Bayes pk models and Applications to Drug Interaction Simulations Lang LI Associate Professor

Bayes PK Models and Applications to Drug Interaction Simulations

• Lang Li

• Associate Professor

• Division of Biostatistics/Clinical Pharmacology

• School of Medicine

• Indiana University

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

A Midazolam/Ketoconazole Interaction Example

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.

Drug Interaction Model Development

Literature Data Extraction (Data Mining) - A Midazolam (MDZ) Example

Result Comparison with DiDB (number of numerical data in abstracts)

Drug Interaction Model Development

Initial Drug Interaction PK Model - A Midazolam/Ketoconazole Example

Published Ketoconazole Data Sets (sample mean profiles)

Published MDZ Data Sets (sample mean profiles)

Bayes Meta Analysis on Sample Mean Data

MCMC vs Stochastic-EM (SEM)

DDI Prediction

Drug Interaction Model Development

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

Population-Average vs Subject-Specific DDI

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)

Initial Drug Interaction PK Model - A Midazolam/Ketoconazole Example

Drug Interaction Model Development

Michaelis-Menten (MM) Kinetics

• MM Kinetics Equation:

• When the concentrations (C) are much less than Km:

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)

Group Gibbs Sampling (GGS) vs Single Gibbs Sampling (SGS)

Drug Interaction Model Development

Metabolic Enzyme Based Drug-Drug Interaction Studies — Decision Tree

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)

Thank you!