Bayes PK Models and Applications to Drug Interaction Simulations

1. Bayes PK Models and Applications to Drug Interaction Simulations Lang Li Associate Professor Division of Biostatistics/Clinical Pharmacology School of Medicine Indiana University

2. What is a drug-drug interaction? • Drug-drug interaction (DDI) is usually referred as one drug’s pharmacokinetics (absorption, distribution, elimination, or its effect) is affected by the existence of another drug. • DDI: Substrate and Inducer/Inhibitor • Possible reasons of a DDI: (1) plasma and/or tissue binding (2) carrier-mediated transport across plasma membranes (3) metabolism Rowland and Toner (1997) Clinical Pharmacokinetics Ito et al. (1998) Pharmacy. Review

3. A Midazolam/Ketoconazole Interaction Example KETO: 200 mg MDZ: 10 mg (Lam, JCP 2003)

4. Inhibitor dose Substrate dose Gut Lumen Gut Lumen Gut Wall Gut Wall Peripheral-ompart-ment Peripheracompartment Portal Vein Portal Vein Systemic Compart-ment Systemic Compart-ment Liver Liver Hepatocyte Hepatocyte PBPK DDI Model • Physiological parameters (Qpv, Vliver, …) • PK parameters measured from in-vitro studies (Vmax, Km, Ki, …) • PK parameters estimated from in-vivo data (Vsys, Vperi, CL12, …) • Prediction Assessment • Model Refinement PK Parameters Prior Distributions Construction Bayes PK Model Fitting and Prediction

5. Statistical Literature Review (Nonlinear Models) • Likelihood based parametric approach: Beal and Sheiner, 1982; Steimer et al. 1987 and Lindstrom and Bates 1992. • Likelihood based nonparametric or semi-parametric approach: Mallet et. al. 1988, Davidian and Gallant 1993, Li et al. 2002. • Likelihood based parametric model with measurement error, Higgins and Davidian 1998, and Li et al. 2004. • Bayesian approach: Wakefield et al. 1996, 1997, 2000; Muller and Rosner 1998, 2002; Gelman et al. 1996. Nonlinear models for subject-specific level data. Division of Biostatistics in the Indiana University

6. Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Literature PK Data Extraction Trial Simulation DDI Trial Data Mining Bayes PK Model Equivalence Tests Bayes PBPK Model Prediction Assessment/ Validation Model Refinement Based on Clinical Data

7. Literature Data Extraction (Data Mining)- A Midazolam (MDZ) Example Search Medline “Midazolam” Information Retrieval ~8000 abstracts Entity template library Entity Recognition Remove Irrelevant Abstracts ~400 left 34 CL data from (3 irrelevant) Information Extraction Extract PK numerical data 43 CL data from 24 abstracts (12 irrelevant) Linear Mixed Meta-Analysis Model Evaluation (Wang et al. 2008, PIII 92)

8. Result Comparison with DiDB (number of numerical data in abstracts) (Wang et al. 2008, manuscript)

9. Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Literature PK Data Extraction Trial Simulation DDI Trial Data Mining Bayes PK Model Equivalence Tests Bayes PBPK Model Prediction Assessment/ Validation Model Refinement Based on Clinical Data

10. Initial Drug Interaction PK Model - A Midazolam/Ketoconazole Example Ketoconazole Midazolam ka CL12 CL12 V1 V1 V2 V2 CL CL

11. Published Ketoconazole Data Sets (sample mean profiles)

12. Published MDZ Data Sets (sample mean profiles)

13. Bayes Meta Analysis on Sample Mean Data Monte Carlo Markov Chain Li et al. Stat in Med. 2007; Yu et al. JBS 2008

14. MCMC vs Stochastic-EM (SEM) SEM is faster than the other MCMC algorithm. Kim et al. 2008 manuscript

15. DDI Prediction Posterior PK Parameter Draws MDZ Alone Profile MDZ Profile with KETO MDZ Alone AUC MDZ AUC with KETO MDZ AUCR

16. Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Literature PK Data Extraction Trial Simulation DDI Trial Data Mining Bayes PK Model Equivalence Tests Bayes PBPK Model Prediction Assessment/ Validation Model Refinement Based on Clinical Data

17. A DDI Prediction Assessment Proposal • Probabilistic Rule • Pr [AUCR in (-inf, 1.25)] > 0.90 clinical insignificant inhibition • Pr [AUCR in (2.00, inf)] > 0.90 clinical significant inhibition • Otherwise inconclusive

18. Population-Average vs Subject-Specific DDI Population – Average DDI Subject-Specific DDI (Zhou et al. 2008, manuscript)

19. Equivalence Test for Simulated and Reported DDI • Reported MDZ(IV)/KETO(PO) interaction: AUCR = 5.1 +/- 0.74, with dose combination 2/200mg (Tsunoda et al. 1999) • How many simulations do we have to run? • What is our maximum power to test the equivalence? Note: AUCR = 5.1 +/- 0.74 <====>logAUCR = 1.629 +/- 0.14 The equivalence bound = log(0.80, 1.25) = (-0.223, 0.223)

20. Observed AUCR = 5.1 +/- 0.74. The equivalence bound Δ = log(0.80, 1.25) = (-0.223, 0.223) (Zhou et al. 2008, manuscript)

21. Initial Drug Interaction PK Model - A Midazolam/Ketoconazole Example Ketoconazole Midazolam ka CL12 CL12 V1 V1 V2 V2 CL CL

22. Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Literature PK Data Extraction Trial Simulation DDI Trial Data Mining Bayes PK Model Equivalence Tests Bayes PBPK Model Prediction Assessment/ Validation Model Refinement Based on Clinical Data

23. Inhibitor dose Substrate dose Gut Lumen Gut Lumen Gut Wall Gut Wall Peripheral-ompart-ment Peripheracompartment Portal Vein Portal Vein Systemic Compart-ment Systemic Compart-ment Liver Liver Hepatocyte Hepatocyte PBPK DDI Model • Non-identifiable system • Fast and reliable computational algorithms.

24. Michaelis-Menten (MM) Kinetics • MM Kinetics Equation: • When the concentrations (C) are much less than Km:

25. Gibbs Sampler • [θ1 , θ2 | y] ~ p(θ1 , θ2 | y) • θ1 and θ2 can be non-identifiable parameters • Draw (θ1 , θ2) by single component Gibbs sampling (SGS) • [θ1 | θ2 , y] ~ p(θ1 | θ2 , y) • [θ2 | θ1 , y] ~ p(θ2 | θ1 , y) • Draw (θ1 , θ2) by grouping Gibbs sampling (GGS) • [θ1 , θ2 | y] ~ p(θ1 , θ2 | y)

26. SGS GGS Group Gibbs Sampling (GGS) vs Single Gibbs Sampling (SGS) Recommended Number of Iterations Identifiable Km ≈ C(t) Unidentifiable Km >>C(t) Prior Variance Kim et al. 2008 (manuscript)

27. Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Literature PK Data Extraction Trial Simulation DDI Trial Data Mining Equivalence Tests Bayes PK Model • In-vitro Data Meta-Analysis • Animal Data Integration • Full Text Mining • Non-compartment • model transformation • to compartment model • Variances Equivalence Bayes PBPK Model Prediction Assessment/ Validation Model Refinement Based on Clinical Data • PBPK Model (DDI mechanisms) • MCMC Speed

28. Metabolic Enzyme Based Drug-Drug Interaction Studies — Decision Tree http://www.fda.gov/cder/guidance/6695dft.htm#_Toc112142815

29. Indiana University Lang Li Pharmacokinetics Lab Seongho Kim, Ph.D. (Statistics) Zhiping Wang, Ph.D. (Bioinformatics) Sara R. Quinney, Ph.D. (Pharmacology) Yuming Zhao, Ph.D. (Computer Science) Eli Lilly and Company Stephen D. Hall, PhD. Jenny Chien, Ph.D. Alergan Company Jihao Zhou, Ph.D. Acknowledgement The research is supported by NIH grants, R01 GM74217 and R01 GM67308.

30. Thank you!