I have a problem in which one of the covariates in my model violates the assumption of proportional hazards, but the interaction it is part of does not.
Lifespan - mosquito time to death (not censored)
feed_time - categorical variable: AM / PM
treatment - categorical variable: infected / uninfected
clutch - continuous variable
cage - cages in which my mosquitoes are housed (i'm using cluster(cage) as mosquitoes within a cage are not independent)
Results of min model: Cox Proportional Hazards Model
cph(formula = Surv(lifespan) ~ feed_time + treatment * clutch1 + cluster(cage), data = df, x = T, y = T) Frequencies of Missing Values Due to Each Variable Surv(lifespan) feed_time treatment clutch1 feed_time 2 0 0 0 0 Model Tests Discrimination Indexes Obs 298 LR chi2 17.47 R2 0.057 Events 298 d.f. 4 Dxy 0.133 Center -0.2016 Pr(> chi2) 0.0016 g 0.281 Score chi2 17.84 gr 1.324 Pr(> chi2) 0.0013 Coef S.E. Wald Z Pr(>|Z|) feed_time=PM -0.3300 0.1402 -2.35 0.0185 treatment=Infected -0.2582 0.1564 -1.65 0.0988 clutch1 -0.0008 0.0017 -0.48 0.6346 treatment=Infected * clutch1 0.0073 0.0023 3.18 0.0015
Results of cox.zph:
rho chisq p feed_time=PM 0.000771 0.000251 0.987 treatment=Infected 0.117886 4.548338 0.033 clutch1 0.072919 1.551721 0.213 treatment=Infected * clutch1 -0.066628 1.084940 0.298
So i've had a read of literature and i'm aware that in cases of violated prop hazard i can either create an interaction between the covariate and time (which wouldn't be ideal as i'm interested in the effect of Treatment) OR stratify my covariate (which i'm not sure you can do with a categorical variable? I've only seen examples with continuous variables).
However, i don't know what is appropriate to do when a covariate lies within an interaction in the same model. If someone could prod me in the right direction for what to do next that would be amazing. I've been knocking my head against this for a while.
edit: Here's the log-log plot for treatment
myfit <- npsurv(Surv(lifespan) ~ treatment, data=df) survplot(myfit, loglog=T)