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
# a. Data set 1 and Breslow estimate
# The data below is not in time order, to also test sorting, and has 1 NA
#
test1 <- data.frame(time= c(9, 3,1,1,6,6,8),
status=c(1,NA,1,0,1,1,0),
x= c(0, 2,1,1,1,0,0))
# Breslow estimate
byhand1 <- function(beta, newx=0) {
r <- exp(beta)
loglik <- 2*beta - (log(3*r+3) + 2*log(r+3))
u <- (6 + 3*r - r^2) / ((r+1)*(r+3))
imat <- r/(r+1)^2 + 6*r/(r+3)^2
x <- c(1,1,1,0,0,0)
status <- c(1,0,1,1,0,1)
xbar <- c(r/(r+1), r/(r+3), 0, 0) # at times 1, 6, 8 and 9
haz <- c(1/(3*r+3), 2/(r+3), 0, 1 )
ties <- c(1,1,2,2,3,4)
wt <- c(r,r,r,1,1,1)
mart <- c(1,0,1,1,0,1) - wt* (cumsum(haz))[ties] #martingale residual
a <- 3*(r+1)^2; b<- (r+3)^2
score <- c((2*r+3)/a, -r/a, -r/a + 3*(3-r)/b, r/a - r*(r+1)/b,
r/a + 2*r/b, r/a + 2*r/b)
# Schoenfeld residual
scho <- c(1/(r+1), 1- (r/(3+r)), 0-(r/(3+r)) , 0)
surv <- exp(-cumsum(haz)* exp(beta*newx))
varhaz.g <- cumsum(c(1/(3*r+3)^2, 2/(r+3)^2, 0, 1 ))
varhaz.d <- cumsum((newx-xbar) * haz)
varhaz <- (varhaz.g + varhaz.d^2/ imat) * exp(2*beta*newx)
names(xbar) <- names(haz) <- 1:4
names(surv) <- names(varhaz) <- 1:4
list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=haz,
mart=mart, score=score,
scho=scho, surv=surv, var=varhaz,
varhaz.g=varhaz.g, varhaz.d=varhaz.d)
}
aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
fit0 <-coxph(Surv(time, status) ~x, test1, iter=0, method='breslow')
truth0 <- byhand1(0,0)
aeq(truth0$loglik, fit0$loglik[1])
aeq(1/truth0$imat, fit0$var)
aeq(truth0$mart, fit0$resid[c(2:6,1)])
aeq(truth0$scho, resid(fit0, 'schoen'))
aeq(truth0$score, resid(fit0, 'score')[c(3:7,1)])
sfit <- survfit(fit0, list(x=0))
aeq(sfit$std.err^2, c(7/180, 2/9, 2/9, 11/9))
aeq(resid(fit0, 'score'), c(5/24, NA, 5/12, -1/12, 7/24, -1/24, 5/24))
fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='breslow')
aeq(fit1$coef, 8/5)
# This next gives an ignorable warning message
fit2 <- coxph(Surv(time, status) ~x, test1, method='breslow', iter=2)
aeq(round(fit2$coef, 6), 1.472724)
fit <- coxph(Surv(time, status) ~x, test1, method='breslow', eps=1e-8)
aeq(round(fit$coef,7), 1.4752849)
truth <- byhand1(fit$coef, 0)
aeq(truth$loglik, fit$loglik[2])
aeq(1/truth$imat, fit$var)
aeq(truth$mart, fit$resid[c(2:6,1)])
aeq(truth$scho, resid(fit, 'schoen'))
aeq(truth$score, resid(fit, 'score')[c(3:7,1)])
sfit <- survfit(fit, list(x=0), censor=FALSE)
aeq(sfit$std.err^2, truth$var[c(1,2,4)]) # sfit skips time 8 (no events there)
aeq(-log(sfit$surv), (cumsum(truth$haz))[c(1,2,4)])
sfit <- survfit(fit, list(x=0), censor=TRUE)
aeq(sfit$std.err^2, truth$var)
aeq(-log(sfit$surv), (cumsum(truth$haz)))
#
# 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)))
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.