s1)\Gamma(s2)/\Gamma(s1+s2)} is the beta function. As \eqn{s_2 \rightarrow \infty}{s2 -> infinity}, the distribution of \eqn{x} tends towards an original generalized gamma distribution with the following parameters: \code{\link{dgengamma.orig}(x, shape=1/sigma, scale=exp(mu) / s1^sigma, k=s1)} See \code{\link{GenGamma.orig}} for how this includes several other common distributions as special cases. The alternative parameterisation of the generalized F distribution, originating from Prentice (1975) and given in this package as \code{\link{GenF}}, is preferred for statistical modelling, since it is more stable as \eqn{s_1}{s1} tends to infinity, and includes a further new class of distributions with negative first shape parameter. The original is provided here for the sake of completion and compatibility. } \references{ R. L. Prentice (1975). Discrimination among some parametric models. Biometrika 62(3):607-614. } \seealso{ \code{\link{GenF}}, \code{\link{GenGamma.orig}}, \code{\link{GenGamma}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/dot-hessian.Rd0000644000176200001440000000162514165570616015427 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/utils.R \name{.hessian} \alias{.hessian} \title{Numerical evaluation of the hessian of a function using numDeriv::hessian} \usage{ .hessian(f, x, seconds.warning = 60, default.r = 6, min.r = 2, ...) } \arguments{ \item{f}{function to compute Hessian for} \item{x}{location to evaluate Hessian at} \item{seconds.warning}{time threshold in seconds to trigger message and reduce the number of iterations for Richardson extrapolation of numDeriv::hessian} \item{default.r}{default number of iterations (high-precision recommendation of numDeriv)} \item{min.r}{minial number of iteration, must be at least 2,} \item{...}{further arguments passed to method.args of numDeriv::hessian} } \description{ We perform a quick check about the expected runtime and adjust the precision accordingly. } \keyword{internal} flexsurv/man/predict.flexsurvreg.Rd0000644000176200001440000001154214644755665017230 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/predict.flexsurvreg.R \name{predict.flexsurvreg} \alias{predict.flexsurvreg} \title{Predictions from flexible survival models} \usage{ \method{predict}{flexsurvreg}( object, newdata, type = "response", times, start = 0, conf.int = FALSE, conf.level = 0.95, se.fit = FALSE, p = c(0.1, 0.9), ... ) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{newdata}{Data frame containing covariate values at which to produce fitted values. There must be a column for every covariate in the model formula used to fit \code{object}, and one row for every combination of covariate values at which to obtain the fitted predictions. If \code{newdata} is omitted, then the original data used to fit the model are used, as extracted by \code{model.frame(object)}. However this will currently not work if the model formula contains functions, e.g. \code{~ factor(x)}. The names of the model frame must correspond to variables in the original data.} \item{type}{Character vector for the type of predictions desired. \itemize{ \item \code{"response"} for mean survival time (the default). \code{"mean"} is an acceptable synonym \item \code{"quantile"} for quantiles of the survival distribution as specified by \code{p} \item \code{"rmst"} for restricted mean survival time \item \code{"survival"} for survival probabilities \item \code{"cumhaz"} for cumulative hazards \item \code{"hazard"} for hazards \item \code{"link"} for fitted values of the location parameter, analogous to the linear predictor in generalized linear models (\code{type = "lp"} and \code{type = "linear"} are acceptable synonyms). This is on the natural scale of the parameter, not the log scale. }} \item{times}{Vector of time horizons at which to compute fitted values. Only applies when \code{type} is \code{"survival"}, \code{"cumhaz"}, \code{"hazard"}, or \code{"rmst"}. Will be silently ignored for all other types. If not specified, predictions for \code{"survival"}, \code{"cumhaz"}, and \code{"hazard"} will be made at each observed event time in \code{model.frame(object)}. For \code{"rmst"}, when \code{times} is not specified predictions will be made at the maximum observed event time from the data used to fit \code{object}. Specifying \code{times = Inf} is valid, and will return mean survival (equal to \code{type = "response"}).} \item{start}{Optional left-truncation time or times. The returned survival, hazard, or cumulative hazard will be conditioned on survival up to this time. \code{start} must be length 1 or the same length as \code{times}. Predicted times returned with \code{type} \code{"rmst"} or \code{"quantile"} will be times since time zero, not times since the \code{start} time.} \item{conf.int}{Logical. Should confidence intervals be returned? Default is \code{FALSE}.} \item{conf.level}{Width of symmetric confidence intervals, relative to 1.} \item{se.fit}{Logical. Should standard errors of fitted values be returned? Default is \code{FALSE}.} \item{p}{Vector of quantiles at which to return fitted values when \code{type = "quantile"}. Default is \code{c(0.1, 0.9)}.} \item{...}{Not currently used.} } \value{ A \code{\link[tibble]{tibble}} with same number of rows as \code{newdata} and in the same order. If multiple predictions are requested, a \code{\link[tibble]{tibble}} containing a single list-column of data frames. For the list-column of data frames - the dimensions of each data frame will be identical. Rows are added for each value of \code{times} or \code{p} requested. This function is a wrapper around \code{\link{summary.flexsurvreg}}, designed to help \pkg{flexsurv} to integrate with the "tidymodels" ecosystem, in particular the \pkg{censored} package. \code{\link{summary.flexsurvreg}} returns the same results but in a more conventional format. } \description{ Predict outcomes from flexible survival models at the covariate values specified in \code{newdata}. } \examples{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") ## Simplest prediction: mean or median, for covariates defined by original dataset predict(fitg) predict(fitg, type = "quantile", p = 0.5) ## Simple prediction for user-defined covariate values predict(fitg, newdata = data.frame(age = c(40, 50, 60))) predict(fitg, type = "quantile", p = 0.5, newdata = data.frame(age = c(40,50,60))) ## Predict multiple quantiles and unnest require(tidyr) pr <- predict(fitg, type = "survival", times = c(600, 800)) tidyr::unnest(pr, .pred) } \seealso{ \code{\link{summary.flexsurvreg}}, \code{\link{residuals.flexsurvreg}} } \author{ Matthew T. Warkentin (\url{https://github.com/mattwarkentin}) } flexsurv/man/pars.fmsm.Rd0000644000176200001440000000275114165570616015120 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{pars.fmsm} \alias{pars.fmsm} \title{Transition-specific parameters in a flexible parametric multi-state model} \usage{ pars.fmsm(x, trans, newdata = NULL, tvar = "trans") } \arguments{ \item{x}{A multi-state model fitted with \code{\link{flexsurvreg}}. See \code{\link{msfit.flexsurvreg}} for the required form of the model and the data. \code{x} can also be a list of \code{\link{flexsurvreg}} models, with one component for each permitted transition in the multi-state model, as illustrated in \code{\link{msfit.flexsurvreg}}.} \item{trans}{Matrix indicating allowed transitions. See \code{\link{msfit.flexsurvreg}}.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. See \code{\link{msfit.flexsurvreg}}.} \item{tvar}{Variable in the data representing the transition type. Not required if \code{x} is a list of models.} } \value{ A list with one component for each permitted transition. Each component has one element for each parameter of the parametric distribution that generates the corresponding event in the multi-state model. } \description{ List of maximum likelihood estimates of transition-specific parameters in a flexible parametric multi-state model, at given covariate values. } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}. } \keyword{models} \keyword{survival} flexsurv/man/flexsurvspline.Rd0000644000176200001440000002644314644767560016317 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/spline.R \name{flexsurvspline} \alias{flexsurvspline} \title{Flexible survival regression using the Royston/Parmar spline model.} \usage{ flexsurvspline( formula, data, weights, bhazard, rtrunc, subset, k = 0, knots = NULL, bknots = NULL, scale = "hazard", timescale = "log", spline = "rp", ... ) } \arguments{ \item{formula}{A formula expression in conventional R linear modelling syntax. The response must be a survival object as returned by the \code{\link[survival]{Surv}} function, and any covariates are given on the right-hand side. For example, \code{Surv(time, dead) ~ age + sex} specifies a model where the log cumulative hazard (by default, see \code{scale}) is a linear function of the covariates \code{age} and \code{sex}. If there are no covariates, specify \code{1} on the right hand side, for example \code{Surv(time, dead) ~ 1}. Time-varying covariate effects can be specified using the method described in \code{\link{flexsurvreg}} for placing covariates on ancillary parameters. The ancillary parameters here are named \code{gamma1}, \ldots{}, \code{gammar} where \code{r} is the number of knots \code{k} plus one (the ``degrees of freedom'' as defined by Royston and Parmar). So for the default Weibull model, there is just one ancillary parameter \code{gamma1}. Therefore a model with one internal spline knot, where the equivalents of the Weibull shape and scale parameters, but not the higher-order term \code{gamma2}, vary with age and sex, can be specified as: \code{Surv(time, dead) ~ age + sex + gamma1(age) + gamma1(sex)} or alternatively (and more safely, see \code{flexsurvreg}) \code{Surv(time, dead) ~ age + sex, anc=list(gamma1=~age + sex)} \code{Surv} objects of \code{type="right"},\code{"counting"}, \code{"interval1"} or \code{"interval2"} are supported, corresponding to right-censored, left-truncated or interval-censored observations.} \item{data}{A data frame in which to find variables supplied in \code{formula}. If not given, the variables should be in the working environment.} \item{weights}{Optional variable giving case weights.} \item{bhazard}{Optional variable giving expected hazards for relative survival models.} \item{rtrunc}{Optional variable giving individual right-truncation times (see \code{\link{flexsurvreg}}). Note that these models can suffer from weakly identifiable parameters and badly-behaved likelihood functions, and it is advised to compare convergence for different initial values by supplying different \code{inits} arguments to \code{flexsurvspline}.} \item{subset}{Vector of integers or logicals specifying the subset of the observations to be used in the fit.} \item{k}{Number of knots in the spline. The default \code{k=0} gives a Weibull, log-logistic or lognormal model, if \code{"scale"} is \code{"hazard"}, \code{"odds"} or \code{"normal"} respectively. \code{k} is equivalent to \code{df-1} in the notation of \code{stpm} for Stata. The knots are then chosen as equally-spaced quantiles of the log uncensored survival times, for example, at the median with one knot, or at the 33\% and 67\% quantiles of log time (or time, see \code{"timescale"}) with two knots. To override this default knot placement, specify \code{knots} instead.} \item{knots}{Locations of knots on the axis of log time (or time, see \code{"timescale"}). If not specified, knot locations are chosen as described in \code{k} above. Either \code{k} or \code{knots} must be specified. If both are specified, \code{knots} overrides \code{k}.} \item{bknots}{Locations of boundary knots, on the axis of log time (or time, see \code{"timescale"}). If not supplied, these are are chosen as the minimum and maximum log death time.} \item{scale}{If \code{"hazard"}, the log cumulative hazard is modelled as a spline function. If \code{"odds"}, the log cumulative odds is modelled as a spline function. If \code{"normal"}, \eqn{-\Phi^{-1}(S(t))}{-InvPhi(S(t))} is modelled as a spline function, where \eqn{\Phi^{-1}()}{InvPhi()} is the inverse normal distribution function \code{\link{qnorm}}.} \item{timescale}{If \code{"log"} (the default) the log cumulative hazard (or alternative) is modelled as a spline function of log time. If \code{"identity"}, it is modelled as a spline function of time, however this model would not satisfy the desirable property that the cumulative hazard (or alternative) should approach 0 at time zero.} \item{spline}{\code{"rp"} to use the natural cubic spline basis described in Royston and Parmar. \code{"splines2ns"} to use the alternative natural cubic spline basis from the \code{splines2} package (Wang and Yan 2021), which may be better behaved due to the basis being orthogonal.} \item{...}{Any other arguments to be passed to or through \code{\link{flexsurvreg}}, for example, \code{anc}, \code{inits}, \code{fixedpars}, \code{weights}, \code{subset}, \code{na.action}, and any options to control optimisation. See \code{\link{flexsurvreg}}.} } \value{ A list of class \code{"flexsurvreg"} with the same elements as described in \code{\link{flexsurvreg}}, and including extra components describing the spline model. See in particular: \item{k}{Number of knots.} \item{knots}{Location of knots on the log time axis.} \item{scale}{The \code{scale} of the model, hazard, odds or normal.} \item{res}{Matrix of maximum likelihood estimates and confidence limits. Spline coefficients are labelled \code{"gamma..."}, and covariate effects are labelled with the names of the covariates. Coefficients \code{gamma1,gamma2,...} here are the equivalent of \code{s0,s1,...} in Stata \code{streg}, and \code{gamma0} is the equivalent of the \code{xb} constant term. To reproduce results, use the \code{noorthog} option in Stata, since no orthogonalisation is performed on the spline basis here. In the Weibull model, for example, \code{gamma0,gamma1} are \code{-shape*log(scale), shape} respectively in \code{\link{dweibull}} or \code{\link{flexsurvreg}} notation, or (\code{-Intercept/scale}, \code{1/scale}) in \code{\link[survival]{survreg}} notation. In the log-logistic model with shape \code{a} and scale \code{b} (as in \code{\link[eha:Loglogistic]{eha::dllogis}} from the \pkg{eha} package), \code{1/b^a} is equivalent to \code{exp(gamma0)}, and \code{a} is equivalent to \code{gamma1}. In the log-normal model with log-scale mean \code{mu} and standard deviation \code{sigma}, \code{-mu/sigma} is equivalent to \code{gamma0} and \code{1/sigma} is equivalent to \code{gamma1}. } \item{loglik}{The maximised log-likelihood. This will differ from Stata, where the sum of the log uncensored survival times is added to the log-likelihood in survival models, to remove dependency on the time scale.} } \description{ Flexible parametric modelling of time-to-event data using the spline model of Royston and Parmar (2002). } \details{ This function works as a wrapper around \code{\link{flexsurvreg}} by dynamically constructing a custom distribution using \code{\link{dsurvspline}}, \code{\link{psurvspline}} and \code{\link{unroll.function}}. In the spline-based survival model of Royston and Parmar (2002), a transformation \eqn{g(S(t,z))} of the survival function is modelled as a natural cubic spline function of log time \eqn{x = \log(t)}{x = log(t)} plus linear effects of covariates \eqn{z}. \deqn{g(S(t,z)) = s(x, \bm{\gamma}) + \bm{\beta}^T \mathbf{z}}{g(S(t,z)) = s(x, gamma) + beta^T z} The proportional hazards model (\code{scale="hazard"}) defines \eqn{g(S(t,\mathbf{z})) = \log(-\log(S(t,\mathbf{z}))) = \log(H(t,\mathbf{z}))}{g(S(t,z)) = log(-log(S(t,z))) = log(H(t,z))}, the log cumulative hazard. The proportional odds model (\code{scale="odds"}) defines \eqn{g(S(t,\mathbf{z})) }{g(S(t,z)) = log(1/S(t,z) - 1)}\eqn{ = \log(S(t,\mathbf{z})^{-1} - 1)}{g(S(t,z)) = log(1/S(t,z) - 1)}, the log cumulative odds. The probit model (\code{scale="normal"}) defines \eqn{g(S(t,\mathbf{z})) = }{g(S(t,z)) = -InvPhi(S(t,z))}\eqn{ -\Phi^{-1}(S(t,\mathbf{z}))}{g(S(t,z)) = -InvPhi(S(t,z))}, where \eqn{\Phi^{-1}()}{InvPhi()} is the inverse normal distribution function \code{\link{qnorm}}. With no knots, the spline reduces to a linear function, and these models are equivalent to Weibull, log-logistic and lognormal models respectively. The spline coefficients \eqn{\gamma_j: j=1, 2 \ldots }{gamma_j: j=1, 2 \ldots}, which are called the "ancillary parameters" above, may also be modelled as linear functions of covariates \eqn{\mathbf{z}}, as \deqn{\gamma_j(\mathbf{z}) = \gamma_{j0} + \gamma_{j1}z_1 + \gamma_{j2}z_2 + ... }{gamma_j(z) = \gamma_{j0} + \gamma_{j1}z_1 + \gamma_{j2}z_2 + ... } giving a model where the effects of covariates are arbitrarily flexible functions of time: a non-proportional hazards or odds model. Natural cubic splines are cubic splines constrained to be linear beyond boundary knots \eqn{k_{min},k_{max}}{kmin,kmax}. The spline function is defined as \deqn{s(x,\boldsymbol{\gamma}) = \gamma_0 + \gamma_1 x + \gamma_2 v_1(x) + \ldots + }{s(x,gamma) = gamma0 + gamma1 x + gamma2 v1(x) + ... + gamma_{m+1} vm(x)}\deqn{ \gamma_{m+1} v_m(x)}{s(x,gamma) = gamma0 + gamma1 x + gamma2 v1(x) + ... + gamma_{m+1} vm(x)} where \eqn{v_j(x)}{vj(x)} is the \eqn{j}th basis function \deqn{v_j(x) = (x - k_j)^3_+ - \lambda_j(x - k_{min})^3_+ - (1 - }{vj(x) = (x - kj)^3_+ - \lambda_j(x - kmin)^3_+ - (1 -\lambda_j) (x - kmax)^3_+}\deqn{ \lambda_j) (x - k_{max})^3_+}{vj(x) = (x - kj)^3_+ - \lambda_j(x - kmin)^3_+ - (1 -\lambda_j) (x - kmax)^3_+} \deqn{\lambda_j = \frac{k_{max} - k_j}{k_{max} - k_{min}}}{\lambda_j = (kmax - kj) / (kmax - kmin)} and \eqn{(x - a)_+ = max(0, x - a)}. } \examples{ ## Best-fitting model to breast cancer data from Royston and Parmar (2002) ## One internal knot (2 df) and cumulative odds scale spl <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=1, scale="odds") ## Fitted survival plot(spl, lwd=3, ci=FALSE) ## Simple Weibull model fits much less well splw <- flexsurvspline(Surv(recyrs, censrec) ~ group, data=bc, k=0, scale="hazard") lines(splw, col="blue", ci=FALSE) ## Alternative way of fitting the Weibull \dontrun{ splw2 <- flexsurvreg(Surv(recyrs, censrec) ~ group, data=bc, dist="weibull") } } \references{ Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197. Wang W, Yan J (2021). Shape-Restricted Regression Splines with R Package splines2. Journal of Data Science, 19(3), 498-517. Jackson, C. (2016). flexsurv: A Platform for Parametric Survival Modeling in R. Journal of Statistical Software, 70(8), 1-33. doi:10.18637/jss.v070.i08 } \seealso{ \code{\link{flexsurvreg}} for flexible survival modelling using general parametric distributions. \code{\link{plot.flexsurvreg}} and \code{\link{lines.flexsurvreg}} to plot fitted survival, hazards and cumulative hazards from models fitted by \code{\link{flexsurvspline}} and \code{\link{flexsurvreg}}. } \author{ Christopher Jackson } \keyword{models} \keyword{survival} flexsurv/man/hazard.Rd0000644000176200001440000000373014165570616014461 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/Exp.R, R/Gamma.R, R/Lnorm.R, R/Weibull.R, % R/flexsurv-package.R \name{hexp} \alias{hexp} \alias{Hexp} \alias{hgamma} \alias{Hgamma} \alias{hlnorm} \alias{Hlnorm} \alias{hweibull} \alias{Hweibull} \alias{hazard} \title{Hazard and cumulative hazard functions} \usage{ hexp(x, rate = 1, log = FALSE) Hexp(x, rate = 1, log = FALSE) hgamma(x, shape, rate = 1, log = FALSE) Hgamma(x, shape, rate = 1, log = FALSE) hlnorm(x, meanlog = 0, sdlog = 1, log = FALSE) Hlnorm(x, meanlog = 0, sdlog = 1, log = FALSE) hweibull(x, shape, scale = 1, log = FALSE) Hweibull(x, shape, scale = 1, log = FALSE) } \arguments{ \item{x}{Vector of quantiles} \item{rate}{Rate parameter (exponential and gamma)} \item{log}{Compute log hazard or log cumulative hazard} \item{shape}{Shape parameter (Weibull and gamma)} \item{meanlog}{Mean on the log scale (log normal)} \item{sdlog}{Standard deviation on the log scale (log normal)} \item{scale}{Scale parameter (Weibull)} } \value{ Hazard (functions beginning 'h') or cumulative hazard (functions beginning 'H'). } \description{ Hazard and cumulative hazard functions for distributions which are built into flexsurv, and whose distribution functions are in base R. } \details{ For the exponential and the Weibull these are available analytically, and so are programmed here in numerically stable and efficient forms. For the gamma and log-normal, these are simply computed as minus the log of the survivor function (cumulative hazard) or the ratio of the density and survivor function (hazard), so are not expected to be robust to extreme values or quick to compute. } \seealso{ \code{\link{dexp}},\code{\link{dweibull}},\code{\link{dgamma}},\code{\link{dlnorm}},\code{\link{dgompertz}},\code{\link{dgengamma}},\code{\link{dgenf}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/ajfit.Rd0000644000176200001440000000355614165570616014313 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{ajfit} \alias{ajfit} \title{Aalen-Johansen nonparametric estimates comparable to a fitted flexsurvmix model} \usage{ ajfit(x, newdata = NULL, tidy = TRUE) } \arguments{ \item{x}{Fitted model returned by \code{\link{flexsurvmix}}.} \item{newdata}{Data frame of alternative covariate values to check fit for. Only factor covariates are supported.} \item{tidy}{If \code{TRUE} then a single tidy data frame is returned. Otherwise the function returns the object returned by \code{survfit}, or a list of these objects if we are computing subset-specific estimates.} } \description{ Given a fitted flexsurvmix model, return the Aalen-Johansen estimates of the probability of occupying each state at a series of times covering the observed data. State 1 represents not having experienced any of the competing events, while state 2 and any further states correspond to having experienced each of the competing events respectively. These estimates can be compared with the fitted probabilities returned by \code{\link{p_flexsurvmix}} to check the fit of a \code{flexsurvmix} model. } \details{ This is only supported for models with no covariates or models containing only factor covariates. For models with factor covariates, the Aalen-Johansen estimates are computed for the subsets of the data defined in \code{newdata}. If \code{newdata} is not supplied, then this function returns state occupancy probabilities for all possible combinations of the factor levels. The Aalen-Johansen estimates are computed using \code{\link[survival]{survfit}} from the \code{survival} package (Therneau 2020). } \references{ Therneau T (2020). _A Package for Survival Analysis in R_. R package version 3.2-3, . } flexsurv/man/means.Rd0000644000176200001440000000711714171772374014320 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/Exp.R, R/Gamma.R, R/GenF.R, R/GenGamma.R, % R/Gompertz.R, R/Llogis.R, R/Lnorm.R, R/Weibull.R, R/WeibullPH.R, % R/flexsurv-package.R \name{mean_exp} \alias{mean_exp} \alias{rmst_exp} \alias{mean_gamma} \alias{rmst_gamma} \alias{rmst_genf} \alias{mean_genf} \alias{rmst_genf.orig} \alias{mean_genf.orig} \alias{rmst_gengamma} \alias{mean_gengamma} \alias{rmst_gengamma.orig} \alias{mean_gengamma.orig} \alias{rmst_gompertz} \alias{mean_gompertz} \alias{mean_llogis} \alias{rmst_llogis} \alias{mean_lnorm} \alias{rmst_lnorm} \alias{mean_weibull} \alias{rmst_weibull} \alias{rmst_weibullPH} \alias{mean_weibullPH} \alias{means} \title{Mean and restricted mean survival functions} \usage{ mean_exp(rate = 1) rmst_exp(t, rate = 1, start = 0) mean_gamma(shape, rate = 1) rmst_gamma(t, shape, rate = 1, start = 0) rmst_genf(t, mu, sigma, Q, P, start = 0) mean_genf(mu, sigma, Q, P) rmst_genf.orig(t, mu, sigma, s1, s2, start = 0) mean_genf.orig(mu, sigma, s1, s2) rmst_gengamma(t, mu = 0, sigma = 1, Q, start = 0) mean_gengamma(mu = 0, sigma = 1, Q) rmst_gengamma.orig(t, shape, scale = 1, k, start = 0) mean_gengamma.orig(shape, scale = 1, k) rmst_gompertz(t, shape, rate = 1, start = 0) mean_gompertz(shape, rate = 1) mean_llogis(shape = 1, scale = 1) rmst_llogis(t, shape = 1, scale = 1, start = 0) mean_lnorm(meanlog = 0, sdlog = 1) rmst_lnorm(t, meanlog = 0, sdlog = 1, start = 0) mean_weibull(shape, scale = 1) rmst_weibull(t, shape, scale = 1, start = 0) rmst_weibullPH(t, shape, scale = 1, start = 0) mean_weibullPH(shape, scale = 1) } \arguments{ \item{rate}{Rate parameter (exponential and gamma)} \item{t}{Vector of times to which restricted mean survival time is evaluated} \item{start}{Optional left-truncation time or times. The returned restricted mean survival will be conditioned on survival up to this time.} \item{shape}{Shape parameter (Weibull, gamma, log-logistic, generalized gamma [orig], generalized F [orig])} \item{mu}{Mean on the log scale (generalized gamma, generalized F)} \item{sigma}{Standard deviation on the log scale (generalized gamma, generalized F)} \item{Q}{Vector of first shape parameters (generalized gamma, generalized F)} \item{P}{Vector of second shape parameters (generalized F)} \item{s1}{Vector of first F shape parameters (generalized F [orig])} \item{s2}{vector of second F shape parameters (generalized F [orig])} \item{scale}{Scale parameter (Weibull, log-logistic, generalized gamma [orig], generalized F [orig])} \item{k}{vector of shape parameters (generalized gamma [orig]).} \item{meanlog}{Mean on the log scale (log normal)} \item{sdlog}{Standard deviation on the log scale (log normal)} } \value{ mean survival (functions beginning 'mean') or restricted mean survival (functions beginning 'rmst_'). } \description{ Mean and restricted mean survival time functions for distributions which are built into flexsurv. } \details{ For the exponential, Weibull, log-logistic, lognormal, and gamma, mean survival is provided analytically. Restricted mean survival for the exponential distribution is also provided analytically. Mean and restricted means for other distributions are calculated via numeric integration. } \seealso{ \code{\link{dexp}},\code{\link{dweibull}},\code{\link{dgamma}},\code{\link{dlnorm}},\code{\link{dgompertz}},\code{\link{dgengamma}},\code{\link{dgenf}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/mean_flexsurvmix.Rd0000644000176200001440000000227114165570616016603 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{mean_flexsurvmix} \alias{mean_flexsurvmix} \title{Mean times to events from a flexsurvmix model} \usage{ mean_flexsurvmix(x, newdata = NULL, B = NULL) } \arguments{ \item{x}{Fitted model object returned from \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} } \value{ Mean times to next event conditionally on each alternative event, given the specified covariate values. } \description{ This returns the mean of each event-specific parametric time-to-event distribution in the mixture model, which is the mean time to event conditionally on that event being the one that happens. } flexsurv/man/bc.Rd0000644000176200001440000000301514165570616013570 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurv-package.R \docType{data} \name{bc} \alias{bc} \title{Breast cancer survival data} \format{ A data frame with 686 rows. \tabular{rll}{ \code{censrec} \tab (numeric) \tab 1=dead, 0=censored \cr \code{rectime} \tab (numeric) \tab Time of death or censoring in days\cr \code{group} \tab (numeric) \tab Prognostic group: \code{"Good"},\code{"Medium"} or \code{"Poor"}, \cr \tab \tab from a regression model developed by Sauerbrei and Royston (1999).\cr } } \source{ German Breast Cancer Study Group, 1984-1989. Used as a reference dataset for the spline-based survival model of Royston and Parmar (2002), implemented here in \code{\link{flexsurvspline}}. Originally provided with the \code{stpm} (Royston 2001, 2004) and \code{stpm2} (Lambert 2009, 2010) Stata modules. } \usage{ bc } \description{ Survival times of 686 patients with primary node positive breast cancer. } \references{ Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197. Sauerbrei, W. and Royston, P. (1999). Building multivariable prognostic and diagnostic models: transformation of the predictors using fractional polynomials. Journal of the Royal Statistical Society, Series A 162:71-94. } \seealso{ \code{\link{flexsurvspline}} } \keyword{datasets} flexsurv/man/bootci.fmsm.Rd0000644000176200001440000000536714470653203015431 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{bootci.fmsm} \alias{bootci.fmsm} \title{Bootstrap confidence intervals for flexsurv output functions} \usage{ bootci.fmsm( x, B, fn, cl = 0.95, attrs = NULL, cores = NULL, sample = FALSE, ... ) } \arguments{ \item{x}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object. Or a list of such objects, defining a multi-state model.} \item{B}{Number of parameter draws to use} \item{fn}{Function to bootstrap the results of. It must have an argument named \code{x} giving a fitted flexsurv model object. This may return a value with any format, e.g. list, matrix or vector, as long as it can be converted to a numeric vector with \code{unlist}. See the example below.} \item{cl}{Width of symmetric confidence interval, by default 0.95} \item{attrs}{Any attributes of the value returned from \code{fn} which we want confidence intervals for. These will be unlisted, if possible, and appended to the result vector.} \item{cores}{Number of cores to use for parallel processing.} \item{sample}{If \code{TRUE} then the bootstrap sample itself is returned. If \code{FALSE} then the quantiles of the sample are returned giving a confidence interval.} \item{...}{Additional arguments to pass to \code{fn}.} } \value{ A matrix with two rows, giving the upper and lower confidence limits respectively. Each row is a vector of the same length as the unlisted result of the function corresponding to \code{fncall}. } \description{ Calculate a confidence interval for a model output by repeatedly replacing the parameters in a fitted model object with a draw from the multivariate normal distribution of the maximum likelihood estimates, then recalculating the output function. } \examples{ ## How to use bootci.fmsm ## Write a function with one argument called x giving a fitted model, ## and returning some results of the model. The results may be in any form. tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, data=bosms3, dist="exp") summfn <- function(x, t){ resp <- flexsurv::pmatrix.fs(x, trans=tmat, t=t) rest <- flexsurv::totlos.fs(x, trans=tmat, t=t) list(resp, rest) } ## Use bootci.fmsm to obtain the confidence interval ## The matrix columns are in the order of the unlisted results of the original ## summfn. You will have to rearrange them into the format that you want. ## If summfn has any extra arguments, in this case \code{t}, make sure they are ## passed through via the ... argument to bootci.fmsm bootci.fmsm(bexp, B=3, fn=summfn, t=10) bootci.fmsm(bexp, B=3, fn=summfn, t=5) } flexsurv/man/ppath_fmixmsm.Rd0000644000176200001440000000253614165570616016067 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/fmixmsm.R \name{ppath_fmixmsm} \alias{ppath_fmixmsm} \title{Probability of each pathway taken through a mixture multi-state model} \usage{ ppath_fmixmsm(x, newdata = NULL, final = FALSE, B = NULL) } \arguments{ \item{x}{Object returned by \code{\link{fmixmsm}}, representing a multi-state model built from piecing together mixture models fitted by \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{final}{If \code{TRUE} then the probabilities of pathways with the same final state are added together, to produce the probability of each ultimate outcome or absorbing state from the multi-state model.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} } \value{ Data frame of pathway probabilities by covariate value and pathway. } \description{ Probability of each pathway taken through a mixture multi-state model } flexsurv/man/glance.flexsurvreg.Rd0000644000176200001440000000221014644755013017002 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/broom-funs.R \name{glance.flexsurvreg} \alias{glance.flexsurvreg} \title{Glance at a flexsurv model object} \usage{ \method{glance}{flexsurvreg}(x, ...) } \arguments{ \item{x}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{...}{Not currently used.} } \value{ A one-row \code{\link[tibble]{tibble}} containing columns: \itemize{ \item \code{N} Number of observations used in fitting \item \code{events} Number of events \item \code{censored} Number of censored events \item \code{trisk} Total length of time-at-risk (i.e. follow-up) \item \code{df} Degrees of freedom (i.e. number of estimated parameters) \item \code{logLik} Log-likelihood \item \code{AIC} Akaike's "An Information Criteria" \item \code{BIC} Bayesian Information Criteria } } \description{ Glance accepts a model object and returns a tibble with exactly one row of model summaries. } \examples{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") glance(fitg) } flexsurv/man/fmsm.Rd0000644000176200001440000000227214165570616014152 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{fmsm} \alias{fmsm} \title{Construct a multi-state model from a set of parametric survival models} \usage{ fmsm(..., trans) } \arguments{ \item{...}{Objects returned by \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} representing fitted survival models.} \item{trans}{A matrix of integers specifying which models correspond to which transitions. The \eqn{r,s} entry is \code{i} if the \eqn{i}th argument specified in \code{...} is the model for the state \eqn{r} to state \eqn{s} transition. The entry should be \code{NA} if the transition is disallowed.} } \value{ A list containing the objects given in \code{...}, and with attributes \code{"trans"} and \code{"statenames"} defining the transition structure matrix and state names, and with list components named to describe the transitions they correspond to. If any of the arguments in \code{...} are named, then these are used to define the transition names, otherwise default names are chosen based on the state names. } \description{ Construct a multi-state model from a set of parametric survival models } flexsurv/man/p_flexsurvmix.Rd0000644000176200001440000000341614165570616016124 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{p_flexsurvmix} \alias{p_flexsurvmix} \title{Transition probabilities from a flexsurvmix model} \usage{ p_flexsurvmix(x, newdata = NULL, startname = "start", t = 1, B = NULL) } \arguments{ \item{x}{Fitted model object returned from \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{startname}{Name of the state where individuals start. This considers the model as a multi-state model where people start in this state, and may transition to one of the competing events.} \item{t}{Vector of times \code{t} to calculate the probabilities of transition by.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} } \value{ A data frame with transition probabilities by time, covariate value and destination state. } \description{ These quantities are variously known as transition probabilities, or state occupancy probabilities, or values of the "cumulative incidence" function, or values of the "subdistribution" function. They are the probabilities that an individual has experienced an event of a particular kind by time \code{t}. } \details{ Note that "cumulative incidence" is a misnomer, as "incidence" typically means a hazard, and the quantities computed here are not cumulative hazards, but probabilities. } flexsurv/man/dot-hess_to_cov.Rd0000644000176200001440000000127414523723773016312 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/utils.R \name{.hess_to_cov} \alias{.hess_to_cov} \title{helper function to safely convert a Hessian matrix to covariance matrix} \usage{ .hess_to_cov(hessian, tol.solve = 1e-09, tol.evalues = 1e-05, ...) } \arguments{ \item{hessian}{hessian matrix to convert to covariance matrix (must be evaluated at MLE)} \item{tol.solve}{tolerance used for solve()} \item{tol.evalues}{accepted tolerance for negative eigenvalues of the covariance matrix} \item{...}{arguments passed to Matrix::nearPD} } \description{ helper function to safely convert a Hessian matrix to covariance matrix } \keyword{internal} flexsurv/man/summary.flexsurvreg.Rd0000644000176200001440000001766414362520136017262 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvreg.R \name{summary.flexsurvreg} \alias{summary.flexsurvreg} \title{Summaries of fitted flexible survival models} \usage{ \method{summary}{flexsurvreg}( object, newdata = NULL, X = NULL, type = "survival", fn = NULL, t = NULL, quantiles = 0.5, start = 0, cross = TRUE, ci = TRUE, se = FALSE, B = 1000, cl = 0.95, tidy = FALSE, na.action = na.pass, ... ) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{newdata}{Data frame containing covariate values to produce fitted values for. Or a list that can be coerced to such a data frame. There must be a column for every covariate in the model formula, and one row for every combination of covariates the fitted values are wanted for. These are in the same format as the original data, with factors as a single variable, not 0/1 contrasts. If this is omitted, if there are any continuous covariates, then a single summary is provided with all covariates set to their mean values in the data - for categorical covariates, the means of the 0/1 indicator variables are taken. If there are only factor covariates in the model, then all distinct groups are used by default.} \item{X}{Alternative way of defining covariate values to produce fitted values for. Since version 0.4, \code{newdata} is an easier way that doesn't require the user to create factor contrasts, but \code{X} has been kept for backwards compatibility. Columns of \code{X} represent different covariates, and rows represent multiple combinations of covariate values. For example \code{matrix(c(1,2),nrow=2)} if there is only one covariate in the model, and we want survival for covariate values of 1 and 2. A vector can also be supplied if just one combination of covariates is needed. For ``factor'' (categorical) covariates, the values of the contrasts representing factor levels (as returned by the \code{\link{contrasts}} function) should be used. For example, for a covariate \code{agegroup} specified as an unordered factor with levels \code{20-29, 30-39, 40-49, 50-59}, and baseline level \code{20-29}, there are three contrasts. To return summaries for groups \code{20-29} and \code{40-49}, supply \code{X = rbind(c(0,0,0), c(0,1,0))}, since all contrasts are zero for the baseline level, and the second contrast is ``turned on'' for the third level \code{40-49}.} \item{type}{\code{"survival"} for survival probabilities. \code{"cumhaz"} for cumulative hazards. \code{"hazard"} for hazards. \code{"rmst"} for restricted mean survival. \code{"mean"} for mean survival. \code{"median"} for median survival (alternative to \code{type="quantile"} with \code{quantiles=0.5}). \code{"quantile"} for quantiles of the survival time distribution. \code{"link"} for the fitted value of the location parameter (i.e. the "linear predictor" but on the natural scale of the parameter, not on the log scale) Ignored if \code{"fn"} is specified.} \item{fn}{Custom function of the parameters to summarise against time. This has optional first two arguments \code{t} representing time, and \code{start} representing left-truncation points, and any remaining arguments must be parameters of the distribution. It should be vectorised, and return a vector corresponding to the vectors given by \code{t}, \code{start} and the parameter vectors.} \item{t}{Times to calculate fitted values for. By default, these are the sorted unique observation (including censoring) times in the data - for left-truncated datasets these are the "stop" times.} \item{quantiles}{If \code{type="quantile"}, this specifies the quantiles of the survival time distribution to return estimates for.} \item{start}{Optional left-truncation time or times. The returned survival, hazard or cumulative hazard will be conditioned on survival up to this time. Predicted times returned with \code{"rmst"}, \code{"mean"}, \code{"median"} or \code{"quantile"} will be times since time zero, not times since the \code{start} time. A vector of the same length as \code{t} can be supplied to allow different truncation times for each prediction time, though this doesn't make sense in the usual case where this function is used to calculate a predicted trajectory for a single individual. This is why the default \code{start} time was changed for version 0.4 of \pkg{flexsurv} - this was previously a vector of the start times observed in the data.} \item{cross}{If \code{TRUE} (the default) then summaries are calculated for all combinations of times specified in \code{t} and covariate vectors specifed in \code{newdata}. If \code{FALSE}, then the times \code{t} should be of length equal to the number of rows in \code{newdata}, and one summary is produced for each row of \code{newdata} paired with the corresponding element of \code{t}. This is used, e.g. when determining Cox-Snell residuals.} \item{ci}{Set to \code{FALSE} to omit confidence intervals.} \item{se}{Set to \code{TRUE} to include standard errors.} \item{B}{Number of simulations from the normal asymptotic distribution of the estimates used to calculate confidence intervals or standard errors. Decrease for greater speed at the expense of accuracy, or set \code{B=0} to turn off calculation of CIs and SEs.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{tidy}{If \code{TRUE}, then the results are returned as a tidy data frame instead of a list. This can help with using the \pkg{ggplot2} package to compare summaries for different covariate values.} \item{na.action}{Function determining what should be done with missing values in \code{newdata}. If \code{na.pass} (the default) then summaries of \code{NA} are produced for missing covariate values. If \code{na.omit}, then missing values are dropped, the behaviour of \code{summary.flexsurvreg} before \code{flexsurv} version 1.2.} \item{...}{Further arguments passed to or from other methods. Currently unused.} } \value{ If \code{tidy=FALSE}, a list with one component for each unique covariate value (if there are only categorical covariates) or one component (if there are no covariates or any continuous covariates). Each of these components is a matrix with one row for each time in \code{t}, giving the estimated survival (or cumulative hazard, or hazard) and 95\% confidence limits. These list components are named with the covariate names and values which define them. If \code{tidy=TRUE}, a data frame is returned instead. This is formed by stacking the above list components, with additional columns to identify the covariate values that each block corresponds to. If there are multiple summaries, an additional list component named \code{X} contains a matrix with the exact values of contrasts (dummy covariates) defining each summary. The \code{\link{plot.flexsurvreg}} function can be used to quickly plot these model-based summaries against empirical summaries such as Kaplan-Meier curves, to diagnose model fit. Confidence intervals are obtained by sampling randomly from the asymptotic normal distribution of the maximum likelihood estimates and then taking quantiles (see, e.g. Mandel (2013)). } \description{ Return fitted survival, cumulative hazard or hazard at a series of times from a fitted \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} model. } \details{ Time-dependent covariates are not currently supported. The covariate values are assumed to be constant through time for each fitted curve. } \references{ Mandel, M. (2013). "Simulation based confidence intervals for functions with complicated derivatives." The American Statistician (in press). } \seealso{ \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}. } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{models} flexsurv/man/flexsurvrtrunc.Rd0000644000176200001440000002255514644755663016343 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvrtrunc.R \name{flexsurvrtrunc} \alias{flexsurvrtrunc} \title{Flexible parametric models for right-truncated, uncensored data defined by times of initial and final events.} \usage{ flexsurvrtrunc( t, tinit, rtrunc, tmax, data = NULL, method = "joint", dist, theta = NULL, fixed.theta = TRUE, inits = NULL, fixedpars = NULL, dfns = NULL, integ.opts = NULL, cl = 0.95, optim_control = list() ) } \arguments{ \item{t}{Vector of time differences between an initial and final event for a set of individuals.} \item{tinit}{Absolute time of the initial event for each individual.} \item{rtrunc}{Individual-specific right truncation points on the same scale as \code{t}, so that each individual's survival time \code{t} would not have been observed if it was greater than the corresponding element of \code{rtrunc}. Only used in \code{method="joint"}. In \code{method="final"}, the right-truncation is implicit.} \item{tmax}{Maximum possible time between initial and final events that could have been observed. This is only used in \code{method="joint"}, and is ignored in \code{method="final"}.} \item{data}{Data frame containing \code{t}, \code{rtrunc} and \code{tinit}.} \item{method}{If \code{"joint"} then the "joint-conditional" method is used. If \code{"final"} then the "conditional-on-final" method is used. The "conditional-on-initial" method can be implemented by using \code{\link{flexsurvreg}} with a \code{rtrunc} argument. These methods are all described in Seaman et al. (2020).} \item{dist}{Typically, one of the strings in the first column of the following table, identifying a built-in distribution. This table also identifies the location parameters, and whether covariates on these parameters represent a proportional hazards (PH) or accelerated failure time (AFT) model. In an accelerated failure time model, the covariate speeds up or slows down the passage of time. So if the coefficient (presented on the log scale) is log(2), then doubling the covariate value would give half the expected survival time. \tabular{llll}{ \code{"gengamma"} \tab Generalized gamma (stable) \tab mu \tab AFT \cr \code{"gengamma.orig"} \tab Generalized gamma (original) \tab scale \tab AFT \cr \code{"genf"} \tab Generalized F (stable) \tab mu \tab AFT \cr \code{"genf.orig"} \tab Generalized F (original) \tab mu \tab AFT \cr \code{"weibull"} \tab Weibull \tab scale \tab AFT \cr \code{"gamma"} \tab Gamma \tab rate \tab AFT \cr \code{"exp"} \tab Exponential \tab rate \tab PH \cr \code{"llogis"} \tab Log-logistic \tab scale \tab AFT \cr \code{"lnorm"} \tab Log-normal \tab meanlog \tab AFT \cr \code{"gompertz"} \tab Gompertz \tab rate \tab PH \cr } \code{"exponential"} and \code{"lognormal"} can be used as aliases for \code{"exp"} and \code{"lnorm"}, for compatibility with \code{\link[survival]{survreg}}. Alternatively, \code{dist} can be a list specifying a custom distribution. See section ``Custom distributions'' below for how to construct this list. Very flexible spline-based distributions can also be fitted with \code{\link{flexsurvspline}}. The parameterisations of the built-in distributions used here are the same as in their built-in distribution functions: \code{\link{dgengamma}}, \code{\link{dgengamma.orig}}, \code{\link{dgenf}}, \code{\link{dgenf.orig}}, \code{\link{dweibull}}, \code{\link{dgamma}}, \code{\link{dexp}}, \code{\link{dlnorm}}, \code{\link{dgompertz}}, respectively. The functions in base R are used where available, otherwise, they are provided in this package. A package vignette "Distributions reference" lists the survivor functions and covariate effect parameterisations used by each built-in distribution. For the Weibull, exponential and log-normal distributions, \code{\link{flexsurvreg}} simply works by calling \code{\link[survival]{survreg}} to obtain the maximum likelihood estimates, then calling \code{\link{optim}} to double-check convergence and obtain the covariance matrix for \code{\link{flexsurvreg}}'s preferred parameterisation. The Weibull parameterisation is different from that in \code{\link[survival]{survreg}}, instead it is consistent with \code{\link{dweibull}}. The \code{"scale"} reported by \code{\link[survival]{survreg}} is equivalent to \code{1/shape} as defined by \code{\link{dweibull}} and hence \code{\link{flexsurvreg}}. The first coefficient \code{(Intercept)} reported by \code{\link[survival]{survreg}} is equivalent to \code{log(scale)} in \code{\link{dweibull}} and \code{\link{flexsurvreg}}. Similarly in the exponential distribution, the rate, rather than the mean, is modelled on covariates. The object \code{flexsurv.dists} lists the names of the built-in distributions, their parameters, location parameter, functions used to transform the parameter ranges to and from the real line, and the functions used to generate initial values of each parameter for estimation.} \item{theta}{Initial value (or fixed value) for the exponential growth rate \code{theta}. Defaults to 1.} \item{fixed.theta}{Should \code{theta} be fixed at its initial value or estimated. This only applies to \code{method="joint"}. For \code{method="final"}, \code{theta} must be fixed.} \item{inits}{Initial values for the parameters of the parametric survival distributon. If not supplied, a heuristic is used. as is done in \code{\link{flexsurvreg}}.} \item{fixedpars}{Integer indices of the parameters of the survival distribution that should be fixed to their values supplied in \code{inits}. Same length as \code{inits}.} \item{dfns}{An alternative way to define a custom survival distribution (see section ``Custom distributions'' below). A list whose components may include \code{"d"}, \code{"p"}, \code{"h"}, or \code{"H"} containing the probability density, cumulative distribution, hazard, or cumulative hazard functions of the distribution. For example, \code{list(d=dllogis, p=pllogis)}. If \code{dfns} is used, a custom \code{dlist} must still be provided, but \code{dllogis} and \code{pllogis} need not be visible from the global environment. This is useful if \code{flexsurvreg} is called within other functions or environments where the distribution functions are also defined dynamically.} \item{integ.opts}{List of named arguments to pass to \code{\link{integrate}}, if a custom density or hazard is provided without its cumulative version. For example, \code{integ.opts = list(rel.tol=1e-12)}} \item{cl}{Width of symmetric confidence intervals for maximum likelihood estimates, by default 0.95.} \item{optim_control}{List to supply as the \code{control} argument to \code{\link{optim}} to control the likelihood maximisation.} } \description{ This function estimates the distribution of the time between an initial and final event, in situations where individuals are only observed if they have experienced both events before a certain time, thus they are right-truncated at this time. The time of the initial event provides information about the time from initial to final event, given the truncated observation scheme, and initial events are assumed to occur with an exponential growth rate. } \details{ Covariates are not currently supported. Note that \code{\link{flexsurvreg}}, with an \code{rtrunc} argument, can fit models for a similar kind of data, but those models ignore the information provided by the time of the initial event. A nonparametric estimator of survival under right-truncation is also provided in \code{\link{survrtrunc}}. See Seaman et al. (2020) for a full comparison of the alternative models. } \examples{ set.seed(1) ## simulate time to initial event X <- rexp(1000, 0.2) ## simulate time between initial and final event T <- rgamma(1000, 2, 10) ## right-truncate to keep only those with final event time ## before tmax tmax <- 40 obs <- X + T < tmax rtrunc <- tmax - X dat <- data.frame(X, T, rtrunc)[obs,] flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gamma", theta=0.2) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gamma", theta=0.2, fixed.theta=FALSE) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gamma", theta=0.2, inits=c(1, 8)) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gamma", theta=0.2, method="final") flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gamma", fixed.theta=TRUE) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="weibull", fixed.theta=TRUE) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="lnorm", fixed.theta=TRUE) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gengamma", fixed.theta=TRUE) flexsurvrtrunc(t=T, rtrunc=rtrunc, tinit=X, tmax=40, data=dat, dist="gompertz", fixed.theta=TRUE) } \references{ Seaman, S., Presanis, A. and Jackson, C. (2020) Estimating a Time-to-Event Distribution from Right-Truncated Data in an Epidemic: a Review of Methods } \seealso{ \code{\link{flexsurvreg}}, \code{\link{survrtrunc}}. } flexsurv/man/GenGamma.Rd0000644000176200001440000001131714165570616014664 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/GenGamma.R \name{GenGamma} \alias{GenGamma} \alias{dgengamma} \alias{pgengamma} \alias{qgengamma} \alias{rgengamma} \alias{Hgengamma} \alias{hgengamma} \title{Generalized gamma distribution} \usage{ dgengamma(x, mu = 0, sigma = 1, Q, log = FALSE) pgengamma(q, mu = 0, sigma = 1, Q, lower.tail = TRUE, log.p = FALSE) Hgengamma(x, mu = 0, sigma = 1, Q) hgengamma(x, mu = 0, sigma = 1, Q) qgengamma(p, mu = 0, sigma = 1, Q, lower.tail = TRUE, log.p = FALSE) rgengamma(n, mu = 0, sigma = 1, Q) } \arguments{ \item{x, q}{vector of quantiles.} \item{mu}{Vector of ``location'' parameters.} \item{sigma}{Vector of ``scale'' parameters. Note the inconsistent meanings of the term ``scale'' - this parameter is analogous to the (log-scale) standard deviation of the log-normal distribution, ``sdlog'' in \code{\link{dlnorm}}, rather than the ``scale'' parameter of the gamma distribution \code{\link{dgamma}}. Constrained to be positive.} \item{Q}{Vector of shape parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dgengamma} gives the density, \code{pgengamma} gives the distribution function, \code{qgengamma} gives the quantile function, \code{rgengamma} generates random deviates, \code{Hgengamma} retuns the cumulative hazard and \code{hgengamma} the hazard. } \description{ Density, distribution function, hazards, quantile function and random generation for the generalized gamma distribution, using the parameterisation originating from Prentice (1974). Also known as the (generalized) log-gamma distribution. } \details{ If \eqn{\gamma \sim Gamma(Q^{-2}, 1)}{g ~ Gamma(Q^{-2}, 1)} , and \eqn{w = log(Q^2 \gamma) / Q}{w = log(Q^2*g) / Q}, then \eqn{x = \exp(\mu + \sigma w)}{x = exp(mu + sigma w)} follows the generalized gamma distribution with probability density function \deqn{f(x | \mu, \sigma, Q) = \frac{|Q|(Q^{-2})^{Q^{-2}}}{\sigma x \Gamma(Q^{-2})} \exp(Q^{-2}(Qw - \exp(Qw)))}{ f(x | mu, sigma, Q) = |Q| (Q^{-2})^{Q^{-2}} / (sigma * x * Gamma(Q^{-2})) exp(Q^{-2}*(Q*w - exp(Q*w)))} This parameterisation is preferred to the original parameterisation of the generalized gamma by Stacy (1962) since it is more numerically stable near to \eqn{Q=0} (the log-normal distribution), and allows \eqn{Q<=0}. The original is available in this package as \code{\link{dgengamma.orig}}, for the sake of completion and compatibility with other software - this is implicitly restricted to \code{Q}>0 (or \code{k}>0 in the original notation). The parameters of \code{\link{dgengamma}} and \code{\link{dgengamma.orig}} are related as follows. \code{dgengamma.orig(x, shape=shape, scale=scale, k=k) = } \code{dgengamma(x, mu=log(scale) + log(k)/shape, sigma=1/(shape*sqrt(k)), Q=1/sqrt(k))} The generalized gamma distribution simplifies to the gamma, log-normal and Weibull distributions with the following parameterisations: \tabular{lcl}{ \code{dgengamma(x, mu, sigma, Q=0)} \tab \code{=} \tab \code{dlnorm(x, mu, sigma)} \cr \code{dgengamma(x, mu, sigma, Q=1)} \tab \code{=} \tab \code{dweibull(x, shape=1/sigma, scale=exp(mu))} \cr \code{dgengamma(x, mu, sigma, Q=sigma)} \tab \code{=} \tab \code{dgamma(x, shape=1/sigma^2, rate=exp(-mu) / sigma^2)} \cr } The properties of the generalized gamma and its applications to survival analysis are discussed in detail by Cox (2007). The generalized F distribution \code{\link{GenF}} extends the generalized gamma to four parameters. } \references{ Prentice, R. L. (1974). A log gamma model and its maximum likelihood estimation. Biometrika 61(3):539-544. Farewell, V. T. and Prentice, R. L. (1977). A study of distributional shape in life testing. Technometrics 19(1):69-75. Lawless, J. F. (1980). Inference in the generalized gamma and log gamma distributions. Technometrics 22(3):409-419. Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine 26:4252-4374 Stacy, E. W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statistics 33:1187-92 } \seealso{ \code{\link{GenGamma.orig}}, \code{\link{GenF}}, \code{\link{Lognormal}}, \code{\link{GammaDist}}, \code{\link{Weibull}}. } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/plot.standsurv.Rd0000644000176200001440000000475014247336547016225 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/standsurv.R \name{plot.standsurv} \alias{plot.standsurv} \title{Plot standardized metrics from a fitted flexsurv model} \usage{ \method{plot}{standsurv}(x, contrast = FALSE, ci = FALSE, expected = FALSE, ...) } \arguments{ \item{x}{A standsurv object returned by \code{standsurv}} \item{contrast}{Should contrasts of standardized metrics be plotted. Defaults to FALSE} \item{ci}{Should confidence intervals be plotted (if calculated in \code{standsurv})?} \item{expected}{Should the marginal expected survival / hazard also be plotted? This can only be invoked if \code{rmap} and \code{ratetable} have been passed to \code{standsurv}} \item{...}{Not currently used} } \value{ A ggplot showing the standardized metric calculated by \code{standsurv} over time. Modification of the plot is possible by adding further ggplot objects, see Examples. } \description{ Plot standardized metrics such as the marginal survival, restricted mean survival and hazard, based on a fitted flexsurv model. } \examples{ ## Use bc dataset, with an age variable appended ## mean age is higher in those with smaller observed survival times newbc <- bc newbc$age <- rnorm(dim(bc)[1], mean = 65-scale(newbc$recyrs, scale=FALSE), sd = 5) ## Fit a Weibull flexsurv model with group and age as covariates weib_age <- flexsurvreg(Surv(recyrs, censrec) ~ group+age, data=newbc, dist="weibull") ## Calculate standardized survival and the difference in standardized survival ## for the three levels of group across a grid of survival times standsurv_weib_age <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length=100), contrast = "difference", ci=TRUE, boot = TRUE, B=10, seed=123) plot(standsurv_weib_age) plot(standsurv_weib_age) + ggplot2::theme_bw() + ggplot2::ylab("Survival") + ggplot2::xlab("Time (years)") + ggplot2::guides(color=ggplot2::guide_legend(title="Prognosis"), fill=ggplot2::guide_legend(title="Prognosis")) plot(standsurv_weib_age, contrast=TRUE, ci=TRUE) + ggplot2::ylab("Difference in survival") } flexsurv/man/residuals.flexsurvreg.Rd0000644000176200001440000000306414165570616017556 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/residuals.flexsurvreg.R \name{residuals.flexsurvreg} \alias{residuals.flexsurvreg} \title{Calculate residuals for flexible survival models} \usage{ \method{residuals}{flexsurvreg}(object, type = "response", ...) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{type}{Character string for the type of residual desired. Currently only \code{"response"} and \code{"coxsnell"} are supported. More residual types may become available in future versions.} \item{...}{Not currently used.} } \value{ Numeric vector with the same length as \code{nobs(object)}. } \description{ Calculates residuals for \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} model fits. } \details{ Residuals of \code{type = "response"} are calculated as the naive difference between the observed survival and the covariate-specific predicted mean survival from \code{\link{predict.flexsurvreg}}, ignoring whether the event time is observed or censored. \code{type="coxsnell"} returns the Cox-Snell residual, defined as the estimated cumulative hazard at each data point. To check the fit of the A more fully featured utility for this is provided in the function \code{\link{coxsnell_flexsurvreg}}. } \examples{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") residuals(fitg, type="response") } \seealso{ \code{\link{predict.flexsurvreg}} } flexsurv/man/qfinal_fmixmsm.Rd0000644000176200001440000000364214165570616016224 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/fmixmsm.R \name{qfinal_fmixmsm} \alias{qfinal_fmixmsm} \title{Quantiles of the distribution of the time until reaching a final state in a mixture multi-state model} \usage{ qfinal_fmixmsm( x, newdata = NULL, final = FALSE, B = NULL, n = 10000, probs = c(0.025, 0.5, 0.975) ) } \arguments{ \item{x}{Object returned by \code{\link{fmixmsm}}, representing a multi-state model built from piecing together mixture models fitted by \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{final}{If \code{TRUE} then the mean time to the final state is calculated for each final state, by taking a weighted average of the mean time to travel each pathway ending in that final state, weighted by the probability of the pathway. If \code{FALSE} (the default) then a separate mean is calculated for each pathway.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} \item{n}{Number of individual-level simulations to use to characterise the time-to-event distributions} \item{probs}{Quantiles to calculate, by default, \code{c(0.025, 0.5, 0.975)}} } \value{ Data frame of quantiles of the time to final state by pathway and covariate value, or by final state and covariate value. } \description{ Calculate the quantiles of the time from the start of the process to each possible final (or "absorbing") state in a mixture multi-state model. Models with cycles are not supported. } flexsurv/man/pdf_flexsurvmix.Rd0000644000176200001440000000201314165570616016426 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{pdf_flexsurvmix} \alias{pdf_flexsurvmix} \title{Fitted densities for times to events in a flexsurvmix model} \usage{ pdf_flexsurvmix(x, newdata = NULL, t = NULL) } \arguments{ \item{x}{Fitted model object returned from \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{t}{Vector of times at which to evaluate the probability density} } \value{ A data frame with each row giving the fitted density \code{dens} for a combination of covariate values, time and competing event. } \description{ This returns an estimate of the probability density for the time to each competing event, at a vector of times supplied by the user. } flexsurv/man/model.frame.flexsurvmix.Rd0000644000176200001440000000107414471126735017772 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvmix.R \name{model.frame.flexsurvmix} \alias{model.frame.flexsurvmix} \title{Model frame from a flexsurvmix object} \usage{ \method{model.frame}{flexsurvmix}(formula, ...) } \arguments{ \item{formula}{Fitted model object from \code{\link{flexsurvmix}}.} \item{...}{Further arguments (currently unused).} } \value{ A list of data frames } \description{ Returns a list of data frames, with each component containing the data that were used for the model fit for that mixture component. } flexsurv/man/model.frame.flexsurvreg.Rd0000644000176200001440000000307514165570616017756 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{model.frame.flexsurvreg} \alias{model.frame.flexsurvreg} \alias{model.matrix.flexsurvreg} \title{Extract original data from \code{flexsurvreg} objects.} \usage{ \method{model.frame}{flexsurvreg}(formula, ...) \method{model.matrix}{flexsurvreg}(object, par = NULL, ...) } \arguments{ \item{formula}{A fitted model object, as returned by \code{\link{flexsurvreg}}.} \item{...}{Further arguments (not used).} \item{object}{A fitted model object, as returned by \code{\link{flexsurvreg}}.} \item{par}{String naming the parameter whose linear model matrix is desired. The default value of \code{par=NULL} returns a matrix consisting of the model matrices for all models in the object \code{cbind}ed together, with the intercepts excluded. This is not really a ``model matrix'' in the usual sense, however, the columns directly correspond to the covariate coefficients in the matrix of estimates from the fitted model.} } \value{ \code{model.frame} returns a data frame with all the original variables used for the model fit. \code{model.matrix} returns a design matrix for a part of the model that includes covariates. The required part is indicated by the \code{"par"} argument (see above). } \description{ Extract the data from a model fitted with \code{flexsurvreg}. } \seealso{ \code{\link{flexsurvreg}}, \code{\link{model.frame}}, \code{\link{model.matrix}}. } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{models} flexsurv/man/flexsurv-package.Rd0000644000176200001440000001004514554242022016441 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurv-package.R \docType{package} \name{flexsurv-package} \alias{flexsurv-package} \alias{flexsurv} \title{flexsurv: Flexible parametric survival and multi-state models} \description{ flexsurv: Flexible parametric models for time-to-event data, including the generalized gamma, the generalized F and the Royston-Parmar spline model, and extensible to user-defined distributions. } \details{ \code{\link{flexsurvreg}} fits parametric models for time-to-event (survival) data. Data may be right-censored, and/or left-censored, and/or left-truncated. Several built-in parametric distributions are available. Any user-defined parametric model can also be employed by supplying a list with basic information about the distribution, including the density or hazard and ideally also the cumulative distribution or hazard. Covariates can be included using a linear model on any parameter of the distribution, log-transformed to the real line if necessary. This typically defines an accelerated failure time or proportional hazards model, depending on the distribution and parameter. \code{\link{flexsurvspline}} fits the flexible survival model of Royston and Parmar (2002) in which the log cumulative hazard is modelled as a natural cubic spline function of log time. Covariates can be included on any of the spline parameters, giving either a proportional hazards model or an arbitrarily-flexible time-dependent effect. Alternative proportional odds or probit parameterisations are available. Output from the models can be presented as survivor, cumulative hazard and hazard functions (\code{\link{summary.flexsurvreg}}). These can be plotted against nonparametric estimates (\code{\link{plot.flexsurvreg}}) to assess goodness-of-fit. Any other user-defined function of the parameters may be summarised in the same way. Multi-state models for time-to-event data can also be fitted with the same functions. Predictions from those models can then be made using the functions \code{\link{pmatrix.fs}}, \code{\link{pmatrix.simfs}}, \code{\link{totlos.fs}}, \code{\link{totlos.simfs}}, or \code{\link{sim.fmsm}}, or alternatively by \code{\link{msfit.flexsurvreg}} followed by \code{mssample} or \code{probtrans} from the package \pkg{mstate}. Distribution (``dpqr'') functions for the generalized gamma and F distributions are given in \code{\link{GenGamma}}, \code{\link{GenF}} (preferred parameterisations) and \code{\link{GenGamma.orig}}, \code{\link{GenF.orig}} (original parameterisations). \code{\link{flexsurv}} also includes the standard Gompertz distribution with unrestricted shape parameter, see \code{\link{Gompertz}}. } \section{User guide}{ The \bold{flexsurv user guide} vignette explains the methods in detail, and gives several worked examples. A further vignette \bold{flexsurv-examples} gives a few more complicated examples, and users are encouraged to submit their own. } \references{ Jackson, C. (2016). flexsurv: A Platform for Parametric Survival Modeling in R. Journal of Statistical Software, 70(8), 1-33. doi:10.18637/jss.v070.i08 Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197. Cox, C. (2008). The generalized \eqn{F} distribution: An umbrella for parametric survival analysis. Statistics in Medicine 27:4301-4312. Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine 26:4252-4374 } \seealso{ Useful links: \itemize{ \item \url{https://github.com/chjackson/flexsurv} \item \url{http://chjackson.github.io/flexsurv/} \item Report bugs at \url{https://github.com/chjackson/flexsurv/issues} } } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{package} flexsurv/man/AIC.fmsm.Rd0000644000176200001440000000116714471126735014546 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{AIC.fmsm} \alias{AIC.fmsm} \title{Akaike's information criterion from a flexible parametric multistate model} \usage{ \method{AIC}{fmsm}(object, ..., k = 2) } \arguments{ \item{object}{Object returned by \code{\link{fmsm}} representing a multistate model.} \item{...}{Further arguments (currently unused).} \item{k}{Penalty applied to number of parameters (defaults to the standard 2).} } \value{ The sum of the AICs of the transition-specific models. } \description{ Defined as the sum of the AICs of the transition-specific models. } flexsurv/man/BIC.flexsurvreg.Rd0000644000176200001440000000520114470703452016146 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{BIC.flexsurvreg} \alias{BIC.flexsurvreg} \title{Bayesian Information Criterion (BIC) for comparison of flexsurvreg models} \usage{ \method{BIC}{flexsurvreg}(object, cens = TRUE, ...) } \arguments{ \item{object}{Fitted model returned by \code{\link{flexsurvreg}} (or \code{\link{flexsurvspline}}).} \item{cens}{Include censored observations in the sample size term (\code{n}) used in the calculation of BIC.} \item{...}{Other arguments (currently unused).} } \value{ The BIC of the fitted model. This is minus twice the log likelihood plus \code{p*log(n)}, where \code{p} is the number of parameters and \code{n} is the sample size of the data. If \code{weights} was supplied to \code{flexsurv}, the sample size is defined as the sum of the weights. } \description{ Bayesian Information Criterion (BIC) for comparison of flexsurvreg models } \details{ There is no "official" definition of what the sample size should be for the use of BIC in censored survival analysis. BIC is based on an approximation to Bayesian model comparison using Bayes factors and an implicit vague prior. Informally, the sample size describes the number of "units" giving rise to a distinct piece of information (Kass and Raftery 1995). However censored observations provide less information than observed events, in principle. The default used here is the number of individuals, for consistency with more familiar kinds of statistical modelling. However if censoring is heavy, then the number of events may be a better represent the amount of information. Following these principles, the best approximation would be expected to be somewere in between. AIC and BIC are intended to measure different things. Briefly, AIC measures predictive ability, whereas BIC is expected to choose the true model from a set of models where one of them is the truth. Therefore BIC chooses simpler models for all but the tiniest sample sizes (\eqn{log(n)>2}, \eqn{n>7}). AIC might be preferred in the typical situation where "all models are wrong but some are useful". AIC also gives similar results to cross-validation (Stone 1977). } \references{ Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773-795. Stone, M. (1977). An asymptotic equivalence of choice of model by crossâ€validation and Akaike's criterion. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 44-47. } \seealso{ \code{\link{BIC}}, \code{\link{AIC}}, \code{\link{AICC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}} } flexsurv/man/ajfit_flexsurvmix.Rd0000644000176200001440000000265714165570616016770 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{ajfit_flexsurvmix} \alias{ajfit_flexsurvmix} \title{Forms a tidy data frame for plotting the fit of parametric mixture multi-state models against nonparametric estimates} \usage{ ajfit_flexsurvmix(x, maxt = NULL, startname = "Start", B = NULL) } \arguments{ \item{x}{Fitted model returned by \code{\link{flexsurvmix}}.} \item{maxt}{Maximum time to produce parametric estimates for. By default this is the maximum event time in the data, the maximum time we have nonparametric estimates for.} \item{startname}{Label to give the state corresponding to "no event happened yet". By default this is \code{"Start"}.} \item{B}{Number of simulation replications to use to calculate a confidence interval for the parametric estimates in \code{\link{p_flexsurvmix}}. Comparable intervals for the Aalen-Johansen estimates are returned if this is set. Otherwise if \code{B=NULL} then no intervals are returned.} } \description{ This computes Aalen-Johansen estimates of the probability of occupying each state at a series of times, using \code{\link{ajfit}}. The equivalent estimates from the parametric model are then produced using \code{\link{p_flexsurvmix}}, and concatenated with the nonparametric estimates to form a tidy data frame. This data frame can then simply be plotted using \code{\link[ggplot2]{ggplot}}. } flexsurv/man/totlos.fs.Rd0000644000176200001440000001336114644767560015154 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{totlos.fs} \alias{totlos.fs} \title{Total length of stay in particular states for a fully-parametric, time-inhomogeneous Markov multi-state model} \usage{ totlos.fs( x, trans = NULL, t = 1, newdata = NULL, ci = FALSE, tvar = "trans", sing.inf = 1e+10, B = 1000, cl = 0.95, ... ) } \arguments{ \item{x}{A model fitted with \code{\link{flexsurvreg}}. See \code{\link{msfit.flexsurvreg}} for the required form of the model and the data. Additionally, this must be a Markov / clock-forward model, but can be time-inhomogeneous. See the package vignette for further explanation. \code{x} can also be a list of models, with one component for each permitted transition, as illustrated in \code{\link{msfit.flexsurvreg}}.} \item{trans}{Matrix indicating allowed transitions. See \code{\link{msfit.flexsurvreg}}.} \item{t}{Time or vector of times to predict up to. Must be finite.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. See \code{\link{msfit.flexsurvreg}}.} \item{ci}{Return a confidence interval calculated by simulating from the asymptotic normal distribution of the maximum likelihood estimates. Turned off by default, since this is computationally intensive. If turned on, users should increase \code{B} until the results reach the desired precision.} \item{tvar}{Variable in the data representing the transition type. Not required if \code{x} is a list of models.} \item{sing.inf}{If there is a singularity in the observed hazard, for example a Weibull distribution with \code{shape < 1} has infinite hazard at \code{t=0}, then as a workaround, the hazard is assumed to be a large finite number, \code{sing.inf}, at this time. The results should not be sensitive to the exact value assumed, but users should make sure by adjusting this parameter in these cases.} \item{B}{Number of simulations from the normal asymptotic distribution used to calculate variances. Decrease for greater speed at the expense of accuracy.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{...}{Arguments passed to \code{\link[deSolve]{ode}} in \pkg{deSolve}.} } \value{ The matrix of lengths of stay \eqn{T(t)}, if \code{t} is of length 1, or a list of matrices if \code{t} is longer. If \code{ci=TRUE}, each element has attributes \code{"lower"} and \code{"upper"} giving matrices of the corresponding confidence limits. These are formatted for printing but may be extracted using \code{attr()}. The result also has an attribute \code{P} giving the transition probability matrices, since these are unavoidably computed as a side effect. These are suppressed for printing, but can be extracted with \code{attr(...,"P")}. } \description{ The matrix whose \eqn{r,s} entry is the expected amount of time spent in state \eqn{s} for a time-inhomogeneous, continuous-time Markov multi-state process that starts in state \eqn{r}, up to a maximum time \eqn{t}. This is defined as the integral of the corresponding transition probability up to that time. } \details{ This is computed by solving a second order extension of the Kolmogorov forward differential equation numerically, using the methods in the \pkg{deSolve} package. The equation is expressed as a linear system \deqn{\frac{dT(t)}{dt} = P(t)} \deqn{\frac{dP(t)}{dt} = P(t) Q(t)} and solved for \eqn{T(t)} and \eqn{P(t)} simultaneously, where \eqn{T(t)} is the matrix of total lengths of stay, \eqn{P(t)} is the transition probability matrix for time \eqn{t}, and \eqn{Q(t)} is the transition hazard or intensity as a function of \eqn{t}. The initial conditions are \eqn{T(0) = 0} and \eqn{P(0) = I}. Note that the package \pkg{msm} has a similar method \code{totlos.msm}. \code{totlos.fs} should give the same results as \code{totlos.msm} when both of these conditions hold: \itemize{ \item the time-to-event distribution is exponential for all transitions, thus the \code{flexsurvreg} model was fitted with \code{dist="exp"}, and is time-homogeneous. \item the \pkg{msm} model was fitted with \code{exacttimes=TRUE}, thus all the event times are known, and there are no time-dependent covariates. } \pkg{msm} only allows exponential or piecewise-exponential time-to-event distributions, while \pkg{flexsurvreg} allows more flexible models. \pkg{msm} however was designed in particular for panel data, where the process is observed only at arbitrary times, thus the times of transition are unknown, which makes flexible models difficult. This function is only valid for Markov ("clock-forward") multi-state models, though no warning or error is currently given if the model is not Markov. See \code{\link{totlos.simfs}} for the equivalent for semi-Markov ("clock-reset") models. } \examples{ # BOS example in vignette, and in msfit.flexsurvreg bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) # predict 4 years spent without BOS, 3 years with BOS, before death # As t increases, this should converge totlos.fs(bexp, t=10, trans=tmat) totlos.fs(bexp, t=1000, trans=tmat) totlos.fs(bexp, t=c(5,10), trans=tmat) # Answers should match results in help(totlos.simfs) up to Monte Carlo # error there / ODE solving precision here, since with an exponential # distribution, the "semi-Markov" model there is the same as the Markov # model here } \seealso{ \code{\link{totlos.simfs}}, \code{\link{pmatrix.fs}}, \code{\link{msfit.flexsurvreg}}. } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}. } \keyword{models} \keyword{survival} flexsurv/man/GenGamma.orig.Rd0000644000176200001440000001010414165570616015614 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/GenGamma.R \name{GenGamma.orig} \alias{GenGamma.orig} \alias{dgengamma.orig} \alias{pgengamma.orig} \alias{qgengamma.orig} \alias{rgengamma.orig} \alias{Hgengamma.orig} \alias{hgengamma.orig} \title{Generalized gamma distribution (original parameterisation)} \usage{ dgengamma.orig(x, shape, scale = 1, k, log = FALSE) pgengamma.orig(q, shape, scale = 1, k, lower.tail = TRUE, log.p = FALSE) Hgengamma.orig(x, shape, scale = 1, k) hgengamma.orig(x, shape, scale = 1, k) qgengamma.orig(p, shape, scale = 1, k, lower.tail = TRUE, log.p = FALSE) rgengamma.orig(n, shape, scale = 1, k) } \arguments{ \item{x, q}{vector of quantiles.} \item{shape}{vector of ``Weibull'' shape parameters.} \item{scale}{vector of scale parameters.} \item{k}{vector of ``Gamma'' shape parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dgengamma.orig} gives the density, \code{pgengamma.orig} gives the distribution function, \code{qgengamma.orig} gives the quantile function, \code{rgengamma.orig} generates random deviates, \code{Hgengamma.orig} retuns the cumulative hazard and \code{hgengamma.orig} the hazard. } \description{ Density, distribution function, hazards, quantile function and random generation for the generalized gamma distribution, using the original parameterisation from Stacy (1962). } \details{ If \eqn{w \sim Gamma(k,1)}{w ~ Gamma(k, 1)}, then \eqn{x = \exp(w/shape + \log(scale))}{x = exp(w/shape + log(scale))} follows the original generalised gamma distribution with the parameterisation given here (Stacy 1962). Defining \code{shape}\eqn{=b>0}, \code{scale}\eqn{=a>0}, \eqn{x} has probability density \deqn{f(x | a, b, k) = \frac{b}{\Gamma(k)} \frac{x^{bk - 1}}{a^{bk}} }{ f(x | a, b, k) = (b / \Gamma(k)) (x^{bk -1} / a^{bk}) exp(-(x/a)^b)}\deqn{ \exp(-(x/a)^b)}{ f(x | a, b, k) = (b / \Gamma(k)) (x^{bk -1} / a^{bk}) exp(-(x/a)^b)} The original generalized gamma distribution simplifies to the gamma, exponential and Weibull distributions with the following parameterisations: \tabular{lcl}{ \code{dgengamma.orig(x, shape, scale, k=1)} \tab \code{=} \tab \code{\link{dweibull}(x, shape, scale)} \cr \code{dgengamma.orig(x, shape=1, scale, k)} \tab \code{=} \tab \code{\link{dgamma}(x, shape=k, scale)} \cr \code{dgengamma.orig(x, shape=1, scale, k=1)} \tab \code{=} \tab \code{\link{dexp}(x, rate=1/scale)} \cr } Also as k tends to infinity, it tends to the log normal (as in \code{\link{dlnorm}}) with the following parameters (Lawless, 1980): \code{dlnorm(x, meanlog=log(scale) + log(k)/shape, sdlog=1/(shape*sqrt(k)))} For more stable behaviour as the distribution tends to the log-normal, an alternative parameterisation was developed by Prentice (1974). This is given in \code{\link{dgengamma}}, and is now preferred for statistical modelling. It is also more flexible, including a further new class of distributions with negative shape \code{k}. The generalized F distribution \code{\link{GenF.orig}}, and its similar alternative parameterisation \code{\link{GenF}}, extend the generalized gamma to four parameters. } \references{ Stacy, E. W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statistics 33:1187-92. Prentice, R. L. (1974). A log gamma model and its maximum likelihood estimation. Biometrika 61(3):539-544. Lawless, J. F. (1980). Inference in the generalized gamma and log gamma distributions. Technometrics 22(3):409-419. } \seealso{ \code{\link{GenGamma}}, \code{\link{GenF.orig}}, \code{\link{GenF}}, \code{\link{Lognormal}}, \code{\link{GammaDist}}, \code{\link{Weibull}}. } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/unroll.function.Rd0000644000176200001440000000547014165570616016352 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/unroll.function.R \name{unroll.function} \alias{unroll.function} \title{Convert a function with matrix arguments to a function with vector arguments.} \usage{ unroll.function(mat.fn, ...) } \arguments{ \item{mat.fn}{A function with any number of arguments, some of which are matrices.} \item{\dots}{A series of other arguments. Their names define which arguments of \code{mat.fn} are matrices. Their values define a vector of strings to be appended to the names of the arguments in the new function. For example \code{fn <- unroll.function(oldfn, gamma=1:3, alpha=0:1)} will make a new function \code{fn} with arguments \code{gamma1},\code{gamma2},\code{gamma3},\code{alpha0},\code{alpha1}. Calling \code{fn(gamma1=a,gamma2=b,gamma3=c,alpha0=d,alpha1=e)} should give the same answer as \code{oldfn(gamma=cbind(a,b,c),alpha=cbind(d,e))}} } \value{ The new function, with vector arguments. } \description{ Given a function with matrix arguments, construct an equivalent function which takes vector arguments defined by the columns of the matrix. The new function simply uses \code{cbind} on the vector arguments to make a matrix, and calls the old one. } \section{Usage in \pkg{flexsurv}}{ This is used by \code{\link{flexsurvspline}} to allow spline models, which have an arbitrary number of parameters, to be fitted using \code{\link{flexsurvreg}}. The ``custom distributions'' facility of \code{\link{flexsurvreg}} expects the user-supplied probability density and distribution functions to have one explicitly named argument for each scalar parameter, and given R vectorisation, each of those arguments could be supplied as a vector of alternative parameter values. However, spline models have a varying number of scalar parameters, determined by the number of knots in the spline. \code{\link{dsurvspline}} and \code{\link{psurvspline}} have an argument called \code{gamma}. This can be supplied as a matrix, with number of columns \code{n} determined by the number of knots (plus 2), and rows referring to alternative parameter values. The following statements are used in the source of \code{flexsurvspline}: \preformatted{ dfn <- unroll.function(dsurvspline, gamma=0:(nk-1)) pfn <- unroll.function(psurvspline, gamma=0:(nk-1)) } to convert these into functions with arguments \code{gamma0}, \code{gamma1},\ldots{},\code{gamman}, corresponding to the columns of \code{gamma}, where \code{n = nk-1}, and with other arguments in the same format. } \examples{ fn <- unroll.function(ncol, x=1:3) fn(1:3, 1:3, 1:3) # equivalent to... ncol(cbind(1:3,1:3,1:3)) } \seealso{ \code{\link{flexsurvspline}},\code{\link{flexsurvreg}} } \author{ Christopher Jackson } flexsurv/man/hr_flexsurvreg.Rd0000644000176200001440000000560014366167215016253 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hr_flexsurvreg.R \name{hr_flexsurvreg} \alias{hr_flexsurvreg} \title{Hazard ratio as a function of time from a parametric survival model} \usage{ hr_flexsurvreg( x, newdata = NULL, t = NULL, start = 0, ci = TRUE, B = 1000, cl = 0.95, na.action = na.pass ) } \arguments{ \item{x}{Object returned by \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}.} \item{newdata}{A data frame with two rows, each specifying a set of covariate values. The hazard ratio is calculated as hazard(z2)/hazard(z1), where z1 is the first row of \code{newdata} and z2 is the second row. \code{newdata} must be supplied unless the model \code{x} includes just one covariate. With one covariate, a default is constructed, which defines the hazard ratio between the second and first level of the factor (if the covariate is a factor), or between a value of 1 and a value of 0 (if the covariate is numeric).} \item{t}{Times to calculate fitted values for. By default, these are the sorted unique observation (including censoring) times in the data - for left-truncated datasets these are the "stop" times.} \item{start}{Optional left-truncation time or times. The returned survival, hazard or cumulative hazard will be conditioned on survival up to this time. Predicted times returned with \code{"rmst"}, \code{"mean"}, \code{"median"} or \code{"quantile"} will be times since time zero, not times since the \code{start} time. A vector of the same length as \code{t} can be supplied to allow different truncation times for each prediction time, though this doesn't make sense in the usual case where this function is used to calculate a predicted trajectory for a single individual. This is why the default \code{start} time was changed for version 0.4 of \pkg{flexsurv} - this was previously a vector of the start times observed in the data.} \item{ci}{Set to \code{FALSE} to omit confidence intervals.} \item{B}{Number of simulations from the normal asymptotic distribution of the estimates used to calculate confidence intervals or standard errors. Decrease for greater speed at the expense of accuracy, or set \code{B=0} to turn off calculation of CIs and SEs.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{na.action}{Function determining what should be done with missing values in \code{newdata}. If \code{na.pass} (the default) then summaries of \code{NA} are produced for missing covariate values. If \code{na.omit}, then missing values are dropped, the behaviour of \code{summary.flexsurvreg} before \code{flexsurv} version 1.2.} } \value{ A data frame with estimate and confidence limits for the hazard ratio, and one row for each of the times requested in \code{t}. } \description{ Hazard ratio as a function of time from a parametric survival model } flexsurv/man/AICc.flexsurvreg.Rd0000644000176200001440000000306114470703452016312 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{AICc.flexsurvreg} \alias{AICc.flexsurvreg} \alias{AICC.flexsurvreg} \title{Second-order Akaike information criterion} \usage{ \method{AICc}{flexsurvreg}(object, cens = TRUE, ...) \method{AICC}{flexsurvreg}(object, cens = TRUE, ...) } \arguments{ \item{object}{Fitted model returned by \code{\link{flexsurvreg}} (or \code{\link{flexsurvspline}}).} \item{cens}{Include censored observations in the sample size term (\code{n}) used in this calculation. See \code{\link{BIC.flexsurvreg}} for a discussion of the issues with defining the sample size.} \item{...}{Other arguments (currently unused).} } \value{ The second-order AIC of the fitted model. } \description{ Second-order or "corrected" Akaike information criterion, often known as AICc (see, e.g. Burnham and Anderson 2002). This is defined as -2 log-likelihood + \code{(2*p*n)/(n - p -1)}, whereas the standard AIC is defined as -2 log-likelihood + \code{2*p}, where \code{p} is the number of parameters and \code{n} is the sample size. The correction is intended to adjust AIC for small-sample bias, hence it only makes a difference to the result for small \code{n}. } \details{ This can be spelt either as \code{AICC} or \code{AICc}. } \references{ Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York. } \seealso{ \code{\link{BIC}}, \code{\link{AIC}}, \code{\link{BIC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}} } flexsurv/man/coxsnell_flexsurvreg.Rd0000644000176200001440000000267114335160720017464 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/residuals.flexsurvreg.R \name{coxsnell_flexsurvreg} \alias{coxsnell_flexsurvreg} \title{Cox-Snell residuals from a parametric survival model} \usage{ coxsnell_flexsurvreg(x) } \arguments{ \item{x}{Object returned by \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}} representing a fitted survival model} } \value{ A data frame with a column called \code{est} giving the Cox-Snell residual, defined as the fitted cumulative hazard at each data point. fitted cumulative hazard at the given observed data point, and other columns indicating the observation time, observed event status, and covariate values defining the data at this point. The cumulative hazards \code{est} should form a censored sample from an Exponential(1). Therefore to check the fit of the model, plot a nonparametric estimate of the cumulative hazard curve against a diagonal line through the origin, which is the theoretical cumulative hazard trajectory of the Exponential(1). } \description{ Cox-Snell residuals from a parametric survival model } \examples{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") cs <- coxsnell_flexsurvreg(fitg) ## Model appears to fit well, with some small sample noise surv <- survfit(Surv(cs$est, ovarian$fustat) ~ 1) plot(surv, fun="cumhaz") abline(0, 1, col="red") } flexsurv/man/flexsurvmix.Rd0000644000176200001440000003462414644755662015622 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvmix.R \name{flexsurvmix} \alias{flexsurvmix} \title{Flexible parametric mixture models for times to competing events} \usage{ flexsurvmix( formula, data, event, dists, pformula = NULL, anc = NULL, partial_events = NULL, initp = NULL, inits = NULL, fixedpars = NULL, dfns = NULL, method = "direct", em.control = NULL, optim.control = NULL, aux = NULL, sr.control = survreg.control(), integ.opts, hess.control = NULL, ... ) } \arguments{ \item{formula}{Survival model formula. The left hand side is a \code{Surv} object specified as in \code{\link{flexsurvreg}}. This may define various kinds of censoring, as described in \code{\link[survival]{Surv}}. Any covariates on the right hand side of this formula will be placed on the location parameter for every component-specific distribution. Covariates on other parameters of the component-specific distributions may be supplied using the \code{anc} argument. Alternatively, \code{formula} may be a list of formulae, with one component for each alternative event. This may be used to specify different covariates on the location parameter for different components. A list of formulae may also be used to indicate that for particular individuals, different events may be observed in different ways, with different censoring mechanisms. Each list component specifies the data and censoring scheme for that mixture component. For example, suppose we are studying people admitted to hospital,and the competing states are death in hospital and discharge from hospital. At time t we know that a particular individual is still alive, but we do not know whether they are still in hospital, or have been discharged. In this case, if the individual were to die in hospital, their death time would be right censored at t. If the individual will be (or has been) discharged before death, their discharge time is completely unknown, thus interval-censored on (0,Inf). Therefore, we need to store different event time and status variables in the data for different alternative events. This is specified here as \code{formula = list("discharge" = Surv(t1di, t2di, type="interval2"), "death" = Surv(t1de, status_de))} where for this individual, \code{(t1di, t2di) = (0, Inf)} and \code{(t1de, status_de) = (t, 0)}. The "dot" notation commonly used to indicate "all remaining variables" in a formula is not supported in \code{flexsurvmix}.} \item{data}{Data frame containing variables mentioned in \code{formula}, \code{event} and \code{anc}.} \item{event}{Variable in the data that specifies which of the alternative events is observed for which individual. If the individual's follow-up is right-censored, or if the event is otherwise unknown, this variable must have the value \code{NA}. Ideally this should be a factor, since the mixture components can then be easily identified in the results with a name instead of a number. If this is not already a factor, it is coerced to one. Then the levels of the factor define the required order for the components of the list arguments \code{dists}, \code{anc}, \code{inits} and \code{dfns}. Alternatively, if the components of the list arguments are named according to the levels of \code{event}, then the components can be arranged in any order.} \item{dists}{Vector specifying the parametric distribution to use for each component. The same distributions are supported as in \code{\link{flexsurvreg}}.} \item{pformula}{Formula describing covariates to include on the component membership proabilities by multinomial logistic regression. The first component is treated as the baseline. The "dot" notation commonly used to indicate "all remaining variables" in a formula is not supported.} \item{anc}{List of component-specific lists, of length equal to the number of components. Each component-specific list is a list of formulae representing covariate effects on parameters of the distribution. If there are covariates for one component but not others, then a list containing one null formula on the location parameter should be supplied for the component with no covariates, e.g \code{list(rate=~1)} if the location parameter is called \code{rate}. Covariates on the location parameter may also be supplied here instead of in \code{formula}. Supplying them in \code{anc} allows some components but not others to have covariates on their location parameter. If a covariate on the location parameter was provided in \code{formula}, and there are covariates on other parameters, then a null formula should be included for the location parameter in \code{anc}, e.g \code{list(rate=~1)}} \item{partial_events}{List specifying the factor levels of \code{event} which indicate knowledge that an individual will not experience particular events, but may experience others. The names of the list indicate codes that indicate partial knowledge for some individuals. The list component is a vector, which must be a subset of \code{levels(event)} defining the events that a person with the corresponding event code may experience. For example, suppose there are three alternative events called \code{"disease1"},\code{"disease2"} and \code{"disease3"}, and for some individuals we know that they will not experience \code{"disease2"}, but they may experience the other two events. In that case we must create a new factor level, called, for example \code{"disease1or3"}, and set the value of \code{event} to be \code{"disease1or3"} for those individuals. Then we use the \code{"partial_events"} argument to tell \code{flexsurvmix} what the potential events are for individuals with this new factor level. \code{partial_events = list("disease1or3" = c("disease1","disease3"))}} \item{initp}{Initial values for component membership probabilities. By default, these are assumed to be equal for each component.} \item{inits}{List of component-specific vectors. Each component-specific vector contains the initial values for the parameters of the component-specific model, as would be supplied as the \code{inits} argument of \code{\link{flexsurvreg}}. By default, a heuristic is used to obtain initial values, which depends on the parametric distribution being used, but is usually based on the empirical mean and/or variance of the survival times.} \item{fixedpars}{Indexes of parameters to fix at their initial values and not optimise. Arranged in the order: baseline mixing probabilities, covariates on mixing probabilities, time-to-event parameters by mixing component. Within mixing components, time-to-event parameters are ordered in the same way as in \code{\link{flexsurvreg}}. If \code{fixedpars=TRUE} then all parameters will be fixed and the function simply calculates the log-likelihood at the initial values. Not currently supported when using the EM algorithm.} \item{dfns}{List of lists of user-defined distribution functions, one for each mixture component. Each list component is specified as the \code{dfns} argument of \code{\link{flexsurvreg}}.} \item{method}{Method for maximising the likelihood. Either \code{"em"} for the EM algorithm, or \code{"direct"} for direct maximisation.} \item{em.control}{List of settings to control EM algorithm fitting. The only options currently available are \code{trace} set to 1 to print the parameter estimates at each iteration of the EM algorithm \code{reltol} convergence criterion. The algorithm stops if the log likelihood changes by a relative amount less than \code{reltol}. The default is the same as in \code{\link{optim}}, that is, \code{sqrt(.Machine$double.eps)}. \code{var.method} method to compute the covariance matrix. \code{"louis"} for the method of Louis (1982), or \code{"direct"}for direct numerical calculation of the Hessian of the log likelihood. \code{optim.p.control} A list that is passed as the \code{control} argument to \code{optim} in the M step for the component membership probability parameters. The optimisation in the M step for the time-to-event parameters can be controlled by the \code{optim.control} argument to \code{flexsurvmix}. For example, \code{em.control = list(trace=1, reltol=1e-12)}.} \item{optim.control}{List of options to pass as the \code{control} argument to \code{\link{optim}}, which is used by \code{method="direct"} or in the M step for the time-to-event parameters in \code{method="em"}. By default, this uses \code{fnscale=10000} and \code{ndeps=rep(1e-06,p)} where \code{p} is the number of parameters being estimated, unless the user specifies these options explicitly.} \item{aux}{A named list of other arguments to pass to custom distribution functions. This is used, for example, by \code{\link{flexsurvspline}} to supply the knot locations and modelling scale (e.g. hazard or odds). This cannot be used to fix parameters of a distribution --- use \code{fixedpars} for that.} \item{sr.control}{For the models which use \code{\link[survival]{survreg}} to find the maximum likelihood estimates (Weibull, exponential, log-normal), this list is passed as the \code{control} argument to \code{\link[survival]{survreg}}.} \item{integ.opts}{List of named arguments to pass to \code{\link{integrate}}, if a custom density or hazard is provided without its cumulative version. For example, \code{integ.opts = list(rel.tol=1e-12)}} \item{hess.control}{List of options to control covariance matrix computation. Available options are: \code{numeric}. If \code{TRUE} then numerical methods are used to compute the Hessian for models where an analytic Hessian is available. These models include the Weibull (both versions), exponential, Gompertz and spline models with hazard or odds scale. The default is to use the analytic Hessian for these models. For all other models, numerical methods are always used to compute the Hessian, whether or not this option is set. \code{tol.solve}. The tolerance used for \code{\link{solve}} when inverting the Hessian (default \code{.Machine$double.eps}) \code{tol.evalues} The accepted tolerance for negative eigenvalues in the covariance matrix (default \code{1e-05}). The Hessian is positive definite, thus invertible, at the maximum likelihood. If the Hessian computed after optimisation convergence can't be inverted, this is either because the converged result is not the maximum likelihood (e.g. it could be a "saddle point"), or because the numerical methods used to obtain the Hessian were inaccurate. If you suspect that the Hessian was computed wrongly enough that it is not invertible, but not wrongly enough that the nearest valid inverse would be an inaccurate estimate of the covariance matrix, then these tolerance values can be modified (reducing \code{tol.solve} or increasing \code{tol.evalues}) to allow the inverse to be computed.} \item{...}{Optional arguments to the general-purpose optimisation routine \code{\link{optim}}. For example, the BFGS optimisation algorithm is the default in \code{\link{flexsurvreg}}, but this can be changed, for example to \code{method="Nelder-Mead"} which can be more robust to poor initial values. If the optimisation fails to converge, consider normalising the problem using, for example, \code{control=list(fnscale = 2500)}, for example, replacing 2500 by a number of the order of magnitude of the likelihood. If 'false' convergence is reported with a non-positive-definite Hessian, then consider tightening the tolerance criteria for convergence. If the optimisation takes a long time, intermediate steps can be printed using the \code{trace} argument of the control list. See \code{\link{optim}} for details.} } \value{ List of objects containing information about the fitted model. The important one is \code{res}, a data frame containing the parameter estimates and associated information. } \description{ In a mixture model for competing events, an individual can experience one of a set of different events. We specify a model for the probability that they will experience each event before the others, and a model for the time to the event conditionally on that event occurring first. } \details{ This differs from the more usual "competing risks" models, where we specify "cause-specific hazards" describing the time to each competing event. This time will not be observed for an individual if one of the competing events happens first. The event that happens first is defined by the minimum of the times to the alternative events. The \code{flexsurvmix} function fits a mixture model to data consisting of a single time to an event for each individual, and an indicator for what type of event occurs for that individual. The time to event may be observed or censored, just as in \code{\link{flexsurvreg}}, and the type of event may be known or unknown. In a typical application, where we follow up a set of individuals until they experience an event or a maximum follow-up time is reached, the event type is known if the time is observed, and the event type is unknown when follow-up ends and the time is right-censored. The model is fitted by maximum likelihood, either directly or by using an expectation-maximisation (EM) algorithm, by wrapping \code{\link{flexsurvreg}} to compute the likelihood or to implement the E and M steps. Some worked examples are given in the package vignette about multi-state modelling, which can be viewed by running \code{vignette("multistate", package="flexsurv")}. } \references{ Jackson, C. H. and Tom, B. D. M. and Kirwan, P. D. and Mandal, S. and Seaman, S. R. and Kunzmann, K. and Presanis, A. M. and De Angelis, D. (2022) A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19. Statistical Methods in Medical Research 31(9) 1656-1674. Larson, M. G., & Dinse, G. E. (1985). A mixture model for the regression analysis of competing risks data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 34(3), 201-211. Lau, B., Cole, S. R., & Gange, S. J. (2009). Competing risk regression models for epidemiologic data. American Journal of Epidemiology, 170(2), 244-256. } flexsurv/man/summary.flexsurvrtrunc.Rd0000644000176200001440000000463314165570616020023 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvrtrunc.R \name{summary.flexsurvrtrunc} \alias{summary.flexsurvrtrunc} \title{Summarise quantities of interest from fitted flexsurvrtrunc models} \usage{ \method{summary}{flexsurvrtrunc}( object, type = "survival", fn = NULL, t = NULL, quantiles = 0.5, ci = TRUE, se = FALSE, B = 1000, cl = 0.95, ... ) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{type}{\code{"survival"} for survival probabilities. \code{"cumhaz"} for cumulative hazards. \code{"hazard"} for hazards. \code{"rmst"} for restricted mean survival. \code{"mean"} for mean survival. \code{"median"} for median survival (alternative to \code{type="quantile"} with \code{quantiles=0.5}). \code{"quantile"} for quantiles of the survival time distribution. Ignored if \code{"fn"} is specified.} \item{fn}{Custom function of the parameters to summarise against time. This has optional first argument \code{t} representing time, and any remaining arguments must be parameters of the distribution. It should return a vector of the same length as \code{t}.} \item{t}{Times to calculate fitted values for. By default, these are the sorted unique observation (including censoring) times in the data - for left-truncated datasets these are the "stop" times.} \item{quantiles}{If \code{type="quantile"}, this specifies the quantiles of the survival time distribution to return estimates for.} \item{ci}{Set to \code{FALSE} to omit confidence intervals.} \item{se}{Set to \code{TRUE} to include standard errors.} \item{B}{Number of simulations from the normal asymptotic distribution of the estimates used to calculate confidence intervals or standard errors. Decrease for greater speed at the expense of accuracy, or set \code{B=0} to turn off calculation of CIs and SEs.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{...}{Further arguments passed to or from other methods. Currently unused.} } \description{ This function extracts quantities of interest from the untruncated version of a model with individual-specific right truncation points fitted by \code{\link{flexsurvrtrunc}}. Note that covariates are currently not supported by \code{\link{flexsurvrtrunc}}. } flexsurv/man/qgeneric.Rd0000644000176200001440000000523114165570616015003 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/utils.R \name{qgeneric} \alias{qgeneric} \title{Generic function to find quantiles of a distribution} \usage{ qgeneric(pdist, p, matargs = NULL, scalarargs = NULL, ...) } \arguments{ \item{pdist}{Probability distribution function, for example, \code{\link{pnorm}} for the normal distribution, which must be defined in the current workspace. This should accept and return vectorised parameters and values. It should also return the correct values for the entire real line, for example a positive distribution should have \code{pdist(x)==0} for \eqn{x<0}.} \item{p}{Vector of probabilities to find the quantiles for.} \item{matargs}{Character vector giving the elements of \code{...} which represent vector parameters of the distribution. Empty by default. When vectorised, these will become matrices. This is used for the arguments \code{gamma} and \code{knots} in \code{\link{qsurvspline}}.} \item{scalarargs}{Character vector naming scalar arguments of the distribution function that cannot be vectorised. This is used for the arguments \code{scale} and \code{timescale} in \code{\link{qsurvspline}}.} \item{...}{The remaining arguments define parameters of the distribution \code{pdist}. These MUST be named explicitly. This may also contain the standard arguments \code{log.p} (logical; default \code{FALSE}, if \code{TRUE}, probabilities p are given as log(p)), and \code{lower.tail} (logical; if \code{TRUE} (default), probabilities are P[X <= x] otherwise, P[X > x].). If the distribution is bounded above or below, then this should contain arguments \code{lbound} and \code{ubound} respectively, and these will be returned if \code{p} is 0 or 1 respectively. Defaults to \code{-Inf} and \code{Inf} respectively.} } \value{ Vector of quantiles of the distribution at \code{p}. } \description{ Generic function to find the quantiles of a distribution, given the equivalent probability distribution function. } \details{ This function is used by default for custom distributions for which a quantile function is not provided. It works by finding the root of the equation \eqn{h(q) = pdist(q) - p = 0}. Starting from the interval \eqn{(-1, 1)}, the interval width is expanded by 50\% until \eqn{h()} is of opposite sign at either end. The root is then found using \code{\link{uniroot}}. This assumes a suitably smooth, continuous distribution. } \examples{ qnorm(c(0.025, 0.975), 0, 1) qgeneric(pnorm, c(0.025, 0.975), mean=0, sd=1) # must name the arguments } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/lines.flexsurvreg.Rd0000644000176200001440000000435014165570616016674 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plot.flexsurvreg.R \name{lines.flexsurvreg} \alias{lines.flexsurvreg} \title{Add fitted flexible survival curves to a plot} \usage{ \method{lines}{flexsurvreg}( x, newdata = NULL, X = NULL, type = "survival", t = NULL, est = TRUE, ci = NULL, B = 1000, cl = 0.95, col = "red", lty = 1, lwd = 2, col.ci = NULL, lty.ci = 2, lwd.ci = 1, ... ) } \arguments{ \item{x}{Output from \code{\link{flexsurvreg}}, representing a fitted survival model object.} \item{newdata}{Covariate values to produce fitted curves for, as a data frame, as described in \code{\link{plot.flexsurvreg}}.} \item{X}{Covariate values to produce fitted curves for, as a matrix, as described in \code{\link{plot.flexsurvreg}}.} \item{type}{\code{"survival"} for survival, \code{"cumhaz"} for cumulative hazard, or \code{"hazard"} for hazard, as in \code{\link{plot.flexsurvreg}}.} \item{t}{Vector of times to plot fitted values for.} \item{est}{Plot fitted curves (\code{TRUE} or \code{FALSE}.)} \item{ci}{Plot confidence intervals for fitted curves.} \item{B}{Number of simulations controlling accuracy of confidence intervals, as used in \code{\link[=summary.flexsurvreg]{summary}}.} \item{cl}{Width of confidence intervals, by default 0.95 for 95\% intervals.} \item{col}{Colour of the fitted curve(s).} \item{lty}{Line type of the fitted curve(s).} \item{lwd}{Line width of the fitted curve(s).} \item{col.ci}{Colour of the confidence limits, defaulting to the same as for the fitted curve.} \item{lty.ci}{Line type of the confidence limits.} \item{lwd.ci}{Line width of the confidence limits, defaulting to the same as for the fitted curve.} \item{...}{Other arguments to be passed to the generic \code{\link{plot}} and \code{\link{lines}} functions.} } \description{ Add fitted survival (or hazard or cumulative hazard) curves from a \code{\link{flexsurvreg}} model fit to an existing plot. } \details{ Equivalent to \code{\link{plot.flexsurvreg}(...,add=TRUE)}. } \seealso{ \code{\link{flexsurvreg}} } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{aplot} \keyword{models} flexsurv/man/pmatrix.fs.Rd0000644000176200001440000001354514644755663015321 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{pmatrix.fs} \alias{pmatrix.fs} \title{Transition probability matrix from a fully-parametric, time-inhomogeneous Markov multi-state model} \usage{ pmatrix.fs( x, trans = NULL, t = 1, newdata = NULL, condstates = NULL, ci = FALSE, tvar = "trans", sing.inf = 1e+10, B = 1000, cl = 0.95, tidy = FALSE, ... ) } \arguments{ \item{x}{A model fitted with \code{\link{flexsurvreg}}. See \code{\link{msfit.flexsurvreg}} for the required form of the model and the data. Additionally, this must be a Markov / clock-forward model, but can be time-inhomogeneous. See the package vignette for further explanation. \code{x} can also be a list of models, with one component for each permitted transition, as illustrated in \code{\link{msfit.flexsurvreg}}.} \item{trans}{Matrix indicating allowed transitions. See \code{\link{msfit.flexsurvreg}}.} \item{t}{Time or vector of times to predict state occupancy probabilities for.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. See \code{\link{msfit.flexsurvreg}}.} \item{condstates}{xInstead of the unconditional probability of being in state \eqn{s} at time \eqn{t} given state \eqn{r} at time 0, return the probability conditional on being in a particular subset of states at time \eqn{t}. This subset is specified in the \code{condstates} argument, as a vector of character labels or integers. This is used, for example, in competing risks situations, e.g. if the competing states are death or recovery from a disease, and we want to compute the probability a patient has died, given they have died or recovered. If these are absorbing states, then as \eqn{t} increases, this converges to the case fatality ratio. To compute this, set \eqn{t} to a very large number, \code{Inf} will not work.} \item{ci}{Return a confidence interval calculated by simulating from the asymptotic normal distribution of the maximum likelihood estimates. Turned off by default, since this is computationally intensive. If turned on, users should increase \code{B} until the results reach the desired precision.} \item{tvar}{Variable in the data representing the transition type. Not required if \code{x} is a list of models.} \item{sing.inf}{If there is a singularity in the observed hazard, for example a Weibull distribution with \code{shape < 1} has infinite hazard at \code{t=0}, then as a workaround, the hazard is assumed to be a large finite number, \code{sing.inf}, at this time. The results should not be sensitive to the exact value assumed, but users should make sure by adjusting this parameter in these cases.} \item{B}{Number of simulations from the normal asymptotic distribution used to calculate variances. Decrease for greater speed at the expense of accuracy.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{tidy}{If TRUE then return the results as a tidy data frame} \item{...}{Arguments passed to \code{\link[deSolve]{ode}} in \pkg{deSolve}.} } \value{ The transition probability matrix, if \code{t} is of length 1. If \code{t} is longer, return a list of matrices, or a data frame if \code{tidy} is TRUE. If \code{ci=TRUE}, each element has attributes \code{"lower"} and \code{"upper"} giving matrices of the corresponding confidence limits. These are formatted for printing but may be extracted using \code{attr()}. } \description{ The transition probability matrix for time-inhomogeneous Markov multi-state models fitted to time-to-event data with \code{\link{flexsurvreg}}. This has \eqn{r,s} entry giving the probability that an individual is in state \eqn{s} at time \eqn{t}, given they are in state \eqn{r} at time \eqn{0}. } \details{ This is computed by solving the Kolmogorov forward differential equation numerically, using the methods in the \pkg{deSolve} package. The equation is \deqn{\frac{dP(t)}{dt} = P(t) Q(t)} where \eqn{P(t)} is the transition probability matrix for time \eqn{t}, and \eqn{Q(t)} is the transition hazard or intensity as a function of \eqn{t}. The initial condition is \eqn{P(0) = I}. Note that the package \pkg{msm} has a similar method \code{pmatrix.msm}. \code{pmatrix.fs} should give the same results as \code{pmatrix.msm} when both of these conditions hold: \itemize{ \item the time-to-event distribution is exponential for all transitions, thus the \code{flexsurvreg} model was fitted with \code{dist="exp"} and the model is time-homogeneous. \item the \pkg{msm} model was fitted with \code{exacttimes=TRUE}, thus all the event times are known, and there are no time-dependent covariates. } \pkg{msm} only allows exponential or piecewise-exponential time-to-event distributions, while \pkg{flexsurvreg} allows more flexible models. \pkg{msm} however was designed in particular for panel data, where the process is observed only at arbitrary times, thus the times of transition are unknown, which makes flexible models difficult. This function is only valid for Markov ("clock-forward") multi-state models, though no warning or error is currently given if the model is not Markov. See \code{\link{pmatrix.simfs}} for the equivalent for semi-Markov ("clock-reset") models. } \examples{ # BOS example in vignette, and in msfit.flexsurvreg bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) # more likely to be dead (state 3) as time moves on, or if start with # BOS (state 2) pmatrix.fs(bexp, t=c(5,10), trans=tmat) } \seealso{ \code{\link{pmatrix.simfs}}, \code{\link{totlos.fs}}, \code{\link{msfit.flexsurvreg}}. } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}. } \keyword{models} \keyword{survival} flexsurv/man/vcov.flexsurvreg.Rd0000644000176200001440000000125214471101454016523 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{vcov.flexsurvreg} \alias{vcov.flexsurvreg} \title{Variance-covariance matrix from a flexsurvreg model} \usage{ \method{vcov}{flexsurvreg}(object, ...) } \arguments{ \item{object}{A fitted model object of class \code{\link{flexsurvreg}}, e.g. as returned by \code{flexsurvreg} or \code{flexsurvspline}.} \item{...}{Other arguments (currently unused).} } \value{ Variance-covariance matrix of the estimated parameters, on the scale that they were estimated on (for positive parameters this is the log scale). } \description{ Variance-covariance matrix from a flexsurvreg model } flexsurv/man/pmatrix.simfs.Rd0000644000176200001440000001222014523723770016005 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{pmatrix.simfs} \alias{pmatrix.simfs} \title{Transition probability matrix from a fully-parametric, semi-Markov multi-state model} \usage{ pmatrix.simfs( x, trans, t = 1, newdata = NULL, ci = FALSE, tvar = "trans", tcovs = NULL, M = 1e+05, B = 1000, cl = 0.95, cores = NULL, tidy = FALSE ) } \arguments{ \item{x}{A model fitted with \code{\link{flexsurvreg}}. See \code{\link{msfit.flexsurvreg}} for the required form of the model and the data. Additionally this should be semi-Markov, so that the time variable represents the time since the last transition. In other words the response should be of the form \code{Surv(time,status)}. See the package vignette for further explanation. \code{x} can also be a list of \code{\link{flexsurvreg}} models, with one component for each permitted transition, as illustrated in \code{\link{msfit.flexsurvreg}}. This can be constructed by \code{\link{fmsm}}.} \item{trans}{Matrix indicating allowed transitions. See \code{\link{msfit.flexsurvreg}}. This is not required if \code{x} is a list constructed by \code{\link{fmsm}}.} \item{t}{Time to predict state occupancy probabilities for. This can be a single number or a vector of different numbers.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. See \code{\link{msfit.flexsurvreg}}.} \item{ci}{Return a confidence interval calculated by simulating from the asymptotic normal distribution of the maximum likelihood estimates. This is turned off by default, since two levels of simulation are required. If turned on, users should adjust \code{B} and/or \code{M} until the results reach the desired precision. The simulation over \code{M} is generally vectorised, therefore increasing \code{B} is usually more expensive than increasing \code{M}.} \item{tvar}{Variable in the data representing the transition type. Not required if \code{x} is a list of models.} \item{tcovs}{Predictable time-dependent covariates such as age, see \code{\link{sim.fmsm}}.} \item{M}{Number of individuals to simulate in order to approximate the transition probabilities. Users should adjust this to obtain the required precision.} \item{B}{Number of simulations from the normal asymptotic distribution used to calculate confidence limits. Decrease for greater speed at the expense of accuracy.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{cores}{Number of processor cores used when calculating confidence limits by repeated simulation. The default uses single-core processing.} \item{tidy}{If \code{TRUE} then the results are returned as a tidy data frame with columns for the estimate and confidence limits, and rows per state transition and time interval.} } \value{ The transition probability matrix. If \code{ci=TRUE}, there are attributes \code{"lower"} and \code{"upper"} giving matrices of the corresponding confidence limits. These are formatted for printing but may be extracted using \code{attr()}. } \description{ The transition probability matrix for semi-Markov multi-state models fitted to time-to-event data with \code{\link{flexsurvreg}}. This has \eqn{r,s} entry giving the probability that an individual is in state \eqn{s} at time \eqn{t}, given they are in state \eqn{r} at time \eqn{0}. } \details{ This is computed by simulating a large number of individuals \code{M} using the maximum likelihood estimates of the fitted model and the function \code{\link{sim.fmsm}}. Therefore this requires a random sampling function for the parametric survival model to be available: see the "Details" section of \code{\link{sim.fmsm}}. This will be available for all built-in distributions, though users may need to write this for custom models. Note the random sampling method for \code{flexsurvspline} models is currently very inefficient, so that looping over the \code{M} individuals will be very slow. \code{\link{pmatrix.fs}} is a more efficient method based on solving the Kolmogorov forward equation numerically, which requires the multi-state model to be Markov. No error or warning is given if running \code{\link{pmatrix.simfs}} with a Markov model, but this is still invalid. } \examples{ # BOS example in vignette, and in msfit.flexsurvreg bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) # more likely to be dead (state 3) as time moves on, or if start with # BOS (state 2) pmatrix.simfs(bexp, t=5, trans=tmat) pmatrix.simfs(bexp, t=10, trans=tmat) # these results should converge to those in help(pmatrix.fs), as M # increases here and ODE solving precision increases there, since with # an exponential distribution, the semi-Markov model is the same as the # Markov model. } \seealso{ \code{\link{pmatrix.fs}},\code{\link{sim.fmsm}},\code{\link{totlos.simfs}}, \code{\link{msfit.flexsurvreg}}. } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}. } \keyword{models} \keyword{survival} flexsurv/man/reexports.Rd0000644000176200001440000000077714165570616015253 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/broom-funs.R \docType{import} \name{reexports} \alias{reexports} \alias{tidy} \alias{glance} \alias{augment} \title{Objects exported from other packages} \keyword{internal} \description{ These objects are imported from other packages. Follow the links below to see their documentation. \describe{ \item{generics}{\code{\link[generics]{augment}}, \code{\link[generics]{glance}}, \code{\link[generics]{tidy}}} }} flexsurv/man/WeibullPH.Rd0000644000176200001440000000556614171772374015056 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/WeibullPH.R \name{WeibullPH} \alias{WeibullPH} \alias{dweibullPH} \alias{pweibullPH} \alias{qweibullPH} \alias{rweibullPH} \alias{HweibullPH} \alias{hweibullPH} \title{Weibull distribution in proportional hazards parameterisation} \usage{ dweibullPH(x, shape, scale = 1, log = FALSE) pweibullPH(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) qweibullPH(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) hweibullPH(x, shape, scale = 1, log = FALSE) HweibullPH(x, shape, scale = 1, log = FALSE) rweibullPH(n, shape, scale = 1) } \arguments{ \item{x, q}{Vector of quantiles.} \item{shape}{Vector of shape parameters.} \item{scale}{Vector of scale parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{Vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dweibullPH} gives the density, \code{pweibullPH} gives the distribution function, \code{qweibullPH} gives the quantile function, \code{rweibullPH} generates random deviates, \code{HweibullPH} retuns the cumulative hazard and \code{hweibullPH} the hazard. } \description{ Density, distribution function, hazards, quantile function and random generation for the Weibull distribution in its proportional hazards parameterisation. } \details{ The Weibull distribution in proportional hazards parameterisation with `shape' parameter a and `scale' parameter m has density given by \deqn{f(x) = a m x^{a-1} exp(- m x^a) } cumulative distribution function \eqn{F(x) = 1 - exp( -m x^a )}, survivor function \eqn{S(x) = exp( -m x^a )}, cumulative hazard \eqn{m x^a} and hazard \eqn{a m x^{a-1}}. \code{\link{dweibull}} in base R has the alternative 'accelerated failure time' (AFT) parameterisation with shape a and scale b. The shape parameter \eqn{a} is the same in both versions. The scale parameters are related as \eqn{b = m^{-1/a}}, equivalently m = b^-a. In survival modelling, covariates are typically included through a linear model on the log scale parameter. Thus, in the proportional hazards model, the coefficients in such a model on \eqn{m} are interpreted as log hazard ratios. In the AFT model, covariates on \eqn{b} are interpreted as time acceleration factors. For example, doubling the value of a covariate with coefficient \eqn{beta=log(2)} would give half the expected survival time. These coefficients are related to the log hazard ratios \eqn{\gamma} as \eqn{\beta = -\gamma / a}. } \seealso{ \code{\link{dweibull}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/totlos.simfs.Rd0000644000176200001440000001143414523723770015653 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{totlos.simfs} \alias{totlos.simfs} \title{Expected total length of stay in specific states, from a fully-parametric, semi-Markov multi-state model} \usage{ totlos.simfs( x, trans, t = 1, start = 1, newdata = NULL, ci = FALSE, tvar = "trans", tcovs = NULL, group = NULL, M = 1e+05, B = 1000, cl = 0.95, cores = NULL ) } \arguments{ \item{x}{A model fitted with \code{\link{flexsurvreg}}. See \code{\link{msfit.flexsurvreg}} for the required form of the model and the data. Additionally this should be semi-Markov, so that the time variable represents the time since the last transition. In other words the response should be of the form \code{Surv(time,status)}. See the package vignette for further explanation. \code{x} can also be a list of \code{\link{flexsurvreg}} models, with one component for each permitted transition, as illustrated in \code{\link{msfit.flexsurvreg}}. This can be constructed by \code{\link{fmsm}}.} \item{trans}{Matrix indicating allowed transitions. See \code{\link{msfit.flexsurvreg}}. This is not required if \code{x} is a list constructed by \code{\link{fmsm}}.} \item{t}{Maximum time to predict to.} \item{start}{Starting state.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. See \code{\link{msfit.flexsurvreg}}.} \item{ci}{Return a confidence interval calculated by simulating from the asymptotic normal distribution of the maximum likelihood estimates. This is turned off by default, since two levels of simulation are required. If turned on, users should adjust \code{B} and/or \code{M} until the results reach the desired precision. The simulation over \code{M} is generally vectorised, therefore increasing \code{B} is usually more expensive than increasing \code{M}.} \item{tvar}{Variable in the data representing the transition type. Not required if \code{x} is a list of models.} \item{tcovs}{Predictable time-dependent covariates such as age, see \code{\link{sim.fmsm}}.} \item{group}{Optional grouping for the states. For example, if there are four states, and \code{group=c(1,1,2,2)}, then \code{\link{totlos.simfs}} returns the expected total time in states 1 and 2 combined, and states 3 and 4 combined.} \item{M}{Number of individuals to simulate in order to approximate the transition probabilities. Users should adjust this to obtain the required precision.} \item{B}{Number of simulations from the normal asymptotic distribution used to calculate confidence limits. Decrease for greater speed at the expense of accuracy.} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{cores}{Number of processor cores used when calculating confidence limits by repeated simulation. The default uses single-core processing.} } \value{ The expected total time spent in each state (or group of states given by \code{group}) up to time \code{t}, and corresponding confidence intervals if requested. } \description{ The expected total time spent in each state for semi-Markov multi-state models fitted to time-to-event data with \code{\link{flexsurvreg}}. This is defined by the integral of the transition probability matrix, though this is not analytically possible and is computed by simulation. } \details{ This is computed by simulating a large number of individuals \code{M} using the maximum likelihood estimates of the fitted model and the function \code{\link{sim.fmsm}}. Therefore this requires a random sampling function for the parametric survival model to be available: see the "Details" section of \code{\link{sim.fmsm}}. This will be available for all built-in distributions, though users may need to write this for custom models. Note the random sampling method for \code{flexsurvspline} models is currently very inefficient, so that looping over \code{M} will be very slow. The equivalent function for time-inhomogeneous Markov models is \code{\link{totlos.fs}}. Note neither of these functions give errors or warnings if used with the wrong type of model, but the results will be invalid. } \examples{ # BOS example in vignette, and in msfit.flexsurvreg bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) # predict 4 years spent without BOS, 3 years with BOS, before death # As t increases, this should converge totlos.simfs(bexp, t=10, trans=tmat) totlos.simfs(bexp, t=1000, trans=tmat) } \seealso{ \code{\link{pmatrix.simfs}},\code{\link{sim.fmsm}},\code{\link{msfit.flexsurvreg}}. } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}. } \keyword{models} \keyword{survival} flexsurv/man/plot_survtrunc.Rd0000644000176200001440000000125314644755665016332 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/survrtrunc.R \name{plot.survrtrunc} \alias{plot.survrtrunc} \alias{lines.survrtrunc} \title{Plot nonparametric estimates of survival from right-truncated data.} \usage{ \method{plot}{survrtrunc}(x, ...) \method{lines}{survrtrunc}(x, ...) } \arguments{ \item{x}{Object of class \code{"survrtrunc"} as returned by \code{\link{survrtrunc}}.} \item{...}{Other arguments to be passed to \code{\link[survival]{plot.survfit}} or \code{\link[survival]{lines.survfit}}.} } \description{ \code{plot.survrtrunc} creates a new plot, while \code{lines.survrtrunc} adds lines to an exising plot. } flexsurv/man/logLik.flexsurvreg.Rd0000644000176200001440000000133714471101454016773 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{logLik.flexsurvreg} \alias{logLik.flexsurvreg} \title{Log likelihood from a flexsurvreg model} \usage{ \method{logLik}{flexsurvreg}(object, ...) } \arguments{ \item{object}{A fitted model object of class \code{\link{flexsurvreg}}, e.g. as returned by \code{flexsurvreg} or \code{flexsurvspline}.} \item{...}{Other arguments (currently unused).} } \value{ Log-likelihood (numeric) with additional attributes \code{df} (degrees of freedom, or number of parameters that were estimated), and number of observations \code{nobs} (including observed events and censored observations). } \description{ Log likelihood from a flexsurvreg model } flexsurv/man/ajfit_fmsm.Rd0000644000176200001440000000316014476637567015342 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ajfit.R \name{ajfit_fmsm} \alias{ajfit_fmsm} \title{Check the fit of Markov flexible parametric multi-state models against nonparametric estimates.} \usage{ ajfit_fmsm(x, maxt = NULL, newdata = NULL) } \arguments{ \item{x}{Object returned by \code{\link{fmsm}} representing a flexible parametric multi-state model. This must be Markov, rather than semi-Markov, and no check is performed for this. Note that all "competing risks" style models, with just one source state and multiple destination states, are Markov, so those are fine here.} \item{maxt}{Maximum time to compute parametric estimates to.} \item{newdata}{Data frame defining the subgroups to consider. This must have a column for each covariate in the model. If omitted, then all potential subgroups defined by combinations of factor covariates are included. Continuous covariates are not supported.} } \value{ Tidy data frame containing both Aalen-Johansen and parametric estimates of state occupancy over time, and by subgroup if subgroups are included. } \description{ Computes both parametric and comparable Aalen-Johansen nonparametric estimates from a flexible parametric multi-state model, and returns them together in a tidy data frame. Only models with no covariates, or only factor covariates, are supported. If there are factor covariates, then the nonparametric estimates are computed for subgroups defined by combinations of the covariates. Another restriction of this function is that all transitions must have the same covariates on them. } flexsurv/man/Survspline.Rd0000644000176200001440000001420114532367563015360 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/spline.R \name{Survspline} \alias{Survspline} \alias{dsurvspline} \alias{psurvspline} \alias{qsurvspline} \alias{rsurvspline} \alias{hsurvspline} \alias{Hsurvspline} \alias{mean_survspline} \alias{rmst_survspline} \title{Royston/Parmar spline survival distribution} \usage{ dsurvspline( x, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0, log = FALSE ) psurvspline( q, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0, lower.tail = TRUE, log.p = FALSE ) qsurvspline( p, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0, lower.tail = TRUE, log.p = FALSE ) rsurvspline( n, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0 ) Hsurvspline( x, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0 ) hsurvspline( x, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0 ) rmst_survspline( t, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0, start = 0 ) mean_survspline( gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", offset = 0 ) } \arguments{ \item{x, q, t}{Vector of times.} \item{gamma}{Parameters describing the baseline spline function, as described in \code{\link{flexsurvspline}}. This may be supplied as a vector with number of elements equal to the length of \code{knots}, in which case the parameters are common to all times. Alternatively a matrix may be supplied, with rows corresponding to different times, and columns corresponding to \code{knots}.} \item{beta}{Vector of covariate effects. Not supported and ignored since version 2.3, and this argument will be removed in 2.4.} \item{X}{Matrix of covariate values. Not supported and ignored since version 2.3, and this argument will be removed in 2.4.} \item{knots}{Locations of knots on the axis of log time, supplied in increasing order. Unlike in \code{\link{flexsurvspline}}, these include the two boundary knots. If there are no additional knots, the boundary locations are not used. If there are one or more additional knots, the boundary knots should be at or beyond the minimum and maximum values of the log times. In \code{\link{flexsurvspline}} these are exactly at the minimum and maximum values. This may in principle be supplied as a matrix, in the same way as for \code{gamma}, but in most applications the knots will be fixed.} \item{scale}{\code{"hazard"}, \code{"odds"}, or \code{"normal"}, as described in \code{\link{flexsurvspline}}. With the default of no knots in addition to the boundaries, this model reduces to the Weibull, log-logistic and log-normal respectively. The scale must be common to all times.} \item{timescale}{\code{"log"} or \code{"identity"} as described in \code{\link{flexsurvspline}}.} \item{spline}{\code{"rp"} to use the natural cubic spline basis described in Royston and Parmar. \code{"splines2ns"} to use the alternative natural cubic spline basis from the \code{splines2} package (Wang and Yan 2021), which may be better behaved due to the basis being orthogonal.} \item{offset}{An extra constant to add to the linear predictor \eqn{\eta}{eta}. Not supported and ignored since version 2.3, and this argument will be removed in 2.4.} \item{log, log.p}{Return log density or probability.} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{Vector of probabilities.} \item{n}{Number of random numbers to simulate.} \item{start}{Optional left-truncation time or times. The returned restricted mean survival will be conditioned on survival up to this time.} } \value{ \code{dsurvspline} gives the density, \code{psurvspline} gives the distribution function, \code{hsurvspline} gives the hazard and \code{Hsurvspline} gives the cumulative hazard, as described in \code{\link{flexsurvspline}}. \code{qsurvspline} gives the quantile function, which is computed by crude numerical inversion (using \code{\link{qgeneric}}). \code{rsurvspline} generates random survival times by using \code{qsurvspline} on a sample of uniform random numbers. Due to the numerical root-finding involved in \code{qsurvspline}, it is slow compared to typical random number generation functions. } \description{ Probability density, distribution, quantile, random generation, hazard, cumulative hazard, mean and restricted mean functions for the Royston/Parmar spline model. These functions have all parameters of the distribution collected together in a single argument \code{gamma}. For the equivalent functions with one argument per parameter, see \code{\link{Survsplinek}}. } \examples{ ## reduces to the weibull regscale <- 0.786; cf <- 1.82 a <- 1/regscale; b <- exp(cf) dweibull(1, shape=a, scale=b) dsurvspline(1, gamma=c(log(1 / b^a), a)) # should be the same ## reduces to the log-normal meanlog <- 1.52; sdlog <- 1.11 dlnorm(1, meanlog, sdlog) dsurvspline(1, gamma = c(-meanlog/sdlog, 1/sdlog), scale="normal") # should be the same } \references{ Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197. Wang W, Yan J (2021). Shape-Restricted Regression Splines with R Package splines2. Journal of Data Science, 19(3), 498-517. } \seealso{ \code{\link{flexsurvspline}}. } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/normboot.flexsurvreg.Rd0000644000176200001440000000624314366167215017424 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvreg.R \name{normboot.flexsurvreg} \alias{normboot.flexsurvreg} \title{Simulate from the asymptotic normal distribution of parameter estimates.} \usage{ normboot.flexsurvreg( x, B, newdata = NULL, X = NULL, transform = FALSE, raw = FALSE, tidy = FALSE, rawsim = NULL ) } \arguments{ \item{x}{A fitted model from \code{\link{flexsurvreg}} (or \code{\link{flexsurvspline}}).} \item{B}{Number of samples.} \item{newdata}{Data frame or list containing the covariate values to evaluate the parameters at. If there are covariates in the model, at least one of \code{newdata} or \code{X} must be supplied, unless \code{raw=TRUE}.} \item{X}{Alternative (less convenient) format for covariate values: a matrix with one row, with one column for each covariate or factor contrast. Formed from all the "model matrices", one for each named parameter of the distribution, with intercepts excluded, \code{cbind}ed together.} \item{transform}{\code{TRUE} if the results should be transformed to the real-line scale, typically by log if the parameter is defined as positive. The default \code{FALSE} returns parameters on the natural scale.} \item{raw}{Return samples of the baseline parameters and the covariate effects, rather than the default of adjusting the baseline parameters for covariates.} \item{tidy}{If \code{FALSE} (the default) then a list is returned. If \code{TRUE} a data frame is returned, consisting of the list elements \code{rbind}ed together, with integer variables labelling the covariate number and simulation replicate number.} \item{rawsim}{allows input of raw samples from a previous run of \code{normboot.flexsurvreg}. This is useful if running \code{normboot.flexsurvreg} multiple time on the same dataset but with counterfactual contrasts, e.g. treat =0 vs. treat =1. Used in \code{standsurv.flexsurvreg}.} } \value{ If \code{newdata} includes only one covariate combination, a matrix will be returned with \code{B} rows, and one column for each named parameter of the survival distribution. If more than one covariate combination is requested (e.g. \code{newdata} is a data frame with more than one row), then a list of matrices will be returned, one for each covariate combination. } \description{ Produce a matrix of alternative parameter estimates under sampling uncertainty, at covariate values supplied by the user. Used by \code{\link{summary.flexsurvreg}} for obtaining confidence intervals around functions of parameters. } \examples{ fite <- flexsurvreg(Surv(futime, fustat) ~ age, data = ovarian, dist="exp") normboot.flexsurvreg(fite, B=10, newdata=list(age=50)) normboot.flexsurvreg(fite, B=10, X=matrix(50,nrow=1)) normboot.flexsurvreg(fite, B=10, newdata=list(age=0)) ## closer to... fite$res } \references{ Mandel, M. (2013). "Simulation based confidence intervals for functions with complicated derivatives." The American Statistician (in press). } \seealso{ \code{\link{summary.flexsurvreg}} } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{models} flexsurv/man/augment.flexsurvreg.Rd0000644000176200001440000000523714644755661017236 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/broom-funs.R \name{augment.flexsurvreg} \alias{augment.flexsurvreg} \title{Augment data with information from a flexsurv model object} \usage{ \method{augment}{flexsurvreg}( x, data = NULL, newdata = NULL, type.predict = "response", type.residuals = "response", ... ) } \arguments{ \item{x}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{data}{A \code{\link{data.frame}} or \code{\link[tibble]{tibble}} containing the original data that was used to produce the object \code{x}.} \item{newdata}{A \code{\link{data.frame}} or \code{\link[tibble]{tibble}} containing all the original predictors used to create \code{x}. Defaults to \code{NULL}, indicating that nothing has been passed to \code{newdata}. If \code{newdata} is specified, the \code{data} argument will be ignored.} \item{type.predict}{Character indicating type of prediction to use. Passed to the \code{type} argument of the \code{\link{predict}} generic. Allowed arguments vary with model class, so be sure to read the \code{predict.my_class} documentation.} \item{type.residuals}{Character indicating type of residuals to use. Passed to the type argument of \code{\link{residuals}} generic. Allowed arguments vary with model class, so be sure to read the \code{residuals.my_class} documentation.} \item{...}{Additional arguments. Not currently used.} } \value{ A \code{\link[tibble]{tibble}} containing \code{data} or \code{newdata} and possible additional columns: \itemize{ \item \code{.fitted} Fitted values of model \item \code{.se.fit} Standard errors of fitted values \item \code{.resid} Residuals (not present if \code{newdata} specified) } } \description{ Augment accepts a model object and a dataset and adds information about each observation in the dataset. Most commonly, this includes predicted values in the \code{.fitted} column, residuals in the \code{.resid} column, and standard errors for the fitted values in a \code{.se.fit} column. New columns always begin with a . prefix to avoid overwriting columns in the original dataset. } \details{ If neither of \code{data} or \code{newdata} are specified, then \code{model.frame(x)} will be used. It is worth noting that \code{model.frame(x)} will include a \code{\link[survival]{Surv}} object and not the original time-to-event variables used when fitting the \code{flexsurvreg} object. If the original data is desired, specify \code{data}. } \examples{ fit <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "exp") augment(fit, data = ovarian) } flexsurv/man/figures/0000755000176200001440000000000014531453561014356 5ustar liggesusersflexsurv/man/figures/flexsurv_hex.png0000644000176200001440000002332314523512617017610 0ustar liggesusers‰PNG  IHDRX.eÞ|PLTEýþý..3334445556667778889999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGFHHGIIHM®IKKJLLKMMLNNMOONPPOQQPRRQSSRTTRUUSUUSVVTWWUXXVYYWZZX[[Y\\Z]][^^\__]``^aa_bb_cc`ddaeebffcggdhheiifjjgkkhllimmjnnkoolpplqqmrrnssottpuuqvvrwwsxxtyyuzzv{{w||x}}x~~yz€€{|‚‚}ƒƒ~„„……€††‡‡‚ˆˆƒ‰‰„ŠŠ…‹‹…ŒŒ†‡ŽŽˆ‰Š‘‘‹’’Œ““””Ž••––——‘˜˜‘™™’™™’šš“››”œœ•–žž—ŸŸ˜  ™™™™¡¡š¢¢›££œ¤¤¥¥ž¦¦ž§§Ÿ¨¨ ©©¡ªª¢««£¬¬¤­­¥®®¦¯¯§°°¨±±©²²ª³³«´´«µµ¬¶¶­··®¸¸¯¹¹°ºº±»»²¼¼³½½´¾¾µ¿¿¶ÀÀ·ÁÁ·Â¸ÃùÄĺÅÅ»ÆƼÇǽÈȾÉÉ¿ÊÊÀËËÁÌÌÂÍÍÃÎÎÄÏÏÄÐÐÅÑÑÆÒÒÇÓÓÈÔÔÉÕÕÊÖÖË××ÌØØÍÙÙÎÚÚÏÛÛÐÜÜÐÝÝÑÝÝÑÞÞÒßßÓààÔááÕââÖãã×ääØååÙææÚççÛèèÜééÝêêÝëëÞììßííàîîáïïâððãññäòòåóóæôôçõõèööé÷÷êøøêùùëúúìûûíüüîýýïþþðÿÿýþýñ¨sèÔtRNSÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿƒ€‚= pHYs.#.#x¥?v IDATxœíÝû£EýpžåÎP0AA!EDÅÔ@ÑBÅ$5óŠT–”fj¦Ò·‡’ ù"jŠ©h˜"^ ÅÄ[DáAPtÎðuöyfö:³³—¹Ïçýìî³;»ó:{qØçqtEoFè.€Æéè.ŽÎøË ÈGw‘ôÅ[;ð”ǼdÀDà-"ð‚ ¸ |tàƒ|„àƒ’üƒàƒ |ƒàƒŠ ¼rà ƒÊ¼‚à ƒZ<‚àƒÚ |qàƒ|à>^-#„‚ë ¸ë•pà<Ç”BP‚”Fà=‡TBà9gðê4¯ÀçSWÔ@àóÁM5ø ÁE ø ÁA xéÀ9x Á1BxÁ)¼º+¯À·‹G—DàÛÁ‚øÁøÁ ¼Úª«À›S'HCàÍÁRxÁzÒxÁvJ¸ïÀnŠ¸Áf ¸Á^¼Z­Àé‹Gk(GP‚îR;–2ЂÀaV2ІÀY2àÕƒ\nž"ØÇ@3‚2to¢ê±\„`C¸Á*)pÌE ŒBàk‡À)–0àmo= ܹx´ƒ¡Ê@нéÊÅ#p‚ù GÆ~¦3àma8pŠ`8+„±ÜÑ ¬AÆj3° A‹!˜ËÀ:6;0•…ÂØ ÁL–"c'ð¶¤É ,½x4ÕÂXèÀ8Ö#cÃ8 ŒeŒbÀÛvö(°íÁ$!c“s8† Œ=Laà ‚0¶@0„£ ¬q`g„±‚ œFÆÚð¶‘ý l¸xÔÍÀaLw —'˜ A'„1‚>¼­âš£O´1ðAchbà%‚0†BÐÂÀ[aŒ„ ƒ× Ìt žç˜A5@ЉiÔ2à­½/ Œ»xTÊ$b”… A&APÆPb E xëë§sNÔ0̘á@@P Èg¸ÑA:PP"ÚHfJF3© A…h… ‘o½@A:Üí%¯ª$2•£Ï,€ VtAÃÔŽ2ðÖ…»õ$Ô˜ € a48Έr‚AQ A,P ,jˆd„F%q 𨃠Š¯Ä  N¸[UPí‰b$E‘! 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If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{final}{If \code{TRUE} then the mean time to the final state is calculated for each final state, by taking a weighted average of the mean time to travel each pathway ending in that final state, weighted by the probability of the pathway. If \code{FALSE} (the default) then a separate mean is calculated for each pathway.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} } \value{ A data frame of mean times to absorption, by covariate values and pathway (or by final state) } \description{ Calculate the mean time from the start of the process to a final (or "absorbing") state in a mixture multi-state model. Models with cycles are not supported. } flexsurv/man/simt_flexsurvmix.Rd0000644000176200001440000000216614165570616016642 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/fmixmsm.R \name{simt_flexsurvmix} \alias{simt_flexsurvmix} \title{Simulate times to competing events from a mixture multi-state model} \usage{ simt_flexsurvmix(x, newdata = NULL, n) } \arguments{ \item{x}{Fitted model object returned from \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{n}{Number of simulations} } \value{ Data frame with \code{n*m} rows and a column for each competing event, where \code{m} is the number of alternative covariate values, that is the number of rows of \code{newdata}. The simulated time represents the time to that event conditionally on that event being the one that occurs. This function doesn't simulate which event occurs. } \description{ Simulate times to competing events from a mixture multi-state model } flexsurv/man/plot.flexsurvreg.Rd0000644000176200001440000001251214644755664016551 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plot.flexsurvreg.R \name{plot.flexsurvreg} \alias{plot.flexsurvreg} \title{Plots of fitted flexible survival models} \usage{ \method{plot}{flexsurvreg}( x, newdata = NULL, X = NULL, type = "survival", fn = NULL, t = NULL, start = 0, est = TRUE, ci = NULL, B = 1000, cl = 0.95, col.obs = "black", lty.obs = 1, lwd.obs = 1, col = "red", lty = 1, lwd = 2, col.ci = NULL, lty.ci = 2, lwd.ci = 1, ylim = NULL, add = FALSE, ... ) } \arguments{ \item{x}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{newdata}{Data frame containing covariate values to produce fitted values for. See \code{\link{summary.flexsurvreg}}. If there are only factor covariates in the model, then Kaplan-Meier (or nonparametric hazard...) curves are plotted for all distinct groups, and by default, fitted curves are also plotted for these groups. To plot Kaplan-Meier and fitted curves for only a subset of groups, use \code{plot(survfit())} followed by \code{lines.flexsurvreg()}. If there are any continuous covariates, then a single population Kaplan-Meier curve is drawn. By default, a single fitted curve is drawn with the covariates set to their mean values in the data - for categorical covariates, the means of the 0/1 indicator variables are taken.} \item{X}{Alternative way to supply covariate values, as a model matrix. See \code{\link{summary.flexsurvreg}}. \code{newdata} is an easier way.} \item{type}{\code{"survival"} for survival, to be plotted against Kaplan-Meier estimates from \code{\link[survival]{plot.survfit}}. \code{"cumhaz"} for cumulative hazard, plotted against transformed Kaplan-Meier estimates from \code{\link[survival]{plot.survfit}}. \code{"hazard"} for hazard, to be plotted against smooth nonparametric estimates from \code{\link[muhaz]{muhaz}}. The nonparametric estimates tend to be unstable, and these plots are intended just to roughly indicate the shape of the hazards through time. The \code{min.time} and \code{max.time} options to \code{\link[muhaz]{muhaz}} may sometimes need to be passed as arguments to \code{\link{plot.flexsurvreg}} to avoid an error here. Ignored if \code{"fn"} is specified.} \item{fn}{Custom function of the parameters to summarise against time. The first two arguments of the function must be \code{t} representing time, and \code{start} representing left-truncation points, and any remaining arguments must be parameters of the distribution. It should return a vector of the same length as \code{t}.} \item{t}{Vector of times to plot fitted values for, see \code{\link{summary.flexsurvreg}}.} \item{start}{Left-truncation points, see \code{\link{summary.flexsurvreg}}.} \item{est}{Plot fitted curves (\code{TRUE} or \code{FALSE}.)} \item{ci}{Plot confidence intervals for fitted curves. By default, this is \code{TRUE} if one observed/fitted curve is plotted, and \code{FALSE} if multiple curves are plotted.} \item{B}{Number of simulations controlling accuracy of confidence intervals, as used in \code{\link[=summary.flexsurvreg]{summary}}. Decrease for greater speed at the expense of accuracy, or set \code{B=0} to turn off calculation of CIs.} \item{cl}{Width of confidence intervals, by default 0.95 for 95\% intervals.} \item{col.obs}{Colour of the nonparametric curve.} \item{lty.obs}{Line type of the nonparametric curve.} \item{lwd.obs}{Line width of the nonparametric curve.} \item{col}{Colour of the fitted parametric curve(s).} \item{lty}{Line type of the fitted parametric curve(s).} \item{lwd}{Line width of the fitted parametric curve(s).} \item{col.ci}{Colour of the fitted confidence limits, defaulting to the same as for the fitted curve.} \item{lty.ci}{Line type of the fitted confidence limits.} \item{lwd.ci}{Line width of the fitted confidence limits.} \item{ylim}{y-axis limits: vector of two elements.} \item{add}{If \code{TRUE}, add lines to an existing plot, otherwise new axes are drawn.} \item{...}{Other options to be passed to \code{\link[survival]{plot.survfit}} or \code{\link[muhaz]{muhaz}}, for example, to control the smoothness of the nonparametric hazard estimates. The \code{min.time} and \code{max.time} options to \code{\link[muhaz]{muhaz}} may sometimes need to be changed from the defaults.} } \description{ Plot fitted survival, cumulative hazard or hazard from a parametric model against nonparametric estimates to diagnose goodness-of-fit. Alternatively plot a user-defined function of the model parameters against time. } \note{ Some standard plot arguments such as \code{"xlim","xlab"} may not work. This function was designed as a quick check of model fit. Users wanting publication-quality graphs are advised to set up an empty plot with the desired axes first (e.g. with \code{plot(...,type="n",...)}), then use suitable \code{\link{lines}} functions to add lines. If case weights were used to fit the model, these are used when producing nonparametric estimates of survival and cumulative hazard, but not for the hazard estimates. } \seealso{ \code{\link{flexsurvreg}} } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{hplot} \keyword{models} flexsurv/man/AICc.Rd0000644000176200001440000000113214470701435013733 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{AICc} \alias{AICc} \alias{AICC} \title{Second-order Akaike information criterion} \usage{ AICc(object, ...) AICC(object, ...) } \arguments{ \item{object}{Fitted model object.} \item{...}{Other arguments (currently unused).} } \description{ Generic function for the second-order Akaike information criterion. The only current implementation of this in \pkg{flexsurv} is in \code{\link{AICc.flexsurvreg}}, see there for more details. } \details{ This can be spelt either as \code{AICC} or \code{AICc}. } flexsurv/man/tidy.standsurv.Rd0000644000176200001440000000106314247336547016212 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/standsurv.R \name{tidy.standsurv} \alias{tidy.standsurv} \title{Tidy a standsurv object.} \usage{ \method{tidy}{standsurv}(x, ...) } \arguments{ \item{x}{A standsurv object.} \item{...}{Not currently used.} } \value{ Returns additional tidy data.frames (tibbles) stored as attributes named standpred_at and standpred_contrast. } \description{ This function is used internally by \code{standsurv} and tidy data.frames are automatically returned by the function. } flexsurv/man/tidy.flexsurvreg.Rd0000644000176200001440000000604414644755013016533 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/broom-funs.R \name{tidy.flexsurvreg} \alias{tidy.flexsurvreg} \title{Tidy a flexsurv model object} \usage{ \method{tidy}{flexsurvreg}( x, conf.int = FALSE, conf.level = 0.95, pars = "all", transform = "none", ... ) } \arguments{ \item{x}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{conf.int}{Logical. Should confidence intervals be returned? Default is \code{FALSE}.} \item{conf.level}{The confidence level to use for the confidence interval if \code{conf.int = TRUE}. Default is \code{0.95}.} \item{pars}{One of \code{"all"}, \code{"baseline"}, or \code{"coefs"} for all parameters, baseline distribution parameters, or covariate effects (i.e. regression betas), respectively. Default is \code{"all"}.} \item{transform}{Character vector of transformations to apply to requested \code{pars}. Default is \code{"none"}, which returns \code{pars} as-is. Users can specify one or both types of transformations: \itemize{ \item \code{"baseline.real"} which transforms the baseline distribution parameters to the real number line used for estimation. \item \code{"coefs.exp"} which exponentiates the covariate effects. } See \code{Details} for a more complete explanation.} \item{...}{Not currently used.} } \value{ A \code{\link[tibble]{tibble}} containing the columns: \code{term}, \code{estimate}, \code{std.error}, \code{statistic}, \code{p.value}, \code{conf.low}, and \code{conf.high}, by default. \code{statistic} and \code{p.value} are only provided for covariate effects (\code{NA} for baseline distribution parameters). These are computed as Wald-type test statistics with p-values from a standard normal distribution. } \description{ Tidy summarizes information about the components of the model into a tidy data frame. } \details{ \code{flexsurvreg} models estimate two types of coefficients, baseline distribution parameters, and covariate effects which act on the baseline distribution. By design, \code{flexsurvreg} returns distribution parameters on the same scale as is found in the relevant \code{d/p/q/r} functions. Covariate effects are returned on the log-scale, which represents either log-time ratios (accelerated failure time models) or log-hazard ratios for proportional hazard models. By default, \code{tidy()} will return baseline distribution parameters on their natural scale and covariate effects on the log-scale. To transform the baseline distribution parameters to the real-value number line (the scale used for estimation), pass the character argument \code{"baseline.real"} to \code{transform}. To get time ratios or hazard ratios, pass \code{"coefs.exp"} to \code{transform}. These transformations may be done together by submitting both arguments as a character vector. } \examples{ fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ age, data = ovarian, dist = "gengamma") tidy(fitg) tidy(fitg, pars = "coefs", transform = "coefs.exp") } flexsurv/man/standsurv.Rd0000644000176200001440000003065214523723772015245 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/standsurv.R \name{standsurv} \alias{standsurv} \title{Marginal survival and hazards of fitted flexsurvreg models} \usage{ standsurv( object, newdata = NULL, at = list(list()), atreference = 1, type = "survival", t = NULL, ci = FALSE, se = FALSE, boot = FALSE, B = NULL, cl = 0.95, trans = "log", contrast = NULL, trans.contrast = NULL, seed = NULL, rmap, ratetable, scale.ratetable = 365.25, n.gauss.quad = 100, quantiles = 0.5, interval = c(1e-08, 500) ) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{newdata}{Data frame containing covariate values to produce marginal values for. If not specified then the fitted model data.frame is used. There must be a column for every covariate in the model formula for which the user wishes to standardize over. These are in the same format as the original data, with factors as a single variable, not 0/1 contrasts. Any covariates that are to be fixed should be specified in \code{at}. There should be one row for every combination of covariates in which to standardize over. If newdata contains a variable named '(weights)' then a weighted mean will be used to create the standardized estimates. This is the default behaviour if the fitted model contains case weights, which are stored in the fitted model data.frame.} \item{at}{A list of scenarios in which specific covariates are fixed to certain values. Each element of \code{at} must itself be a list. For example, for a covariate \code{group} with levels "Good", "Medium" and "Poor", the standardized survival plots for each group averaging over all other covariates is specified using \code{at=list(list(group="Good"), list(group="Medium"), list(group="Poor"))}.} \item{atreference}{The reference scenario for making contrasts. Default is 1 (i.e. the first element of \code{at}).} \item{type}{\code{"survival"} for marginal survival probabilities. In a relative survival framework this returns the marginal all-cause survival (see details). \code{"hazard"} for the hazard of the marginal survival probability. In a relative survival framework this returns the marginal all-cause hazard (see details). \code{"rmst"} for standardized restricted mean survival. \code{"relsurvival"} for marginal relative survival (can only be specified if a relative survival model has been fitted in flexsurv). \code{"excesshazard"} for marginal excess hazards (can only be specified if a relative survival model has been fitted in flexsurv). \code{"quantile"} for quantiles of the marginal all-cause survival distribution. The \code{quantiles} option also needs to be provided.} \item{t}{Times to calculate marginal values at.} \item{ci}{Should confidence intervals be calculated? Defaults to FALSE} \item{se}{Should standard errors be calculated? Defaults to FALSE} \item{boot}{Should bootstrapping be used to calculate standard error and confidence intervals? Defaults to FALSE, in which case the delta method is used} \item{B}{Number of bootstrap simulations from the normal asymptotic distribution of the estimates used to calculate confidence intervals or standard errors. Decrease for greater speed at the expense of accuracy. Only specify if \code{boot = TRUE}} \item{cl}{Width of symmetric confidence intervals, relative to 1.} \item{trans}{Transformation to apply when calculating standard errors via the delta method to obtain confidence intervals. The default transformation is "log". Other possible names are "none", "loglog", "logit".} \item{contrast}{Contrasts between standardized measures defined by \code{at} scenarios. Options are \code{"difference"} and \code{"ratio"}. There will be n-1 new columns created where n is the number of \code{at} scenarios. Default is NULL (i.e. no contrasts are calculated).} \item{trans.contrast}{Transformation to apply when calculating standard errors for contrasts via the delta method to obtain confidence intervals. The default transformation is "none" for differences in survival, hazard, quantiles, or RMST, and "log" for ratios of survival, hazard, quantiles or RMST.} \item{seed}{The random seed to use (for bootstrapping confidence intervals)} \item{rmap}{An list that maps data set names to expected ratetable names. This must be specified if all-cause survival and hazards are required after fitting a relative survival model. This can also be specified if expected rates are required for plotting purposes. See the details section below.} \item{ratetable}{A table of expected event rates (see \code{\link[survival]{ratetable}})} \item{scale.ratetable}{Transformation from the time scale of the fitted flexsurv model to the time scale in \code{ratetable}. For example, if the analysis time of the fitted model is in years and the ratetable is in units/day then we should use \code{scale.ratetable = 365.25}. This is the default as often the ratetable will be in units/day (see example).} \item{n.gauss.quad}{Number of Gaussian quadrature points used for integrating the all-cause survival function when calculating RMST in a relative survival framework (default = 100)} \item{quantiles}{If \code{type="quantile"}, this specifies the quantiles of the survival time distribution to return estimates for.} \item{interval}{Interval of survival times for quantile root finding. Default is c(1e-08, 500).} } \value{ A \code{tibble} containing one row for each time-point. The column naming convention is \code{at{i}} for the ith scenario with corresponding confidence intervals (if specified) named \code{at{i}_lci} and \code{at{i}_uci}. Contrasts are named \code{contrast{k}_{j}} for the comparison of the kth versus the jth \code{at} scenario. In addition tidy long-format data.frames are returned in the attributes \code{standsurv_at} and \code{standsurv_contrast}. These can be passed to \code{ggplot} for plotting purposes (see \code{\link{plot.standsurv}}). } \description{ Returns a tidy data.frame of marginal survival probabilities, or hazards, restricted mean survival, or quantiles of the marginal survival function at user-defined time points and covariate patterns. Standardization is performed over any undefined covariates in the model. The user provides the data to standardize over. Contrasts can be calculated resulting in estimates of the average treatment effect or the average treatment effect in the treated if a treated subset of the data are supplied. } \details{ The syntax of \code{standsurv} follows closely that of Stata's \code{standsurv} command written by Paul Lambert and Michael Crowther. The function calculates standardized (marginal) measures including standardized survival functions, standardized restricted mean survival times, quantiles and the hazard of standardized survival. The standardized survival is defined as \deqn{S_s(t|X=x) = E(S(t|X=x,Z)) = \frac{1}{N} \sum_{i=1}^N S(t|X=x,Z=z_i)}{S(t|X=x) = E[S(t|X=x,Z)] = 1/N * sum(S(t|X=x,Z=z_i))} The hazard of the standardized survival is a weighted average of individual hazard functions at time t, weighted by the survival function at this time: \deqn{h_s(t|X=x) = \frac{\sum_{i=1}^N S(t|X=x,Z=z_i)h(t|X=x,Z=z_i)}{\sum_{i=1}^N S(t|X=x,Z=z_i)}}{h(t|X=x) = sum(S(t|X=x,Z=z_i) * h(t|X=x,Z=z_i)) / sum(S(t|X=x,Z=z_i))} Marginal expected survival and hazards can be calculated by providing a population-based lifetable of class ratetable in \code{ratetable} and a mapping between stratification factors in the lifetable and the user dataset using \code{rmap}. If these stratification factors are not in the fitted survival model then the user must specify them in \code{newdata} along with the covariates of the model. The marginal expected survival is calculated using the "Ederer" method that assumes no censoring as this is most relevant approach for forecasting (see \code{\link[survival]{survexp}}). A worked example is given below. Marginal all-cause survival and hazards can be calculated after fitting a relative survival model, which utilise the expected survival from a population ratetable. See Rutherford et al. (Chapter 6) for further details. } \examples{ ## mean age is higher in those with smaller observed survival times newbc <- bc set.seed(1) newbc$age <- rnorm(dim(bc)[1], mean = 65-scale(newbc$recyrs, scale=FALSE), sd = 5) ## Fit a Weibull flexsurv model with group and age as covariates weib_age <- flexsurvreg(Surv(recyrs, censrec) ~ group+age, data=newbc, dist="weibull") ## Calculate standardized survival and the difference in standardized survival ## for the three levels of group across a grid of survival times standsurv_weib_age <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length.out=100), contrast = "difference", ci=FALSE) standsurv_weib_age ## Calculate hazard of standardized survival and the marginal hazard ratio ## for the three levels of group across a grid of survival times ## 10 bootstraps for confidence intervals (this should be larger) \dontrun{ haz_standsurv_weib_age <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length.out=100), type="hazard", contrast = "ratio", boot = TRUE, B=10, ci=TRUE) haz_standsurv_weib_age plot(haz_standsurv_weib_age, ci=TRUE) ## Hazard ratio plot shows a decreasing marginal HR ## Whereas the conditional HR is constant (model is a PH model) plot(haz_standsurv_weib_age, contrast=TRUE, ci=TRUE) ## Calculate standardized survival from a Weibull model together with expected ## survival matching to US lifetables # age at diagnosis in days. This is required to match to US ratetable, whose # timescale is measured in days newbc$agedays <- floor(newbc$age * 365.25) ## Create some random diagnosis dates centred on 01/01/2010 with SD=1 year ## These will be used to match to expected rates in the lifetable newbc$diag <- as.Date(floor(rnorm(dim(newbc)[1], mean = as.Date("01/01/2010", "\%d/\%m/\%Y"), sd=365)), origin="1970-01-01") ## Create sex (assume all are female) newbc$sex <- factor("female") standsurv_weib_expected <- standsurv(weib_age, at = list(list(group="Good"), list(group="Medium"), list(group="Poor")), t=seq(0,7, length.out=100), rmap=list(sex = sex, year = diag, age = agedays), ratetable = survival::survexp.us, scale.ratetable = 365.25, newdata = newbc) ## Plot marginal survival with expected survival superimposed plot(standsurv_weib_expected, expected=TRUE) } } \references{ Paul Lambert, 2021. "STANDSURV: Stata module to compute standardized (marginal) survival and related functions," Statistical Software Components S458991, Boston College Department of Economics. https://ideas.repec.org/c/boc/bocode/s458991.html Rutherford, MJ, Lambert PC, Sweeting MJ, Pennington B, Crowther MJ, Abrams KR, Latimer NR. 2020. "NICE DSU Technical Support Document 21: Flexible Methods for Survival Analysis" https://nicedsu.sites.sheffield.ac.uk/tsds/flexible-methods-for-survival-analysis-tsd } \author{ Michael Sweeting } flexsurv/man/flexsurvreg.Rd0000644000176200001440000006073314644755662015602 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{flexsurvreg} \alias{flexsurvreg} \alias{flexsurv.dists} \title{Flexible parametric regression for time-to-event data} \usage{ flexsurvreg( formula, anc = NULL, data, weights, bhazard, rtrunc, subset, na.action, dist, inits, fixedpars = NULL, dfns = NULL, aux = NULL, cl = 0.95, integ.opts = NULL, sr.control = survreg.control(), hessian = TRUE, hess.control = NULL, ... ) } \arguments{ \item{formula}{A formula expression in conventional R linear modelling syntax. The response must be a survival object as returned by the \code{\link[survival]{Surv}} function, and any covariates are given on the right-hand side. For example, \code{Surv(time, dead) ~ age + sex} \code{Surv} objects of \code{type="right"},\code{"counting"}, \code{"interval1"} or \code{"interval2"} are supported, corresponding to right-censored, left-truncated or interval-censored observations. If there are no covariates, specify \code{1} on the right hand side, for example \code{Surv(time, dead) ~ 1}. If the right hand side is specified as \code{.} all remaining variables are included as covariates. For example, \code{Surv(time, dead) ~ .} corresponds to \code{Surv(time, dead) ~ age + sex} if \code{data} contains the variables \code{time}, \code{dead}, \code{age}, and \code{sex}. By default, covariates are placed on the ``location'' parameter of the distribution, typically the "scale" or "rate" parameter, through a linear model, or a log-linear model if this parameter must be positive. This gives an accelerated failure time model or a proportional hazards model (see \code{dist} below) depending on how the distribution is parameterised. Covariates can be placed on other (``ancillary'') parameters by using the name of the parameter as a ``function'' in the formula. For example, in a Weibull model, the following expresses the scale parameter in terms of age and a treatment variable \code{treat}, and the shape parameter in terms of sex and treatment. \code{Surv(time, dead) ~ age + treat + shape(sex) + shape(treat)} However, if the names of the ancillary parameters clash with any real functions that might be used in formulae (such as \code{I()}, or \code{factor()}), then those functions will not work in the formula. A safer way to model covariates on ancillary parameters is through the \code{anc} argument to \code{\link{flexsurvreg}}. \code{\link[survival]{survreg}} users should also note that the function \code{strata()} is ignored, so that any covariates surrounded by \code{strata()} are applied to the location parameter. Likewise the function \code{frailty()} is not handled.} \item{anc}{An alternative and safer way to model covariates on ancillary parameters, that is, parameters other than the main location parameter of the distribution. This is a named list of formulae, with the name of each component giving the parameter to be modelled. The model above can also be defined as: \code{Surv(time, dead) ~ age + treat, anc = list(shape = ~ sex + treat)}} \item{data}{A data frame in which to find variables supplied in \code{formula}. If not given, the variables should be in the working environment.} \item{weights}{Optional numeric variable giving weights for each individual in the data. The fitted model is then defined by maximising the weighted sum of the individual-specific log-likelihoods.} \item{bhazard}{Optional variable giving expected hazards for relative survival models. The model is described by Nelson et al. (2007). \code{bhazard} should contain a vector of values for each person in the data. \itemize{ \item For people with observed events, \code{bhazard} refers to the hazard at the observed event time. \item For people whose event time is left-censored or interval-censored, \code{bhazard} should contain the probability of dying by the end of the corresponding interval, conditionally on being alive at the start. \item For people whose event time is right-censored, the value of \code{bhazard} is ignored and does not need to be specified. } If \code{bhazard} is supplied, then the parameter estimates returned by \code{flexsurvreg} and the outputs returned by \code{summary.flexsurvreg} describe the parametric model for relative survival. For relative survival models, the log-likelihood returned by \code{flexsurvreg} is a partial log-likelihood, which omits a constant term defined by the sum of the cumulative hazards at the event or censoring time for each individual. Hence this constant must be added if a full likelihood is needed.} \item{rtrunc}{Optional variable giving individual-specific right-truncation times. Used for analysing data with "retrospective ascertainment". For example, suppose we want to estimate the distribution of the time from onset of a disease to death, but have only observed cases known to have died by the current date. In this case, times from onset to death for individuals in the data are right-truncated by the current date minus the onset date. Predicted survival times for new cases can then be described by an un-truncated version of the fitted distribution. These models can suffer from weakly identifiable parameters and badly-behaved likelihood functions, and it is advised to compare convergence for different initial values by supplying different \code{inits} arguments to \code{flexsurvreg}.} \item{subset}{Vector of integers or logicals specifying the subset of the observations to be used in the fit.} \item{na.action}{a missing-data filter function, applied after any 'subset' argument has been used. Default is \code{options()$na.action}.} \item{dist}{Typically, one of the strings in the first column of the following table, identifying a built-in distribution. This table also identifies the location parameters, and whether covariates on these parameters represent a proportional hazards (PH) or accelerated failure time (AFT) model. In an accelerated failure time model, the covariate speeds up or slows down the passage of time. So if the coefficient (presented on the log scale) is log(2), then doubling the covariate value would give half the expected survival time. \tabular{llll}{ \code{"gengamma"} \tab Generalized gamma (stable) \tab mu \tab AFT \cr \code{"gengamma.orig"} \tab Generalized gamma (original) \tab scale \tab AFT \cr \code{"genf"} \tab Generalized F (stable) \tab mu \tab AFT \cr \code{"genf.orig"} \tab Generalized F (original) \tab mu \tab AFT \cr \code{"weibull"} \tab Weibull \tab scale \tab AFT \cr \code{"gamma"} \tab Gamma \tab rate \tab AFT \cr \code{"exp"} \tab Exponential \tab rate \tab PH \cr \code{"llogis"} \tab Log-logistic \tab scale \tab AFT \cr \code{"lnorm"} \tab Log-normal \tab meanlog \tab AFT \cr \code{"gompertz"} \tab Gompertz \tab rate \tab PH \cr } \code{"exponential"} and \code{"lognormal"} can be used as aliases for \code{"exp"} and \code{"lnorm"}, for compatibility with \code{\link[survival]{survreg}}. Alternatively, \code{dist} can be a list specifying a custom distribution. See section ``Custom distributions'' below for how to construct this list. Very flexible spline-based distributions can also be fitted with \code{\link{flexsurvspline}}. The parameterisations of the built-in distributions used here are the same as in their built-in distribution functions: \code{\link{dgengamma}}, \code{\link{dgengamma.orig}}, \code{\link{dgenf}}, \code{\link{dgenf.orig}}, \code{\link{dweibull}}, \code{\link{dgamma}}, \code{\link{dexp}}, \code{\link{dlnorm}}, \code{\link{dgompertz}}, respectively. The functions in base R are used where available, otherwise, they are provided in this package. A package vignette "Distributions reference" lists the survivor functions and covariate effect parameterisations used by each built-in distribution. For the Weibull, exponential and log-normal distributions, \code{\link{flexsurvreg}} simply works by calling \code{\link[survival]{survreg}} to obtain the maximum likelihood estimates, then calling \code{\link{optim}} to double-check convergence and obtain the covariance matrix for \code{\link{flexsurvreg}}'s preferred parameterisation. The Weibull parameterisation is different from that in \code{\link[survival]{survreg}}, instead it is consistent with \code{\link{dweibull}}. The \code{"scale"} reported by \code{\link[survival]{survreg}} is equivalent to \code{1/shape} as defined by \code{\link{dweibull}} and hence \code{\link{flexsurvreg}}. The first coefficient \code{(Intercept)} reported by \code{\link[survival]{survreg}} is equivalent to \code{log(scale)} in \code{\link{dweibull}} and \code{\link{flexsurvreg}}. Similarly in the exponential distribution, the rate, rather than the mean, is modelled on covariates. The object \code{flexsurv.dists} lists the names of the built-in distributions, their parameters, location parameter, functions used to transform the parameter ranges to and from the real line, and the functions used to generate initial values of each parameter for estimation.} \item{inits}{An optional numeric vector giving initial values for each unknown parameter. These are numbered in the order: baseline parameters (in the order they appear in the distribution function, e.g. shape before scale in the Weibull), covariate effects on the location parameter, covariate effects on the remaining parameters. This is the same order as the printed estimates in the fitted model. If not specified, default initial values are chosen from a simple summary of the survival or censoring times, for example the mean is often used to initialize scale parameters. See the object \code{flexsurv.dists} for the exact methods used. If the likelihood surface may be uneven, it is advised to run the optimisation starting from various different initial values to ensure convergence to the true global maximum.} \item{fixedpars}{Vector of indices of parameters whose values will be fixed at their initial values during the optimisation. The indices are ordered as in \code{inits}. For example, in a stable generalized Gamma model with two covariates, to fix the third of three generalized gamma parameters (the shape \code{Q}, see the help for \code{\link{GenGamma}}) and the second covariate, specify \code{fixedpars = c(3, 5)}} \item{dfns}{An alternative way to define a custom survival distribution (see section ``Custom distributions'' below). A list whose components may include \code{"d"}, \code{"p"}, \code{"h"}, or \code{"H"} containing the probability density, cumulative distribution, hazard, or cumulative hazard functions of the distribution. For example, \code{list(d=dllogis, p=pllogis)}. If \code{dfns} is used, a custom \code{dlist} must still be provided, but \code{dllogis} and \code{pllogis} need not be visible from the global environment. This is useful if \code{flexsurvreg} is called within other functions or environments where the distribution functions are also defined dynamically.} \item{aux}{A named list of other arguments to pass to custom distribution functions. This is used, for example, by \code{\link{flexsurvspline}} to supply the knot locations and modelling scale (e.g. hazard or odds). This cannot be used to fix parameters of a distribution --- use \code{fixedpars} for that.} \item{cl}{Width of symmetric confidence intervals for maximum likelihood estimates, by default 0.95.} \item{integ.opts}{List of named arguments to pass to \code{\link{integrate}}, if a custom density or hazard is provided without its cumulative version. For example, \code{integ.opts = list(rel.tol=1e-12)}} \item{sr.control}{For the models which use \code{\link[survival]{survreg}} to find the maximum likelihood estimates (Weibull, exponential, log-normal), this list is passed as the \code{control} argument to \code{\link[survival]{survreg}}.} \item{hessian}{Calculate the covariances and confidence intervals for the parameters. Defaults to \code{TRUE}.} \item{hess.control}{List of options to control covariance matrix computation. Available options are: \code{numeric}. If \code{TRUE} then numerical methods are used to compute the Hessian for models where an analytic Hessian is available. These models include the Weibull (both versions), exponential, Gompertz and spline models with hazard or odds scale. The default is to use the analytic Hessian for these models. For all other models, numerical methods are always used to compute the Hessian, whether or not this option is set. \code{tol.solve}. The tolerance used for \code{\link{solve}} when inverting the Hessian (default \code{.Machine$double.eps}) \code{tol.evalues} The accepted tolerance for negative eigenvalues in the covariance matrix (default \code{1e-05}). The Hessian is positive definite, thus invertible, at the maximum likelihood. If the Hessian computed after optimisation convergence can't be inverted, this is either because the converged result is not the maximum likelihood (e.g. it could be a "saddle point"), or because the numerical methods used to obtain the Hessian were inaccurate. If you suspect that the Hessian was computed wrongly enough that it is not invertible, but not wrongly enough that the nearest valid inverse would be an inaccurate estimate of the covariance matrix, then these tolerance values can be modified (reducing \code{tol.solve} or increasing \code{tol.evalues}) to allow the inverse to be computed.} \item{...}{Optional arguments to the general-purpose optimisation routine \code{\link{optim}}. For example, the BFGS optimisation algorithm is the default in \code{\link{flexsurvreg}}, but this can be changed, for example to \code{method="Nelder-Mead"} which can be more robust to poor initial values. If the optimisation fails to converge, consider normalising the problem using, for example, \code{control=list(fnscale = 2500)}, for example, replacing 2500 by a number of the order of magnitude of the likelihood. If 'false' convergence is reported with a non-positive-definite Hessian, then consider tightening the tolerance criteria for convergence. If the optimisation takes a long time, intermediate steps can be printed using the \code{trace} argument of the control list. See \code{\link{optim}} for details.} } \value{ A list of class \code{"flexsurvreg"} containing information about the fitted model. Components of interest to users may include: \item{call}{A copy of the function call, for use in post-processing.} \item{dlist}{List defining the survival distribution used.} \item{res}{Matrix of maximum likelihood estimates and confidence limits, with parameters on their natural scales.} \item{res.t}{Matrix of maximum likelihood estimates and confidence limits, with parameters all transformed to the real line (using a log transform for all built-in models where this is necessary). The \code{\link{coef}}, \code{\link{vcov}} and \code{\link{confint}} methods for \code{flexsurvreg} objects work on this scale.} \item{coefficients}{The transformed maximum likelihood estimates, as in \code{res.t}. Calling \code{coef()} on a \code{\link{flexsurvreg}} object simply returns this component.} \item{loglik}{Log-likelihood. This will differ from Stata, where the sum of the log uncensored survival times is added to the log-likelihood in survival models, to remove dependency on the time scale. For relative survival models specified with \code{bhazard}, this is a partial log-likelihood which omits a constant term defined by the sum of the cumulative hazards over all event or censoring times. } \item{logliki}{Vector of individual contributions to the log-likelihood} \item{AIC}{Akaike's information criterion (-2*log likelihood + 2*number of estimated parameters)} \item{cov}{Covariance matrix of the parameters, on the real-line scale (e.g. log scale), which can be extracted with \code{\link{vcov}}.} \item{data}{Data used in the model fit. To extract this in the standard R formats, use use \code{\link{model.frame.flexsurvreg}} or \code{\link{model.matrix.flexsurvreg}}.} } \description{ Parametric modelling or regression for time-to-event data. Several built-in distributions are available, and users may supply their own. } \details{ Parameters are estimated by maximum likelihood using the algorithms available in the standard R \code{\link{optim}} function. Parameters defined to be positive are estimated on the log scale. Confidence intervals are estimated from the Hessian at the maximum, and transformed back to the original scale of the parameters. The usage of \code{\link{flexsurvreg}} is intended to be similar to \code{\link[survival]{survreg}} in the \pkg{survival} package. } \section{Custom distributions}{ \code{\link{flexsurvreg}} is intended to be easy to extend to handle new distributions. To define a new distribution for use in \code{\link{flexsurvreg}}, construct a list with the following elements: \describe{ \item{\code{"name"}}{A string naming the distribution. If this is called \code{"dist"}, for example, then there must be visible in the working environment, at least, either a) a function called \code{ddist} which defines the probability density, or b) a function called \code{hdist} which defines the hazard. Ideally, in case a) there should also be a function called \code{pdist} which defines the probability distribution or cumulative density, and in case b) there should be a function called \code{Hdist} defining the cumulative hazard. If these additional functions are not provided, \pkg{flexsurv} attempts to automatically create them by numerically integrating the density or hazard function. However, model fitting will be much slower, or may not even work at all, if the analytic versions of these functions are not available. The functions must accept vector arguments (representing different times, or alternative values for each parameter) and return the results as a vector. The function \code{\link{Vectorize}} may be helpful for doing this: see the example below. These functions may be in an add-on package (see below for an example) or may be user-written. If they are user-written they must be defined in the global environment, or supplied explicitly through the \code{dfns} argument to \code{flexsurvreg}. The latter may be useful if the functions are created dynamically (as in the source of \code{flexsurvspline}) and thus not visible through R's scoping rules. Arguments other than parameters must be named in the conventional way -- for example \code{x} for the first argument of the density function or hazard, as in \code{\link{dnorm}(x, ...)} and \code{q} for the first argument of the probability function. Density functions should also have an argument \code{log}, after the parameters, which when \code{TRUE}, computes the log density, using a numerically stable additive formula if possible. Additional functions with names beginning with \code{"DLd"} and \code{"DLS"} may be defined to calculate the derivatives of the log density and log survival probability, with respect to the parameters of the distribution. The parameters are expressed on the real line, for example after log transformation if they are defined as positive. The first argument must be named \code{t}, representing the time, and the remaining arguments must be named as the parameters of the density function. The function must return a matrix with rows corresponding to times, and columns corresponding to the parameters of the distribution. The derivatives are used, if available, to speed up the model fitting with \code{\link{optim}}. } \item{\code{"pars"}}{Vector of strings naming the parameters of the distribution. These must be the same names as the arguments of the density and probability functions. } \item{\code{"location"}}{Name of the main parameter governing the mean of the distribution. This is the default parameter on which covariates are placed in the \code{formula} supplied to \code{flexsurvreg}. } \item{\code{"transforms"}}{List of R functions which transform the range of values taken by each parameter onto the real line. For example, \code{c(log, log)} for a distribution with two positive parameters. } \item{\code{"inv.transforms"}}{List of R functions defining the corresponding inverse transformations. Note these must be lists, even for single parameter distributions they should be supplied as, e.g. \code{c(exp)} or \code{list(exp)}. } \item{\code{"inits"}}{A function of the observed survival times \code{t} (including right-censoring times, and using the halfway point for interval-censored times) which returns a vector of reasonable initial values for maximum likelihood estimation of each parameter. For example, \code{function(t){ c(1, mean(t)) }} will always initialize the first of two parameters at 1, and the second (a scale parameter, for instance) at the mean of \code{t}. } } For example, suppose we want to use an extreme value survival distribution. This is available in the CRAN package \pkg{eha}, which provides conventionally-defined density and probability functions called \code{\link[eha:EV]{eha::dEV}} and \code{\link[eha:EV]{eha::pEV}}. See the Examples below for the custom list in this case, and the subsequent command to fit the model. } \examples{ ## Compare generalized gamma fit with Weibull fitg <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="gengamma") fitg fitw <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist="weibull") fitw plot(fitg) lines(fitw, col="blue", lwd.ci=1, lty.ci=1) ## Identical AIC, probably not enough data in this simple example for a ## very flexible model to be worthwhile. ## Custom distribution ## make "dEV" and "pEV" from eha package (if installed) ## available to the working environment if (require("eha")) { custom.ev <- list(name="EV", pars=c("shape","scale"), location="scale", transforms=c(log, log), inv.transforms=c(exp, exp), inits=function(t){ c(1, median(t)) }) fitev <- flexsurvreg(formula = Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.ev) fitev lines(fitev, col="purple", col.ci="purple") } ## Custom distribution: supply the hazard function only hexp2 <- function(x, rate=1){ rate } # exponential distribution hexp2 <- Vectorize(hexp2) custom.exp2 <- list(name="exp2", pars=c("rate"), location="rate", transforms=c(log), inv.transforms=c(exp), inits=function(t)1/mean(t)) flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist=custom.exp2) flexsurvreg(Surv(futime, fustat) ~ 1, data = ovarian, dist="exp") ## should give same answer } \references{ Jackson, C. (2016). flexsurv: A Platform for Parametric Survival Modeling in R. Journal of Statistical Software, 70(8), 1-33. doi:10.18637/jss.v070.i08 Cox, C. (2008) The generalized \eqn{F} distribution: An umbrella for parametric survival analysis. Statistics in Medicine 27:4301-4312. Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007) Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine 26:4252-4374 Jackson, C. H. and Sharples, L. D. and Thompson, S. G. (2010) Survival models in health economic evaluations: balancing fit and parsimony to improve prediction. International Journal of Biostatistics 6(1):Article 34. Nelson, C. P., Lambert, P. C., Squire, I. B., & Jones, D. R. (2007). Flexible parametric models for relative survival, with application in coronary heart disease. Statistics in medicine, 26(30), 5486-5498. } \seealso{ \code{\link{flexsurvspline}} for flexible survival modelling using the spline model of Royston and Parmar. \code{\link{plot.flexsurvreg}} and \code{\link{lines.flexsurvreg}} to plot fitted survival, hazards and cumulative hazards from models fitted by \code{\link{flexsurvreg}} and \code{\link{flexsurvspline}}. } \author{ Christopher Jackson } \keyword{models} \keyword{survival} flexsurv/man/pfinal_fmsm.Rd0000644000176200001440000000442014523723771015500 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{pfinal_fmsm} \alias{pfinal_fmsm} \title{Probabilities of final states in a flexible parametric competing risks model} \usage{ pfinal_fmsm(x, newdata = NULL, fromstate, maxt = 1e+05, B = 0, cores = NULL) } \arguments{ \item{x}{Object returned by \code{\link{fmsm}}, representing a multi-state model formed from transition-specific time-to-event models fitted by \code{\link{flexsurvreg}}.} \item{newdata}{Data frame of covariate values, with one column per covariate, and one row per alternative value.} \item{fromstate}{State from which to calculate the transition probability state. This should refer to the name of a row of the transition matrix \code{attr(x,trans)}.} \item{maxt}{Large time to use for forecasting final state probabilities. The transition probability from zero to this time is used. Note \code{Inf} will not work. The default is \code{100000}.} \item{B}{Number of simulations to use to calculate 95\% confidence intervals based on the asymptotic normal distribution of the basic parameter estimates. If \code{B=0} then no intervals are calculated.} \item{cores}{Number of processor cores to use. If \code{NULL} (the default) then a single core is used.} } \value{ A data frame with one row per covariate value and destination state, giving the state in column \code{state}, and probability in column \code{val}. Additional columns \code{lower} and \code{upper} for the confidence limits are returned if \code{B=0}. } \description{ This requires the model to be Markov, and is not valid for semi-Markov models, as it works by wrapping \code{\link{pmatrix.fs}} to calculate the transition probability over a very large time. As it also works on a \code{fmsm} object formed from transition-specific time-to-event models, it therefore only works on competing risks models, defined by just one starting state with multiple destination states representing competing events. For these models, this function returns the probability governing which competing event happens next. However this function simply wraps \code{pmatrix.fs}, so for other models, \code{pmatrix.fs} or \code{pmatrix.simfs} can be used with a large forecast time \code{t}. } flexsurv/man/basis.Rd0000644000176200001440000000353114531442444014302 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/spline.R \name{basis} \alias{basis} \alias{dbasis} \alias{fss} \alias{dfss} \title{Natural cubic spline basis} \usage{ basis(knots, x, spline = "rp") } \arguments{ \item{knots}{Vector of knot locations in increasing order, including the boundary knots at the beginning and end.} \item{x}{Vector of ordinates to compute the basis for.} \item{spline}{\code{"rp"} to use the natural cubic spline basis described in Royston and Parmar. \code{"splines2ns"} to use the alternative natural cubic spline basis from the \code{splines2} package (Wang and Yan 2021), which may be better behaved due to the basis being orthogonal.} } \value{ A matrix with one row for each ordinate and one column for each knot. \code{basis} returns the basis, and \code{dbasis} returns its derivative with respect to \code{x}. \code{fss} and \code{dfss} are the same, but with the order of the arguments swapped around for consistency with similar functions in other R packages. } \description{ Compute a basis for a natural cubic spline, by default using the parameterisation described by Royston and Parmar (2002). Used for flexible parametric survival models. } \details{ The exact formula for the basis is given in \code{\link{flexsurvspline}}. } \references{ Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197. Wang W, Yan J (2021). Shape-Restricted Regression Splines with R Package splines2. Journal of Data Science, 19(3), 498-517. } \seealso{ \code{\link{flexsurvspline}}. } \author{ Christopher Jackson } \keyword{models} flexsurv/man/survrtrunc.Rd0000644000176200001440000001122114174025317015430 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/survrtrunc.R \name{survrtrunc} \alias{survrtrunc} \title{Nonparametric estimator of survival from right-truncated, uncensored data} \usage{ survrtrunc(t, rtrunc, tmax, data = NULL, eps = 0.001, conf.int = 0.95) } \arguments{ \item{t}{Vector of observed times from an initial event to a final event.} \item{rtrunc}{Individual-specific right truncation points, so that each individual's survival time \code{t} would not have been observed if it was greater than the corresponding element of \code{rtrunc}. If any of these are greater than \code{tmax}, then the actual individual-level truncation point for these individuals is taken to be \code{tmax}.} \item{tmax}{Maximum possible time to event that could have been observed.} \item{data}{Data frame to find \code{t} and \code{rtrunc} in. If not supplied, these should be in the working environment.} \item{eps}{Small number that is added to \code{t} before implementing the time-reversed estimator, to ensure the risk set is consistent between forward and reverse time scales. It should be just large enough that \code{t+eps} is not \code{==t}. This should not need changing from the default of 0.001, unless \code{t} are extremely large or small and the data are rounded to integer.} \item{conf.int}{Confidence level, defaulting to 0.95.} } \value{ A list with components: \code{time} Time points where the estimated survival changes. \code{surv} Estimated survival at \code{time}, truncated above at \code{tmax}. \code{se.surv} Standard error of survival. \code{std.err} Standard error of -log(survival). Named this way for consistency with \code{survfit}. \code{lower} Lower confidence limits for survival. \code{upper} Upper confidence limits for survival. } \description{ Estimates the survivor function from right-truncated, uncensored data by reversing time, interpreting the data as left-truncated, applying the Kaplan-Meier / Lynden-Bell estimator and transforming back. } \details{ Note that this does not estimate the untruncated survivor function - instead it estimates the survivor function truncated above at a time defined by the maximum possible time that might have been observed in the data. Define \eqn{X} as the time of the initial event, \eqn{Y} as the time of the final event, then we wish to determine the distribution of \eqn{T = Y- X}. Observations are only recorded if \eqn{Y \leq t_{max}}. Then the distribution of \eqn{T} in the resulting sample is right-truncated by \code{rtrunc} \eqn{ = t_{max} - X}. Equivalently, the distribution of \eqn{t_{max} - T} is left-truncated, since it is only observed if \eqn{t_{max} - T \geq X}. Then the standard Kaplan-Meier type estimator as implemented in \code{\link[survival]{survfit}} is used (as described by Lynden-Bell, 1971) and the results transformed back. This situation might happen in a disease epidemic, where \eqn{X} is the date of disease onset for an individual, \eqn{Y} is the date of death, and we wish to estimate the distribution of the time \eqn{T} from onset to death, given we have only observed people who have died by the date \eqn{t_{max}}. If the estimated survival is unstable at the highest times, then consider replacing \code{tmax} by a slightly lower value, then if necessary, removing individuals with \code{t > tmax}, so that the estimand is changed to the survivor function truncated over a slightly narrower interval. } \examples{ ## simulate some event time data set.seed(1) X <- rweibull(100, 2, 10) T <- rweibull(100, 2, 10) ## truncate above tmax <- 20 obs <- X + T < tmax rtrunc <- tmax - X dat <- data.frame(X, T, rtrunc)[obs,] sf <- survrtrunc(T, rtrunc, data=dat, tmax=tmax) plot(sf, conf.int=TRUE) ## Kaplan-Meier estimate ignoring truncation is biased sfnaive <- survfit(Surv(T) ~ 1, data=dat) lines(sfnaive, conf.int=TRUE, lty=2, col="red") ## truncate above the maximum observed time tmax <- max(X + T) + 10 obs <- X + T < tmax rtrunc <- tmax - X dat <- data.frame(X, T, rtrunc)[obs,] sf <- survrtrunc(T, rtrunc, data=dat, tmax=tmax) plot(sf, conf.int=TRUE) ## estimates identical to the standard Kaplan-Meier sfnaive <- survfit(Surv(T) ~ 1, data=dat) lines(sfnaive, conf.int=TRUE, lty=2, col="red") } \references{ D. Lynden-Bell (1971) A method of allowing for known observational selection in small samples applied to 3CR quasars. Monthly Notices of the Royal Astronomical Society, 155:95–118. Seaman, S., Presanis, A. and Jackson, C. (2020) Review of methods for estimating distribution of time to event from right-truncated data. } flexsurv/man/quantile_flexsurvmix.Rd0000644000176200001440000000241214165570616017502 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{quantile_flexsurvmix} \alias{quantile_flexsurvmix} \title{Quantiles of time-to-event distributions in a flexsurvmix model} \usage{ quantile_flexsurvmix(x, newdata = NULL, B = NULL, probs = c(0.025, 0.5, 0.975)) } \arguments{ \item{x}{Fitted model object returned from \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} \item{probs}{Vector of alternative quantiles, by default \code{c(0.025, 0.95, 0.975)} giving the median and a 95\% interval.} } \description{ This returns the quantiles of each event-specific parametric time-to-event distribution in the mixture model, which describes the time to the event conditionally on that event being the one that happens. } flexsurv/man/Llogis.Rd0000644000176200001440000000564614171772374014453 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/Llogis.R \name{Llogis} \alias{Llogis} \alias{dllogis} \alias{pllogis} \alias{qllogis} \alias{hllogis} \alias{Hllogis} \alias{rllogis} \title{The log-logistic distribution} \usage{ dllogis(x, shape = 1, scale = 1, log = FALSE) pllogis(q, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) qllogis(p, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) rllogis(n, shape = 1, scale = 1) hllogis(x, shape = 1, scale = 1, log = FALSE) Hllogis(x, shape = 1, scale = 1, log = FALSE) } \arguments{ \item{x, q}{vector of quantiles.} \item{shape, scale}{vector of shape and scale parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dllogis} gives the density, \code{pllogis} gives the distribution function, \code{qllogis} gives the quantile function, \code{hllogis} gives the hazard function, \code{Hllogis} gives the cumulative hazard function, and \code{rllogis} generates random deviates. } \description{ Density, distribution function, hazards, quantile function and random generation for the log-logistic distribution. } \details{ The log-logistic distribution with \code{shape} parameter \eqn{a>0} and \code{scale} parameter \eqn{b>0} has probability density function \deqn{f(x | a, b) = (a/b) (x/b)^{a-1} / (1 + (x/b)^a)^2} and hazard \deqn{h(x | a, b) = (a/b) (x/b)^{a-1} / (1 + (x/b)^a)} for \eqn{x>0}. The hazard is decreasing for shape \eqn{a\leq 1}{a <= 1}, and unimodal for \eqn{a > 1}. The probability distribution function is \deqn{F(x | a, b) = 1 - 1 / (1 + (x/b)^a)} If \eqn{a > 1}, the mean is \eqn{b c / sin(c)}, and if \eqn{a > 2} the variance is \eqn{b^2 * (2*c/sin(2*c) - c^2/sin(c)^2)}, where \eqn{c = \pi/a}, otherwise these are undefined. } \note{ Various different parameterisations of this distribution are used. In the one used here, the interpretation of the parameters is the same as in the standard Weibull distribution (\code{\link{dweibull}}). Like the Weibull, the survivor function is a transformation of \eqn{(x/b)^a} from the non-negative real line to [0,1], but with a different link function. Covariates on \eqn{b} represent time acceleration factors, or ratios of expected survival. The same parameterisation is also used in \code{\link[eha:Loglogistic]{eha::dllogis}} in the \pkg{eha} package. } \references{ Stata Press (2007) Stata release 10 manual: Survival analysis and epidemiological tables. } \seealso{ \code{\link{dweibull}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/coef.flexsurvreg.Rd0000644000176200001440000000277414165570616016506 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{coef.flexsurvreg} \alias{coef.flexsurvreg} \title{Extract model coefficients from fitted flexible survival models} \usage{ \method{coef}{flexsurvreg}(object, ...) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{...}{Further arguments passed to or from other methods. Currently unused.} } \value{ This returns the \code{mod$res.t[,"est"]} component of the fitted model object \code{mod}. See \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}} for full documentation of all components. } \description{ Extract model coefficients from fitted flexible survival models. This presents all parameter estimates, transformed to the real line if necessary. For example, shape or scale parameters, which are constrained to be positive, are returned on the log scale. } \details{ This matches the behaviour of \code{coef.default} for standard R model families such as \code{\link[stats]{glm}}, where intercepts in regression models are presented on the same scale as the covariate effects. Note that any parameter in a distribution fitted by \code{\link{flexsurvreg}} or \code{\link{flexsurvreg}} may be an intercept in a regression model. } \seealso{ \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}. } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{models} flexsurv/man/GenF.Rd0000644000176200001440000001144214603767242014026 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/GenF.R \name{GenF} \alias{GenF} \alias{dgenf} \alias{pgenf} \alias{qgenf} \alias{rgenf} \alias{Hgenf} \alias{hgenf} \title{Generalized F distribution} \usage{ dgenf(x, mu = 0, sigma = 1, Q, P, log = FALSE) pgenf(q, mu = 0, sigma = 1, Q, P, lower.tail = TRUE, log.p = FALSE) Hgenf(x, mu = 0, sigma = 1, Q, P) hgenf(x, mu = 0, sigma = 1, Q, P) qgenf(p, mu = 0, sigma = 1, Q, P, lower.tail = TRUE, log.p = FALSE) rgenf(n, mu = 0, sigma = 1, Q, P) } \arguments{ \item{x, q}{Vector of quantiles.} \item{mu}{Vector of location parameters.} \item{sigma}{Vector of scale parameters.} \item{Q}{Vector of first shape parameters.} \item{P}{Vector of second shape parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{Vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dgenf} gives the density, \code{pgenf} gives the distribution function, \code{qgenf} gives the quantile function, \code{rgenf} generates random deviates, \code{Hgenf} retuns the cumulative hazard and \code{hgenf} the hazard. } \description{ Density, distribution function, hazards, quantile function and random generation for the generalized F distribution, using the reparameterisation by Prentice (1975). } \details{ If \eqn{y \sim F(2s_1, 2s_2)}{y ~ F(2*s1, 2*s2)}, and \eqn{w = }{w = log(y)}\eqn{ \log(y)}{w = log(y)} then \eqn{x = \exp(w\sigma + \mu)}{x = exp(w*sigma + mu)} has the original generalized F distribution with location parameter \eqn{\mu}{mu}, scale parameter \eqn{\sigma>0}{sigma>0} and shape parameters \eqn{s_1,s_2}{s1,s2}. In this more stable version described by Prentice (1975), \eqn{s_1,s_2}{s1,s2} are replaced by shape parameters \eqn{Q,P}, with \eqn{P>0}, and \deqn{s_1 = 2(Q^2 + 2P + Q\delta)^{-1}, \quad s_2 = 2(Q^2 + 2P - Q\delta)^{-1}}{s1 = 2 / (Q^2 + 2P + Q*delta), s2 = 2 / (Q^2 + 2P - Q*delta)} equivalently \deqn{Q = \left(\frac{1}{s_1} - \frac{1}{s_2}\right)\left(\frac{1}{s_1} + \frac{1}{s_2}\right)^{-1/2}, \quad P = \frac{2}{s_1 + s_2} }{Q = (1/s1 - 1/s2) / (1/s1 + 1/s2)^{-1/2}, P = 2 / (s1 + s2) } Define \eqn{\delta = (Q^2 + 2P)^{1/2}}{delta = (Q^2 + 2P)^{1/2}}, and \eqn{w = (\log(x) - \mu)\delta /\sigma}{w = (log(x) - mu)delta / sigma}, then the probability density function of \eqn{x} is \deqn{ f(x) = \frac{\delta (s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 + s_2)} B(s_1, s_2)} }{ f(x) = (delta (s1/s2)^{s1} e^{s1 w}) / (sigma t (1 + s1 e^w/s2) ^ {(s1 + s2)} B(s1, s2)) } The original parameterisation is available in this package as \code{\link{dgenf.orig}}, for the sake of completion / compatibility. With the above definitions, \code{dgenf(x, mu=mu, sigma=sigma, Q=Q, P=P) = dgenf.orig(x, mu=mu, sigma=sigma/delta, s1=s1, s2=s2)} The generalized F distribution with \code{P=0} is equivalent to the generalized gamma distribution \code{\link{dgengamma}}, so that \code{dgenf(x, mu, sigma, Q, P=0)} equals \code{dgengamma(x, mu, sigma, Q)}. The generalized gamma reduces further to several common distributions, as described in the \code{\link{GenGamma}} help page. The generalized F distribution includes the log-logistic distribution (see \code{\link[eha:Loglogistic]{eha::dllogis}}) as a further special case: \code{dgenf(x, mu=mu, sigma=sigma, Q=0, P=1) = \link[eha:Loglogistic]{eha::dllogis}(x, shape=sqrt(2)/sigma, scale=exp(mu))} The range of hazard trajectories available under this distribution are discussed in detail by Cox (2008). Jackson et al. (2010) give an application to modelling oral cancer survival for use in a health economic evaluation of screening. } \note{ The parameters \code{Q} and \code{P} are usually called \eqn{q} and \eqn{p} in the literature - they were made upper-case in these R functions to avoid clashing with the conventional arguments \code{q} in the probability function and \code{p} in the quantile function. } \references{ R. L. Prentice (1975). Discrimination among some parametric models. Biometrika 62(3):607-614. Cox, C. (2008). The generalized \eqn{F} distribution: An umbrella for parametric survival analysis. Statistics in Medicine 27:4301-4312. Jackson, C. H. and Sharples, L. D. and Thompson, S. G. (2010). Survival models in health economic evaluations: balancing fit and parsimony to improve prediction. International Journal of Biostatistics 6(1):Article 34. } \seealso{ \code{\link{GenF.orig}}, \code{\link{GenGamma}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/Gompertz.Rd0000644000176200001440000000644014165570616015020 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/Gompertz.R \name{Gompertz} \alias{Gompertz} \alias{dgompertz} \alias{pgompertz} \alias{qgompertz} \alias{hgompertz} \alias{Hgompertz} \alias{rgompertz} \title{The Gompertz distribution} \usage{ dgompertz(x, shape, rate = 1, log = FALSE) pgompertz(q, shape, rate = 1, lower.tail = TRUE, log.p = FALSE) qgompertz(p, shape, rate = 1, lower.tail = TRUE, log.p = FALSE) rgompertz(n, shape = 1, rate = 1) hgompertz(x, shape, rate = 1, log = FALSE) Hgompertz(x, shape, rate = 1, log = FALSE) } \arguments{ \item{x, q}{vector of quantiles.} \item{shape, rate}{vector of shape and rate parameters.} \item{log, log.p}{logical; if TRUE, probabilities p are given as log(p).} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{vector of probabilities.} \item{n}{number of observations. If \code{length(n) > 1}, the length is taken to be the number required.} } \value{ \code{dgompertz} gives the density, \code{pgompertz} gives the distribution function, \code{qgompertz} gives the quantile function, \code{hgompertz} gives the hazard function, \code{Hgompertz} gives the cumulative hazard function, and \code{rgompertz} generates random deviates. } \description{ Density, distribution function, hazards, quantile function and random generation for the Gompertz distribution with unrestricted shape. } \details{ The Gompertz distribution with \code{shape} parameter \eqn{a} and \code{rate} parameter \eqn{b}{b} has probability density function \deqn{f(x | a, b) = be^{ax}\exp(-b/a (e^{ax} - 1))}{f(x | a, b) = b exp(ax) exp(-b/a (exp(ax) - 1))} and hazard \deqn{h(x | a, b) = b e^{ax}}{h(x | a, b) = b exp(ax)} The hazard is increasing for shape \eqn{a>0} and decreasing for \eqn{a<0}. For \eqn{a=0} the Gompertz is equivalent to the exponential distribution with constant hazard and rate \eqn{b}. The probability distribution function is \deqn{F(x | a, b) = 1 - \exp(-b/a (e^{ax} - 1))}{F(x | a, b) = 1 - exp(-b/a (exp(ax) - 1))} Thus if \eqn{a} is negative, letting \eqn{x} tend to infinity shows that there is a non-zero probability \eqn{\exp(b/a)}{exp(b/a)} of living forever. On these occasions \code{qgompertz} and \code{rgompertz} will return \code{Inf}. } \note{ Some implementations of the Gompertz restrict \eqn{a} to be strictly positive, which ensures that the probability of survival decreases to zero as \eqn{x} increases to infinity. The more flexible implementation given here is consistent with \code{streg} in Stata. The functions \code{\link[eha:Gompertz]{eha::dgompertz}} and similar available in the package \pkg{eha} label the parameters the other way round, so that what is called the \code{shape} there is called the \code{rate} here, and what is called \code{1 / scale} there is called the \code{shape} here. The terminology here is consistent with the exponential \code{\link{dexp}} and Weibull \code{\link{dweibull}} distributions in R. } \references{ Stata Press (2007) Stata release 10 manual: Survival analysis and epidemiological tables. } \seealso{ \code{\link{dexp}} } \author{ Christopher Jackson } \keyword{distribution} flexsurv/man/probs_flexsurvmix.Rd0000644000176200001440000000217114165570616017007 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/summary.flexsurvmix.R \name{probs_flexsurvmix} \alias{probs_flexsurvmix} \title{Probabilities of competing events from a flexsurvmix model} \usage{ probs_flexsurvmix(x, newdata = NULL, B = NULL) } \arguments{ \item{x}{Fitted model object returned from \code{\link{flexsurvmix}}.} \item{newdata}{Data frame or list of covariate values. If omitted for a model with covariates, a default is used, defined by all combinations of factors if the only covariates in the model are factors, or all covariate values of zero if there are any non-factor covariates in the model.} \item{B}{Number of simulations to use to compute 95\% confidence intervals, based on the asymptotic multivariate normal distribution of the basic parameter estimates. If \code{B=NULL} then intervals are not computed.} } \value{ A data frame containing the probability that each of the competing events will occur next, by event and by any covariate values specified in \code{newdata}. } \description{ Probabilities of competing events from a flexsurvmix model } flexsurv/man/msfit.flexsurvreg.Rd0000644000176200001440000001565214644755663016724 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{msfit.flexsurvreg} \alias{msfit.flexsurvreg} \title{Cumulative intensity function for parametric multi-state models} \usage{ msfit.flexsurvreg( object, t, newdata = NULL, variance = TRUE, tvar = "trans", trans, B = 1000 ) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object. The model should have been fitted to data consisting of one row for each observed transition and additional rows corresponding to censored times to competing transitions. This is the "long" format, or counting process format, as explained in the \pkg{flexsurv} vignette. The model should contain a categorical covariate indicating the transition. In \code{flexsurv} this variable can have any name, indicated here by the \code{tvar} argument. In the Cox models demonstrated by \pkg{mstate} it is usually included in model formulae as \code{strata(trans)}, but note that the \code{strata} function does not do anything in \pkg{flexsurv}. The formula supplied to \code{\link{flexsurvreg}} should be precise about which parameters are assumed to vary with the transition type. Alternatively, if the parameters (including covariate effects) are assumed to be different between different transitions, then a list of transition-specific models can be formed. This list has one component for each permitted transition in the multi-state model. This is more computationally efficient, particularly for larger models and datasets. See the example below, and the vignette.} \item{t}{Vector of times. These do not need to be the same as the observed event times, and since the model is parametric, they can be outside the range of the data. A grid of more frequent times will provide a better approximation to the cumulative hazard trajectory for prediction with \code{\link[mstate]{probtrans}} or \code{\link[mstate]{mssample}}, at the cost of greater computational expense.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. This must be specified if there are other covariates. The variable names should be the same as those in the fitted model formula. There must be either one value per covariate (the typical situation) or \eqn{n} values per covariate, a different one for each of the \eqn{n} allowed transitions.} \item{variance}{Calculate the variances and covariances of the transition cumulative hazards (\code{TRUE} or \code{FALSE}). This is based on simulation from the normal asymptotic distribution of the estimates, which is computationally-expensive.} \item{tvar}{Name of the categorical variable in the model formula that represents the transition number. This should have been defined as a factor, with factor levels that correspond to elements of \code{trans}, conventionally a sequence of integers starting from 1. Not required if \code{x} is a list of transition-specific models.} \item{trans}{Matrix indicating allowed transitions in the multi-state model, in the format understood by \pkg{mstate}: a matrix of integers whose \eqn{r,s} entry is \eqn{i} if the \eqn{i}th transition type (reading across rows) is \eqn{r,s}, and has \code{NA}s on the diagonal and where the \eqn{r,s} transition is disallowed.} \item{B}{Number of simulations from the normal asymptotic distribution used to calculate variances. Decrease for greater speed at the expense of accuracy.} } \value{ An object of class \code{"msfit"}, in the same form as the objects used in the \pkg{mstate} package. The \code{\link[mstate]{msfit}} method from \pkg{mstate} returns the equivalent cumulative intensities for Cox regression models fitted with \code{\link[survival]{coxph}}. } \description{ Cumulative transition-specific intensity/hazard functions for fully-parametric multi-state or competing risks models, using a piecewise-constant approximation that will allow prediction using the functions in the \pkg{mstate} package. } \examples{ ## 3 state illness-death model for bronchiolitis obliterans ## Compare clock-reset / semi-Markov multi-state models ## Simple exponential model (reduces to Markov) bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) mexp <- msfit.flexsurvreg(bexp, t=seq(0,12,by=0.1), trans=tmat, tvar="trans", variance=FALSE) ## Cox semi-parametric model within each transition bcox <- coxph(Surv(years, status) ~ strata(trans), data=bosms3) if (require("mstate")){ mcox <- mstate::msfit(bcox, trans=tmat) ## Flexible parametric spline-based model bspl <- flexsurvspline(Surv(years, status) ~ trans + gamma1(trans), data=bosms3, k=3) mspl <- msfit.flexsurvreg(bspl, t=seq(0,12,by=0.1), trans=tmat, tvar="trans", variance=FALSE) ## Compare fit: exponential model is OK but the spline is better plot(mcox, lwd=1, xlim=c(0, 12), ylim=c(0,4)) cols <- c("black","red","green") for (i in 1:3){ lines(mexp$Haz$time[mexp$Haz$trans==i], mexp$Haz$Haz[mexp$Haz$trans==i], col=cols[i], lwd=2, lty=2) lines(mspl$Haz$time[mspl$Haz$trans==i], mspl$Haz$Haz[mspl$Haz$trans==i], col=cols[i], lwd=3) } legend("topright", lwd=c(1,2,3), lty=c(1,2,1), c("Cox", "Exponential", "Flexible parametric"), bty="n") } ## Fit a list of models, one for each transition ## More computationally efficient, but only valid if parameters ## are different between transitions. \dontrun{ bexp.list <- vector(3, mode="list") for (i in 1:3) { bexp.list[[i]] <- flexsurvreg(Surv(years, status) ~ 1, subset=(trans==i), data=bosms3, dist="exp") } ## The list of models can be passed to this and other functions, ## as if it were a single multi-state model. msfit.flexsurvreg(bexp.list, t=seq(0,12,by=0.1), trans=tmat) } } \references{ Liesbeth C. de Wreede, Marta Fiocco, Hein Putter (2011). \pkg{mstate}: An R Package for the Analysis of Competing Risks and Multi-State Models. \emph{Journal of Statistical Software}, 38(7), 1-30. \doi{10.18637/jss.v038.i07} Mandel, M. (2013). "Simulation based confidence intervals for functions with complicated derivatives." The American Statistician 67(2):76-81 } \seealso{ \pkg{flexsurv} provides alternative functions designed specifically for predicting from parametric multi-state models without calling \pkg{mstate}. These include \code{\link{pmatrix.fs}} and \code{\link{pmatrix.simfs}} for the transition probability matrix, and \code{\link{totlos.fs}} and \code{\link{totlos.simfs}} for expected total lengths of stay in states. These are generally more efficient than going via \pkg{mstate}. } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{models} flexsurv/man/simfinal_fmsm.Rd0000644000176200001440000000443514523723770016036 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{simfinal_fmsm} \alias{simfinal_fmsm} \title{Simulate and summarise final outcomes from a flexible parametric multi-state model} \usage{ simfinal_fmsm( x, newdata = NULL, probs = c(0.025, 0.5, 0.975), t = 1000, M = 1e+05, B = 0, cores = NULL ) } \arguments{ \item{x}{Object returned by \code{\link{fmsm}}, representing a multi-state model formed from transition-specific time-to-event models fitted by \code{\link{flexsurvreg}}.} \item{newdata}{Data frame of covariate values, with one column per covariate, and one row per alternative value.} \item{probs}{Quantiles to calculate, by default, \code{c(0.025, 0.5, 0.975)} for a median and 95\% interval.} \item{t}{Maximum time to simulate to, passed to \code{\link{sim.fmsm}}, so that the summaries are taken from the subset of individuals in the simulated data who are in the absorbing state at this time.} \item{M}{Number of individuals to simulate.} \item{B}{Number of simulations to use to calculate 95\% confidence intervals based on the asymptotic normal distribution of the basic parameter estimates. If \code{B=0} then no intervals are calculated.} \item{cores}{Number of processor cores to use. If \code{NULL} (the default) then a single core is used.} } \value{ A tidy data frame with rows for each combination of covariate values and quantity of interest. The quantity of interest is identified in the column \code{quantity}, and the value of the quantity is in \code{val}, with additional columns \code{lower} and \code{upper} giving 95\% confidence intervals for the quantity, if \code{B>0}. } \description{ Estimates the probability of each final outcome ("absorbing" state), and the mean and quantiles of the time to that outcome for people who experience it, by simulating a large sample of individuals from the model. This can be used for both Markov and semi-Markov models. } \details{ For a competing risks model, i.e. a model defined by just one starting state and multiple destination states representing competing events, this returns the probability governing the next event that happens, and the distribution of the time to each event conditionally on that event happening. } flexsurv/man/nobs.flexsurvreg.Rd0000644000176200001440000000277114470654461016530 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/flexsurvreg.R \name{nobs.flexsurvreg} \alias{nobs.flexsurvreg} \title{Number of observations contributing to a fitted flexible survival model} \usage{ \method{nobs}{flexsurvreg}(object, cens = TRUE, ...) } \arguments{ \item{object}{Output from \code{\link{flexsurvreg}} or \code{\link{flexsurvspline}}, representing a fitted survival model object.} \item{cens}{Include censored observations in the number. \code{TRUE} by default. If \code{FALSE} then the number of observed events is returned. See \code{\link{BIC.flexsurvreg}} for a discussion of the issues with defining the sample size for censored data.} \item{...}{Further arguments passed to or from other methods. Currently unused.} } \value{ This returns the \code{mod$N} component of the fitted model object \code{mod}. See \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}} for full documentation of all components. } \description{ Number of observations contributing to a fitted flexible survival model } \details{ By default, this matches the behaviour of the \code{nobs} method for \code{\link[survival]{survreg}} objects, including both censored and uncensored observations. If a weighted \code{flexsurvreg} analysis was done, then this function returns the sum of the weights. } \seealso{ \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}. } \author{ C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk} } \keyword{models} flexsurv/man/sim.fmsm.Rd0000644000176200001440000001113314623361304014724 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mstate.R \name{sim.fmsm} \alias{sim.fmsm} \title{Simulate paths through a fully parametric semi-Markov multi-state model} \usage{ sim.fmsm( x, trans = NULL, t, newdata = NULL, start = 1, M = 10, tvar = "trans", tcovs = NULL, tidy = FALSE ) } \arguments{ \item{x}{A model fitted with \code{\link{flexsurvreg}}. See \code{\link{msfit.flexsurvreg}} for the required form of the model and the data. Alternatively \code{x} can be a list of fitted \code{\link{flexsurvreg}} model objects. The \code{i}th element of this list is the model corresponding to the \code{i}th transition in \code{trans}. This is a more efficient way to fit a multi-state model, but only valid if the parameters are different between different transitions.} \item{trans}{Matrix indicating allowed transitions. See \code{\link{msfit.flexsurvreg}}.} \item{t}{Time, or vector of times for each of the \code{M} individuals, to simulate trajectories until.} \item{newdata}{A data frame specifying the values of covariates in the fitted model, other than the transition number. See \code{\link{msfit.flexsurvreg}}.} \item{start}{Starting state, or vector of starting states for each of the \code{M} individuals.} \item{M}{Number of individual trajectories to simulate.} \item{tvar}{Variable in the data representing the transition type. Not required if \code{x} is a list of models.} \item{tcovs}{Names of "predictable" time-dependent covariates in \code{newdata}, i.e. those whose values change at the same rate as time. Age is a typical example. During simulation, their values will be updated after each transition time, by adding the current time to the value supplied in \code{newdata}. This assumes the covariate is measured in the same unit as time. \code{tcovs} is supplied as a character vector.} \item{tidy}{If \code{TRUE} then the simulated data are returned as a tidy data frame with one row per simulated transition. See \code{\link{simfs_bytrans}} for a function to rearrange the data into this format if it was simulated in non-tidy format. Currently this includes only event times, and excludes any times of censoring that are reported when \code{tidy=FALSE}.} } \value{ If \code{tidy=TRUE}, a data frame with one row for each simulated transition, giving the individual ID \code{id}, start state \code{start}, end state \code{end}, transition label \code{trans}, time of the transition since the start of the process (\code{time}), and time since the previous transition (\code{delay}). If \code{tidy=FALSE}, a list of two matrices named \code{st} and \code{t}. The rows of each matrix represent simulated individuals. The columns of \code{t} contain the times when the individual changes state, to the corresponding states in \code{st}. The first columns will always contain the starting states and the starting times. The last column of \code{t} represents either the time when the individual moves to an absorbing state, or right-censoring in a transient state at the time given in the \code{t} argument to \code{sim.fmsm}. } \description{ Simulate changes of state and transition times from a semi-Markov multi-state model fitted using \code{\link{flexsurvreg}}. } \details{ \code{sim.fmsm} relies on the presence of a function to sample random numbers from the parametric survival distribution used in the fitted model \code{x}, for example \code{\link{rweibull}} for Weibull models. If \code{x} was fitted using a custom distribution, called \code{dist} say, then there must be a function called (something like) \code{rdist} either in the working environment, or supplied through the \code{dfns} argument to \code{\link{flexsurvreg}}. This must be in the same format as standard R functions such as \code{\link{rweibull}}, with first argument \code{n}, and remaining arguments giving the parameters of the distribution. It must be vectorised with respect to the parameter arguments. This function is only valid for semi-Markov ("clock-reset") models, though no warning or error is currently given if the model is not of this type. An equivalent for time-inhomogeneous Markov ("clock-forward") models has currently not been implemented. } \examples{ bexp <- flexsurvreg(Surv(years, status) ~ trans, data=bosms3, dist="exp") tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA)) sim.fmsm(bexp, M=10, t=5, trans=tmat) } \seealso{ \code{\link{pmatrix.simfs}},\code{\link{totlos.simfs}} } \author{ Christopher Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}. } \keyword{models} \keyword{survival} flexsurv/man/Survsplinek.Rd0000644000176200001440000003564614603754465015553 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/survsplinek.R \name{Survsplinek} \alias{Survsplinek} \alias{dsurvspline0} \alias{dsurvspline1} \alias{dsurvspline2} \alias{dsurvspline3} \alias{dsurvspline4} \alias{dsurvspline5} \alias{dsurvspline6} \alias{dsurvspline7} \alias{psurvspline0} \alias{psurvspline1} \alias{psurvspline2} \alias{psurvspline3} \alias{psurvspline4} \alias{psurvspline5} \alias{psurvspline6} \alias{psurvspline7} \alias{qsurvspline0} \alias{qsurvspline1} \alias{qsurvspline2} \alias{qsurvspline3} \alias{qsurvspline4} \alias{qsurvspline5} \alias{qsurvspline6} \alias{qsurvspline7} \alias{rsurvspline0} \alias{rsurvspline1} \alias{rsurvspline2} \alias{rsurvspline3} \alias{rsurvspline4} \alias{rsurvspline5} \alias{rsurvspline6} \alias{rsurvspline7} \alias{hsurvspline0} \alias{hsurvspline1} \alias{hsurvspline2} \alias{hsurvspline3} \alias{hsurvspline4} \alias{hsurvspline5} \alias{hsurvspline6} \alias{hsurvspline7} \alias{Hsurvspline0} \alias{Hsurvspline1} \alias{Hsurvspline2} \alias{Hsurvspline3} \alias{Hsurvspline4} \alias{Hsurvspline5} \alias{Hsurvspline6} \alias{Hsurvspline7} \alias{mean_survspline0} \alias{mean_survspline1} \alias{mean_survspline2} \alias{mean_survspline3} \alias{mean_survspline4} \alias{mean_survspline5} \alias{mean_survspline6} \alias{mean_survspline7} \alias{rmst_survspline0} \alias{rmst_survspline1} \alias{rmst_survspline2} \alias{rmst_survspline3} \alias{rmst_survspline4} \alias{rmst_survspline5} \alias{rmst_survspline6} \alias{rmst_survspline7} \title{Royston/Parmar spline survival distribution functions with one argument per parameter} \usage{ mean_survspline0( gamma0, gamma1, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline1( gamma0, gamma1, gamma2, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline2( gamma0, gamma1, gamma2, gamma3, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline3( gamma0, gamma1, gamma2, gamma3, gamma4, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline4( gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline5( gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline6( gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) mean_survspline7( gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp" ) rmst_survspline0( t, gamma0, gamma1, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline1( t, gamma0, gamma1, gamma2, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline2( t, gamma0, gamma1, gamma2, gamma3, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline3( t, gamma0, gamma1, gamma2, gamma3, gamma4, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline4( t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline5( t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline6( t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) rmst_survspline7( t, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots = c(-10, 10), scale = "hazard", timescale = "log", spline = "rp", start = 0 ) dsurvspline0( x, gamma0, gamma1, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline1( x, gamma0, gamma1, gamma2, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline2( x, gamma0, gamma1, gamma2, gamma3, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline3( x, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline4( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline5( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline6( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) dsurvspline7( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale = "hazard", timescale = "log", spline = "rp", log = FALSE ) psurvspline0( q, gamma0, gamma1, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline1( q, gamma0, gamma1, gamma2, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline2( q, gamma0, gamma1, gamma2, gamma3, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline3( q, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline4( q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline5( q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline6( q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) psurvspline7( q, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline0( p, gamma0, gamma1, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline1( p, gamma0, gamma1, gamma2, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline2( p, gamma0, gamma1, gamma2, gamma3, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline3( p, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline4( p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline5( p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline6( p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) qsurvspline7( p, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale = "hazard", timescale = "log", spline = "rp", lower.tail = TRUE, log.p = FALSE ) rsurvspline0( n, gamma0, gamma1, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline1( n, gamma0, gamma1, gamma2, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline2( n, gamma0, gamma1, gamma2, gamma3, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline3( n, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline4( n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline5( n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline6( n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale = "hazard", timescale = "log", spline = "rp" ) rsurvspline7( n, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline0( x, gamma0, gamma1, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline1( x, gamma0, gamma1, gamma2, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline2( x, gamma0, gamma1, gamma2, gamma3, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline3( x, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline4( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline5( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline6( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale = "hazard", timescale = "log", spline = "rp" ) hsurvspline7( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline0( x, gamma0, gamma1, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline1( x, gamma0, gamma1, gamma2, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline2( x, gamma0, gamma1, gamma2, gamma3, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline3( x, gamma0, gamma1, gamma2, gamma3, gamma4, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline4( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline5( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline6( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, knots, scale = "hazard", timescale = "log", spline = "rp" ) Hsurvspline7( x, gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8, knots, scale = "hazard", timescale = "log", spline = "rp" ) } \arguments{ \item{gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7, gamma8}{Parameters describing the baseline spline function, as described in \code{\link{flexsurvspline}}.} \item{knots}{Locations of knots on the axis of log time, supplied in increasing order. Unlike in \code{\link{flexsurvspline}}, these include the two boundary knots. If there are no additional knots, the boundary locations are not used. If there are one or more additional knots, the boundary knots should be at or beyond the minimum and maximum values of the log times. In \code{\link{flexsurvspline}} these are exactly at the minimum and maximum values. This may in principle be supplied as a matrix, in the same way as for \code{gamma}, but in most applications the knots will be fixed.} \item{scale}{\code{"hazard"}, \code{"odds"}, or \code{"normal"}, as described in \code{\link{flexsurvspline}}. With the default of no knots in addition to the boundaries, this model reduces to the Weibull, log-logistic and log-normal respectively. The scale must be common to all times.} \item{timescale}{\code{"log"} or \code{"identity"} as described in \code{\link{flexsurvspline}}.} \item{spline}{\code{"rp"} to use the natural cubic spline basis described in Royston and Parmar. \code{"splines2ns"} to use the alternative natural cubic spline basis from the \code{splines2} package (Wang and Yan 2021), which may be better behaved due to the basis being orthogonal.} \item{start}{Optional left-truncation time or times. The returned restricted mean survival will be conditioned on survival up to this time.} \item{x, q, t}{Vector of times.} \item{log, log.p}{Return log density or probability.} \item{lower.tail}{logical; if TRUE (default), probabilities are \eqn{P(X \le x)}{P(X <= x)}, otherwise, \eqn{P(X > x)}{P(X > x)}.} \item{p}{Vector of probabilities.} \item{n}{Number of random numbers to simulate.} } \description{ Probability density, distribution, quantile, random generation, hazard, cumulative hazard, mean and restricted mean functions for the Royston/Parmar spline model, with one argument per parameter. For the equivalent functions with all parameters collected together in a single argument, see \code{\link{Survspline}}. } \details{ These functions go up to 7 spline knots, or 9 parameters. } \author{ Christopher Jackson } flexsurv/DESCRIPTION0000644000176200001440000000376014660035012013641 0ustar liggesusersPackage: flexsurv Type: Package Title: Flexible Parametric Survival and Multi-State Models Version: 2.3.2 Date: 2024-08-16 Authors@R: c(person("Christopher", "Jackson", email="chris.jackson@mrc-bsu.cam.ac.uk", role=c("aut", "cre")), person("Paul", "Metcalfe", role=c("ctb")), person("Jordan", "Amdahl", role=c("ctb")), person("Matthew T.", "Warkentin", role = c("ctb")), person("Michael", "Sweeting", role = c("ctb")), person("Kevin", "Kunzmann", role = c("ctb")) ) Description: Flexible parametric models for time-to-event data, including the Royston-Parmar spline model, generalized gamma and generalized F distributions. Any user-defined parametric distribution can be fitted, given at least an R function defining the probability density or hazard. There are also tools for fitting and predicting from fully parametric multi-state models, based on either cause-specific hazards or mixture models. License: GPL (>= 2) Depends: survival, R (>= 2.15.0) Imports: assertthat, deSolve, generics, magrittr, mstate (>= 0.2.10), Matrix, muhaz, mvtnorm, numDeriv, quadprog, Rcpp (>= 0.11.5), rlang, rstpm2, purrr, statmod, tibble, tidyr, dplyr, tidyselect, ggplot2 Encoding: UTF-8 Suggests: splines2, flexsurvcure, survminer, lubridate, rmarkdown, colorspace, eha, knitr, msm, testthat, TH.data, broom, covr URL: https://github.com/chjackson/flexsurv, http://chjackson.github.io/flexsurv/ BugReports: https://github.com/chjackson/flexsurv/issues VignetteBuilder: knitr LazyData: yes LinkingTo: Rcpp RoxygenNote: 7.3.1 NeedsCompilation: yes Packaged: 2024-08-16 15:05:50 UTC; Chris Author: Christopher Jackson [aut, cre], Paul Metcalfe [ctb], Jordan Amdahl [ctb], Matthew T. Warkentin [ctb], Michael Sweeting [ctb], Kevin Kunzmann [ctb] Maintainer: Christopher Jackson Repository: CRAN Date/Publication: 2024-08-17 05:50:02 UTC