Joint Model for Assessing the Effect of Frailty and Longitudinal Measures in Time‐To‐Event Outcome

Abstract

Joint modeling provides a robust statistical framework for simultaneously modeling longitudinal covariate and time‐to‐event outcome. Apart from the interdependence between longitudinal and survival outcomes there may exist some unobserved random heterogeneity which can be modeled using a joint frailty model (JFM). Unlike existing JFMs, where two survival events are modeled using a frailty, our framework incorporates frailty into the survival sub‐model to accommodate an additional source of variation at the survival endpoint. So here we developed a novel JFM and estimated the parameters using maximum‐likelihood estimation method. The analyses were performed using R Software and illustrated using colorectal cancer data. The frailty component was introduced in colorectal cancer data to account for the unobserved variability in survival risk beyond the observed clinical characteristics. The highly significant frailty variance confirmed the presence of unobserved heterogeneity in survival outcomes. When compared with the standard Joint model (JM), the JFM demonstrated improved model fit and captured additional unexplained heterogeneity among individuals, leading to more precise hazard estimates. Further we conducted Monte Carlo simulations to compare the performance of the proposed model under various simulation scenarios (censoring [20% and 50%], frailty variance (≈0, 0.5, 1), and sample sizes [ n = 100, 250, 500]). Performance was assessed using bias, root mean squared error and model fit indices. The findings highlight the importance of incorporating the frailty term in joint modeling, particularly in cancer prognostic studies where individual heterogeneity plays a crucial role.