Online Bayesian Inference for Cox Proportional Hazards Model

In this article, we develop an online Bayesian inferential method for the Cox proportional hazards model with right-censored data. The proposed method is designed to analyze datasets where mini-batches of the entire data are sequentially available. As each mini-batch arrives, the method updates the current prior to the posterior distribution, which is then used as the prior for the next step. Each update consists of two steps: updating the marginal posterior of the regression coefficients using the partial likelihood and updating the remaining conditional posterior using the Poisson form Bayesian bootstrap likelihood. Our method is capable of inferring both the regression coefficients and the baseline cumulative hazard function. To the best of our knowledge, this is the first online Bayesian method for the Cox proportional hazards model. Through numerical experiments and real data analysis, we demonstrate that the proposed method outperforms existing frequentist online methods and is comparable to batch learning on the entire dataset, even when the size of mini-batches is moderately small. Supplementary materials for this article are available online.