Manifold-constrained Gaussian processes for inference of mixed-effects ordinary differential equations with application to pharmacokinetics

Dynamic systems involving a population of subjects often feature significant variability among the individual trajectories. Mixed-effects ordinary differential equations (ODEs) provide a natural modeling framework for such systems, where subjects share the same functional form for the ODEs but have subject-specific parameters. However, inference for nonlinear mixed-effects ODE models remains challenging, particularly in settings where the system is only partially observed or the trajectories are highly sensitive to the model parameters. In pharmacokinetic modeling, for example, the observed data also tend to be sparse and noisy. To address these challenges, we propose an extension of manifold-constrained Gaussian processes for inference of general mixed-effects ODE models within a Bayesian statistical framework. We evaluate our method on simulated examples, demonstrating its ability to provide fast and accurate inference for parameters and trajectories using nested optimization. To illustrate the practical efficacy of the proposed method, we provide a real data analysis of a pharmacokinetic model used for an HIV combination therapy study.