Benjamin Maurel 1,2,3, Agathe Guilloux 1,2,3, Sarah Zohar 1,2,3, Moreno Ursino 1,2,3, Jean Baptiste Woillard 4,5
1 INSERM (Paris, France), 2 INRIA (Paris, France), 3 Université Paris Cité (Paris, France), 4 P&T U1248, CHU Limoges (Limoges, France), 5 Service de Pharmacologie, Toxicologie et Pharmacovigilance (Limoges, France)
Introduction & Objectives
Model-Informed Precision Dosing of drugs with a narrow therapeutic index, such as tacrolimus, routinely relies on estimating individual exposure (AUC) from limited sampling strategies (e.g., 2 to 3 points). In standard pharmacometrics practice, this is often achieved using Empirical Bayes Estimation (EBE) based on population pharmacokinetic models [1]. While non-linear mixed-effects (NLME) models are highly robust, they inherently depend on rigid, pre-specified compartmental equations. When patient pharmacokinetics deviate from these predefined structures (due to complex unmodeled absorption, saturable kinetics or missing covariates for example) the EBE estimator is forced to shrink individual predictions toward an incorrect structural curve, leading to biased AUC estimates. We introduce a data-driven alternative based on Latent Neural Ordinary Differential Equations (Latent ODEs) [2, 3]. The objective of this study was to evaluate the capacity of this non-parametric, continuous-time framework to predict individualized tacrolimus AUCs and assess its robustness against standard NLME-EBE estimators under conditions of structural and covariate misspecification.
Methods
A probabilistic generative framework based on Latent ODEs was developed to bypass traditional compartmental equations. The architecture consists of an ODE-RNN (recurrent neural networks) encoder and a Neural ODE decoder. The recurrent encoder processes sparse, irregularly sampled clinical observations backwards in time to infer the patient’s initial latent state (analogous to the individual EBE step in NLME setting). To capture multimodal subpopulation heterogeneity (e.g. distinct metabolic phenotypes),a Gaussian Mixture Model (GMM) prior replaced the standard unimodal normal distribution typically used for random effects. The continuous-time derivative function governing drug disposition is then learned directly from data via a neural network.
Model training utilizes rich PK profiles (10–12 samples/patient) to learn the underlying population dynamics. Individual AUC prediction is subsequently performed using only standard sparse clinical inputs C0, C1, C3 sampled at time 0h, 1h and 3h. Predictive performance was first evaluated via a controlled simulation study (100 runs of 200 patients) using a published tacrolimus structural model (transit absorption, two-compartment distribution) [4]. We tested three scenarios: (1) correct structural specification (2) unaccounted covariate effect and (3) structural misspecification. Finally, the framework was validated on two real-world clinical datasets of renal transplant recipients: a development cohort for internal cross-validation (n=178) and an unseen external dataset (n=75) [5]. Benchmarks included MAP-BE (Maximum a Posteriori and SAEM algorithm via Monolix) and the Iterative Two-Stage Bayesian (IT2B) method via the ISBA clinical software [6].
Results
In the simulation study, under perfectly correct specification (Scenario 1), the Latent ODE matched the precision of MAP-BE (Root Mean Squared Percentage Error [RMSPE] 16.7% vs. 16.6%), confirming the neural architecture does not degrade performance under ideal parametric conditions. Under misspecification, the Latent ODE exhibited superior robustness. In Scenario 2 (missing covariate) and Scenario 3 (structural misspecification), MAP-BE higher precision errors (RMSPE 23.0% and 23.6%, respectively) than Latent ODE (RMSPE 20.4% and 15.4%, respectively).
During cross-validation on real-world data, the Latent ODE yielded significantly more precise predictions than the clinical standard IT2B (RMSPE 7.99% vs 9.24%, p < 0.001) with lower bias (Mean Percentage Error [MPE] 1.11% vs 4.74%). On the external validation cohort, the Latent ODE was able to generalize, achieving an RMSPE of 10.82%, which was comparable to MAP-BE SAEM (11.48%) and IT2B (11.58%) fitted directly on the development set. Furthermore, an unsupervised Principal Component Analysis of the learned latent space revealed a physiologically meaningful topological organization. The model successfully clustered patients according to CYP3A5 genotype and formulation. Experiments also showed that even when the dataset is very limited (25 patients), our model achieved comparable performance to NLME methods. Conclusions The Latent ODE framework offers a viable, highly flexible alternative to classical NLME models for AUC-guided precision dosing. By avoiding pre-specified structural equations, this data-driven approach demonstrates superior robustness to model misspecification while achieving clinical accuracy comparable to gold-standard Bayesian estimators. The model's parsimonious design also allows for robust training on small clinical cohorts. Ultimately, the natural organization of the probabilistic latent space provides a powerful, unsupervised tool for covariate discovery, establishing an extensible foundation for next-generation, multi-modal pharmacometrics. References: [1] Sheiner, L. B., & Beal, S. L. (1982). Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-Bayesian methods. Journal of Pharmaceutical Sciences, 71(12), 1344-1348. [2] Chen, R. T., Rubanova, Y., Bettencourt, J., & Duvenaud, D. K. (2018). Neural ordinary differential equations. Advances in Neural Information Processing Systems, 31. [3] Rubanova, Y., Chen, R. T., & Duvenaud, D. K. (2019). Latent ordinary differential equations for irregularly-sampled time series. Advances in Neural Information Processing Systems, 32. [4] Woillard, J.-B., de Winter, B. C., Kamar, N., Marquet, P., Rostaing, L., & Rousseau, A. (2011). Population pharmacokinetic model and Bayesian estimator for two tacrolimus formulations. British Journal of Clinical Pharmacology, 71(3), 391-402. [5] Marquet, P., Albano, L., Woillard, J.-B., Rostaing, L., Kamar, N., Sakarovitch, C., ... & Thervet, E. (2018). Comparative clinical trial of the variability factors of the exposure indices used for the drug monitoring of two tacrolimus formulations in kidney transplant recipients. Pharmacological Research, 129, 84-94. [6] Saint-Marcoux, F., Woillard, J.-B., Jurado, C., & Marquet, P. (2013). Lessons from routine dose adjustment of tacrolimus in renal transplant patients based on global exposure. Therapeutic Drug Monitoring, 35(3), 322-327.
Reference: PAGE 34 (2026) Abstr 12053 [www.page-meeting.org/?abstract=12053]
Poster: Methodology – AI/Machine Learning