R Under development (unstable) (2023-08-12 r84939 ucrt) -- "Unsuffered Consequences"
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> options(na.action=na.exclude) # preserve missings
> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
> library(survival)
> 
> #
> # Simple test of (start, stop] Kaplan-Meier curves, using the test2 data
> #   set
> #
> test1 <- data.frame(time=  c(9, 3,1,1,6,6,8),
+                     status=c(1,NA,1,0,1,1,0),
+                     x=     c(0, 2,1,1,1,0,0))
> test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8),
+                     stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17),
+                     event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0),
+                     x    =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0),
+                     wt   = 1:10)
> aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
> test2 <- test2[c(1,6,2,7,3,8,4,9,5,10),]  # unsorted data is a harder test
> 
> fit1 <- survfit(Surv(start, stop, event) ~1, test2, type='fh2',
+                 error='tsiatis')
> fit2 <- survfit(Surv(start, stop, event) ~x, test2, start.time=3,
+ 		type='fh2')
> 
> cfit1<- survfit(coxph(Surv(start, stop, event)~1, test2))
> cfit2<- survfit(coxph(Surv(start, stop, event) ~ strata(x), test2, subset=-1))
> 
> deaths <- (fit1$n.event + fit1$n.censor)>0
> aeq(fit1$time[deaths], cfit1$time)
[1] TRUE
> aeq(fit1$n.risk[deaths], cfit1$n.risk)
[1] TRUE
> aeq(fit1$n.event[deaths], cfit1$n.event)
[1] TRUE
> aeq(fit1$surv[deaths], cfit1$surv)
[1] TRUE
> aeq(fit1$std.err[deaths], cfit1$std.err)
[1] TRUE
> 
> deaths <- (fit2$n.event + fit2$n.censor)>0
> aeq(fit2$time[deaths], cfit2$time)
[1] TRUE
> aeq(fit2$n.risk[deaths], cfit2$n.risk)
[1] TRUE
> aeq(fit2$n.event[deaths], cfit2$n.event)
[1] TRUE
> aeq(fit2$surv[deaths], cfit2$surv)
[1] TRUE
> 
> fit3 <- survfit(Surv(start, stop, event) ~1, test2) #Kaplan-Meier
> aeq(fit3$n, 10)
[1] TRUE
> aeq(fit3$time, sort(unique(test2$stop)))
[1] TRUE
> aeq(fit3$n.risk, c(2,3,5,4,4,5,2,1))
[1] TRUE
> aeq(fit3$n.event,c(1,1,1,1,1,2,0,0))
[1] TRUE
> aeq(fit3$surv[fit3$n.event>0], c(.5, 1/3, 4/15, 1/5, 3/20, 9/100))
[1] TRUE
> temp <- with(fit3, n.event/(n.risk * (n.risk - n.event)))
> aeq(fit3$std.err, sqrt(cumsum(temp)))
[1] TRUE
> 
> #
> #  Verify that both surv AND n.risk are right between time points.
> #
> fit <- survfit(Surv(time, status) ~1, test1)
> temp <- summary(fit, time=c(.5,1, 1.5, 6, 7.5, 8, 8.9, 9, 10), extend=TRUE)
> 
> aeq(temp$n.risk, c(6,6,4,4,2,2,1,1,0))
[1] TRUE
> aeq(temp$surv, c(1, fit$surv[c(1,1,2,2,3,3,4,4)]))
[1] TRUE
> aeq(temp$n.event, c(0,1,0,2,0,0,0,1,0))
[1] TRUE
> aeq(temp$std.err, c(0, (fit$surv*fit$std.err)[c(1,1,2,2,3,3,4,4)]))
[1] TRUE
> 
> 
> fit <- survfit(Surv(start, stop, event) ~1, test2)
> temp <- summary(fit, times=c(.5, 1.5, 2.5, 3, 6.5, 14.5, 16.5))
> aeq(temp$surv, c(1, 1, fit$surv[c(1,2,3,6,6)]))
[1] TRUE
> 
> # This next fails.  With start-stop data the number at risk at intermediate
> #  endpoints is not known precisely, since the underlying routine does not report
> #  time points at which only an addition occured. 
> if (FALSE) aeq(temp$n.risk, c(0, 2, 3, 3, 4, 1,1))
> 
> # compute conditional survival
> fit1 <- survfit(Surv(start, stop, event)~1, test2, weights=wt)
> fit2 <- survfit(Surv(start, stop, event)~1, test2, weights=wt, start.time=5)
> 
> aeq(fit1$surv[2], summary(fit1, time=5)$surv)  # verify my subscript
[1] TRUE
> aeq(fit2$surv, fit1$surv[3:8]/fit1$surv[2])
[1] TRUE
> aeq(fit2$std.err^2,   fit1$std.err[3:8]^2 - fit1$std.err[2]^2)
[1] TRUE
> aeq(fit2$cumhaz, fit1$cumhaz[3:8] - fit1$cumhaz[2])
[1] TRUE
> aeq(fit2$std.chaz^2,   fit1$std.chaz[3:8]^2 - fit1$std.chaz[2]^2)
[1] TRUE
> 
> # Now with a Cox model
> cfit <- coxph(Surv(start, stop, event)~1, test2, weights=wt)
> fit1 <- survfit(cfit)
> fit2 <- survfit(cfit, start.time=5)
> aeq(fit2$surv, fit1$surv[3:8]/fit1$surv[2])
[1] TRUE
> aeq(fit2$std.err^2,   fit1$std.err[3:8]^2 - fit1$std.err[2]^2)
[1] TRUE
> aeq(fit2$cumhaz, fit1$cumhaz[3:8] - fit1$cumhaz[2])
[1] TRUE
> aeq(fit2$std.chaz^2,   fit1$std.chaz[3:8]^2 - fit1$std.chaz[2]^2)
[1] TRUE
> 
> 
> # bigger data set, with covariates and some tied event times
> mfit <- coxph(Surv(age, age+futime/12, death) ~ sex + mspike, mgus2)
> dummy <- data.frame(sex='F', mspike=1.3)
> 
> msurv1 <- survfit(mfit, newdata=dummy)
> msurv2 <- survfit(mfit, newdata=dummy, start.time=80)
> j <- max(which(msurv1$time < 80))
> k <- seq(j+1, length(msurv1$time))
> aeq(msurv2$surv, msurv1$surv[k] / msurv1$surv[j])
[1] TRUE
> aeq(msurv2$cumhaz, msurv1$cumhaz[k] - msurv1$cumhaz[j])
[1] TRUE
> # standard errors now have a term due to vmat(mfit), so don't factor
> #  into a simple sum
> 
> proc.time()
   user  system elapsed 
   0.96    0.09    1.06