The Empirical Bayes Variational Autoencoder—A Neural ODE Approach for Population Modeling in Pharmacology

Abstract

Variational autoencoders (VAEs) combined with neural ordinary differential equations provide a flexible framework for exploring neural latent-variable models in population pharmacokinetics. In this work, we investigate an empirical Bayes VAE formulation that integrates encoder–decoder architectures with covariate-dependent population priors, enabling correlated latent representations and probabilistic inference. We evaluate the proposed framework using controlled simulation studies and a small clinical benchmark dataset. The simulation experiments assess the ability to recover known population structures and covariate effects, while the clinical study evaluates subject-specific prediction and model diagnostics. In simulation studies with correlated individual parameters, the empirical Bayes VAE consistently captured population-level variability, whereas a fixed-prior VAE baseline exhibited systematic biases. In our experiments, extrapolation beyond the training dosing schedules showed more stable predictive behavior when using the proposed input–response normalization, relative to models trained without normalization, within a limited range. Diagnostic analyses indicated clear relationships between inferred latent variables and true parameters, and estimated observation noise was consistent with simulated values. In the clinical case study, cross-validation experiments suggested predictive performance comparable to previously reported neural ODE–based approaches. Overall, the results illustrate the feasibility of combining empirical Bayes inference with neural ODE–based decoders for population modeling. The proposed framework should be viewed as a methodological proof-of-concept, highlighting both the potential and the current limitations of variational neural approaches in pharmacometric applications.