Variable selection for high-dimensional partly linear additive Cox model with application to Alzheimer's disease

Variable selection has been discussed under many contexts and especially, a large literature has been established for the analysis of right-censored failure time data. In this article, we discuss an interval-censored failure time situation where there exist two sets of covariates with one being low-dimensional and having possible nonlinear effects and the other being high-dimensional. For the problem, we present a penalized estimation procedure for simultaneous variable selection and estimation, and in the method, Bernstein polynomials are used to approximate the involved nonlinear functions. Furthermore, for implementation, a coordinate-wise optimization algorithm, which can accommodate most commonly used penalty functions, is developed. A numerical study is performed for the evaluation of the proposed approach and suggests that it works well in practical situations. Finally the method is applied to an Alzheimer's disease study that motivated this investigation.