# A General Framework for Joint Multi-State Models

arXiv: https://arxiv.org/abs/2510.07128 · HTML: https://mlsanity.com/paper/2510.07128/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 46 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Estimation of extended mixed models using latent classes and latent processes: the R package lcmm](https://mlsanity.com/paper/1503.00890/) (2015)
- [Estimation of Semi-Markov Multi-state Models: A Comparison of the Sojourn Times and Transition Intensities Approaches](https://mlsanity.com/paper/2005.14462/) (2020)

## Abstract (arXiv)

Conventional joint modeling approaches generally characterize the relationship between longitudinal biomarkers and discrete event occurrences within terminal, recurring or competing risk settings, thereby offering a limited representation of complex, multi-state trajectories. 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 also accomodates 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, model selection criteria, 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.