Abstract
Joint modeling of longitudinal data and survival data has gained great attention in the last two decades. However, most of the existing studies have focused on right-censored survival data. In this article, we study joint analysis of longitudinal data and interval-censored survival data and conduct Bayesian variable selection in this framework. A new joint model is proposed with a shared frailty to characterize the dependence between the two types of responses, where the longitudinal response is modeled with a semiparametric linear mixed-effects submodel and the survival time is modeled by a semiparametric normal fraility probit sub-model. Several Bayesian variable selection approaches are developed by adopting Bayesian Lasso, adaptive Lasso, and spike-and-slab priors in order to simultaneously select significant covariates and estimate their effects on the two types of responses. Efficient Gibbs samplers are proposed with all unknown parameters and latent variables being sampled directly from well recognized full conditional distributions. Our simulation study shows that these methods perform well in both variable selection and parameter estimation. A real-life data application to joint analysis of blood cholesterol level and hypertension is provided as an illustration.