Bayesian Joint Modeling of Zero-Inflated Longitudinal Data and Survival with a Cure Fraction: Application to AIDS Data

Abstract: We propose a comprehensive Bayesian joint modeling framework for zero-inflated longitudinal count data and time-to-event outcomes, explicitly incorporating a cure fraction to account for subjects who never experience the event. The longitudinal sub-model employs a flexible mixed-effects Hurdle model, with distributional options including zero-inflated Poisson and zero-inflated negative binomial, accommodating excess zeros and overdispersion common in count data. The survival component is modeled using a Cox proportional hazards model combined with a mixture cure model to distinguish cured from susceptible individuals. To link the longitudinal and survival processes, we include a linear combination of current longitudinal values as predictors in the survival model. Inference is performed via Hamiltonian Monte Carlo, enabling efficient and robust parameter estimation. The joint model supports dynamic predictions, facilitating real-time risk assessment and personalized medicine. Model performance and estimation accuracy are validated through simulation studies. Finally, we illustrate the methodology using a real-world HIV cohort dataset, demonstrating its practical utility in predicting patient survival outcomes and supporting personalized treatment decisions. Our results highlight the benefits of integrating complex longitudinal count data with survival information in clinical research.