Neural ODE enhanced linear mixed effect models for estimating complex association patterns of time-varying covariates with the marker trajectory
Abstract
Longitudinal cohort studies produce repeated data that enable the assessment of time-varying association patterns between exposures and health outcomes. Classical linear mixed-effects models (LMMs) can accommodate a large variety of association patterns while accounting for the irregularly spaced, partially observed measurement. But they require the analyst to pre-specify the functional form linking the exposure history to the outcome. We propose the Neural ODE-LMM, which embeds a Neural Ordinary Differential Equation (Neural ODE) within the linear mixed-effects framework: a learned vector field encodes covariate trajectories into a continuous-time latent state that drives both the fixed- and random-effect design, while preserving the standard LMM observation model. This retains classical likelihood-based inference while learning complex, potentially cumulative, covariate effects flexibly. All parameters are estimated by maximising a penalised marginal likelihood. To quantify covariate effects, we introduce contrasts of counterfactual predictions that compare the expected outcome under alternative covariate trajectories with variance estimated via the delta method. In simulations, the model recovers both instantaneous and cumulative-burden effects without prior specification of the functional form. Applied to the Trois-Cités (3C) cohort, a population-based study of 7{,}324 participants, the method reveals trajectory-dependent associations of BMI and fasting glucose with cognitive decline.
Related
- Neural ODE enhanced linear mixed effect models for estimating complex association patterns of time-varying covariates with the marker trajectory Supplementary Materials
- Back to the Definition: Estimating Step-Level Advantages via Trajectory Graphs for Agentic Reinforcement Learning
- Search-Trajectory Patterns as Feedback for Adaptive Metaheuristic Configuration Control
- Estimating marginal association between paired outcomes in clustered data with an application to analyzing caries and periodontal disease data from the National Health and Nutrition Examination Survey
- Kernel Density Regression Estimation with Covariates on Riemannian Manifolds
BibTeX
@misc{li2026neural,
title = {{Neural ODE enhanced linear mixed effect models for estimating complex association patterns of time-varying covariates with the marker trajectory}},
author = {Zhe Aurore Li and Quentin Clairon and Cécilia Samieri and Rodolphe Thiébaut and Mélanie Prague and Cécile Proust-Lima},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29714},
eprint = {2608.29714},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29714},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Neural ODE enhanced linear mixed effect models for estimating complex association patterns of time-varying covariates with the marker trajectory
AU - Zhe Aurore Li
AU - Quentin Clairon
AU - Cécilia Samieri
AU - Rodolphe Thiébaut
AU - Mélanie Prague
AU - Cécile Proust-Lima
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29714
UR - https://arxiv.org/abs/2608.29714
AB - Longitudinal cohort studies produce repeated data that enable the assessment of time-varying association patterns between exposures and health outcomes. Classical linear mixed-effects models (LMMs) can accommodate a large variety of association patterns while accounting for the irregularly spaced, partially observed measurement. But they require the analyst to pre-specify the functional form linking the exposure history to the outcome. We propose the Neural ODE-LMM, which embeds a Neural Ordinary Differential Equation (Neural ODE) within the linear mixed-effects framework: a learned vector field encodes covariate trajectories into a continuous-time latent state that drives both the fixed- and random-effect design, while preserving the standard LMM observation model. This retains classical likelihood-based inference while learning complex, potentially cumulative, covariate effects flexibly. All parameters are estimated by maximising a penalised marginal likelihood. To quantify covariate effects, we introduce contrasts of counterfactual predictions that compare the expected outcome under alternative covariate trajectories with variance estimated via the delta method. In simulations, the model recovers both instantaneous and cumulative-burden effects without prior specification of the functional form. Applied to the Trois-Cités (3C) cohort, a population-based study of 7{,}324 participants, the method reveals trajectory-dependent associations of BMI and fasting glucose with cognitive decline.
ER -