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 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.