Aurore Zhe LI - Neural Ordinary Differential Equations enhanced Linear Mixed-effects Models

par Aurore Zhe LI (BPH)

jeudi 17 sept. 2026, 13:00 → 14:00 Europe/Paris

amphi Louis (ISPED)

Speaker: Aurore Zhe LI from BPH

Title: Neural Ordinary Differential Equations enhanced Linear Mixed-effects Models

Abstract: 

Introduction
Longitudinal cohort studies generate irregularly spaced, partially missing repeated measurements where outcomes may depend on the full trajectory of time-varying exposures rather than their instantaneous values. Classical linear mixed-effects models (LMMs) can incorporate path-dependent or cumulative exposures through hand-engineered functionals like lags, weighted cumulative integrals, or basis expansions of covariate history, whose functional form, time window, and interaction structure must be pre-specified by the analyst, and so cannot be discovered from data. We propose Neural Ordinary Differential Equation enhanced LMMs (NODE-LMMs), a unified framework embedding continuous-time latent dynamics within a mixed-effects model, which learns the form of the path-dependent effect jointly with the rest of the model rather than fixing it a priori.

Methods
Baseline and static covariates are encoded into an initial latent state, which evolves over time via a Neural ODE with autonomous dynamics. The latent process is decoded through a LMMs observation model, enabling estimation of population-level fixed effects and subject-specific random effects, with parameters learned by maximizing the marginal likelihood. To interpret covariate effects, we compute Partial Dependence Plots (PDPs) under counterfactual interventions and define the ∆PDP as the difference in population-averaged predictions between exposure levels with uncertainty quantified via a full-parameter delta method. The approach is evaluated in the simulation studies under diverse data-generating processes, and compared to the classical LMMs. It is also applied to the real population-based aging Trois-Cités (3C) cohort (N=7,324) to assess the association between cardiometabolic health (e.g.,BMI, glycemia) and cognitive decline over 15 years of follow-up.

Results
Under an instantaneous association (X(t) --> Y(t)), our approach achieves ∆PDP estimation performance comparable to the correctly specified classical LMM. Under a cumulative burden process, the NODE-LMMs correctly distinguish sustained early exposure from a late spike to the same level, a discrimination the classical LMMs cannot achieve without committing in advance to a cumulative-burden specification. In the 3C cohort, our method delivers interpretable marginal associations between trajectories of cardiometabolic factors (BMI and glycemia) and cognitive decline via the PDP.

Discussion
The NODE-LMMs extend classical LMMs with continuous-time neural dynamics while preserving their statistical interpretability. Simulation and real-data results demonstrate that the framework matches LMMs performance when covariate effects are instantaneous and outperforms it when effects are path-dependent or cumulative, a setting highly relevant in
life-course epidemiology.

Keywords: Irregular Longitudinal Data, Neural ODE, mixed-effects models

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Biostatistics seminar series from the Department of Public Health from the University of Bordeaux and the Bordeaux Population Health UMR 1219 research center