Bayesian Joint Modeling of Longitudinal Data and Interval-Censored Failure Time Data

Longitudinal data are a collection of repeated observations of the same subjects at different points in time. Interval-censored data arise when the time to the event of interest for each subject is never exactly observed but known to fall between two consecutive points in time. Joint analysis of longitudinal data and interval-censored failure time data can lead to more accurate estimates compared to separate modeling when the correlation among events of interest or intracluster correlation is present. The aim of this dissertation is to develop efficient and reliable joint analyses of longitudinal and interval-censored failure time data using Bayesian methods. Three research projects are conducted in this dissertation. The first project of this dissertation focuses on joint modeling of longitudinal data and interval-censored survival data. The joint modeling of longitudinal and survival data is a popular topic in statistics, but most of the existing studies on joint modeling focus on longitudinal data and right-censored data, and there are only a few works on longitudinal data and interval-censored data. A new joint model is proposed and has several appealing properties. Based on the proposed model, a novel Bayesian approach is developed for the parameter estimation, and the proposed approach is computationally efficient and has good performance as shown in numerical studies. The second project extends the proposed joint analysis of longitudinal data and interval-censored survival data to incorporate variable selection. Variable selection in the context of joint modeling of longitudinal and right-censored survival data has received attention in the recent literature. However, variable selection via Bayesian approaches in the context of joint modeling of longitudinal and interval-censored survival data has not yet been proposed. Bayesian Lasso, Bayesian adaptive Lasso, and spike-and-slab priors are used for simultaneous variable selection and parameter estimation in such context. The proposed approaches are shown to perform better in variable selection as compared to the Bayesian approach under a normal prior via simulation studies. The third project is motivated by tumorigenicity studies conducted at National Toxicology Program. Such studies test the toxicity of chemical agents by exposing rats to some test agent at different dose levels and checking the tumor status at different organs of each rat for typically 2 years. When the onset times of tumor at different organs are of interest, multivariate current status data arise. In the current literature, a limited number of studies have focused on joint analysis of multivariate current status data while there are even fewer works on joint modeling of longitudinal data and multivariate current status data. A joint model considering semiparametric multivariate survival submodels, and a semiparametric longitudinal submodel is proposed. The Bayesian approach developed for the parameter estimation has good performance as shown in simulation studies. The proposed method is further illustrated by application to the data from a 2-year study conducted by NTP that tested isoprene for carcinogenicity in male rats.