Model selection for two-sample problems with right-censored data: An application of Cox model

For investigating differences between two treatment groups in medical science, selecting a suitable model to capture the underlying survival function for each group with some covariates is an important issue. Many methods, such as stratified Cox model and unstratified Cox model, have been proposed for investigating the problem. However, different models generally perform differently under different circumstances and none dominates the others. In this article, we focus on two sample problems with right-censored data and propose a model selection criterion based on an approximately unbiased estimator of Kullback–Leibler loss, which accounts for estimation uncertainty in estimated survival functions obtained by various candidate models. The effectiveness of the proposed method is justified by some simulation studies and it also applied to an HIV+ data set for illustration.