Joint Modeling of Longitudinal and Survival Data: A Bayesian Approach for Predicting Disease Progression

Abstract: Joint modeling of longitudinal and survival data has become increasingly important in medical research, particularly for understanding disease progression in chronic conditions where both repeated biomarker measurements and time-to-event outcomes are available. Traditional two-stage methods, which analyze longitudinal and survival components separately, often result in biased estimates and suboptimal predictions due to failure to account for their interdependence. In this study, we propose a Bayesian hierarchical joint modeling framework with an emphasis on predictive evaluation and clinical interpretability. The model simultaneously characterizes the longitudinal trajectory of a biomarker and the associated survival outcome through shared random effects, capturing the intrinsic association between disease dynamics and event risk. The Bayesian formulation allows flexible incorporation of prior information, accommodates irregular measurement times and missing data, and provides full posterior distributions for uncertainty quantification via credible intervals. We evaluate the proposed framework using both simulated data designed to mimic realistic patient trajectories and a real-world clinical dataset involving patients with chronic liver disease. Results demonstrate that the Bayesian joint model consistently outperforms conventional two-stage approaches in terms of parameter estimation accuracy and predictive performance, as measured by time-dependent area under the curve and Brier scores. The proposed approach provides a robust and interpretable tool for dynamic, patient-specific prognosis, supporting clinical decision-making in personalized medicine.