Manifold-Constrained Gaussian Processes for Inference of Mixed-effects Ordinary Differential Equations with Application to Pharmacokinetics

TL;DR

This paper introduces a Bayesian Gaussian process approach with manifold constraints to improve uncertainty quantification in mixed-effects ODE models for pharmacokinetics, demonstrated through simulations and real HIV therapy data.

Contribution

It extends Gaussian processes with manifold constraints for better inference of mixed-effects ODE models, enabling fast, accurate, and uncertainty-aware parameter estimation.

Findings

Accurate inference of pharmacokinetic parameters demonstrated on simulated data.

Effective application to real HIV therapy pharmacokinetic data.

Provides subject-level uncertainty quantification for key drug concentration measures.

Abstract

Pharmacokinetic modeling using ordinary differential equations (ODEs) has an important role in dose optimization studies, where dosing must balance sustained therapeutic efficacy with the risk of adverse side effects. Such ODE models characterize drug plasma concentration over time and allow pharmacokinetic parameters to be inferred, such as drug absorption and elimination rates. For time-course studies involving treatment groups with multiple subjects, mixed-effects ODE models are commonly used. However, existing methods tend to lack uncertainty quantification on a subject-level, for key measures such as peak or trough concentration and for making predictions of drug concentration. To address such limitations, 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.