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

Bayes PK Models and Applications to Drug Interaction Simulations

Lang LiAssociate ProfessorDivision of Biostatistics/Clinical PharmacologySchool of MedicineIndiana 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 PharmacokineticsIto et al. (1998) Pharmacy. Review

A Midazolam/Ketoconazole Interaction Example

KETO: 200 mgMDZ: 10 mg

(Lam, JCP 2003)

Gut Lumen

Gut Wall

Portal Vein

Liver

Hepatocyte

SystemicCompart-ment

Peripheral-ompart-ment

Inhibitor dose Substrate dose

Gut Lumen

Gut Wall

Portal Vein

Liver

Peripheracompartment


Hepatocyte

Ikd

GLIka ,

GWIka ,

periICL ,

HQ

PVQ

PVQ

Ik12 Ik21

HAQRICL ,

Skd

GLSka ,

GWSCL ,

GWIka ,

periSCL , PVQ

HQ

HAQ

PVQ

RSCL ,

Sk12Sk21

HSCL ,HICL ,

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 ParametersPrior Distributions

Construction

PK ParametersPrior Distributions

Construction

Bayes PK ModelFitting and Prediction

Bayes PK ModelFitting and Prediction

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

Drug Interaction Model Development

Literature PK DataExtraction


Meta Analysis forSimple Drug InteractionModel Development


Prediction Assessment/ Validation


Model RefinementBased on Clinical Data


Trial Simulation

Trial Simulation

Data Mining Bayes PK Model

Bayes PBPK Model

DDITrial

DDITrial

Equivalence Tests

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

InformationRetrieval

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)

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

MDZ DiDB(Dec. 2007)

Mining

AUC 1 4

Clearance 7 34

(Wang et al. 2008, manuscript)










Trial Simulation

Trial Simulation


Bayes PBPK Model

DDITrial

DDITrial

Equivalence Tests

Initial Drug Interaction PK Model - A Midazolam/Ketoconazole Example

int

int

maxint

H

H

keto

Q CLCL

Q CL

VCL

Km C

Ketoconazole Midazolam

ka

CL CL

CL12 CL12

V1 V1 V2V2

int

int

maxint

(1 )

H

H

ketoMDZ

i

Q CLCL

Q CL

VCL

CKm C

k

Published Ketoconazole Data Sets (sample mean profiles)

Published MDZ Data Sets (sample mean profiles)

Bayes Meta Analysis on Sample Mean Data

jkhkni

jkikjkh ntfyk

/),,(,...1

βα

).,,(

],|/)](),,({[

],|/),,([),|(

,...,1

,...,1

jkk

nikkikkT

k

jkk

nikkjkikkjkh

tf

nf

tfE

ntfEyE

k

k

βα

βαβββ

βα

βαβαβα

2v̂ar( | , ) /jkh k jkh ky s n α β

. ] ),,,([),,,|( 22kjkhkjkkjkjkhjkh /nstfNtsyp βαβα

Li et al. Stat in Med. 2007; Yu et al. JBS 2008

.,...,1,)(

)()(),()(

),10,0(),(22

22

4

qlab

pbaUp

Up

lll

βα

,),(~)|( ββ vk Stp

Monte Carlo Markov Chain

MCMC vs Stochastic-EM (SEM)

Kim et al. 2008 manuscript

SEM is faster than the other MCMC algorithm.

DDI Prediction

Posterior PK Parameter Draws

MDZ AloneProfile

MDZ Profilewith KETO

MDZ AloneAUC

MDZ AUCwith KETO

MDZ AUCR










Trial Simulation

Trial Simulation


Bayes PBPK Model

DDITrial

DDITrial

Equivalence Tests

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

Population – Average DDI

Subject-Specific DDI

(Zhou et al. 2008, manuscript)

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)

(Zhou et al. 2008, manuscript)

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

Initial Drug Interaction PK Model - A Midazolam/Ketoconazole Example

int

int

maxint

H

H

keto

Q CLCL

Q CL

VCL

Km C

Ketoconazole Midazolam

ka

CL CL

CL12 CL12

V1 V1 V2V2

int

int

maxint

(1 )

H

H

ketoMDZ

i

Q CLCL

Q CL

VCL

CKm C

k










Trial Simulation

Trial Simulation


Bayes PBPK Model

DDITrial

DDITrial

Equivalence Tests

Gut Lumen

Gut Wall

Portal Vein

Liver

Hepatocyte


Peripheral-ompart-ment

Inhibitor dose Substrate dose

Gut Lumen

Gut Wall

Portal Vein

Liver

Peripheracompartment


Hepatocyte

Ikd

GLIka ,

GWIka ,

periICL ,

HQ

PVQ

PVQ

Ik12 Ik21

HAQRICL ,

Skd

GLSka ,

GWSCL ,

GWIka ,

periSCL , PVQ

HQ

HAQ

PVQ

RSCL ,

Sk12Sk21

HSCL ,HICL ,

PBPK DDI Model

Non-identifiable system

Fast and reliable computational algorithms.

Michaelis-Menten (MM) Kinetics MM Kinetics Equation:

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

maxint

V CCL

Km C

C Km CKm

VCL

maxint

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)

IdentifiableKm ≈ C(t)

UnidentifiableKm >>C(t)

Recommended Number of Iterations

SGSGGS

Kim et al. 2008 (manuscript)

Prior Variance










Trial Simulation

Trial Simulation


Bayes PBPK Model

DDITrial

DDITrial

Equivalence Tests

Full Text Mining

Non-compartmentmodel transformationto compartment model

In-vitro Data Meta-Analysis Animal Data Integration

Variances Equivalence

PBPK Model (DDI mechanisms) MCMC Speed

Metabolic Enzyme Based Drug-Drug Interaction Studies

— Decision Tree

http://www.fda.gov/cder/guidance/6695dft.htm#_Toc112142815

Acknowledgement

Indiana UniversityLang 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 CompanyStephen D. Hall, PhD.Jenny Chien, Ph.D.

Alergan CompanyJihao Zhou, Ph.D.

The research is supported by NIH grants, R01 GM74217 and R01 GM67308.

Thank you!

Documents

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