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



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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!



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