Latent Neural-ODE for Model-Informed Precision Dosing: Overcoming Structural Assumptions in Pharmacokinetics

TL;DR

This work introduces Latent ODEs with a Gaussian Mixture prior to model tacrolimus PK for precision dosing, addressing the rigidity of traditional NLME structures. By integrating a probabilistic generative framework with variational inference, it learns individualized PK dynamics from sparse data and generalizes across unseen populations. In simulations and real-world data, the approach shows robustness to misspecification and competitive external performance, while revealing physiologically meaningful latent structure and enabling data-efficient training. The framework lays the groundwork for flexible, multi-modal pharmacometrics models in personalized medicine and is released as open-source for reproducibility.

Abstract

Accurate estimation of tacrolimus exposure, quantified by the area under the concentration-time curve (AUC), is essential for precision dosing after renal transplantation. Current practice relies on population pharmacokinetic (PopPK) models based on nonlinear mixed-effects (NLME) methods. However, these models depend on rigid, pre-specified assumptions and may struggle to capture complex, patient-specific dynamics, leading to model misspecification. In this study, we introduce a novel data-driven alternative based on Latent Ordinary Differential Equations (Latent ODEs) for tacrolimus AUC prediction. This deep learning approach learns individualized pharmacokinetic dynamics directly from sparse clinical data, enabling greater flexibility in modeling complex biological behavior. The model was evaluated through extensive simulations across multiple scenarios and benchmarked against two standard approaches: NLME-based estimation and the iterative two-stage Bayesian (it2B) method. We further performed a rigorous clinical validation using a development dataset (n = 178) and a completely independent external dataset (n = 75). In simulation, the Latent ODE model demonstrated superior robustness, maintaining high accuracy even when underlying biological mechanisms deviated from standard assumptions. Regarding experiments on clinical datasets, in internal validation, it achieved significantly higher precision with a mean RMSPE of 7.99% compared with 9.24% for it2B (p < 0.001). On the external cohort, it achieved an RMSPE of 10.82%, comparable to the two standard estimators (11.48% and 11.54%). These results establish the Latent ODE as a powerful and reliable tool for AUC prediction. Its flexible architecture provides a promising foundation for next-generation, multi-modal models in personalized medicine.

Figures (8)

• Figure 1: The AUC Prediction. The blue curve represents the patient's true underlying drug concentration over time, and the shaded area corresponds to the target AUC we wish to estimate. The grey dots illustrate a rich sampling strategy (e.g., 12 samples - each point with a measurement error), which allows for accurate AUC estimation but is impractical in routine clinical care. In contrast, only a few measurements (orange points, collected at 0 h, 1 h, and 3 h) are typically available. The objective is to estimate the full 24h-AUC from these limited observations.
• Figure 2: Schematic of the Latent ODE model architecture. The model is organized into two main blocks: the Encoder Network (green), which maps sparse clinical data to the probabilistic latent state $z_0^i$; and the Generative Model (red), which solves the forward problem by integrating the learned dynamics and projecting the continuous state back to the observation space.
• Figure 3: Workflow for the three-scenario simulation study. Each scenario generates a unique dataset to test the models under different conditions.
• Figure 4: Distribution of performance metrics over 50 cross-validation runs. The Latent ODE (blue) shows consistently better precision (lower RMSPE) and less bias (MPE closer to zero) than the it2B benchmark (orange).
• Figure 5: Relative prediction error versus the reference AUC value on the external dataset for the Latent ODE model (dark colors) and the ISBA competitor (light colors). Categories correspond to the two kinds of formulation in the dataset