A General Framework for Joint Multi-State Models
Félix Laplante, Christophe Ambroise
TL;DR
The paper introduces a general nonlinear joint modeling framework that unifies longitudinal biomarker dynamics with multi-state time-to-event processes defined on arbitrary directed graphs, accommodating both Markovian and semi-Markov transitions and recurrent cycles. It links the longitudinal and event processes through shared latent effects within nonlinear mixed-effects models and provides a tractable likelihood-based inference approach using stochastic gradient methods, enabling scalable analysis of high-dimensional data. A dynamic prediction component yields individualized state-transition probabilities and risk assessments along complex trajectories. Through simulations and application to the PAQUID cohort, the framework demonstrates accurate parameter recovery and effective personalized predictions, highlighting its potential for modeling complex disease progression and guiding clinical decision-making.
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.