Kauermann, Göran and Berger, U.
A Smooth Test in Proportional Hazard Survival Models using Local Partial Likelihood Fitting.
Collaborative Research Center 386, Discussion Paper 282
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 with covariate effects smoothly varying with time. A formal test is derived to test the model with proportional hazards against the smooth general model as alternative. The test proves to possess omnibus power. 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.