R version 4.1.2 (2021-11-01) -- "Bird Hippie"
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> #
> # Verify that using multiple states + proportional baselines
> #  will mimic a factor covariate
> #
> library(survival)
> aeq <- function(x, y, ...) all.equal(as.vector(x), as.vector(y), ...)
> 
> tdata <- subset(lung, ph.ecog < 3)  # there is only one row with ph.ecog=3
> tdata$state <- factor(tdata$status, 1:2, c("censor", "death"))
> tdata$cstate<- factor(tdata$ph.ecog, 0:2, c("ph0", "ph1", "ph2"))
> tdata$id  <- 1:nrow(tdata)
> survcheck(Surv(time, state) ~ 1, id=id, istate=cstate, tdata)
Call:
survcheck(formula = Surv(time, state) ~ 1, data = tdata, id = id, 
    istate = cstate)

Unique identifiers       Observations        Transitions 
               226                226                163 

Transitions table:
       to
from    death (censored)
  ph0      37         26
  ph1      82         31
  ph2      44          6
  death     0          0

Number of subjects with 0, 1, ... transitions to each state:
       count
state    0   1
  death 63 163
  (any) 63 163

> 
> # standard coxph fit, stratified by the ph0/1/2 groups
> fit1 <- coxph(Surv(time, status) ~ age + sex + factor(ph.ecog), tdata, 
+                  ties="breslow")
> # multi-state fit, where ph0/1/2 are states with a shared hazard
> fit2 <- coxph(list(Surv(time, state) ~1,
+                    1:4 + 2:4 + 3:4~ age + sex/ common + shared), 
+               id=id, istate=cstate, data= tdata, ties="breslow")
> 
> aeq(coef(fit1), coef(fit2))  # the names are quite different, values the same
[1] TRUE
> all.equal(fit1$loglik, fit2$loglik)
[1] TRUE
> 
> # Three curves in the usual way: ph0, 1, or 2 for all time, common baseline
> csurv1 <- survfit(fit1, newdata=expand.grid(age=65, sex=1, ph.ecog=0:2))
> 
> # Multistate: start in p0, p1, or p2 (the only place to go is death)
> csurv2a <- survfit(fit2, newdata= list(age=65, sex=1), p0=c(1,0,0,0))
> csurv2b <- survfit(fit2, newdata= list(age=65, sex=1), p0=c(0,1,0,0))
> csurv2c <- survfit(fit2, newdata= list(age=65, sex=1), p0=c(0,0,1,0))
> 
> aeq(csurv1[1]$surv, csurv2a$pstate[,1,1])
[1] TRUE
> aeq(csurv1[2]$surv, csurv2b$pstate[,1,2])
[1] TRUE
> aeq(csurv1[3]$surv, csurv2c$pstate[,1,3])
[1] TRUE
> 
> # Note that multi-state defaults to the Breslow, as it implements the Efron
> #  only imperfectly.
> 
> # part 2: predicted survival for a multistate model that has a strata
> mgus2$etime <- with(mgus2, ifelse(pstat==0, futime, ptime))
> temp <- with(mgus2, ifelse(pstat==0, 2*death, 1))
> mgus2$event <- factor(temp, 0:2, labels=c("censor", "pcm", "death"))
> 
> dummy <- expand.grid(age=c(60, 80), mspike=1.2)
> 
> cfit1 <- coxph(Surv(etime, event) ~ age + mspike +strata(sex), mgus2, id=id)
> 
> csurv1 <- survfit(cfit1, newdata=dummy)
> 
> cfit2 <- coxph(Surv(etime, event) ~ age + mspike, id=id,
+                init= coef(cfit1), iter=0, data=mgus2, subset=(sex=='F'))
> csurv3 <- survfit(cfit2, newdata= expand.grid(age=c(60, 80), mspike=1.2))
> test <- c('n', 'time', 'n.risk', 'n.event', 'n.censor', 'pstate', 'cumhaz')
> all.equal(unclass(csurv1[1,,])[test], unclass(csurv3)[test])
[1] TRUE
> 
> 
> 
> proc.time()
   user  system elapsed 
  1.322   0.123   1.498