Variable selection for partially linear proportional hazards model with covariate measurement error.

In survival analysis, we may encounter the following three problems: nonlinear covariate effect, variable selection and measurement error. Existing studies only address one or two of these problems. The goal of this study is to fill the knowledge gap and develop a novel approach to simultaneously address all three problems. Specifically, a partially time-varying coefficient proportional hazards model is proposed to more flexibly describe covariate effects. Corrected score and conditional score approaches are employed to accommodate potential measurement error. For the selection of relevant variables and regularized estimation, a penalization approach is adopted. It is shown that the proposed approach has satisfactory asymptotic properties. It can be effectively realized using an iterative algorithm. The performance of the proposed approach is assessed via simulation studies, and further illustrated by application to data from an AIDS clinical trial.