Bayesian joint and individual component regression for multigroup physiological data

Heterogeneous multigroup data often contain both globally shared and group-specific components, posing challenges for conventional regression models. Such data structures are increasingly common in medical research, particularly in radiology and biomedical imaging, where patient populations are naturally heterogeneous across disease subtypes, demographic groups, or imaging modalities. While methods such as Joint and Individual Component Regression (JICO) address this separation, they lack mechanisms to quantify uncertainty and incorporate prior knowledge. In this study, we propose a Bayesian Joint and Individual Component Regression (Bayesian-JICO) framework that extends JICO with a probabilistic formulation. The Bayesian approach enables uncertainty quantification through posterior distributions and credible intervals, offering more reliable inference, especially with limited sample sizes. Posterior estimation was performed via Markov Chain Monte Carlo (MCMC), and the model was evaluated using both simulated scenarios and the publicly available Australian Institute of Sport (AIS) dataset, which contains physiological and hematological measurements of elite athletes. Results demonstrate that Bayesian-JICO outperforms traditional methods in predictive accuracy, interpretability, and robustness, while providing credible intervals for parameter estimates. This framework offers a comprehensive and uncertainty-aware solution for multigroup regression, with broad applicability across biomedical, radiological, environmental, and social sciences.