Semi-parametric frailty model for clustered interval-censored data

The shared frailty model is a popular tool to analyze correlated right-censored time-to-event 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. In the case of interval-censored time-to-event data, the inclusion of frailties results in complicated intractable likelihoods. Here, we propose a flexible frailty model for analyzing such data by assuming a smooth semi-parametric form for the conditional time-to-event distribution and a parametric or a flexible form for the frailty distribution. The results of a simulation study suggest that the estimation of regression parameters is robust to misspecification of the frailty distribution (even when the frailty distribution is multimodal or skewed). Given sufficiently large sample sizes and number of clusters, the flexible approach produces smooth and accurate posterior estimates for the baseline survival function and for the frailty density, and it can correctly detect and identify unusual frailty density forms. The methodology is illustrated using dental data from the Signal Tandmobiel® study.