APPLICATION OF THE EMPIRICAL LIKELIHOOD METHOD IN PROPORTIONAL HAZARDS MODEL

In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data. Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion.