Bayesian partial likelihood approach for tied observations

The Bayesian analysis based on the partial likelihood for Cox's proportional hazards model is frequently used because of its simplicity. The Bayesian partial likelihood approach is often justified by showing that it approximates the full Bayesian posterior of the regression coefficients with a diffuse prior on the baseline hazard function. This, however, may not be appropriate when ties exist among uncensored observations. In that case, the full Bayesian and Bayesian partial likelihood posteriors can be much different. In this paper, we propose a new Bayesian partial likelihood approach for many tied observations and justify its use.