Bayesian joint analysis of longitudinal data and interval-censored failure time data

Joint modeling of longitudinal responses and survival time has gained great attention in statistics literature over the last few decades. Most existing works focus on joint analysis of longitudinal data and right-censored data. In this article, we propose a new frailty model for joint analysis of a longitudinal response and interval-censored survival time. Such data commonly arise in real-life studies where participants are examined at periodical or irregular follow-up times. The proposed joint model contains a nonlinear mixed effects submodel for the longitudinal response and a semiparametric probit submodel for the survival time given a shared normal frailty. The proposed joint model allows the regression coefficients to be interpreted as the marginal effects up to a multiplicative constant on both the longitudinal and survival responses. Adopting splines allows us to approximate the unknown baseline functions in both submodels with only a finite number of unknown coefficients while providing great modeling flexibility. An efficient Gibbs sampler is developed for posterior computation, in which all parameters and latent variables can be sampled easily from their full conditional distributions. The proposed method shows a good estimation performance in simulation studies and is further illustrated by a real-life application to the patient data from the Aerobics Center Longitudinal Study. The R code for the proposed methodology is made available for public use.