Exploring Appropriate Prior Distributions for Covariance Matrix Estimation in Bayesian Population Pharmacokinetic Analysis

Authors

Sooyoung Lee, PhD - Center for Translational Medicine, University of Maryland School of Pharmacy; Mathangi Gopalakrishnan, Ph.D. - Assistant Professor, Center for Translational Medicine, Department of Pharmacy Practice, University of Maryland School of Pharmacy, Baltimore, MD, USA

Abstract

Objectives: Since Bayesian analysis incorporates prior knowledge from previous studies and quantifies epistemic uncertainty in model parameters, it provides advantages that non-Bayesian methods often lack [1]. The choice of prior distribution can significantly affect the posterior distribution, hence it is crucial to understand the sensitivity of priors. While various prior distributions for the covariance matrix parameters are known, the appropriate distributions for different scenarios are not well-established. This simulation study aims to explore suitable prior distributions for the covariance matrix parameters in a Bayesian population pharmacokinetic analysis. Methods: The data was simulated from a one-compartment IV-bolus model under six scenarios based on three levels of between-subject variability (BSV): low (10%), medium (30%), and high (70%) for clearance (CL) and volume (Vd) with a 0.8 correlation and two sampling schemes: sparse sampling (2 points) and rich sampling (12 points). Each scenario was repeated 100 times. To estimate the covariance matrix, 15 prior distribution scenarios were applied, comprising five distribution (Inverse-Wishart (Inv-W), Wishart (W), Scaled Inverse-Wishart (S Inv-W), Lognormal + LKJ (LogN + LKJ), and Normal + LKJ (N + LKJ)) with varying levels of informativeness (strongly, weakly, and non-informative). For the mean parameters, a strongly informative lognormal prior was used. Bayesian estimation was performed using the no-U-turn sampler in Pumas 2.4.0 across four parallel chains, each with 2,000 samples, 200 adaptation steps, and an acceptance ratio of 0.8. Estimation results were evaluated using performance metrics, rBias and rRMSE. In scenarios with strongly informative priors, the prior mean was used as the true value for performance metrics. In contrast, the simulated data mean was used for weakly and non-informative prior scenarios. The results were compared in NONMEM 7.5.1 for the available prior distributions (Inv-W and LogN + LKJ).< Results: For data with low and high BSV on PK parameters, the following was observed: When using a strongly informative prior, the Inv-W and W distributions showed less than 10% rBias and rRMSE for BSV and correlation estimates, while the other three distributions exceeded 10%. With a non-informative prior, the N + LKJ distribution showed less than 10% rBias and rRMSE for BSV and correlation estimates, while all other distributions exceeded 10%. In scenarios with weakly informative priors, the S Inv-W distribution provided the most stable results. Conclusions: This simulation study explored suitable prior distributions for the covariance matrix parameters in Bayesian population PK analysis. Results suggest using Inv-W or W for strongly informative priors, S Inv-W for weakly informative priors, and N + LKJ for non-informative priors. These findings can guide selecting appropriate prior distributions and enhance the application of Bayesian approaches for future analyses.

Citations: [1] Tarek, M., Storopoli, J., Davis, C., Elrod, C., Krumbiegel, J., Rackauckas, C., & Ivaturi, V. (2023). A Practitioner's Guide to Bayesian Inference in Pharmacometrics using Pumas. arXiv preprint arXiv:2304.04752.

Keywords

Bayesian, Covariance matrix, Prior distribution

Date of Conference

November 10-13, 2024

Conference Location

Phoenix, Arizona, USA

DOI

10.70534/AISO3156