Application of SHAP values for inferring the optimal functional form of covariates in pharmacokinetic modeling

Abstract

In population pharmacokinetic (PK) models, interindividual variability is explained by implementation of covariates in the model. The widely used forward stepwise selection method is sensitive to bias, which may lead to an incorrect inclusion of covariates. Alternatives, such as the full fixed effects model, reduce this bias but are dependent on the chosen implementation of each covariate. As the correct functional forms are unknown, this may still lead to an inaccurate selection of covariates. Machine learning (ML) techniques can potentially be used to learn the optimal functional forms for implementing covariates directly from data. A recent study suggested that using ML resulted in an improved selection of influential covariates. However, how do we select the appropriate functional form for including these covariates? In this work, we use SHapley Additive exPlanations (SHAP) to infer the relationship between covariates and PK parameters from ML models. As a case-study, we use data from 119 patients with hemophilia A receiving clotting factor VIII concentrate peri-operatively. We fit both a random forest and a XGBoost model to predict empirical Bayes estimated clearance and central volume from a base nonlinear mixed effects model. Next, we show that SHAP reveals covariate relationships which match previous findings. In addition, we can reveal subtle effects arising from combinations of covariates difficult to obtain using other methods of covariate analysis. We conclude that the proposed method can be used to extend ML-based covariate selection, and holds potential as a complete full model alternative to classical covariate analyses.