R version 4.4.0 beta (2024-04-15 r86425 ucrt) -- "Puppy Cup"
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> options(na.action=na.exclude) # preserve missings
> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
> library(survival)
> 
> #
> # Test the logic of the penalized code by fitting some no-frailty models
> #  (theta=0).  It should give exactly the same answers as 'ordinary' coxph.
> #
> test1 <- data.frame(time=  c(4, 3,1,1,2,2,3),
+                     status=c(1,NA,1,0,1,1,0),
+                     x=     c(0, 2,1,1,1,0,0))
> 
> 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) )
> 
> zz <- zz2 <- rep(0, nrow(test1))
> tfit1 <- coxph(Surv(time,status) ~x, test1, eps=1e-7)
> tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T), test1)
> tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz2, theta=0, sparse=T), test1)
> 
> temp <- c('coefficients', 'var', 'loglik', 'linear.predictors',
+ 	  'means', 'n', 'concordance')
> 
> all.equal(tfit1[temp], tfit2[temp])
[1] TRUE
> all.equal(tfit2[temp], tfit3[temp])
[1] TRUE
> 
> zz <- rep(0, nrow(test2))
> tfit1 <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-7)
> tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T),
+ 	       test2)
> all.equal(tfit1[temp], tfit2[temp])
[1] TRUE
> 
> 
> #
> # Repeat the above tests, but with a strata added
> #  Because the data set is simply doubled, the loglik will double,
> #   beta is the same, variance is halved.
> #
> test3 <- rbind(test1, test1)
> test3$x2 <- rep(1:2, rep(nrow(test1),2))
> zz <- zz2 <- rep(0, nrow(test3))
> tfit1 <- coxph(Surv(time,status) ~x + strata(x2), test3, eps=1e-7)
> tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T)
+ 	       + strata(x2), test3)
> tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz2, theta=0, sparse=T)
+ 	         + strata(x2), test3)
> 
> all.equal(tfit1[temp], tfit2[temp])
[1] TRUE
> all.equal(tfit2[temp], tfit3[temp])
[1] TRUE
> 
> 
> test4 <- rbind(test2, test2)
> test4$x2 <- rep(1:2, rep(nrow(test2),2))
> zz <- rep(0, nrow(test4))
> tfit1 <- coxph(Surv(start, stop, event) ~x, test4, eps=1e-7)
> tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T),
+ 	       test4)
> all.equal(tfit1[temp], tfit2[temp])
[1] TRUE
> 
> rm(test3, test4, tfit1, tfit2, tfit3, temp, zz, zz2)
> 
> proc.time()
   user  system elapsed 
   0.79    0.10    0.89