A General Framework for Joint Multi-State Models

arXiv:2510.07128v2 Announce Type: replace-cross
Abstract: Classical joint modeling approaches often rely on competing risks or recurrent event formulations to describe complex processes involving evolving longitudinal biomarkers and discrete event occurrences, but these frameworks typically capture only limited aspects of the underlying event dynamics. We propose a general multi-state joint modeling framework that unifies longitudinal biomarker dynamics with multi-state time-to-event processes defined on arbitrary directed graphs. The proposed framework accommodates arbitrary directed transition graphs, nonlinear longitudinal submodels, and scalable inference via stochastic gradient descent. This formulation encompasses both Markovian and semi-Markovian transition structures, allowing recurrent cycles and terminal absorptions to be naturally represented. The longitudinal and event processes are linked through shared latent structures within nonlinear mixed-effects models, extending classical joint modeling formulations. We derive the complete likelihood, establish conditions for identifiability, and develop scalable inference procedures based on stochastic gradient descent to enable high-dimensional and large-scale applications. In addition, we formulate a dynamic prediction framework that provides individualized state-transition probabilities and personalized risk assessments along complex event trajectories. Through simulation and application to the PAQUID cohort, we demonstrate accurate parameter recovery and individualized prediction.