R Under development (unstable) (2023-08-12 r84939 ucrt) -- "Unsuffered Consequences"
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> 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])
[1] TRUE
> aeq(1/truth0$imat, fit0$var)
[1] TRUE
> aeq(truth0$mart, fit0$resid[c(2:6,1)])
[1] TRUE
> 
> fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='exact')
> aeq(fit1$coef, truth0$u*fit0$var)
[1] TRUE
> truth1 <- byhand7(fit1$coef)
> aeq(fit1$loglik[2], truth1$loglik)
[1] TRUE
> aeq(1/truth1$imat, fit1$var)
[1] TRUE
> aeq(truth1$mart, resid(fit1)[c(3:7,1)])
[1] TRUE
> 
> # Beta is infinite for this model, so we will get a warning message
> fit2 <-  coxph(Surv(time, status) ~x, test1, method='exact')
Warning message:
In coxexact.fit(X, Y, istrat, offset, init, control, weights = weights,  :
  Loglik converged before variable  1 ; beta may be infinite. 
> aeq(resid(fit2)[-2], c(0, 2/3, -1/3, -4/3,  1, 0))  #values from the book
[1] TRUE
> 
> 
> #
> # Now a multivariate case: start/stop data uses a different C routine
> #
> zz <- rep(0, nrow(lung))
> fit1 <- coxph(Surv(time, status) ~ age + ph.ecog + sex, lung, method="exact")
> fit2 <- coxph(Surv(zz, time, status) ~ age + ph.ecog + sex, lung,
+               method="exact")
> aeq(fit1$loglik, fit2$loglik)
[1] TRUE
> aeq(fit1$var, fit2$var)
[1] TRUE
> aeq(fit1$score, fit2$score)
[1] TRUE
> aeq(fit1$resid, fit2$resid)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   1.39    0.14    1.53