R version 4.4.0 beta (2024-04-15 r86425 ucrt) -- "Puppy Cup"
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> # A short test on coxph.detail, to ensure that the computed hazard is
> #  equal to the theoretical value
> library(survival)
> aeq <- function(a,b) all.equal(as.vector(a), as.vector(b))
> 
> # taken from book4.R
> 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) + 2*log(3*r+2) + 2*log(3*r+1) +
+         log(2*r +2))
+     u <- 1/(r+1) +  1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) -
+                  ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1))
+     imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 +
+             6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2)
+ 
+     hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1),
+                1/(3*r+2), 1/(2*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,
+                       0,0,0,0,0,.5,.5,1,1,1), ncol=7)
+     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 1:5) dM[i,i] <- dM[i,i] +1  #observed
+     dM[6:7,6:7] <- dM[6:7,6:7] +.5  # 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 add the ties back up (they are symmetric)
+     scho[6:7] <- rep(mean(scho[6:7]), 2)
+ 
+     list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard* exp(beta*newx),
+ 	     mart=mart,  score=score, rmat=resid,
+ 		scho=scho)
+     } 
> 
> # The actual coefficient of the fit is close to zero.  Using a larger
> #  number pushes the test harder, but it should still work without
> #  the init and iter arguments, i.e., for any coefficient.
> fit1 <- coxph(Surv(start, stop, event) ~x, test2,init=-1, iter=0)
> temp <- coxph.detail(fit1)
> temp2 <- byhand(fit1$coef, fit1$means)
> aeq(temp$haz, c(temp2$haz[1:5], sum(temp2$haz[6:7])))
[1] TRUE
>                   
> 
> proc.time()
   user  system elapsed 
   0.89    0.07    0.96