145 lines
5.0 KiB
R
145 lines
5.0 KiB
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])
|
||
|
|
aeq(1/truth0$imat, fit0$var)
|
||
|
|
aeq(truth0$mart, fit0$residuals)
|
||
|
|
aeq(truth0$scho, resid(fit0, 'schoen'))
|
||
|
|
aeq(truth0$score, resid(fit0, 'score'))
|
||
|
|
sfit <- survfit(fit0, list(x=0), censor=FALSE)
|
||
|
|
aeq(sfit$std.err^2, truth0$var)
|
||
|
|
aeq(sfit$surv, truth0$surv)
|
||
|
|
aeq(fit0$score, truth0$u^2/truth0$imat)
|
||
|
|
|
||
|
|
beta1 <- truth0$u/truth0$imat
|
||
|
|
fit1 <- coxph(Surv(start, stop, event) ~x, test2, iter=1, ties="breslow")
|
||
|
|
aeq(beta1, coef(fit1))
|
||
|
|
|
||
|
|
truth <- byhand(-0.084526081, 0)
|
||
|
|
fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8, method='breslow',
|
||
|
|
nocenter= NULL)
|
||
|
|
aeq(truth$loglik, fit$loglik[2])
|
||
|
|
aeq(1/truth$imat, fit$var)
|
||
|
|
aeq(truth$mart, fit$residuals)
|
||
|
|
aeq(truth$scho, resid(fit, 'schoen'))
|
||
|
|
aeq(truth$score, resid(fit, 'score'))
|
||
|
|
expect <- predict(fit, type='expected', newdata=test2) #force recalc
|
||
|
|
aeq(test2$event -fit$residuals, expect) #tests the predict function
|
||
|
|
|
||
|
|
sfit <- survfit(fit, list(x=0), censor=FALSE)
|
||
|
|
aeq(sfit$std.err^2, truth$var)
|
||
|
|
aeq(-log(sfit$surv), (cumsum(truth$haz)))
|
||
|
|
|
||
|
|
# Reprise the test, with strata
|
||
|
|
# offseting the times ensures that we will get the wrong risk sets
|
||
|
|
# if strata were not kept separate
|
||
|
|
test2b <- rbind(test2, test2, test2)
|
||
|
|
test2b$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])
|
||
|
|
aeq(3*truth0$imat, 1/fit0$var)
|
||
|
|
aeq(rep(truth0$mart,3), fit0$residuals)
|
||
|
|
aeq(rep(truth0$scho,3), resid(fit0, 'schoen'))
|
||
|
|
aeq(rep(truth0$score,3), resid(fit0, 'score'))
|
||
|
|
|
||
|
|
fit1 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b,
|
||
|
|
iter=1, method="breslow")
|
||
|
|
aeq(fit1$coefficients, beta1)
|
||
|
|
|
||
|
|
fit3 <- coxph(Surv(start, stop, event) ~x + strata(group),
|
||
|
|
test2b, eps=1e-8, method='breslow')
|
||
|
|
aeq(3*truth$loglik, fit3$loglik[2])
|
||
|
|
aeq(3*truth$imat, 1/fit3$var)
|
||
|
|
aeq(rep(truth$mart,3), fit3$residuals)
|
||
|
|
aeq(rep(truth$scho,3), resid(fit3, 'schoen'))
|
||
|
|
aeq(rep(truth$score,3), resid(fit3, 'score'))
|
||
|
|
|
||
|
|
#
|
||
|
|
# Done with the formal test, now print out lots of bits
|
||
|
|
#
|
||
|
|
resid(fit)
|
||
|
|
resid(fit, 'scor')
|
||
|
|
resid(fit, 'scho')
|
||
|
|
|
||
|
|
predict(fit, type='lp')
|
||
|
|
predict(fit, type='risk')
|
||
|
|
predict(fit, type='expected')
|
||
|
|
predict(fit, type='terms')
|
||
|
|
predict(fit, type='lp', se.fit=T)
|
||
|
|
predict(fit, type='risk', se.fit=T)
|
||
|
|
predict(fit, type='expected', se.fit=T)
|
||
|
|
predict(fit, type='terms', se.fit=T)
|
||
|
|
|
||
|
|
summary(survfit(fit))
|
||
|
|
summary(survfit(fit, list(x=2)))
|