Bayesian analysis of multivariate linear mixed models with censored and intermittent missing responses

Multivariate longitudinal data usually exhibit complex features such as the presence of censored responses due to detection limits of the assay and unavoidable missing values arising when participants make irregular visits that lead to intermittently recorded characteristics. A generalization of the multivariate linear mixed model constructed by taking into account impacts of censored and intermittent missing responses simultaneously, which is named as the MLMM-CM, has been recently proposed for more precisely analyzing such kinds of data. This paper aims at presenting a fully Bayesian sampling-based approach to the MLMM-CM for addressing the uncertainties of censored and missing responses as well as unknown parameters. Two widely accepted Bayesian computational techniques based on the Markov chain Monte Carlo and the inverse Bayes formulas coupled with the Gibbs (IBF-Gibbs) schemes are developed for carrying out posterior inference of the model. The proposed methodology is illustrated through a simulation study and a real-data example from the Adult AIDS Clinical Trials Group 388 study. Numerical results show empirically that the proposed Bayesian methodology performs satisfactorily and offers reliable posterior inference.