The Cox Proportional Hazards Model with a Partially Known Baseline

The Cox proportional hazards regression model has been widely used in the analysis of survival/duration data. It is semiparametric because the model includes a baseline hazard function that is completely unspecified. We study here the statistical inference of the Cox model where some information about the baseline hazard function is available, but it still remains as an infinite dimensional nuisance parameter. We incorporate the information about the baseline hazard into the inference for regression coefficient by using the empirical likelihood method (Owen 2001) and obtained the modified test/estimator and their asymptotic distributions. The modified estimator is shown to be better than the regular Cox partial likelihood estimator in theory and in several simulations.