Variational Bayesian approach for analyzing interval-censored data under the proportional hazards model

Interval -censored failure time data frequently occur in medical follow-up studies among others and include right -censored data as a special case. Their analysis is much difficult than the analysis of the right -censored data due to their much more complicated structures and no partial likelihood. This article presents a variational Bayesian (VB) approach for analyzing such data under a proportional hazards model. The VB approach obtains a direct approximation of the posterior density. Compared to the Markov chain Monte Carlo (MCMC)-based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. An extensive simulation study is conducted to compare the performance of the proposed methods with two main Bayesian methods currently available in the literature and the classic proportional hazards model and indicates that they work well in practical situations.