Partially linear structure selection in Cox models with varying coefficients

To explore the nonlinear interactions between covariates and an index variable, partially linear proportional hazards models have been proposed for censored survival data. However, specification of the partially linear structure was usually carried out in an ad-hoc manner by first fitting a full varying-coefficient model and visually examining the resulting fit to identify the linear part. In this article, we consider the problem of coefficient estimation and constant coefficient identification based on a double shrinkage approach. Variable selection is also considered in a coherent estimation framework, resulting in a double-penalization procedure. Under the mild assumptions, we establish asymptotic properties for the procedure such as consistency, sparesistency, constansistency, and asymptotic normality. We evaluate the performance of the proposed method by numerical simulations and demonstrate its application using a breast cancer data set.