Bayesian Neural Ordinary Differential Equations for Uncertainty-Aware Pharmacokinetic Modeling: Theory, Calibration, and Clinical Validation

Keywords: Bayesian neural ODEs, pharmacokinetics, pharmacodynamics, uncertainty quantification, posterior contraction, calibration, MIMIC-IV, clinical decision support, variational inference

TL;DR: ayesNeuralPK combines compartmental PK/PD with Bayesian neural ODEs for calibrated uncertainty; 23\% lower error and 94.2\% coverage on clinical data.

Abstract: Pharmacokinetic-pharmacodynamic (PK/PD) models are fundamental to drug dosing and personalized medicine, yet traditional compartmental ordinary differential equations (ODEs) cannot adequately capture patient-specific variability, while standard neural ODEs lack the uncertainty quantification critical for clinical safety. We propose **BayesNeuralPK**, a Bayesian neural ODE framework that combines the mechanistic interpretability of compartmental models with the flexibility of data-driven learning and rigorous uncertainty quantification. Our theoretical contributions are threefold: (1) we prove that the posterior distribution over neural ODE parameters concentrates around true PK dynamics at rate $O(n^{-1/(2+d)})$ under a Gaussian process prior on the vector field, establishing the first posterior contraction result for Bayesian neural ODEs; (2) we derive a calibration theorem showing that BayesNeuralPK's predictive intervals achieve asymptotically exact coverage; (3) we establish identifiability conditions under which compartmental structure can be recovered from the learned neural vector field. Evaluated on MIMIC-IV clinical data and PharmaPy synthetic benchmarks, BayesNeuralPK achieves 23\% lower prediction error than standard neural ODEs while providing calibrated 95\% confidence intervals (empirical coverage: 94.2±1.1\%, compared to 78.3\% for MC-Dropout baselines). This work bridges mathematical pharmacology and Bayesian deep learning for safer AI-assisted clinical decision-making.

Submission Number: 149