Fully Bayesian Covariate Selection in Population Pharmacokinetics and Pharmacodynamics Models Using Regularized Horseshoe Priors

Objectives: Covariate selection for population models in pharmacometrics analysis is important for understanding patient attributes associated with observed inter-individual variability, and thus whether doses adjustments should be for specific patient groups. This task often entails the need to explore the effect of several covariates on multiple model subject-level effects. Fitting a single model that includes all such combinations, i.e. a full fixed-effects model (FFEM), is ideal (Yngman, 2022). However, this is often difficult in practice, as the variance of maximum-likelihood estimators of such models often have large variance or may not even be obtainable due to numerical issues. Several approaches to covariate selection exist in the pharmacometrics literature (Sanghavi, 2024) that address this in varying ways, but a Bayesian approach, particularly with sparse regularization, has not been explored to a wide extent.Bayesian covariate selection has gained popularity in recent years in the broader statistics field and several new tools and approaches to Bayesian covariate selection have been developed, including regularized horseshoe (RHS) priors (Piironen, 2017), which like the LASSO, incorporate information about covariate sparsity into the model. Bayesian approaches are attractive for addressing the covariate selection problem because they provide a natural form of regularization via priors, and they provide a way to average over posterior uncertainty to reduce overfitting.We explore a fully Bayesian approach using RHS priors to several covariate selection problems in pharmacometrics.Methods: We use MCMC sampling in Stan (Carpenter, 2017) to fit several pharmacometrics models presented in (Ayral, 2021). We include all covariate relationships of interest and use RHS priors for regularization. We compare the results to the results obtained in (Ayral, 2021) in terms of 1) their predictive error on held-out data 2) the covariates selected and 3) the predicted outcomes as a function of various covariates.Results: A fully Bayesian approach to covariate selection offers several advantages to traditional approaches. First, because of the regularization provided by RHS priors and the accounting of all posterior uncertainty, all covariate relationships of interest can be included in a single model fit. Second, marginal posterior probabilities of the importance of individual covariates can be directly obtained. Third, rather than having to make discrete decision rules on which covariates are included in a model, the posterior provides a natural continuous compromise between all such models, weighted by their ability to explain the data.Conclusions: A fully Bayesian approach to covariate selection using RHS priors provides a promising alternative to traditional approaches used in pharmacometrics analyses and can bring in novel efficiencies in determination of the dose adjustments needed for favorable patient outcomes.Citations: [1] Ayral, G. e. (2021). A novel method based on unbiased correlations tests for covariate selection in nonlinear mixed effects models: The COSSAC approach. CPT: pharmacometrics & systems pharmacology, 318-329.[2] Carpenter, B. e. (2017). Stan: A probabilistic programming language. Journal of statistical software.[3] Piironen, J. a. (2017). "Sparsity information and regularization in the horseshoe and other shrinkage priors.[4] Sanghavi, K. e. (2024). Covariate modeling in pharmacometrics: General points for consideration. CPT: Pharmacometrics & Systems Pharmacology.[5] Yngman, G. e. (2022). An introduction to the full random effects model. CPT: pharmacometrics & systems pharmacology, 149-160.