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Distribution-based covariate assessment using wasserstein distance in population pharmacokinetic models
Nicolas Simon1, Jean-Sebastien Hulot2,3, Katharina von Fabeck1
1Department of Clinical Pharmacology, APHM, Institut de Neurosciences de la Timone, UMR7289, CNRS, Hôpital Sainte Marguerite, CAP-TV, Aix Marseille University, Marseille, France.
Background:
Population pharmacokinetic modeling relies on adequate covariate specification to explain interindividual variability and support model-informed precision dosing. Current validation methods predominantly use likelihood-based criteria and correlation analyses, which may fail to detect complex non-linear or non-monotonic covariate relationships. We propose the Wasserstein distance, derived from optimal transport theory, as a complementary distribution-based metric for covariate specification assessment.
Methods:
Using high-dose methotrexate pharmacokinetic data from 50 patients with lymphoid malignancies, we developed three nested population models: BASE (no covariates), GENET_ALL (ABCC2 -24C>T polymorphism), and FINAL (genetic plus creatinine clearance). We computed Wasserstein distances between empirical distributions of individual parameter deviations stratified by covariate groups, with statistical significance assessed via permutation testing. We defined a Wasserstein-based R2 metric to quantify variance reduction across models. Simulation studies illustrated detection of threshold, U-shaped, and Simpson's paradox-like covariate effects.
Results:
In the FINAL model, both CT01 (W = 0.071, p = 0.741) and creatinine clearance showed no residual distributional differences, confirming adequate specification. The Wasserstein-based R2 demonstrated progressive improvement (GENET_ALL: 21.5%, FINAL: 31.7% reduction). Simulations illustrated the complementary value of the Wasserstein-based approach alongside classical methods, particularly for detecting complex non-linear relationships.
Conclusion:
Wasserstein distance provides a complementary distribution-based framework with limited parametric assumptions for validating covariate specification in population pharmacokinetic models, provided that eta-shrinkage remains sufficiently low when using empirical Bayes estimates. This approach is particularly useful for detecting complex non-linear relationships.
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