I want to run a Cox model to see if there is an interaction between two treatments. However, the test to see if proportional hazard is respected suggests that it is actually not respected. So I don't know what other statistical survival analysis to do because it means I cannot rely on the cox model conclusions? Or that the conclusions may just be less powerful that if proportional hazard would have been respected? What alternative tests I could do in this case? I was thinking about "survreg" models, but I am not sure what distribution to use and with only 4 dates I think it does not make sense to have a timescale distribution with so few dates? In R, I can only run survreg with Gaussian or logistic distributions, but I think none of these should be considered in my case.

Thank you very much if you can help me or guide me on this.

Best wishes and please see below further explanations:

Experiment overview: There is four conditions (a= no treatment, b= antibiotics, c=antihypertensive and d=antibiotics+antihypertensive). I had 150 animals (tiny) per condition, so 600 in total. I followed the survival/death at days 0 (all alive), day 2, day 4 and day 6 of the experiment.

Here is a bit of the Rcode:

fit1 <- coxph(Surv(a$time, a$survival) ~ antibiotics + antihypertensive + antibiotics:antihypertensive, data = a)

summary(fit1)

test.ph <- cox.zph(fit1)

test.ph

> test.ph

rho chisq p

antihypertensiveyes -0.0806 4.34 0.037260

antibioticsyes 0.0794 4.18 0.040944

antihypertensiveyes:antibioticsyes -0.0467 1.45 0.228140

GLOBAL NA 18.36 0.000371

--> no proportional hazard

Thanks a lot,

Best wishes

Rets