141 lines
5.5 KiB
R
141 lines
5.5 KiB
R
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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#
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# Simple tests of concordance
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#
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aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
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grank <- function(x, time, grp, wt)
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unlist(tapply(x, grp, rank))
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grank2 <- function(x, time, grp, wt) { #for case weights
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if (length(wt)==0) wt <- rep(1, length(x))
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z <- double(length(x))
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for (i in unique(grp)) {
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indx <- which(grp==i)
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temp <- tapply(wt[indx], x[indx], sum)
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temp <- temp/2 + c(0, cumsum(temp)[-length(temp)])
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z[indx] <- temp[match(x[indx], names(temp))]
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}
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z
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}
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# Concordance by brute force. O(n^2) algorithm, but ok for n<500 or so
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allpair <- function(x, time, status, wt, all=FALSE) {
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if (missing(wt)) wt <- rep(1, length(x))
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count <- sapply(which(status==1), function(i) {
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atrisk <- (time > time[i]) | (time==time[i] & status==0)
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temp <- tapply(wt[atrisk], factor(sign(x[i] -x[atrisk]), c(1, -1, 0)),
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sum)
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wt[i]* c(ifelse(is.na(temp), 0, temp),
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(sum(wt[time==time[i] & status==1]) - wt[i])/2)
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})
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rownames(count) <- c("concordant", "discordant", "tied.x", "tied.y")
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if (all) {
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colnames(count) <- time[status==1]
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t(count)
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}
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else rowSums(count)
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}
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# The std of C = std(numerator)/(number of comparable pairs)
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# The information matrix of a Cox model is = to the var(C-D)
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cfun <- function(fit) fit$cvar * sum(fit$count[1:3])^2
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tdata <- aml[aml$x=='Maintained', c("time", "status")]
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tdata$x <- c(1,6,2,7,3,7,3,8,4,4,5)
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tdata$wt <- c(1,2,3,2,1,2,3,4,3,2,1)
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fit <- concordance(Surv(time, status) ~x, tdata)
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aeq(fit$count[1:4], c(24,14,2,0))
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cfit <- coxph(Surv(time, status) ~ tt(x), tdata, tt=grank, method='breslow',
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iter=0, x=T)
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cdt <- coxph.detail(cfit)
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aeq(sum(cdt$imat), cfun(fit))
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aeq(sum(2*cdt$score), diff(fit$count[1:2]))
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aeq(with(tdata, allpair(x, time, status)), c(14,24,2,0))
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# Lots of ties
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tempy <- Surv(c(1,2,2,2,3,4,4,4,5,2), c(1,0,1,0,1,0,1,1,0,1))
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tempx <- c(5,5,4,4,3,3,7,6,5,4)
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fit2 <- concordance(tempy ~ tempx)
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addxy <- function(x) c(x[1:3], sum(x[4:5]))
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aeq(addxy(fit2$count), allpair(tempx, tempy[,1], tempy[,2]))
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cfit2 <- coxph(tempy ~ tt(tempx), tt=grank, method='breslow', iter=0)
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aeq(cfit2$var, 1/cfun(fit2))
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# Direct call
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fit2b <- concordancefit(tempy, tempx)
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fit2c <- concordancefit(tempy, tempx, std.err=FALSE)
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all.equal(fit2[1:5], fit2b)
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all.equal(fit2b[1:3], fit2c)
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# Bigger data
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fit3 <- concordance(Surv(time, status) ~ age, lung, reverse=TRUE)
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aeq(addxy(fit3$count), allpair(lung$age, lung$time, lung$status-1))
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cfit3 <- coxph(Surv(time, status) ~ tt(age), lung,
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iter=0, method='breslow', tt=grank, x=T)
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cdt <- coxph.detail(cfit3)
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aeq(sum(cdt$imat), cfun(fit3))
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aeq(2*sum(cdt$score), diff(fit3$count[2:1]))
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# More ties
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fit4 <- concordance(Surv(time, status) ~ ph.ecog, lung, reverse=TRUE)
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aeq(addxy(fit4$count), allpair(lung$ph.ecog, lung$time, lung$status-1))
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aeq(fit4$count[1:5], c(8392, 4258, 7137, 21, 7))
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cfit4 <- coxph(Surv(time, status) ~ tt(ph.ecog), lung,
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iter=0, method='breslow', tt=grank)
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aeq(1/cfit4$var, cfun(fit4))
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# Case weights
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fit5 <- concordance(Surv(time, status) ~ x, tdata, weights=wt, reverse=TRUE)
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fit6 <- concordance(Surv(time, status) ~x, tdata[rep(1:11,tdata$wt),])
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aeq(addxy(fit5$count), with(tdata, allpair(x, time, status, wt)))
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aeq(fit5$count[1:4], c(70, 91, 7, 0)) # checked by hand
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aeq(fit5$count[1:3], fit6$count[c(2,1,3)]) #spurious "tied on time" values, ignore
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aeq(fit5$std, fit6$std)
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cfit5 <- coxph(Surv(time, status) ~ tt(x), tdata, weights=wt,
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iter=0, method='breslow', tt=grank2)
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cfit6 <- coxph(Surv(time, status) ~ tt(x), tdata[rep(1:11,tdata$wt),],
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iter=0, method='breslow', tt=grank)
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aeq(1/cfit6$var, cfun(fit6))
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aeq(cfit5$var, cfit6$var)
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# Start, stop simplest cases
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fit7 <- concordance(Surv(rep(0,11), time, status) ~ x, tdata)
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aeq(fit7$count, fit$count)
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aeq(fit7$std.err, fit$std.err)
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fit7 <- concordance(Surv(rep(0,11), time, status) ~ x, tdata, weights=wt)
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aeq(fit5$count, fit7$count[c(2,1,3:5)]) #one reversed, one not
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# Multiple intervals for some, but same risk sets as tdata
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tdata2 <- data.frame(time1=c(0,3, 5, 6,7, 0, 4,17, 7, 0,16, 2, 0,
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0,9, 5),
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time2=c(3,9, 13, 7,13, 18, 17,23, 28, 16,31, 34, 45,
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9,48, 60),
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status=c(0,1, 1, 0,0, 1, 0,1, 0, 0,1, 1, 0, 0,1, 0),
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x = c(1,1, 6, 2,2, 7, 3,3, 7, 3,3, 8, 4, 4,4, 5),
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wt= c(1,1, 2, 3,3, 2, 1,1, 2, 3,3, 4, 3, 2,2, 1))
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fit8 <- concordance(Surv(time1, time2, status) ~x, tdata2, weights=wt,
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reverse=TRUE)
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aeq(fit5$count, fit8$count)
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aeq(fit5$std.err, fit8$std.err)
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cfit8 <- coxph(Surv(time1, time2, status) ~ tt(x), tdata2, weights=wt,
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iter=0, method='breslow', tt=grank2)
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aeq(1/cfit8$var, cfun(fit8))
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# Stratified
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tdata3 <- data.frame(time1=c(tdata2$time1, rep(0, nrow(lung))),
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time2=c(tdata2$time2, lung$time),
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status = c(tdata2$status, lung$status -1),
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x = c(tdata2$x, lung$ph.ecog),
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wt= c(tdata2$wt, rep(1, nrow(lung))),
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grp=rep(1:2, c(nrow(tdata2), nrow(lung))))
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fit9 <- concordance(Surv(time1, time2, status) ~x + strata(grp),
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data=tdata3, weights=wt, reverse=TRUE)
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aeq(fit9$count[1,], fit5$count)
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aeq(fit9$count[2,], fit4$count)
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