R version 4.4.0 RC (2024-04-16 r86458 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. > library(survival) > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # > # Tests from the appendix of Therneau and Grambsch > # c. Data set 2 and Breslow 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) - 3*log(3*r+2) - 2*log(3*r+1) + u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) - + ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) + imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 + + 3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2 + + hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) ) + xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1), + 3*r/(3*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), ncol=6) + 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 1:6) dM[i,i] <- dM[i,i] +1 #observed + dM[7,6] <- dM[7,6] +1 # 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 split the two tied times up, to match coxph + scho <- c(scho[1:5], scho[6]/2, scho[6]/2) + var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2)) + var.d <- cumsum( (xbar-newx)*hazard) + + surv <- exp(-cumsum(hazard) * exp(beta*newx)) + varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx) + + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, + mart=mart, score=score, rmat=resid, + scho=scho, surv=surv, var=varhaz) + } > > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0, method='breslow') > 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 > sfit <- survfit(fit0, list(x=0), censor=FALSE) > aeq(sfit$std.err^2, truth0$var) [1] TRUE > aeq(sfit$surv, truth0$surv) [1] TRUE > aeq(fit0$score, truth0$u^2/truth0$imat) [1] TRUE > > beta1 <- truth0$u/truth0$imat > fit1 <- coxph(Surv(start, stop, event) ~x, test2, iter=1, ties="breslow") > aeq(beta1, coef(fit1)) [1] TRUE > > truth <- byhand(-0.084526081, 0) > fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8, method='breslow', + nocenter= NULL) > aeq(truth$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$score, resid(fit, 'score')) [1] TRUE > expect <- predict(fit, type='expected', newdata=test2) #force recalc > aeq(test2$event -fit$resid, expect) #tests the predict function [1] TRUE > > sfit <- survfit(fit, list(x=0), censor=FALSE) > aeq(sfit$std.err^2, truth$var) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$haz))) [1] TRUE > > # Reprise the test, with strata > # offseting the times ensures that we will get the wrong risk sets > # if strata were not kept separate > test2b <- rbind(test2, test2, test2) > test2b$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, method="breslow") > 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 > > fit1 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, + iter=1, method="breslow") > aeq(fit1$coef, beta1) [1] TRUE > > fit3 <- coxph(Surv(start, stop, event) ~x + strata(group), + test2b, eps=1e-8, method='breslow') > aeq(3*truth$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 0.52111895 0.65741078 0.78977654 0.24738772 -0.60629349 0.36902492 7 8 9 10 -0.06876579 -1.06876579 -0.42044692 -0.42044692 > resid(fit, 'scor') 1 2 3 4 5 6 0.27156496 -0.20696709 -0.45771743 -0.09586133 0.13608234 0.19288983 7 8 9 10 0.04655651 -0.37389040 0.24367131 0.24367131 > resid(fit, 'scho') 2 3 6 7 8 9 9 0.5211189 -0.3148216 -0.5795531 0.2661809 -0.7338191 0.4204469 0.4204469 > > predict(fit, type='lp') [1] -0.04226304 0.04226304 0.04226304 -0.04226304 0.04226304 -0.04226304 [7] -0.04226304 -0.04226304 0.04226304 0.04226304 > predict(fit, type='risk') [1] 0.9586176 1.0431688 1.0431688 0.9586176 1.0431688 0.9586176 0.9586176 [8] 0.9586176 1.0431688 1.0431688 > predict(fit, type='expected') 1 2 3 4 5 6 7 8 0.4788811 0.3425892 0.2102235 0.7526123 1.6062935 0.6309751 1.0687658 1.0687658 9 10 0.4204469 0.4204469 > predict(fit, type='terms') x 1 -0.04226304 2 0.04226304 3 0.04226304 4 -0.04226304 5 0.04226304 6 -0.04226304 7 -0.04226304 8 -0.04226304 9 0.04226304 10 0.04226304 attr(,"constant") [1] -0.04226304 > predict(fit, type='lp', se.fit=T) $fit 1 2 3 4 5 6 -0.04226304 0.04226304 0.04226304 -0.04226304 0.04226304 -0.04226304 7 8 9 10 -0.04226304 -0.04226304 0.04226304 0.04226304 $se.fit 1 2 3 4 5 6 7 8 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 9 10 0.3969086 0.3969086 > predict(fit, type='risk', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.9586176 1.0431688 1.0431688 0.9586176 1.0431688 0.9586176 0.9586176 0.9586176 9 10 1.0431688 1.0431688 $se.fit 1 2 3 4 5 6 7 8 0.3886094 0.4053852 0.4053852 0.3886094 0.4053852 0.3886094 0.3886094 0.3886094 9 10 0.4053852 0.4053852 > predict(fit, type='expected', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.4788811 0.3425892 0.2102235 0.7526123 1.6062935 0.6309751 1.0687658 1.0687658 9 10 0.4204469 0.4204469 $se.fit [1] 0.5182381 0.3982700 0.3292830 0.6266797 1.0255146 0.5852364 0.7341340 [8] 0.7341340 0.6268550 0.6268550 > predict(fit, type='terms', se.fit=T) $fit x 1 -0.04226304 2 0.04226304 3 0.04226304 4 -0.04226304 5 0.04226304 6 -0.04226304 7 -0.04226304 8 -0.04226304 9 0.04226304 10 0.04226304 attr(,"constant") [1] -0.04226304 $se.fit x 1 0.3969086 2 0.3969086 3 0.3969086 4 0.3969086 5 0.3969086 6 0.3969086 7 0.3969086 8 0.3969086 9 0.3969086 10 0.3969086 > > 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 0.2279 1.000 3 3 1 0.437 0.262 0.1347 1.000 6 5 1 0.357 0.226 0.1034 1.000 7 4 1 0.277 0.188 0.0729 1.000 8 4 1 0.214 0.156 0.0514 0.894 9 5 2 0.143 0.112 0.0308 0.667 > 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 0.644 0.444 0.16657 1 3 3 1 0.482 0.511 0.06055 1 6 5 1 0.404 0.504 0.03491 1 7 4 1 0.322 0.475 0.01801 1 8 4 1 0.258 0.437 0.00928 1 9 5 2 0.181 0.377 0.00302 1 > > proc.time() user system elapsed 1.21 0.14 1.34