In a Cox regression framework, I'd like to implement piecewise continuous time-dependent coefficients. This is for variable that do not satisify the PH assumption.
In this vignette https://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf, there are examples for step functions (p.17), and coefficient with some functional form (p.20). What I'd like is to somehow have a piecewise relationship. Using the example provided in the vignette:
library(survival)
vfit <- coxph(Surv(time, status) ~ trt + prior + karno, veteran)
zp <- cox.zph(vfit, transform= function(time) log(time +20))
## Step functions
vet2 <- survSplit(Surv(time, status) ~ ., data= veteran, cut=c(90, 180),
episode= "tgroup", id="id")
vfit2 <- coxph(Surv(tstart, time, status) ~ trt + prior +
karno:strata(tgroup), data=vet2)
## Functional form
vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + tt(karno),
data=veteran,
tt = function(x, t, ...) x * log(t+20))
plot(zp[3])
abline(coef(vfit3)[3:4], col=2)
From the plot (also on p.21 in the vignette), we might argue that we could have a similar but inverted trend from approx. Time=200. I've tried but without success.
First tried directly with a piecewise function with the tt argument but it does not give two sets of coefficents, only one coef for karno and one for tt(karno). I mean we should have something like ax+b for t<200 and cx+d for t>=200
vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + tt(karno),
data=veteran,
tt = function(x, t, t1, t2, ...) x * log(t1+20) * (t<200) +
x * t2 * (t>=200))
So in a second step, I tried to mix both step functions with some functional form for each. Meaning to split the data in two time periods as for step functions and then fit a function in each. But gives error.
vfit3 <- coxph(Surv(tstart, time, status) ~ trt + prior +
(karno + tt(karno)):strata(tgroup),
data=vet2,
tt = function(x, t, ...) x * log(t+20) * (t<200) -
x * t * (t>=200))
Does someone knows how to implement this?
EDIT:
This is what I've come up with
library(survival)
## Original model
m1 <- coxph(formula = Surv(time, status) ~ trt + prior + karno,
data = veteran)
## Transform to long format as in the link
vet1 <- survSplit(Surv(time, status)~., data = veteran, id = "id",
cut = unique(veteran$time))
## Add a grouping variable (strata) for time before 200 days and after.
vet1$tgroup <- ifelse(vet1$time < 200, 1, 2)
## Add a time-transform function
## Here it is the same function for both strata, but they could be different
## e.g. ifelse(vet1$time < 200, f1(time), f2(time))
## Actually not sure, as we need to be careful with the time scale... Anyway
vet1$time1 <- log(vet1$time + 20)
## Same model as in the link, but then add an interaction with the strata
m2 <- coxph(formula = Surv(tstart, time, status)~
trt + prior + (karno + karno:time1):strata(tgroup), data = vet1)
## Some plots as in the vignette
zp <- cox.zph(m1, transform = function(time) log(time +20))
plot(zp[3])
abline(coef(m2)[c(3,5)], col="tomato")
abline(coef(m2)[c(4,6)], col="tomato")
