A Two-stage Approach for Variable Selection in Joint Modeling of Multiple Longitudinal Markers and Competing Risk Outcomes

Abstract: Background: In clinical and epidemiological research, the integration of longitudinal measurements and time-to-event outcomes is vital for understanding relationships and improving risk prediction. However, as the number of longitudinal markers increases, joint model estimation becomes more complex, leading to long computation times and convergence issues. This study introduces a novel two-stage Bayesian approach for variable selection in joint models, illustrated through a practical application. Methods: Our approach conceptualizes the analysis in two stages. In the first stage, we estimate one-marker joint models for each longitudinal marker related to the event, allowing for bias reduction from informative dropouts through individual marker trajectory predictions. The second stage employs a proportional hazard model that incorporates expected current values of all markers as time-dependent covariates. We explore continuous and Dirac spike-and-slab priors for variable selection, utilizing Markov chain Monte Carlo (MCMC) techniques. Results: The proposed method addresses the challenges of parameter estimation and risk prediction with numerous longitudinal markers, demonstrating robust performance through simulation studies. We further validate our approach by predicting dementia risk using the Three-City (3C) dataset, a longitudinal cohort study from France. Conclusions: This two-stage Bayesian method offers an efficient process for variable selection in joint modeling, enhancing risk prediction capabilities in longitudinal studies. The accompanying R package VSJM, which is freely available at https://github.com/tbaghfalaki/VSJM, facilitates implementation, making this approach accessible for diverse clinical applications.