Semiparametric Bayesian frailty model for clustered interval-censored data

The shared frailty model is one of the popular tool to analyze correlated right-censored time-toevent data. In the shared frailty model, the latent frailty is assumed to be shared by the members of a cluster and is assigned a parametric distribution, typically, a gamma distribution due to its conjugacy. However, in case of interval-censored time-to-event data, the inclusion of gamma frailties results in complicated intractable likelihoods, where the conjugacy property does not hold anymore. Here, we propose a semiparametric Bayesian frailty model for analyzing such data. We discuss three parametric specifications for frailty distribution in the analysis of interval-censored data. Afterwards we call particular attention to nonparametric specification of the frailty distribution. The results of the simulation study suggest that the proposed approach is robust to misspecification of the frailty distribution. Moreover, the performance of the proposed methodology is quite good in practical situations where the frailty distribution is multimodal or skewed. The approach is applied to dental data arising from the Signal Tandmobiel® Study