Post on 07-Feb-2016
description
PK/PD Modeling in Support of Drug
DevelopmentAlan Hartford, Ph.D.
Associate Director Scientific StaffClinical Pharmacology Statistics
Merck Research Laboratories, Inc.alan_hartford@merck.com
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Outline• Introduction • Purpose of PK/PD modeling • The Model• Modeling Procedure• Example from literature: Bevacizumab
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Introduction• Pharmacokinetics is the study of what an
organism does with a dose of a drug– kinetics = motion– Absorbs, Distributes, Metabolizes, Excretes
• Pharmacodynamics is the study of what the drug does to the body– dynamics = change
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Pharmacokinetics• Endpoints
– AUC, Cmax, Tmax, half-life (terminal), C_trough
• The effect of the drug is assumed to be related to some measure of exposure. (AUC, Cmax, C_trough)
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Cmax
Tmax
AUC
Figure 2
Time
Con
cent
ratio
nConcentration of Drug as a Function of Time
Model for Extra-vascular Absorption
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PK/PD Modeling• Procedure:
– Estimate exposure and examine correlation between PD other endpoints (including AE rates)
– Use mechanistic models• Purpose:
– Estimate therapeutic window– Dose selection– Identify mechanism of action– Model probability of AE as function of exposure (and
covariates)– Inform the label of the drug
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Drug Label
• Additional negotiation after drug approval• Need information for prescribing doctors
and pharmacists• Need instructions for patients• Aim for clear summary of PK, efficacy, and
safety information• If instructions are complicated, may
reduce patient ability to properly dose
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Observed or Predicted PK?
• Exposure (AUC) not measured – only modeled
• Concentration in blood or plasma is a biomarker for concentration at site of action
• PK parameters are not directly measured
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The Nonlinear Mixed Effects Model
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Pharmacokineticists use the term ”population” model when the model involves random effects.
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Compartmental Modeling• A person’s body is modeled with a system of differential
equations, one for each “compartment”
• If each equation represents a specific organ or set of organs with similar perfusion rates, then called Physiologically Based PK (PBPK) modeling.
• The mean function f is a solution of this system of differential equations.
• Each equation in the system describes the flow of drug into and out of a specific compartment.
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
Parameterized in terms of “Micro constants”
Ac = Amount of drug in central compartment
Ap = Amount of drug in peripheral compartment
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Web Demonstration
• http://vam.anest.ufl.edu/simulations/simulationportfolio.php
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
cpc AkkAkdtdA
101221
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
pcp
cpc
AkAkdtdA
AkkAkdtdA
2112
101221
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
Dose Bolus0
//
2112
101221
tA
VACVAC
AkAkdtdA
AkkAkdtdA
c
ppp
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
Dose Bolus0
//
2112
101221
tA
VACVAC
AkAkdtdA
AkkAkdtdA
c
ppp
ccc
pcp
cpc
)exp()exp( tBtAtCc Solution in terms of macro constants:
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Modeling CovariatesAssumed: PK parameters vary with respect to a patient’s weight or age.
Covariates can be added to the model in a secondary structure (hierarchical model).
“Population Pharmacokinetics” refers specifically to these mixed effects models with covariates included in the secondary, hierarchical structure
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Nonlinear Mixed Effects Model
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iiiji
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baxg
dtfy
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),(
),,(
With secondary structure for covariates:
Often, is a vector of log Cl, log V, and log ka
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Pharmacodynamic Model
• PK: nonlinear mixed effect model (mechanistic)
• PD: – now assume predicted PK parameters are
true– less PD data per subject– nonlinear fixed effect model (mechanistic)
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Next Step: Simulations
• Using the PK/PD model, clinical trial simulations can be performed to:– Inform adaptive design– Determine good dose or dosing regimen for
future trial– Satisfy regulatory agencies in place of
additional trials– Surrogate for trials for testing biomarkers to
discriminate doses
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Example 1: Bevacizumab
• Recombinant humanized IgG1 antibody• Binds and inhibits effects induced by
vascular endothelial growth factor (VEGF)• (stops tumors from growing by cutting off
supply of blood)• Approved for use with chemotherapy for
colorectal cancer
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Paper: Clinical PK of bevacizumab in patients with solid tumors (Lu et al 2007)
• Objective stated in paper: To characterize the population PK and the influence of demographic factors, disease severity, and concomitantly used chemotherapy agents on it’s PK behavior.
• Purpose: to make conclusions about PK to confirm dosing strategy is appropriate
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Patients and Methods
• 4629 bevacizumab concentration samples• 491 patients with solid tumors• Doses from 1 to 20 mg/kg from weekly to
every 3 weeks• NONMEM software used to fit nonlinear
mixed effects model
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Demographic Variables• Gender (male/female)• Race (caucasian, Black, Hispanic, Asian, Native
American, Other)• ECOG Performance Status (0, 1, 2)• Chemotherapy (6 different therapies)• Weight• Height• Body Surface Area• Lean Body Mass
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Other Covariates
• Serum-asparate aminotransferase (SGPT)• Serum-alanine aminotransferase (SGOT)• Serum-alkaline phosphatase (ALK)• Serum Serum-bilirubin• Total protein• Albumin• Creatinine clearance
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Results
• First-order, two-compartment model fitted data well
• Weight, gender, and albumin had largest effects on CL
• ALK and SGOT also significantly effected CL
• Weight, gender, and Albumin had significant effects on Vc
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Results (cont.)
• Bevacizumab CL was 26% faster in males than females
• Subjects with low serum albumin have 19% faster CL than typical patients
• Subjects with higher ALK have a 23% faster CL than typical patients
• CL was different for different chemo regimens
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Ex 1: Conclusions
• Population PK parameters for Bevacizumab similar to other IGg antibodies
• Weight and gender effects from modeling support weight based dosing
• Linear PK suggest similar exposures can be achieved with flexible dosage regimens (Q2 or Q3 weekly dosing)
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Review
• PK/PD modeling performed to help better understand the drug:– Estimate therapeutic window– Dose selection– Identify mechanism of action– Model probability of AE as function of
exposure (and covariates)
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Reference
• Clinical pharmacokinetics of bevacizumab in patients with solid tumors, Jian-Feng Lu, Rene Bruno, Steve Eppler, William Novotny, Bert Lum, and Jacques Gaudreault, Cancer Chemother Pharmacol., 2008 Jan 19.