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. Gut Lumen Gut Wall Portal Vein Liver Hepatoc yte Systemi c Compar t-ment Peripher al- ompart- ment Inhibitor dose Substrate dose Gut Lumen Gut Wall Portal Vein Liver Peripher acompar tment Systemi c Compar t-ment Hepatoc yte PBPK DDI Model Physiological parameters (Q pv, V liver, …) PK parameters measured from in-vitro studies (Vmax, Km, Ki, …) PK parameters estimated from in-vivo data (V sys, V peri, CL 12, …) Prediction Assessment Model Refinement PK Parameters Prior Distributions Construction PK Parameters Prior Distributions Construction Bayes PK Model Fitting and Prediction Bayes PK Model Fitting and Prediction

5. Statistical Literature Review (Nonlinear Models) (1) Likelihood based parametric approach: Beal and Sheiner, 1982; Steimer et al. 1987 and Lindstrom and Bates 1992. (2) Likelihood based nonparametric or semi-parametric approach: Mallet et. al. 1988, Davidian and Gallant 1993, Li et al. 2002. (3) Likelihood based parametric model with measurement error, Higgins and Davidian 1998, and Li et al. 2004. (4) 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 Literature PK Data Extraction Literature PK Data Extraction Meta Analysis for Simple Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Prediction Assessment/ Validation Model Refinement Based on Clinical Data Model Refinement Based on Clinical Data Trial Simulation Data MiningBayes PK Model Bayes PBPK Model DDI Trial DDI Trial Equivalence Tests

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

8. Result Comparison with DiDB ( number of numerical data in abstracts ) MDZDiDB (Dec. 2007) Mining AUC14 Clearance734 ( Wang et al. 2008, manuscript )

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

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

11. Published Ketoconazole Data Sets (sample mean profiles)

12. Published MDZ Data Sets (sample mean profiles)

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

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

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

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

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

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

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

23. Gut Lumen Gut Wall Portal Vein Liver Hepatoc yte Systemi c Compar t-ment Peripher al- ompart- ment Inhibitor dose Substrate dose Gut Lumen Gut Wall Portal Vein Liver Peripher acompar tment Systemi c Compar t-ment Hepatoc yte 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 [θ 1, θ 2 | y] ~ p(θ 1, θ 2 | y)  θ 1 and θ 2 can be non-identifiable parameters  Draw (θ 1, θ 2 ) by single component Gibbs sampling (SGS) [θ 1 | θ 2, y] ~ p(θ 1 | θ 2, y) [θ 2 | θ 1, y] ~ p(θ 2 | θ 1, y)  Draw (θ 1, θ 2 ) by grouping Gibbs sampling (GGS) [θ 1, θ 2 | y] ~ p(θ 1, θ 2 | y)

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

27. Drug Interaction Model Development Literature PK Data Extraction Literature PK Data Extraction Meta Analysis for Simple Drug Interaction Model Development Meta Analysis for Simple Drug Interaction Model Development Prediction Assessment/ Validation Model Refinement Based on Clinical Data Model Refinement Based on Clinical Data Trial Simulation Data Mining Bayes PK Model Bayes PBPK Model DDI Trial DDI Trial Equivalence Tests  Full Text Mining  Non-compartment model transformation to compartment model  In-vitro Data Meta-Analysis  Animal Data Integration  Variances Equivalence  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. Acknowledgement 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. The research is supported by NIH grants, R01 GM74217 and R01 GM67308.

30. Thank you!