R version 4.4.0 beta (2024-04-12 r86413 ucrt) -- "Puppy Cup"
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> library(survival)
> options(na.action=na.exclude) # preserve missings
> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
> aeq <- function(x,y,...) all.equal(as.vector(x), as.vector(y),...)
> 
> #
> # Test out the results for competing risks.  Survfit does this directly as just
> #   one case of the Aalen-Johansen, but also known as 'cumulative incidence'.
> #
> # First trivial test
> tdata <- data.frame(time=c(1,2,2,3,3,3,5,6),
+                     status = c(0,1,0,1,0,1,0,1),
+                     event =  c(1,1,2,2,1,2,3,2),
+                     grp = c(1,2,1,2,1,2,1,2),
+                     id = 1:8)
> old <- survfit(Surv(time, status*event, type="mstate") ~1, tdata) #old style
> fit <- survfit(Surv(time, factor(status*event)) ~1, tdata)
> 
> # test that the old (should be depricated) form gives the same answer
> indx <- match("call", names(fit))
> all.equal(unclass(old)[-indx], unclass(fit)[-indx])
[1] TRUE
> 
> byhand <- function() {
+     #everyone starts in state 0
+     p1 <- c(1,0,0)
+ 
+     p2 <- c(6/7, 1/7, 0)  # 0-1 transition at time 2
+     u2 <- matrix(rep(c(1/49, -1/49, 0), each=8), ncol=3) #leverage matrix at time 2
+     u2[1,] <- 0  #subject 1 is not present
+     u2[2,1:2] <- u2[2, 1:2] + c(-1/7, 1/7)
+ 
+     p3 <- c((6/7)*(3/5), 1/7, 12/35) # 0-2 transition at time 3, 5 at risk
+     h3 <- matrix(c(3/5, 0, 2/5, 0,1,0, 0,1,0), byrow=T, ncol=3) #hazard mat
+     u3 <- u2 %*% h3
+     u3[4:8,1] <- u3[4:8,1] + p2[1]*2/25
+     u3[4:8,3] <- u3[4:8,3]  -p2[1]*2/25
+     u3[4,] <- u3[4,] + c(-p2[1]/5, 0, p2[1]/5)
+     u3[6,] <- u3[4,]
+  
+     p6 <- c(0, 1/7, 6/7) # 0-2 at time 6, 1 at risk
+     h6 <- matrix(c(-1,0,1,0,1,0,0,1,0), byrow=T, ncol=3)
+     u6 <- cbind(0, u3[,2], -u3[,2])
+     
+     V <- rbind(0, colSums(u2^2), 
+                   colSums(u3^2),
+                   colSums(u3^2),
+                   colSums(u6^2))
+     list(P=rbind(p1, p2, p3, p3, p6), u2=u2, u3=u3, u6=u6, V=V)
+ }
> bfit <- byhand()
> aeq(fit$pstate, bfit$P)
[1] TRUE
> aeq(fit$n.risk[,1], c(8,7,5,2,1))
[1] TRUE
> aeq(fit$n.event[,2:3], c(0,1,0,0,0, 0,0 ,2,0,1))
[1] TRUE
> aeq(fit$std.err, sqrt(bfit$V))
[1] TRUE
> 
> # Check the influence directly, per row
> eps <- 1e-6
> deltaU <- array(0, dim= c(nrow(tdata), dim(fit$pstate))) 
> deltaC <- array(0, dim= c(nrow(tdata), dim(fit$cumhaz)))
> deltaA <- deltaU
> auc <- function(fit) {
+     nr <- length(fit$time)
+     rbind(fit$p0*fit$time[1], 
+           apply(diff(fit$time) * fit$pstate[-nr,], 2, cumsum))
+ }   
> for (i in 1:nrow(tdata)) {
+     twt <- rep(1, nrow(tdata))
+     twt[i] <- twt[i] + eps
+     tfit <- survfit(Surv(time, factor(status*event)) ~1, tdata, id=id,
+                     weights= twt)
+     deltaU[i,,] <- (tfit$pstate - fit$pstate)/eps  # approx derivative
+     deltaC[i,,] <- (tfit$cumhaz - fit$cumhaz)/eps
+     deltaA[i,,] <- (auc(tfit) - auc(fit))/eps
+ }
> aeq(bfit$u2, deltaU[,2,], tol=eps)
[1] TRUE
> aeq(bfit$u3, deltaU[,3,], tol=eps)
[1] TRUE
> aeq(bfit$u6, deltaU[,5,], tol=eps)
[1] TRUE
> 
> sqmean <- function(x) sqrt(sum(x^2))
> aeq(fit$std.chaz, apply(deltaC, 2:3, sqmean), tol=eps)
[1] TRUE
> aeq(fit$std.err,  apply(deltaU, 2:3, sqmean), tol=eps)
[1] TRUE
> aeq(fit$std.auc,  apply(deltaA, 2:3, sqmean), tol=eps)
[1] TRUE
> 
> # Times purposely has values that are before the start, exact, intermediate
> #  and after the end of the observed times
> sfit <- summary(fit, times=c(0, 1, 3.5, 6, 7), extend=TRUE)
> aeq(sfit$pstate, rbind(c(1,0,0), bfit$P[c(1,3,5,5),]))
[1] TRUE
> aeq(sfit$n.risk[,1], c(8,8, 2, 1, 0))
[1] TRUE
> aeq(sfit$n.event,  matrix(c(0,0,0,0,0, 0,0,1,0,0, 0,0,2,1,0), ncol=3))
[1] TRUE
> 
> #
> # For this we need the competing risks MGUS data set, first
> #  event
> #
> tdata <- mgus1[mgus1$enum==1,]
> # Ensure the old-style call using "etype" works (backwards compatability)
> fit1 <- survfit(Surv(stop, status) ~ 1, etype=event, tdata)
> fit1b <-survfit(Surv(stop, event) ~1, tdata)
> indx <- match("call", names(fit1)) 
> all.equal(unclass(fit1)[-indx], unclass(fit1b)[-indx])
[1] TRUE
> 
> # Now get the overall survival, and the hazard for progression
> fit2 <- survfit(Surv(stop, status) ~1, tdata)  #overall to "first bad thing"
> fit3 <- survfit(Surv(stop, status*(event=='pcm')) ~1, tdata,
+                 type='fleming')
> fit4 <- survfit(Surv(stop, status*(event=='death')) ~1, tdata,
+                 type='fleming')
> 
> aeq(fit1$n.risk[,1], fit2$n.risk)
[1] TRUE
> aeq(rowSums(fit1$n.event), fit2$n.event)
[1] TRUE
> 
> # Classic CI formula
> #  integral [hazard(t) S(t-0) dt], where S= "survival to first event"
> haz1 <- diff(c(0, -log(fit3$surv))) #Aalen hazard estimate for progression
> haz2 <- diff(c(0, -log(fit4$surv))) #Aalen estimate for death
> tsurv <- c(1, fit2$surv[-length(fit2$surv)])  #lagged survival
> ci1 <- cumsum(haz1 *tsurv)
> ci2 <- cumsum(haz2 *tsurv)
> aeq(cbind(ci1, ci2), fit1$pstate[,2:3])
[1] TRUE
> 
> #
> # Now, make sure that it works for subgroups
> #
> fit1 <- survfit(Surv(stop, event) ~ sex, tdata)
> fit2 <- survfit(Surv(stop, event) ~ 1, tdata,
+                         subset=(sex=='female'))
> fit3 <- survfit(Surv(stop, event) ~ 1, tdata,
+                    subset=(sex=='male'))
> 
> aeq(fit2$pstate, fit1$pstate[1:fit1$strata[1],])
[1] TRUE
> aeq(fit2$std, fit1$std[1:fit1$strata[1],])
[1] TRUE
> aeq(fit3$pstate, fit1$pstate[-(1:fit1$strata[1]),])
[1] TRUE
> 
> #  A second test of cumulative incidence
> # compare results to Bob Gray's functions
> #  The file gray1 is the result of 
> #    library(cmprsk)
> #    tstat <- ifelse(tdata$status==0, 0, 1+ (tdata$event=='death'))
> #    gray1 <- cuminc(tdata$stop, tstat)
> load("gray1.rda")
> fit2 <- survfit(Surv(stop, event) ~ 1, tdata)
> 
> if (FALSE) {
+     # lines of the two graphs should overlay
+     plot(gray1[[1]]$time, gray1[[1]]$est, type='l',
+          ylim=range(c(gray1[[1]]$est, gray1[[2]]$est)),
+          xlab="Time")
+     lines(gray1[[2]]$time, gray1[[2]]$est, lty=2)
+     matlines(fit2$time, fit2$pstate, col=2, lty=1:2, type='s')
+ }
> # To formally match these is a bit of a nuisance.
> #  The cuminc function returns a full step function, and survfit only
> # the bottoms of the steps.
> temp1 <- tapply(gray1[[1]]$est, gray1[[1]]$time, max)[-1]  #toss time 0
> indx1 <- match(names(temp1), fit2$time)
> aeq(temp1, fit2$pstate[indx1,2])
[1] TRUE
>     
> 
> proc.time()
   user  system elapsed 
   0.89    0.10    1.00