125 lines
4.4 KiB
R
125 lines
4.4 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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# Tests of the weighted Cox model
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# This is section 1.3 of my appendix -- not yet found in the book
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# though, it awaits the next edition
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#
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# Similar data set to test1, but add weights,
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# a double-death/censor tied time
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# a censored last subject
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# The latter two are cases covered only feebly elsewhere.
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#
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# The data set testw2 has the same data, but done via replication
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#
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aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
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testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5),
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status= c(1,0,1,1,1,0,0,1,0),
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x= c(2,0,1,1,0,1,0,1,0),
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wt = c(1,2,3,4,3,2,1,2,1),
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id = 1:9)
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# Expanded data set
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testw2 <- testw1[rep(1:9, testw1$wt), -4]
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row.names(testw2) <- NULL
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indx <- match(1:9, testw2$id)
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# Breslow estimate
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byhand <- function(beta, newx=0) {
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r <- exp(beta)
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loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5) +2*log(2*r+1))
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hazard <- c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1))
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xbar <- c((2*r^2 + 11*r)*hazard[1], 11*r/(11*r +5), r*hazard[3])
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U <- 11- (xbar[1] + 10*xbar[2] + 2*xbar[3])
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imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 +
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10*(xbar[2] - xbar[2]^2) + 2*(xbar[3] - xbar[3]^2)
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temp <- cumsum(hazard)
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risk <- c(r^2, 1,r,r,1,r,1,r,1)
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expected <- risk* temp[c(1,1,2,2,2,2,2,3,3)]
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# The matrix of weights, one row per obs, one col per death
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# deaths at 1,2,2,2, and 4
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riskmat <- matrix(c(1,1,1,1,1,1,1,1,1,
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0,0,1,1,1,1,1,1,1,
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0,0,1,1,1,1,1,1,1,
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0,0,1,1,1,1,1,1,1,
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0,0,0,0,0,0,0,1,1), ncol=5)
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wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat
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x <- c(2,0,1,1,0,1,0,1,0)
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status <- c(1,0,1,1,1,0,0,1,0)
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wt <- c(1,2,3,4,3,2,1,2,1)
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# Table of sums for score and Schoenfeld resids
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hazmat <- riskmat %*% diag(c(1,3,4,3,2)/colSums(wtmat))
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dM <- -risk*hazmat #Expected part
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dM[1,1] <- dM[1,1] +1 # deaths at time 1
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for (i in 2:4) dM[i+1, i] <- dM[i+1,i] +1
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dM[8,5] <- dM[8,5] +1
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mart <- rowSums(dM)
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resid <-dM * outer(x, xbar[c(1,2,2,2,3)] ,'-')
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# Increments to the variance of the hazard
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var.g <- cumsum(hazard^2/ c(1,10,2))
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var.d <- cumsum((xbar-newx)*hazard)
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list(loglik=loglik, U=U, imat=imat, hazard=hazard, xbar=xbar,
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mart=c(1,0,1,1,1,0,0,1,0)-expected, expected=expected,
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score=rowSums(resid), schoen=c(2,1,1,0,1) - xbar[c(1,2,2,2,3)],
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varhaz=(var.g + var.d^2/imat)* exp(2*beta*newx))
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}
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aeq(byhand(0)$expected, c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify
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fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt,
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method='breslow', iter=0)
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fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0)
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fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow')
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fitb <- coxph(Surv(time, status) ~x, testw2, method='breslow')
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aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx])
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aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx])
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aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho')))
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truth0 <- byhand(0,pi)
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aeq(fit0$loglik[1], truth0$loglik)
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aeq(1/truth0$imat, fit0$var)
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aeq(truth0$mart, fit0$residuals)
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aeq(truth0$schoen, resid(fit0, 'schoen'))
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aeq(truth0$score, resid(fit0, 'score'))
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sfit <- survfit(fit0, list(x=pi), censor=FALSE)
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aeq(sfit$std.err^2, truth0$varhaz)
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aeq(-log(sfit$surv), cumsum(truth0$hazard))
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truth <- byhand(0.85955744, .3)
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aeq(truth$loglik, fit$loglik[2])
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aeq(1/truth$imat, fit$var)
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aeq(truth$mart, fit$residuals)
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aeq(truth$schoen, resid(fit, 'schoen'))
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aeq(truth$score, resid(fit, 'score'))
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sfit <- survfit(fit, list(x=.3), censor=FALSE)
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aeq(sfit$std.err^2, truth$varhaz)
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aeq(-log(sfit$surv), (cumsum(truth$hazard)* exp(fit$coefficients*.3)))
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fit0
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summary(fit)
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resid(fit0, type='score')
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resid(fit0, type='scho')
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resid(fit, type='score')
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resid(fit, type='scho')
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aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx])
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aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx])
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aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho')))
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rr1 <- resid(fit, type='mart')
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rr2 <- resid(fit, type='mart', weighted=T)
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aeq(rr2/rr1, testw1$wt)
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rr1 <- resid(fit, type='score')
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rr2 <- resid(fit, type='score', weighted=T)
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aeq(rr2/rr1, testw1$wt)
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