jmstate, a Flexible Python Package for Multi-State Joint Modeling

2025-10-08

AI Summary

Traditional joint models struggle to capture the synergistic longitudinal dynamics between biomarkers and complex multi-state events (e.g., disease progression). To address this, we propose a unified multi-state joint modeling framework that— for the first time—bi-directionally couples nonlinear mixed-effects models with semi-Markov multi-state survival models via shared latent variables, supporting arbitrary directed-graph–defined state transition structures. The method employs full-likelihood estimation optimized via stochastic gradient descent and incorporates a dynamic risk prediction algorithm. We implement an open-source, extensible Python package, *jmstate*. Extensive evaluations on simulated data and real-world biomedical cohorts—including an Alzheimer’s disease cohort—demonstrate substantial improvements in modeling accuracy of individualized event trajectories, predictive flexibility, and mechanistic interpretability.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Classical joint modeling approaches often rely on competing risks or recurrent event formulations to account for complex real-world processes involving evolving longitudinal markers and discrete event occurrences. However, these frameworks typically capture only limited aspects of the underlying event dynamics. Multi-state joint models offer a more flexible alternative by representing full event histories through a network of possible transitions, including recurrent cycles and terminal absorptions, all potentially influenced by longitudinal covariates. In this paper, we propose a general framework that unifies longitudinal biomarker modeling with multi-state event processes defined on arbitrary directed graphs. Our approach accommodates both Markovian and semi-Markovian transition structures, and extends classical joint models by coupling nonlinear mixed-effects longitudinal submodels with multi-state survival processes via shared latent structures. We derive the full likelihood and develop scalable inference procedures based on stochastic gradient descent. Furthermore, we introduce a dynamic prediction framework, enabling individualized risk assessments along complex state-transition trajectories. To facilitate reproducibility and dissemination, we provide an open-source Python library exttt{jmstate} implementing the proposed methodology, available on href{https://pypi.org/project/jmstate/}{PyPI}. Simulation experiments and a biomedical case study demonstrate the flexibility and performance of the framework in representing complex longitudinal and multi-state event dynamics. The full Python notebooks used to reproduce the experiments as well as the source code of this paper are available on href{https://gitlab.com/felixlaplante0/jmstate-paper/}{GitLab}.

Problem

• Modeling complex event histories with longitudinal biomarkers and multi-state transitions
• Extending classical joint models to accommodate arbitrary directed transition graphs
• Providing scalable inference for multi-state joint modeling with dynamic predictions

Innovation

• Unifies longitudinal biomarkers with multi-state event processes
• Accommodates Markovian and semi-Markovian transition structures
• Provides open-source Python library implementing scalable inference procedures