Covariate selection for semiparametric hazard function regression models

We study a flexible class of non-proportional hazard function regression models in which the influence of the covariates splits into the sum of a parametric part and a time-dependent nonparametric part. We develop a method of covariate selection for the parametric part by adjusting for the implicit fitting of the nonparametric part. Our approach is based on the general model selection methodology of Barron, Birgé and Massart, suitably adapted to the censored semiparametric regression framework. Asymptotic consistency of the proposed covariate selection method is established, leading to asymptotically normal estimators of both parametric and nonparametric parts of the model in the presence of covariate selection. The approach is applied to a real data set and a simulation study is presented.