Bayesian joint modeling of high-dimensional discrete multivariate longitudinal data using generalized linear mixed models

Abstract

In routine cancer care, various patient- and clinician-reported symptoms are collected throughout treatment. This informs a crucial part of clinical research, particularly in studying the factors associated with symptom underascertainment. To jointly analyze such discrete, multivariate, and potentially high-dimensional repeated measures, we propose a Bayesian longitudinal generalized linear mixed model (BLGLMM). This model integrates three key methodologies: a low-rank matrix decomposition to approximate the high-dimensional regression coefficient matrix, a sparse factor model to capture the dependence among multiple outcomes, and random effects to account for the dependence among repeated responses. Posterior computation is performed using an efficient Markov chain Monte Carlo algorithm. We conduct simulations and provide an illustrative example examining the factors associated with symptom underascertainment in prostate cancer patients to demonstrate the efficacy and utility of our proposed method.