Neural ODE enhanced linear mixed effect models for estimating complex association patterns of time-varying covariates with the marker trajectory

2026-08-30

AI Summary

该研究提出了一种结合神经ODE和线性混合效应模型的方法，以灵活估计时间变化协变量与标记轨迹之间的复杂关联模式。

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.

Problem

• Longitudinal cohort studies
• time-varying association patterns
• linear mixed-effects models
• functional form
• covariate effects

Innovation

• Neural ODE
• Linear Mixed-Effects Models
• Continuous-time Latent State
• Counterfactual Predictions
• Complex Covariate Effects