Bayesian multivariate linear mixed-effects models with varied association structures

In medicine, multiple continuous outcomes are often repeatedly measured on each subject over time to assess disease severity. Usually, it is of interest to investigate the association between those outcomes, which may be measured at different time points, resulting in unbalanced data. The multivariate linear mixed-effects model (MLMM) is a popular framework for this analysis. It considers the unbalanced nature of the data and accounts for the association of the outcomes via the random effects, often assuming a multivariate normal distribution. However, measuring and understanding the degree of connection between longitudinal outcomes remains challenging. We propose to enhance the MLMM by incorporating various interpretable association structures. Specifically, we consider that multiple longitudinal outcomes are related to the primary outcome through their current value, cumulative effect (total or partial), or both. Our research is motivated by Pompe disease, a rare, inheritable, progressive metabolic myopathy. Clinically, it is important to investigate how patient-reported outcome measures (primary outcomes) are associated with physical outcomes to determine whether improvements in physical outcomes are accompanied by improvements in health-related quality of life and other patient experiences. We found a positive association between them. The proposed models are fitted under the Bayesian framework using Hamiltonian Monte Carlo.