Cox and Proportional Hazard

FORUM QUESTION: BarbaraGrimes - 24 Aug 2009 - 13:09

If the proportional hazards assumption is not met for a predictor in a Cox model, what should I do?

FORUM ANSWER 1: KnutWittkowski - 25 Aug 2009 - 05:13

Like the related assumption of linearity in the linear model the proportional hazard assumption is being made for computational convenience, not biologic plausibility. Depending on your problem, you may use Kaplan-Meier curves or Gehan's test (see Morales 2008, SAGMB, for extensions to several event categories).

FORUM ANSWER 2: PeterBacchetti - 27 Aug 2009 - 20:22

If there is some interest in the predictor, then modeling the non-proportionality may provide insight. This can be done using time-varying covariates. For example, you can divide followup time into early and late eras, and then define two predictors: one equal to the predictor at times in the early era and equal to zero in the late era, and one equal to zero in the early era and equal to the predictor in the late era. You can then obtain estimates for the effect of the predictor early and for its effect late. There are many variations possible on this approach.

This is in keeping with the general good statistical practice of obtaining estimates (with confidence intervals) for quantities that address any important issues.