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. Study Highlights WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?Covariate selection in pharmacokinetic (PK) modeling is a complex process and is sensitive to bias. Machine-learning (ML) techniques might help to simplify and potentially improve this process, but are difficult to interpret as is.

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“…Alternatively, model interpretation methods might be of interest to infer covariate relationships from ML models. We have previously performed an investigation into how one such explanation method can be used to visualize the relationships between covariates and estimated PK parameters [54]. We found that these relationships matched implementations in previous PK models and biological concepts.…”

“…One study used SHAP for the identification of important covariates when using neural networks to predict cyclosporin A clearance [101]. Aside from covariate importance, which only provides a limited interpretation of the model, SHAP can also be used to visualize covariate relationships [54]. To present an example, we performed a SHAP analysis on the prediction of warfarin absorption rate (k a ) by the previous discussed ODE-based neural network (implementation details in Appendix B.3).…”

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“…A subsequent study expanded upon this using SHapley Additive exPlanations (SHAP), 63 a method to explain how features influence ML predictions, to illustrate how covariates affect PK parameters for factor VIII concentrate in patients with hemophilia A. 64 A random forest model was identified as the best model and was used to predict Bayesian estimated clearance and volume of distribution parameters. The relationships between individual PK parameters and SHAP values for individual covariates, as well as the interactive effects between covariates, were evaluated.…”