A Bayesian Approach for PK/PD Modeling with PD Data Below Limit of Quantification

Abstract

A Bayesian approach to handling below limit of quantification (BLOQ) pharmacodynamic (PD) data in pharmacokinetic/pharmacodynamic (PK/PD) modeling is described. The inhibitory sigmoid Emax model is used to illustrate the implementation of the Bayesian approach for modeling BLOQ PD data. Details on how to implement this Bayesian approach via the Markov-chain Monte Carlo (MCMC) technique using WinBUGS software are presented. A simulation study was conducted to evaluate the performance of the proposed Bayesian approach and to compare the Bayesian approach with two other ad hoc approaches: replacing BLOQ data with LOQ, and ignoring the BLOQ data. The simulation study indicates that the proposed Bayesian approach performs better than the other two ad hoc approaches and should be considered in practice as a complementary tool for BLOQ data analysis. A case study with real PK/PD data is provided to illustrate the application of the Bayesian approach of handling BLOQ PD data in PK/PD modeling.

Key Words:

• Bayesian
• Below limit of quantification (BLOQ)
• Markov-chain Monte Carlo (MCMC)
• Pharmacodynamics (PD)
• WinBUGS

ACKNOWLEDGMENTS

The authors are grateful to their former colleague William Denney at Merck for providing computational assistance in conducting the simulation study on a Linux cluster. They also thank the associate editor and the referee for valuable comments that greatly improved the content and presentation of this paper.

Notes

Note. “All data” means that the analysis is on the complete data set without any observations set to BLOQ; BLC represents the Bayesian approach for left-censoring data analysis; RPL represents the ad hoc approach of replacing BLOQ data with LOQ; and IGN represents the ad hoc approach of ignoring the BLOQ data.