Distribution-based covariate assessment using wasserstein distance in population pharmacokinetic models

Area of Science:

• Pharmacometrics
• Pharmacokinetics
• Systems Biology

Background:

• Population pharmacokinetic (PopPK) modeling is crucial for explaining interindividual variability and enabling model-informed precision dosing.
• Existing validation methods using likelihood-based criteria and correlation analyses may miss complex non-linear covariate relationships.
• There is a need for complementary methods to assess covariate specification in PopPK models.

Purpose of the Study:

• To introduce and validate the Wasserstein distance as a complementary metric for assessing covariate specification in PopPK models.
• To evaluate the Wasserstein distance's ability to detect complex non-linear and non-monotonic covariate relationships.
• To quantify variance reduction using a Wasserstein-based R² metric.

Main Methods:

• Developed three nested PopPK models for high-dose methotrexate in 50 patients with lymphoid malignancies.
• Calculated Wasserstein distances between empirical parameter deviation distributions stratified by covariate groups (e.g., ABCC2 polymorphism, creatinine clearance).
• Assessed statistical significance using permutation testing and defined a Wasserstein-based R² for variance reduction. Simulation studies were used to illustrate detection of various covariate effects.

Main Results:

• The FINAL model, incorporating genetic and creatinine clearance covariates, showed no residual distributional differences (CT01: W = 0.071, p = 0.741), indicating adequate specification.
• The Wasserstein-based R² demonstrated progressive variance reduction: 21.5% for the GENET_ALL model and 31.7% for the FINAL model.
• Simulation studies confirmed the utility of the Wasserstein-based approach in identifying complex non-linear covariate relationships, complementing traditional methods.

Conclusions:

• Wasserstein distance provides a robust, distribution-based framework for validating covariate specification in PopPK models with minimal parametric assumptions.
• This method is particularly valuable for detecting complex non-linear covariate relationships that might be missed by conventional techniques.
• The approach is reliable when eta-shrinkage is sufficiently low with empirical Bayes estimates.