R version 4.4.0 RC (2024-04-16 r86458 ucrt) -- "Puppy Cup"
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> #
> # Tests for multi-state Cox models
> #
> library(survival)
> 
> aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
> 
> #  There are a few subjects with progression and death on the same day. In the
> # usual multi-state data set only one will count. 
> data1 <- mgus2
> data1$etime <- with(data1, ifelse(pstat==1, ptime, futime))
> data1$event <- factor(ifelse(data1$pstat==1, 1, 2L*data1$death),
+                       0:2, c("censor", "PCM", "death"))
> 
> # direct data set with 2 rows per subject, much like mstate package would do
> data2 <- mgus2[rep(1:nrow(mgus2) ,2), c("id", "age", "sex", "mspike")]
> data2$time <- rep(data1$etime, 2)
> data2$status <- 1* c(data1$event=="PCM", data1$event=="death")
> data2$type   <- rep(c(2:3), each=nrow(mgus2))
> 
> fit1 <- coxph(Surv(etime, event) ~ age + sex + mspike, data1, id=id, x=TRUE,
+               robust=FALSE)
> fit1a <- coxph(Surv(etime, event=="PCM") ~ age + sex + mspike, data1)
> fit1b <- coxph(Surv(etime, event=='death') ~ age + sex + mspike, data1)
> fit1c <- coxph(Surv(time, status) ~ strata(type)/(age + sex+ mspike), 
+                data2, x=TRUE)
> 
> aeq(fit1$loglik, fit1a$loglik + fit1b$loglik)
[1] TRUE
> aeq(fit1$coef, c(fit1a$coef, fit1b$coef))
[1] TRUE
> aeq(fit1$var[1:3, 1:3], fit1a$var)
[1] TRUE
> aeq(fit1$var[4:6, 4:6], fit1b$var)
[1] TRUE
> aeq(fit1$coef[c(1,4,2,5,3,6)], fit1c$coef)
[1] TRUE
> 
> # force a common age effect across all states
> fit2 <- coxph(list(Surv(etime, event) ~ sex,
+                                   1:0 ~ age / common), 
+               data1, id=id)
> 
> data2 <- rbind(cbind(data1, status= (data1$event=="PCM"), etype=1),
+                cbind(data1, status= (data1$event=='death'), etype=2))
> fit2a <- coxph(Surv(etime, status) ~ age + strata(etype)/sex, data2)
> 
> aeq(coef(fit2), coef(fit2a)[c(2,1,3)])  # not in the same order
[1] TRUE
> aeq(fit2$loglik, fit2a$loglik)
[1] TRUE
> 
> #same fit in more complex ways
> data1$entry <- "Entry"
> fit2b <-  coxph(list(Surv(etime, event) ~ sex,
+                      "Entry":"PCM" + "Entry":"death" ~ age / common),
+                 istate=entry, data1, id=id)
> fit2c <-  coxph(list(Surv(etime, event) ~ sex,
+                      "Entry":state(c("PCM", "death")) ~ age / common),
+                 istate=entry, data1, id=id)
> 
> aeq(fit2b$loglik, fit2$loglik)
[1] TRUE
> aeq(fit2c$coef, fit2$coef)
[1] TRUE
> 
> # mspike size as a covariate for PCM only
> # first, 4 different ways to write the same
> fit3 <- coxph(list(Surv(etime, event) ~ age + sex,
+                    1:state("PCM") ~ mspike),
+               data1, id=id)
> fit3b <- coxph(list(Surv(etime, event) ~ age + sex,
+                    1:"PCM" ~ mspike),
+               data1, id=id)
> fit3c <- coxph(list(Surv(etime, event) ~ age + sex,
+                    1:c("PCM") ~ mspike),
+               data1, id=id)
> fit3d <- coxph(list(Surv(etime, event) ~ age + sex + mspike,
+                     1:3 ~ -mspike), data1, id=id)
> 
> aeq(fit3b$coef, fit3$coef)
[1] TRUE
> aeq(fit3c$coef, fit3$coef)
[1] TRUE
> aeq(fit3d$coef, fit3$coef)
[1] TRUE
> 
> data3 <- data2
> data3$mspike[data3$etype==2] <- 0
> fit3a <-  coxph(Surv(etime, status) ~ strata(etype)/(age + sex + mspike), data3)
> aeq(fit3$loglik, fit3a$loglik)
[1] TRUE
> aeq(fit3$coef, fit3a$coef[c(1,3,5,2,4)])
[1] TRUE
> 
> # models with strata
> test1 <-  coxph(Surv(etime, event=="PCM") ~ age + mspike + strata(sex), data1)
> test2 <-  coxph(Surv(etime, event=="death") ~ age + strata(sex), data1)
> 
> sfit1 <-  coxph(list(Surv(etime, event) ~ age + strata(sex), 
+                    1:state("PCM") ~ mspike),
+               data1, id=id)
> aeq(coef(sfit1), c(coef(test1), coef(test2)))
[1] TRUE
> 
> test3 <- coxph(Surv(etime, event=="death") ~ age +sex, data1)
> sfit2 <- coxph(list(Surv(etime, event) ~ age + sex,
+                     1:2 ~ mspike + strata(sex) - sex),  data1, id=id)
> aeq(coef(sfit2), c(coef(test1), coef(test3)))
[1] TRUE
> 
> 
> proc.time()
   user  system elapsed 
   1.25    0.25    1.48