Abstract: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.
| Comments: | 34 pages, 12 figures |
| Subjects: | Methodology (stat.ME); Machine Learning (stat.ML) |
| Cite as: | arXiv:2510.07128 [stat.ME] |
| (or arXiv:2510.07128v5 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2510.07128 arXiv-issued DOI via DataCite |
From: Félix Laplante [view email]
[v1]
Wed, 8 Oct 2025 15:24:51 UTC (933 KB)
[v2]
Wed, 14 Jan 2026 16:46:00 UTC (406 KB)
[v3]
Fri, 30 Jan 2026 18:10:17 UTC (406 KB)
[v4]
Wed, 25 Feb 2026 23:59:18 UTC (807 KB)
[v5]
Mon, 25 May 2026 17:58:14 UTC (949 KB)
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