A unified joint modelling of zero-inflated longitudinal measurements and time-to-event outcomes with applications to HIV and colorectal cancer data

In this manuscript, we develop a unified joint modelling and estimation framework for zero-inflated count and longitudinal semi-continuous data, with a focus on models structured around the exponential family and two-part hurdle formulations. We first review and synthesize existing longitudinal hurdle models, identifying a common structure across diverse approaches. Motivated by this foundation, we introduce novel joint models that integrate semi-continuous longitudinal outcomes with time-to-event data, and propose new methods for dynamic prediction in the presence of semi-continuous outcomes. To facilitate flexible estimation and inference across this class of models, we propose a Bayesian estimation strategy based on a Markov Chain Monte Carlo (MCMC) algorithm. We have implemented these methods in the R package UHJM (available at https://github.com/tbaghfalaki/UHJM), providing accessible tools for parameter estimation and risk prediction. The utility of our framework is demonstrated through simulation studies and two real-world applications characterized by excess zeros.