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

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Multivariate longitudinal data often contain censored responses and intermittent missing values.
• Existing models may not adequately address these complex data features.
• Accurate analysis is crucial for understanding disease progression and treatment effects.

Purpose of the Study:

• To present a Bayesian sampling-based approach for the multivariate linear mixed model with censored and missing responses (MLMM-CM).
• To address uncertainties associated with censored/missing data and unknown model parameters.
• To provide a robust statistical framework for analyzing complex longitudinal datasets.

Main Methods:

• Developed a fully Bayesian approach utilizing Markov chain Monte Carlo (MCMC) and Inverse Bayes Formulas coupled with Gibbs (IBF-Gibbs) sampling.
• Applied the methodology to the MLMM-CM, a generalized multivariate linear mixed model.
• Validated the approach through simulation studies and a real-world dataset from the Adult AIDS Clinical Trials Group 388 study.

Main Results:

• The proposed Bayesian methodology for MLMM-CM demonstrated satisfactory performance in simulations.
• Empirical results confirmed the reliability of the posterior inference.
• The approach effectively handles both censored and intermittently missing data in multivariate longitudinal studies.

Conclusions:

• The developed Bayesian methodology offers a reliable approach for analyzing multivariate longitudinal data with censored and missing values.
• The MLMM-CM with the proposed Bayesian inference provides accurate statistical insights.
• This method enhances the analysis of complex health-related longitudinal data.