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Could you help me to proceed with a request by a reviewer?

I have a Cox model like this

time_1year | status ~ p1 + p2 + p3 + p4

I was not able to perform Cox regression at 2 year as the proportional hazard assumption was violated.

Reviewer asked us to do the following:

Conduct an analysis that includes time x covariate interactions to address non-proportional hazards, so that mortality risk at 2 year can be assessed.

What and how should I do it? I can use R and SPSS.

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Before you jump to time*covariate interactions, consider other ways of handling violation of proportional hazards (PH). This page contains several recommendations, including using a log-normal model that wouldn't require PH. If any of your predictors are continuous, a transformation might help.

Failing those, the time-dependent vignette for the R survival package shows ways to proceed. One simple approach that sometimes works is to split the time scale in a way that PH is met within each of the time epochs. A full interaction of a covariate with an arbitrary continuous function of time is provided by the tt() functionality of that package, but be careful to follow the instructions carefully lest you fall into a very common error.

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