Transcript Slide 1

PK/PD Modeling in
Support of Drug
Development
Alan Hartford, Ph.D.
Associate Director Scientific Staff
Clinical Pharmacology Statistics
Merck Research Laboratories, Inc.
[email protected]
Outline
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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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Concentration of Drug as a Function of Time
Model for Extra-vascular Absorption
Concentration
Cmax
AUC
Tmax
Time
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Figure 2
PK/PD Modeling
• Procedure:
– Estimate exposure and examine correlation between
PD other endpoints (including AE rates)
– Use mechanistic models
• Purpose:
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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
yij is the jth responsefor the i th subject
yij  f (tij ,  i , d i )   ij
 i ~ N  , D 
 i ~ N 0, Ri 
f is a scalar functionnonlinear in 
 is a k  1 parametervector
tij is the jth timefor the i th subject
d i is thei th subject's dose
j ranges from1 to ni
 ij is residual error
D is a k  k covariancematrix
Ri is an ni  ni covariancematrix
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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Example: First-Order 2-Compartment
Model (Intravenous Dose)
Input
k12
Peripheral
Central
Vp
Vc
Parameterized in terms of
“Micro constants”
k21
Elimination
k10
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/simula
tionportfolio.php
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Example: First-Order 2-Compartment
Model (Intravenous Dose)
dAc
 k 21 Ap  k12  k10 Ac
dt
Input
k12
Peripheral
Central
Vp
Vc
k21
Elimination
k10
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Example: First-Order 2-Compartment
Model (Intravenous Dose)
Input
k12
Peripheral
Central
dAc
 k 21 Ap  k12  k10 Ac
dt
dAp
 k12 Ac  k 21 Ap
dt
Vp
Vc
k21
Elimination
k10
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Example: First-Order 2-Compartment
Model (Intravenous Dose)
Input
k12
Peripheral
Central
Vp
Vc
k21
Elimination
k10
dAc
 k 21 Ap  k12  k10 Ac
dt
dAp
 k12 Ac  k 21 Ap
dt
Cc  Ac / Vc
C p  Ap / V p
Ac t  0  Bolus Dose
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Example: First-Order 2-Compartment
Model (Intravenous Dose)
Input
k12
Peripheral
Central
Vp
Vc
k21
Elimination
k10
Solution in terms of
macro constants:
dAc
 k 21 Ap  k12  k10 Ac
dt
dAp
 k12 Ac  k 21 Ap
dt
Cc  Ac / Vc
C p  Ap / V p
Ac t  0  Bolus Dose
Cc t   A exp(t )  B exp(t )
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Modeling Covariates
Assumed: 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
With secondary structure for covariates:
yij  f (tij ,  i , d i )   ij
 i  g ( x ij , ai )  b i
b i ~ N 0, B 
 i ~ N 0, Ri 
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
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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.
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