bayes pk models and applications to drug interaction simulations
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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?. - PowerPoint PPT PresentationTRANSCRIPT
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
SystemicCompart-ment
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
Literature PK DataExtraction
Meta Analysis forSimple Drug InteractionModel Development
Meta Analysis forSimple Drug InteractionModel Development
Prediction Assessment/ Validation
Prediction Assessment/ Validation
Model RefinementBased on Clinical Data
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)
Drug Interaction Model Development
Literature PK DataExtraction
Literature PK DataExtraction
Meta Analysis forSimple Drug InteractionModel Development
Meta Analysis forSimple Drug InteractionModel Development
Prediction Assessment/ Validation
Prediction Assessment/ Validation
Model RefinementBased on Clinical Data
Model RefinementBased on Clinical Data
Trial Simulation
Trial Simulation
Data Mining Bayes PK Model
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
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],|/),,([),|(
,...,1
,...,1
jkk
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k
jkk
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tf
nf
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k
k
βα
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βα
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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
Drug Interaction Model Development
Literature PK DataExtraction
Literature PK DataExtraction
Meta Analysis forSimple Drug InteractionModel Development
Meta Analysis forSimple Drug InteractionModel Development
Prediction Assessment/ Validation
Prediction Assessment/ Validation
Model RefinementBased on Clinical Data
Model RefinementBased on Clinical Data
Trial Simulation
Trial Simulation
Data Mining Bayes PK Model
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
Drug Interaction Model Development
Literature PK DataExtraction
Literature PK DataExtraction
Meta Analysis forSimple Drug InteractionModel Development
Meta Analysis forSimple Drug InteractionModel Development
Prediction Assessment/ Validation
Prediction Assessment/ Validation
Model RefinementBased on Clinical Data
Model RefinementBased on Clinical Data
Trial Simulation
Trial Simulation
Data Mining Bayes PK Model
Bayes PBPK Model
DDITrial
DDITrial
Equivalence Tests
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
SystemicCompart-ment
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
Drug Interaction Model Development
Literature PK DataExtraction
Literature PK DataExtraction
Meta Analysis forSimple Drug InteractionModel Development
Meta Analysis forSimple Drug InteractionModel Development
Prediction Assessment/ Validation
Prediction Assessment/ Validation
Model RefinementBased on Clinical Data
Model RefinementBased on Clinical Data
Trial Simulation
Trial Simulation
Data Mining Bayes PK Model
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!