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Type 'q()' to quit R. > library(survival) > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # Tests of the weighted Cox model > # This is section 1.3 of my appendix -- no yet found in any of the > # printings though, it awaits the next edition > # > # Efron approximation > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), + status= c(1,0,1,1,1,0,0,1,0), + x= c(2,0,1,1,0,1,0,1,0), + wt = c(1,2,3,4,3,2,1,2,1)) > xx <- testw1$wt > > # Efron estimate > byhand <- function(beta, newx=0) { + r <- exp(beta) + a <- 7*r +3; b<- 4*r+2 + loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5)/3 + + 10*log(a*2/3 +b)/3 + 10*log(a/3 +b)/3 +2*log(2*r+1)) + + hazard <- c(1/(r^2 + 11*r +7), + 10/(3*c(11*r +5, a*2/3 +b, a/3+b)), 2/(2*r+1)) + temp <- c(hazard[1], hazard[1]+hazard[2] + hazard[3]*2/3 + hazard[4]/3, + cumsum(hazard)[4:5]) + risk <- c(r^2, 1,r,r,1,r,1,r,1) + expected <- risk* temp[c(1,1,2,2,2,3,3,4,4)] + + # The matrix of weights, one row per obs, one col per death + # deaths at 1,2,2,2, and 4 + riskmat <- matrix(c(1,1,1,1,1,1,1,1,1, + 0,0,1,1,1,1,1,1,1, + 0,0,2/3,2/3,2/3,1,1,1,1, + 0,0,1/3,1/3,1/3,1,1,1,1, + 0,0,0,0,0,0,0,1,1), ncol=5) + wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat + + x <- c(2,0,1,1,0,1,0,1,0) + xbar <- colSums(x*wtmat)/ colSums(wtmat) + imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 + + 10* mean(xbar[2:4] - xbar[2:4]^2) + 2*(xbar[5] - xbar[5]^2) + + status <- c(1,0,1,1,1,0,0,1,0) + wt <- c(1,2,3,4,3,2,1,2,1) + # Table of sums for score resids + hazmat <- riskmat %*% diag(c(1,10/3,10/3, 10/3,2)/colSums(wtmat)) + dM <- -risk*hazmat #Expected part + dM[1,1] <- dM[1,1] +1 # deaths at time 1 + for (i in 2:4) dM[3:5, i] <- dM[3:5,i] + 1/3 + dM[8,5] <- dM[8,5] +1 + mart <- rowSums(dM) + resid <-dM * outer(x, xbar ,'-') + + # Increments to the variance of the hazard + var.g <- cumsum(hazard^2* c(1,3/10, 3/10, 3/10, 1/2)) + var.d <- cumsum((xbar-newx)*hazard) + + sxbar <- c(xbar[1], mean(xbar[2:4]), xbar[5]) #xbar for Schoen + list(loglik=loglik, imat=imat, hazard=hazard, xbar=xbar, + mart=status-expected, expected=expected, + score=rowSums(resid), schoen=c(2,1,1,0,1) - sxbar[c(1,2,2,2,3)], + varhaz=((var.g + var.d^2/imat)* exp(2*beta*newx))[c(1,4,5)]) + } > > # Verify > temp <- byhand(0,0) > aeq(temp$xbar, c(13/19, 11/16, 26/38, 19/28, 2/3)) [1] TRUE > aeq(temp$hazard, c(1/19, 5/24, 5/19, 5/14, 2/3)) [1] TRUE > > fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, iter=0) > fit <- coxph(Surv(time, status) ~x, testw1, weights=wt) > > truth0 <- byhand(0,pi) > aeq(fit0$loglik[1], truth0$loglik) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$residuals) [1] TRUE > aeq(truth0$schoen, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')) [1] TRUE > sfit <- survfit(fit0, list(x=pi), censor=FALSE) > aeq(sfit$std.err^2, truth0$varhaz) [1] TRUE > aeq(-log(sfit$surv), cumsum(truth0$hazard)[c(1,4,5)]) [1] TRUE > > truth <- byhand(fit$coefficients, .3) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$residuals) [1] TRUE > aeq(truth$schoen, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')) [1] TRUE > > sfit <- survfit(fit, list(x=.3), censor=FALSE) > aeq(sfit$std.err^2, truth$varhaz) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$hazard)* exp(fit$coefficients*.3))[c(1,4,5)]) [1] TRUE > > > fit0 Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, iter = 0) coef exp(coef) se(coef) z p x 0.0000 1.0000 0.5843 0 1 Likelihood ratio test=0 on 1 df, p=1 n= 9, number of events= 5 > summary(fit) Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt) n= 9, number of events= 5 coef exp(coef) se(coef) z Pr(>|z|) x 0.8726 2.3931 0.7126 1.225 0.221 exp(coef) exp(-coef) lower .95 upper .95 x 2.393 0.4179 0.5921 9.672 Concordance= 0.637 (se = 0.161 ) Likelihood ratio test= 1.75 on 1 df, p=0.2 Wald test = 1.5 on 1 df, p=0.2 Score (logrank) test = 1.58 on 1 df, p=0.2 > resid(fit0, type='score') 1 2 3 4 5 6 1.24653740 0.03601108 0.14118105 0.14118105 -0.30336782 -0.27962308 7 8 9 0.60164259 -0.16851197 1.04608703 > resid(fit0, type='scho') 1 2 2 2 4 1.3157895 0.3165727 0.3165727 -0.6834273 0.3333333 > > resid(fit, type='score') 1 2 3 4 5 6 0.88116056 0.02477248 0.06057806 0.06057806 -0.59724033 -0.16737066 7 8 9 0.38040295 -0.13750290 0.66631324 > resid(fit, type='scho') 1 2 2 2 4 1.0325955 0.1621759 0.1621759 -0.8378241 0.1728229 > > rr1 <- resid(fit, type='mart') > rr2 <- resid(fit, type='mart', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > rr1 <- resid(fit, type='score') > rr2 <- resid(fit, type='score', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > > proc.time() user system elapsed 0.89 0.09 0.96