Toward Joint Prediction of a Longitudinal Marker and a Terminal Event: A bivariate discrete-time framework
Sudden cardiac death (SCD) is a leading cause of death in the U.S. Patients at elevated risk of SCD are primarily treated with an implantable cardioverter-defibrillator (ICD), which may prevent death from cardiovascular causes but may cause severe side effects, such as reduced quality of life from shock-induced pain. Decisions about ICD treatment therefore involve complex personal trade-offs across multiple health events, including mortality and quality of life. While prediction tools could help weigh these trade-offs, they commonly focus on univariate outcomes; at best, they treat other clinical endpoints as inputs, so trade-offs cannot be directly informed. To address this, we propose a novel general Bayesian framework that jointly models a terminal event and a longitudinal marker as a bivariate process over discrete time, for settings where prediction is the primary goal. Discretization of study time lets the framework capture the dynamic interplay between outcomes while avoiding implicit extrapolation beyond truncation by a terminal event. The framework flexibly accommodates phenomena arising in applied contexts, including global time-invariant and local time-dependent dependence structures between the terminal event and the longitudinal marker, and latent association via a shared frailty term. Estimation proceeds via the Bayesian paradigm, yielding patient-specific joint posterior predictions for the time to terminal event and the future marker trajectory. We introduce the framework with a focus on its modeling flexibility, provide guidance on discretization and on Bayesian model construction and selection, and discuss insights from the joint posterior predictions. Finally, we demonstrate the framework's clinical relevance and practicality for SCD and ICD therapy using data from the Sudden Cardiac Death in Heart Failure Trial (SCD-HeFT), an important ICD-related benchmark trial.