I run a Cox model with 2 covariates, in addition to the variable of interest. For one covariate, the assumption of proportional hazards is violated. I know different methods developed to cope with non proportionality in Cox models but they seem to be restricted to the case when the violation of the assumption of PH concerns the prognosis variable of interest. Does anyone know what to do when the violation of the assumption of PH concerns one of the covariates? I would be grateful if someone could help.
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1$\begingroup$ How many cases and events are there, over what range of ages? Have you tried any transformations of the age variable? $\endgroup$– EdMCommented Feb 15, 2017 at 16:52
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1$\begingroup$ I have approximately 6000 cases aged 0 to 15 yo, 20% had an event. N, I haven't tried any transformation yet. $\endgroup$– Julie RobinsCommented Feb 15, 2017 at 17:04
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With about 6000 cases and 1200 events, the simplest way to proceed would be to stratify on subgroups of age. That would allow different baseline hazards for the different age subgroups, with the proportional hazards then limited to the influences of sex and your "prognosis variable of interest" around those different baseline hazards. Although it's generally not recommended to categorize a continuous variable this way, that's less of an issue here as your primary interest is not in the effect of age itself; you merely want to account for age as best you can. In principle, you might be able to model age with a polynomial or spline in a way that provided proportional hazards, but in this case the stratification on age subgroups would seem adequate. You can also check for interactions of the other predictors with the age subgroups.
In any event, you should examine carefully the survival curves in the different age subgroups. If you are really covering ages from birth to 15 years, the biologic differences as infants become children and then teenagers don't seem likely to be adequately modeled by a hazard proportional to age.
