The Regularized Horseshoe for Covariate Selection Improves Convenience and Predictive Performance in Population <scp>PK</scp> / <scp>PD</scp> Models

We introduce the Regularized Horseshoe (RHS) in the context of covariate selection for population PK/PD models. Unlike stepwise approaches which are commonly used in this context, the RHS can simultaneously assess all possible parameter-covariate relationships in a single model fit by leveraging the fact that such relationships are usually sparse in practice. Furthermore, the RHS avoids the over-estimation of effect sizes that commonly occurs with stepwise approaches and avoids overfitting by averaging over the posterior uncertainty of possible parameter-covariate relationships. This leads to improved predictive performance on held-out data. We first give an overview of common covariate selection methods for population PK/PD modeling, then we define the RHS and provide intuition for how the method works. We then provide Stan code and a set of hyperparameters applicable to general population PK/PD models that can readily be applied by practitioners. Using an extensive simulation study, the beneficial properties of the RHS are illustrated and compared to popular covariate selection methods that are commonly used on population PK/PD models. Lastly, we compare the RHS to other commonly used methods on four real-world PK/PD datasets and illustrate its superior predictive performance on held-out data.