Semiparametric 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 exible
frailty model for analyzing such data by assuming a smooth semiparametric form for the
conditional time-to-event distribution and a parametric or a exible form for the frailty
distribution. The results of a simulation study suggest that the estimation of regression
parameters is robust to misspeci cation of the frailty distribution (even when the frailty
distribution is multimodal or skewed). Given su ciently large sample sizes and number
of clusters, the exible approach produces smooth and accurate posterior estimates for the
baseline survival function and for the frailty density, and can correctly detect and identify
unusual frailty density forms. The methodology is illustrated using dental data from the
Signal Tandmobiel® Study.