Joint models for recurrent event data combining with a longitudinal internal covariate

In survival analysis, the primary focus is often the time until an event occurs, but many clinical studies involve recurrent events – such as disease relapses – that require more complex modeling. To understand how these events are influenced by patient-specific factors, researchers often incorporate internal time-dependent covariates like longitudinal biomarkers; for example, tumor size measured over time may affect lesion recurrence in colorectal cancer. Joint modeling provides a robust framework for simultaneously analyzing longitudinal and event processes, enhancing inference through shared information. While the proportional hazards (PH) model is commonly used for the event component, the accelerated failure time (AFT) model offers a valuable alternative when the PH assumption is violated, yet remains underutilized in recurrent event settings. We propose a novel joint modeling framework that integrates both PH and AFT models for longitudinal and recurrent event data, employing a Bayesian approach with efficient computational algorithms. The methodology is validated through extensive simulations and applied to two real-world datasets, demonstrating its flexibility, accuracy, and practical relevance.