Bayesian analysis of joint quantile regression for multi-response longitudinal data with application to primary...

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Longitudinal data with multiple responses present challenges for traditional statistical modeling.
• Estimating conditional quantiles is crucial for understanding data distributions and variability.
• Multivariate mixed-effects models are suitable for correlated longitudinal outcomes.

Purpose of the Study:

• To propose a Bayesian approach for jointly estimating marginal conditional quantiles.
• To handle multi-response longitudinal data using a multivariate mixed-effects model.
• To facilitate high-dimensional inference for complex data structures.

Main Methods:

• Utilized a multivariate asymmetric Laplace distribution for the working likelihood.
• Incorporated penalization priors for Bayesian high-dimensional inference.
• Employed Markov chain Monte Carlo (MCMC) for posterior distribution estimation.

Main Results:

• Developed a robust Bayesian joint quantile regression approach.
• Evaluated the method's performance through Monte Carlo simulations.
• Demonstrated the practical utility with a primary biliary cirrhosis cohort study.

Conclusions:

• The proposed Bayesian method effectively estimates joint conditional quantiles for multi-response longitudinal data.
• The approach is suitable for high-dimensional settings and real-world medical applications.
• Provides a valuable tool for analyzing complex health outcome trajectories.