# tests/book7.R In survival: Survival Analysis

```library(survival)
options(na.action=na.exclude)
options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type

#
# Tests from the appendix of Therneau and Grambsch
#  Data set 1 + exact method

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))

byhand7 <- function(beta) {
r <- exp(beta)
loglik <- 2*(beta - log(3*r + 3))
u <- 2/(r+1)
imat <- 2*r/(r+1)^2
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

list(loglik=loglik, u=u, imat=imat, mart=mart)
}
aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))

fit0 <-coxph(Surv(time, status) ~x, test1, iter=0, method='exact')
truth0 <- byhand7(0)
aeq(truth0\$loglik, fit0\$loglik[1])
aeq(1/truth0\$imat, fit0\$var)
aeq(truth0\$mart, fit0\$resid[c(2:6,1)])

fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='exact')
aeq(fit1\$coef, truth0\$u*fit0\$var)
truth1 <- byhand7(fit1\$coef)
aeq(fit1\$loglik[2], truth1\$loglik)
aeq(1/truth1\$imat, fit1\$var)
aeq(truth1\$mart, resid(fit1)[c(3:7,1)])

# Beta is infinite for this model, so we will get a warning message
fit2 <-  coxph(Surv(time, status) ~x, test1, method='exact')
aeq(resid(fit2)[-2], c(0, 2/3, -1/3, -4/3,  1, 0))  #values from the book

#
# Now a multivariate case: start/stop data uses a different C routine
#
zz <- rep(0, nrow(lung))
fit1 <- coxph(Surv(time, status) ~ age + ph.ecog + sex, lung, method="exact")
fit2 <- coxph(Surv(zz, time, status) ~ age + ph.ecog + sex, lung,
method="exact")
aeq(fit1\$loglik, fit2\$loglik)
aeq(fit1\$var, fit2\$var)
aeq(fit1\$score, fit2\$score)
aeq(fit1\$resid, fit2\$resid)
```

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survival documentation built on Aug. 24, 2021, 5:06 p.m.