File: C:/Program Files/R/R-4.4.0/library/survival/tests/coxsurv5.Rout.save
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> library(survival)
> aeq <- function(x, y) all.equal(as.vector(x), as.vector(y))
> #
> # Compute the hazard functions for a multi-state Cox model
> #
> coxhaz <- function(y, id, risk, wt, expm=TRUE) {
+ # y should be a multi-state survival
+ if (!inherits(y, "Surv") || attr(y, "type") != "mcounting")
+ stop("invalid response")
+
+ n <- nrow(y)
+ if (missing(id) || length(id) !=n) stop("invalid id")
+
+ if (missing(wt)) wt <- rep(1.0, n)
+ else if (length(wt) !=n || any(wt <=0)) stop("invalid wt")
+
+ # get the current state, and the list of transtions
+ # transitions to censor don't count
+ mcheck <- survcheck(y~1, id= id)
+ states <- mcheck$states
+ nstate <- length(states)
+ istate <- mcheck$istate
+
+ event <- y[,3] > 0
+ temp <- attr(y, 'states')[y[event,3]]
+ tmat <- table(y[event,2], from=istate[event], to=temp)
+ tmat2 <- tapply(wt[event], list(y[event,2], from=mcheck$istate[event],
+ to=temp), sum)
+ tmat2 <- ifelse(is.na(tmat2), 0, tmat2)
+
+
+ # Hazards can be done one at a time. For each of them the risk
+ # weight vector for the subjects can be different.
+ # First organize the material as a 2 dim matrix
+ temp <- apply(tmat, 2:3, sum) # count of transtions
+ keep <- which(temp>0)
+ from <- states[row(temp)[keep]]
+ hlab <- outer(match(rownames(temp), states),
+ match(colnames(temp), states), paste, sep=':')[keep]
+ nhaz <- length(keep)
+ nevent <- matrix(tmat2, nrow(tmat2))[,keep]
+ dtime <- sort(unique(y[event,2]))
+ ntime <- length(dtime)
+ dimnames(nevent) <- list(NULL, hlab)
+ aindex <- cbind(as.numeric(substring(hlab,1,1)),
+ as.numeric(substring(hlab,3,3)))
+
+ if (missing(risk)) risk <- matrix(1, nrow=n, ncol=nhaz)
+ if (!is.matrix(risk) || nrow(risk) != n || ncol(risk) != nhaz)
+ stop("invalid risk matrix")
+ risk <- risk * wt
+
+ # get the weighted at risk at each time
+ wtrisk <- matrix(, length(dtime), nhaz)
+ statematch <- outer(istate, from, function(x, y) x==y)
+ risk <- ifelse(statematch, risk, 0)
+ for (i in 1:ntime) {
+ atrisk <- (y[,1]< dtime[i] & y[,2] >= dtime[i])
+ wtrisk[i,] <- colSums(risk[atrisk,, drop=FALSE])
+ }
+
+ haz <- nevent/ifelse(wtrisk==0, 1, wtrisk) # avoid 0/0
+ chaz<- apply(haz, 2, cumsum)
+
+ # compute the probability in state, with p(0)= 1,0, ..
+ pstate <- matrix(0, ntime+1, nstate)
+ pstate[1,1] <- 1
+ for (i in 1:ntime) {
+ tmat <- matrix(0, nstate, nstate)
+ tmat[aindex] <- haz[i,]
+ if (expm) {
+ diag(tmat) <- -rowSums(tmat)
+ pstate[i+1,] <- pstate[i,] %*% as.matrix(Matrix::expm(tmat))
+ } else {
+ diag(tmat) <- 1-rowSums(tmat)
+ pstate[i+1,] <- pstate[i,] %*% tmat
+ }
+ }
+
+ list(time=dtime, nrisk=wtrisk, nevent=nevent,
+ haz=haz, cumhaz=chaz, states=states, pstate= pstate[-1,])
+ }
>
> mtest <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5),
+ t1= c(0, 4, 9, 0, 2, 0, 2, 8, 1, 3),
+ t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11),
+ state= c(1, 2, 1, 2, 3, 1, 3, 0, 2, 0),
+ x = c(0, 0, 0, 1, 1, 0, 0, 0, 2, 2))
> mtest$state <- factor(mtest$state, 0:3, c("censor", "a", "b", "c"))
>
> # True results
> #
> #time at risk events
> # entry a b c
> #
> #2 1245 4 -> a
> #3 1235 4 5 -> b
> #4 123 4 5 1 -> a
> #5 23 14 5 2 -> b, exits
> #8 3 14 5 4 -> c
> #9 3 1 5 4 1->b, 3->c & exit, 4 censored
> #10 15 1->a, exit
> #11 5 censor
>
> # with all coefficients =0
> check1 <- with(mtest, coxhaz(Surv(t1, t2, state), id))
> fit1 <- survfit(Surv(t1, t2, state) ~1, mtest, id=id)
> aeq(check1$cumhaz, fit1$cumhaz[match(check1$time, fit1$time),])
[1] TRUE
>
> dummy <- data.frame(x=1:2)
> cox0 <- coxph(Surv(t1, t2, state) ~x, iter=0, mtest, id=id)
> cfit0 <- survfit(cox0, newdata=dummy)
> indx <- match(check1$time, cfit0$time)
> aeq(check1$cumhaz, cfit0$cumhaz[indx,1,])
[1] TRUE
> aeq(check1$cumhaz, cfit0$cumhaz[indx,2,])
[1] TRUE
> aeq(check1$pstate, cfit0$pstate[indx,1,])
[1] TRUE
>
> # a fixed coefficient
> mfit <- coxph(Surv(t1, t2, state) ~x, iter=0, mtest, id=id,
+ init= log(1:6))
> msurv <- survfit(mfit, newdata=list(x=0:1))
> mrisk <- exp(outer(mtest$x, log(1:6), '*')) # hazards for each transition
> check2 <- with(mtest, coxhaz(Surv(t1, t2, state), id=id, risk=mrisk))
> aeq(check2$cumhaz, msurv$cumhaz[indx,1,])
[1] TRUE
> aeq(check2$pstate, msurv$pstate[indx,1,])
[1] TRUE
>
> # a different predicted x multiplies the risk weights
> # now use exp(x - target) as the risk score
> mrisk2 <- mrisk %*% diag(1/(1:6))
> check2b <- with(mtest, coxhaz(Surv(t1, t2, state), id=id, risk=mrisk2))
> aeq(check2b$cumhaz, msurv$cumhaz[indx,2,])
[1] TRUE
> aeq(check2b$pstate, msurv$pstate[indx,2,])
[1] TRUE
>
> # since pstate depends only on the hazards and p(0), if the hazards are
> # right I don't have to check pstate for every subcase
>
> if (FALSE) {
+ # this graph is very useful
+ temp <- survcheck(Surv(t1, t2, state) ~1, mtest, id=id)
+ plot(c(0,11), c(1,5.1), type='n', xlab="Time", ylab= "Subject")
+ with(mtest, segments(t1+.1, id, t2, id, col=as.numeric(temp$istate)))
+ event <- subset(mtest, state!='censor')
+ text(event$t2, event$id+.2, as.character(event$state))
+ }
>
>
> # slight change, add a few censored subjects
> # all the events happen on even numbered days
> test2 <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5,
+ 6, 7, 8, 9),
+ t1= c(0, 8, 18, 0, 4, 0, 4, 16, 2, 6,
+ 0, 0, 7, 8),
+ t2= c(8, 18, 20, 10, 18, 4, 16, 18, 6, 22,
+ 5, 10, 10, 15),
+ state= c(1, 2, 1, 2, 3, 1, 3, 0, 2, 0,0,0,0,0),
+ x = c(0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 1, 1, 2, 0))
> test2$state <- factor(test2$state, 0:3, c("censor", "a", "b", "c"))
>
> if (FALSE) {
+ # this graph is very useful when debugging
+ temp <- survcheck(Surv(t1, t2, state) ~1, test2, id=id)
+ plot(c(0,22), c(1,9.1), type='n', xlab="Time", ylab= "Subject")
+ with(test2, segments(t1+.1, id, t2, id, col=as.numeric(temp$istate)))
+ event <- subset(test2, state!='censor')
+ text(event$t2, event$id+.2, as.character(event$state))
+ }
>
> # s0 to a, cumhaz of 1/6 (t=4) + 1/5 (t=8)
> # b to a, cumhaz of 1/2 at 20
> # s0 to b, cumhaz of 1/5 at 6, +1/5 at 10
> # a to b, cumhaz of 1/1 at 18
> # s0 to c, cumhaz of 1/1 at 18
> # a to c, cumhaz of 1/2 at 16
> time2 <- c(4,5,6,8,10,15,16,18,20, 22)
> chaz2 <- matrix(0, nrow=10, ncol=6,
+ dimnames=list(time2, c("1:2", "1:3", "1:3", "2:3", "1:4", "2:4")))
> chaz2['4',1] <- 1/6; chaz2['8',1] <- 1/5
> chaz2['20',2] <- 1/2
> chaz2['6', 3] <- 1/5; chaz2['10', 3] <- 1/5
> chaz2['18',4:5] <- 1
> chaz2['16', 6] <- 1/2
> chaz2 <- apply(chaz2, 2, cumsum)
>
>
> cox3 <- coxph(Surv(t1, t2, state) ~x, id=id, test2, iter=0) # no weights
> csurv3 <- survfit(cox3, newdata=data.frame(x=0:1))
> aeq(csurv3$time, time2)
[1] TRUE
> aeq(csurv3$cumhaz[,1,], chaz2)
[1] TRUE
> aeq(csurv3$cumhaz[,2,], chaz2)
[1] TRUE
> check3 <- with(test2, coxhaz(Surv(t1, t2, state), id=id))
> indx3 <- match(check3$time, csurv3$time)
> aeq(check3$cumhaz, chaz2[indx3,]) # a check on the coxhaz function above
[1] TRUE
> aeq(check3$pstate, csurv3$pstate[indx3,1,])
[1] TRUE
>
> cox4 <- coxph(Surv(t1,t2, state) ~ x, id=id, test2,
+ init=log(1:6), iter=0)
> csurv4 <- survfit(cox4, newdata=data.frame(x=0:1))
> mrisk4 <- exp(outer(test2$x, log(1:6), '*')) # hazards for each transition
> check4 <- with(test2, coxhaz(Surv(t1, t2, state), id=id, risk=mrisk4))
> aeq(check4$cumhaz, csurv4$cumhaz[indx3,1,])
[1] TRUE
> aeq(check4$pstate, csurv4$pstate[indx3,1,])
[1] TRUE
> aeq(csurv4$cumhaz[,2,], csurv4$cumhaz[,1,] %*% diag(1:6))
[1] TRUE
>
>
> # Check the stype=1 option
> csurv4b <- survfit(cox4, newdata= data.frame(x=0:1), stype=1)
> check4b <- with(test2, coxhaz(Surv(t1, t2, state), id=id, risk=mrisk4,
+ expm=FALSE))
> aeq(check4b$cumhaz, csurv4b$cumhaz[indx3,1,])
[1] TRUE
> aeq(check4b$pstate, csurv4b$pstate[indx3,1,])
[1] TRUE
>
> proc.time()
user system elapsed
1.224 0.078 1.296