Variable Selection For Marginal Hazard Ratio Based On Penalized GEE

Clustered failure time data often arise in biomedical studies and a marginal regression mod-eling approach is often preferred to avoid assumption on the dependence structure within clus-ters. A novel estimating equation approach is proposed based on a semiparametric marginal proportional hazards model and a penalized generalized estimating equation (GEE) to take the correlation within clusters into account. On one hand, different from the traditional marginal method for clustered failure time data, our method explicitly models the correlation structure within clusters by using a pre-specified working correlation matrix. On the other hand, there ex-ists a variable selection function by adding a penalty into the estimating equation. The estimates from the proposed method are proved to be consistent and asymptotically normal. Simulation studies show the excellent properties of the proposed method. Finally, the model and the pro-posed method are applied to a kidney infections study.The contents of the paper is as follows. Section 1 is the introduction, will introduce the background of clustered failure time data and some previous research outcomes. Some basic knowledge involved in this paper is introduced in Section 2. Section 3 describes the forming pro-cess and specific form of our estimating equation. The asymptotic properties of these estimators and iterative algorithm for solving the estimating functions are listed. Section 4 illustrates the estimation performance with simulation results. In section 5, we evaluate the proposed method by analyzing the infections in kidney patients data. The conditions and a brief discussion are deferred to section 6.