# time-varying coefficients (Cox regression) - interaction terms

I'm fitting a cox regression model that violates the proportionality assumption by breaking the data into three intervals as suggested by Therneau et al. p. 17~ (https://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf)

But because I'm interested in an interaction term, I think I'll ultimately need a three way interaction term (with time). And I'm wondering what lower order interactions I need to put in the model.

i.e., this is their example,

vfit2 <- coxph(Surv(tstart, time, status) ~ trt + prior + karno:strata(tgroup), data=vet2)

And what I'm trying to do is something equivalent to examining gender differences in that karno effect. So

vfit3 <- coxph(Surv(tstart, time, status) ~ trt + prior + karno:sex:strata(tgroup), data=vet2)

I'll need to do this, but do I also need all or any of the following?

karno:sex

karno:strata(tgroup)

sex:strata(tgroup)

When I tested the cox.zph with the following model coxph(Surv(tstart, time, status) ~ trt + prior + karno*sex, I did see that the interaction term also violates the assumption, if this makes a difference.