R version 4.4.0 beta (2024-04-15 r86425 ucrt) -- "Puppy Cup"
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> library(survival)
> library(splines)
> aeq <- function(x, y) all.equal(as.vector(x), as.vector(y))
> 
> # A contrived example for the tt function
> #
> mkdata <- function(n, beta) {
+     age <- runif(n, 20, 60)
+     x <- rbinom(n, 1, .5)
+ 
+     futime <- rep(40, n)   # everyone has 40 years of follow-up
+     status <- rep(0, n)
+     dtime <-  runif(n/2, 1, 40)  # 1/2 of them die
+     dtime <- sort(dtime)
+ 
+     # The risk is set to beta[1]*x + beta[2]* f(current_age)
+     #   where f= 0 up to age 40, rises linear to age 70, flat after that
+     for (i in 1:length(dtime)) {
+         atrisk <- (futime >= dtime[i])
+         c.age <- age + dtime
+         age2 <- pmin(30, pmax(0, c.age-40))
+         xbeta <- beta[1]*x + beta[2]*age2
+         
+         # Select a death according to risk
+         risk <- ifelse(atrisk, exp(xbeta), 0)
+         dead <- sample(1:n, 1, prob=risk/sum(risk))
+         
+         futime[dead] <- dtime[i]
+         status[dead] <- 1
+     }
+     data.frame(futime=round(futime,1), status=status, age=age, x=x, risk=risk,
+                casewt = sample(1:5, n, replace=TRUE),
+ 
+                grp = sample(1:15, n, replace=TRUE))
+ }
> 
> set.seed(1953)  # a good year
> # The functional form won't be well estimated with n=100, but a large
> #  n makes the test slow, and as a validity test n=100 and n=1000 are equally
> #  good.
> tdata <- mkdata(100, c(log(1.5), 2/30))   # data set has many ties
> 
> dtime <- sort(unique(tdata$futime[tdata$status==1]))
> data2 <- survSplit(Surv(futime, status) ~., tdata, cut=dtime)
> data2$c.age <- data2$age + data2$futime  # current age
> 
> # fit1 uses data at the event times, fit2$c.age might have a 
> #  wider range due to censorings.  To make the two fits agree
> #  fix the knots.  I know a priori that 20 to 101 will cover it.
> ns2 <- function(x) ns(x, Boundary.knots=c(20, 101), knots=c(45, 60, 75))
> 
> fit1 <- coxph(Surv(futime, status)~ x + tt(age), tdata,
+               tt= function(x, t, ...) ns2(x+t))
> 
> fit2 <- coxph(Surv(tstart, futime, status) ~ x + ns2(c.age), data2)
> 
> aeq(coef(fit1), coef(fit2))
[1] TRUE
> aeq(vcov(fit1), vcov(fit2))
[1] TRUE
> 
> #
> # Check that cluster, weight, and offset were correctly expanded
> #
> fit3a <- coxph(Surv(futime, status)~ x + tt(age), tdata, weights=casewt, 
+               tt= function(x, t, ...) ns2(x+t))
> fit3b <-  coxph(Surv(tstart, futime, status) ~ x + ns2(c.age), data2,
+                 weights=casewt)
> aeq(coef(fit3a), coef(fit3b))
[1] TRUE
> aeq(vcov(fit3a), vcov(fit3b))
[1] TRUE
> 
> fit4a <- coxph(Surv(futime, status)~ x + tt(age), tdata,
+               tt= function(x, t, ...) ns2(x+t), cluster=grp)
> fit4b <-  coxph(Surv(tstart, futime, status) ~ x + ns2(c.age), data2,
+                 cluster=grp)
> fit4c <- coxph(Surv(tstart, futime, status) ~ x + ns2(c.age) + cluster(grp),
+                data2)
> aeq(coef(fit4a), coef(fit4b))
[1] TRUE
> aeq(vcov(fit4a), vcov(fit4b))
[1] TRUE
> aeq(coef(fit4a), coef(fit4c))
[1] TRUE
> aeq(vcov(fit4a), vcov(fit4c))
[1] TRUE
> 
> fit5a <- coxph(Surv(futime, status)~ x + tt(age) + offset(grp/10), tdata,
+               tt= function(x, t, ...) ns2(x+t),)
> fit5b <-  coxph(Surv(tstart, futime, status) ~ x + ns2(c.age)+ offset(grp/10)
+                 , data=data2)
> aeq(coef(fit5a), coef(fit5b))
[1] TRUE
> aeq(vcov(fit5a), vcov(fit5b))
[1] TRUE
> 
> # Check that strata is correct
> fit6a <- coxph(Surv(futime, status) ~ x + tt(age) + strata(grp), tdata,
+                tt = function(x, t, ...) (x+t)^2)
> fit6b <- coxph(Surv(tstart, futime, status) ~ x + I(c.age^2) +strata(grp), data2)
> aeq(coef(fit6a), coef(fit6b))
[1] TRUE
> aeq(vcov(fit6a), vcov(fit6b))
[1] TRUE
> 
>                                              
> 
> proc.time()
   user  system elapsed 
   1.07    0.17    1.25