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