Joint Modeling of Multiple Longitudinal Biomarkers and Survival Outcomes via Threshold Regression: Variability as a Predictor

Longitudinal biomarker data and health outcomes are routinely collected in many studies to assess how biomarker trajectories predict health outcomes. Existing methods primarily focus on mean biomarker profiles, treating variability as a nuisance. However, excess variability may indicate system dysregulations that may be associated with poor outcomes. In this paper, we address the long-standing problem of using variability information of multiple longitudinal biomarkers in time-to-event analyses by formulating and studying a Bayesian joint model. We first model multiple longitudinal biomarkers, some of which are subject to limit-of-detection censoring. We then model the survival times by incorporating random effects and variances from the longitudinal component as predictors through threshold regression that admits non-proportional hazards. We demonstrate the operating characteristics of the proposed joint model through simulations and apply it to data from the Study of Women's Health Across the Nation (SWAN) to investigate the impact of the mean and variability of follicle-stimulating hormone (FSH) and anti-Mullerian hormone (AMH) on age at the final menstrual period (FMP).