File: C:/Program Files/R/R-4.4.0/library/survival/tests/book3.Rout.save
R Under development (unstable) (2021-01-28 r79896) -- "Unsuffered Consequences"
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> 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
1.079 0.084 1.165