Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data

Abstract

In clinical research, longitudinal biomarkers and time-to-event outcomes are often correlated. Standard separate modeling of these processes leads to biased estimates due to the failure to account for endogeneity. This study investigates the application of the Bayesian joint modeling framework to quantify the association between pulse rate trajectories and mortality risk in cardiac patients. A primary focus is placed on comparing various association structures to determine the most effective parameterization for medical inference. Data from cardiac patients at an Ethiopian cardiac center were analyzed using a linear mixed model for pulse rate and a Cox PH model for time-to-death. Three distinct association structures current value, current value plus slope, and shared random effects were estimated via Markov chain Monte Carlo (MCMC) algorithms. The current value plus slope association structure provided the best model fit, demonstrating that both the current level of pulse rate and its instantaneous rate of change are significant predictors of mortality. Clinical findings also indicated that underweight status and pulmonary complications significantly increase the hazard of death, while corrective surgery serves as a protective factor. Joint modeling offers a robust unified approach for medical research, yielding more efficient and less biased estimates than separate analyses. The choice of association structure is critical; specifically, incorporating the trajectory's slope alongside its current value enhances the predictive performance and interpretability of clinical biomarkers in survival analysis.