R version 4.4.0 beta (2024-04-12 r86413 ucrt) -- "Puppy Cup" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Tests from the appendix of Therneau and Grambsch > # d. Data set 2 and Efron estimate > # > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0)) > > byhand <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 4*beta - (log(r+1) + log(r+2) + 2*log(3*r+2) + 2*log(3*r+1) + + log(2*r +2)) + u <- 1/(r+1) + 1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) - + ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) + imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 + + 6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2) + + hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), + 1/(3*r+2), 1/(2*r +2) ) + + + # The matrix of weights, one row per obs, one col per time + # deaths at 2,3,6,7,8,9 + wtmat <- matrix(c(1,0,0,0,1, 0, 0,0,0,0, + 0,1,0,1,1, 0, 0,0,0,0, + 0,0,1,1,1, 0, 1,1,0,0, + 0,0,0,1,1, 0, 1,1,0,0, + 0,0,0,0,1, 1, 1,1,0,0, + 0,0,0,0,0, 1, 1,1,1,1, + 0,0,0,0,0,.5,.5,1,1,1), ncol=7) + wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat + + x <- c(1,0,0,1,0,1,1,1,0,0) + status <- c(1,1,1,1,1,1,1,0,0,0) + xbar <- colSums(wtmat*x)/ colSums(wtmat) + n <- length(x) + + # Table of sums for score and Schoenfeld resids + hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time + dM <- -hazmat #Expected part + for (i in 1:5) dM[i,i] <- dM[i,i] +1 #observed + dM[6:7,6:7] <- dM[6:7,6:7] +.5 # observed + mart <- rowSums(dM) + + # Table of sums for score and Schoenfeld resids + # Looks like the last table of appendix E.2.1 of the book + resid <- dM * outer(x, xbar, '-') + score <- rowSums(resid) + scho <- colSums(resid) + + # We need to add the ties back up (they are symmetric) + scho[6:7] <- rep(mean(scho[6:7]), 2) + + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, + mart=mart, score=score, rmat=resid, + scho=scho) + } > > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0) > truth0 <- byhand(0,0) > aeq(truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')) [1] TRUE > > > fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8, nocenter=NULL) > truth <- byhand(fit$coef, 0) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')) [1] TRUE > > # Reprise the test, with strata > # offseting the times ensures that we will get the wrong risk sets > # if strata were not kept separate > test2b <- rbind(test2, test2, test2) > test2b$group <- rep(1:3, each= nrow(test2)) > test2b$start <- test2b$start + test2b$group > test2b$stop <- test2b$stop + test2b$group > fit0 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, iter=0) > aeq(3*truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(3*truth0$imat, 1/fit0$var) [1] TRUE > aeq(rep(truth0$mart,3), fit0$resid) [1] TRUE > aeq(rep(truth0$scho,3), resid(fit0, 'schoen')) [1] TRUE > aeq(rep(truth0$score,3), resid(fit0, 'score')) [1] TRUE > > fit3 <- coxph(Surv(start, stop, event) ~x + strata(group), test2b, eps=1e-8) > aeq(3*truth$loglik, fit3$loglik[2]) [1] TRUE > aeq(3*truth$imat, 1/fit3$var) [1] TRUE > aeq(rep(truth$mart,3), fit3$resid) [1] TRUE > aeq(rep(truth$scho,3), resid(fit3, 'schoen')) [1] TRUE > aeq(rep(truth$score,3), resid(fit3, 'score')) [1] TRUE > > # > # Done with the formal test, now print out lots of bits > # > resid(fit) 1 2 3 4 5 6 0.50527611 0.66432995 0.79746211 0.22435805 -0.55144018 0.42933697 7 8 9 10 -0.01764508 -1.14132605 -0.45517594 -0.45517594 > resid(fit, 'scor') 1 2 3 4 5 6 7 0.2553039 -0.2183386 -0.4744295 -0.1101520 0.1137126 0.2491954 0.1057078 8 9 10 -0.4119611 0.2454808 0.2454808 > resid(fit, 'scho') 2 3 6 7 8 9 9 0.5052761 -0.3286599 -0.5949242 0.2539781 -0.7460219 0.4551759 0.4551759 > > predict(fit, type='lp') [1] -0.0105526 0.0105526 0.0105526 -0.0105526 0.0105526 -0.0105526 [7] -0.0105526 -0.0105526 0.0105526 0.0105526 > predict(fit, type='risk') [1] 0.9895029 1.0106085 1.0106085 0.9895029 1.0106085 0.9895029 0.9895029 [8] 0.9895029 1.0106085 1.0106085 > predict(fit, type='expected') 1 2 3 4 5 6 7 8 0.4947239 0.3356701 0.2025379 0.7756420 1.5514402 0.5706630 1.0176451 1.1413261 9 10 0.4551759 0.4551759 > predict(fit, type='terms') x 1 -0.0105526 2 0.0105526 3 0.0105526 4 -0.0105526 5 0.0105526 6 -0.0105526 7 -0.0105526 8 -0.0105526 9 0.0105526 10 0.0105526 attr(,"constant") [1] -0.0105526 > predict(fit, type='lp', se.fit=T) $fit 1 2 3 4 5 6 7 -0.0105526 0.0105526 0.0105526 -0.0105526 0.0105526 -0.0105526 -0.0105526 8 9 10 -0.0105526 0.0105526 0.0105526 $se.fit 1 2 3 4 5 6 7 8 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 9 10 0.3975884 0.3975884 > predict(fit, type='risk', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.9895029 1.0106085 1.0106085 0.9895029 1.0106085 0.9895029 0.9895029 0.9895029 9 10 1.0106085 1.0106085 $se.fit 1 2 3 4 5 6 7 8 0.3954962 0.3996918 0.3996918 0.3954962 0.3996918 0.3954962 0.3954962 0.3954962 9 10 0.3996918 0.3996918 > predict(fit, type='expected', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.4947239 0.3356701 0.2025379 0.7756420 1.5514402 0.5706630 1.0176451 1.1413261 9 10 0.4551759 0.4551759 $se.fit [1] 0.5331623 0.3940109 0.3241963 0.6388491 1.0026838 0.6453101 0.7848594 [8] 0.7848594 0.6401915 0.6401915 > predict(fit, type='terms', se.fit=T) $fit x 1 -0.0105526 2 0.0105526 3 0.0105526 4 -0.0105526 5 0.0105526 6 -0.0105526 7 -0.0105526 8 -0.0105526 9 0.0105526 10 0.0105526 attr(,"constant") [1] -0.0105526 $se.fit x 1 0.3975884 2 0.3975884 3 0.3975884 4 0.3975884 5 0.3975884 6 0.3975884 7 0.3975884 8 0.3975884 9 0.3975884 10 0.3975884 > > summary(survfit(fit)) Call: survfit(formula = fit) time n.risk n.event survival std.err lower 95% CI upper 95% CI 2 2 1 0.607 0.303 0.2277 1.000 3 3 1 0.435 0.262 0.1337 1.000 6 5 1 0.356 0.226 0.1029 1.000 7 4 1 0.277 0.189 0.0729 1.000 8 4 1 0.215 0.157 0.0516 0.899 9 5 2 0.137 0.109 0.0288 0.655 > summary(survfit(fit, list(x=2))) Call: survfit(formula = fit, newdata = list(x = 2)) time n.risk n.event survival std.err lower 95% CI upper 95% CI 2 2 1 0.616 0.465 0.14013 1 3 3 1 0.447 0.519 0.04568 1 6 5 1 0.368 0.504 0.02512 1 7 4 1 0.288 0.464 0.01232 1 8 4 1 0.226 0.418 0.00603 1 9 5 2 0.146 0.343 0.00147 1 > > proc.time() user system elapsed 0.85 0.17 0.96