A smooth test in proportional hazard survival models using local partial likelihood fitting.

Proportional hazard models for survival data, even though popular and numerically handy, suffer from the restrictive assumption that covariate effects are constant over survival time. A number of tests have been proposed to check this assumption. This paper contributes to this area by employing local estimates allowing to fit hazard models in which covariate effects are smoothly varying with time. A formal test is derived to check for proportional hazards against smooth hazards as alternative. The test proves to possess omnibus power in that it is powerful against arbitrary but smooth alternatives. Comparative simulations and two data examples accompany the presentation. Extensions are provided to multiple covariate settings, where the focus of interest is to decide which of the covariate effects vary with time.