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![Page 1: PK/PD Modeling in Support of Drug Development Alan Hartford, Ph.D. Associate Director Scientific Staff Clinical Pharmacology Statistics Merck Research.](https://reader034.fdocuments.net/reader034/viewer/2022051416/56649eb35503460f94bba8b4/html5/thumbnails/1.jpg)
PK/PD Modeling in Support of Drug
DevelopmentAlan Hartford, Ph.D.
Associate Director Scientific StaffClinical Pharmacology Statistics
Merck Research Laboratories, [email protected]
![Page 2: PK/PD Modeling in Support of Drug Development Alan Hartford, Ph.D. Associate Director Scientific Staff Clinical Pharmacology Statistics Merck Research.](https://reader034.fdocuments.net/reader034/viewer/2022051416/56649eb35503460f94bba8b4/html5/thumbnails/2.jpg)
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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
n
Concentration of Drug as a Function of TimeModel 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 AkkAkdt
dA101221
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
pcp
cpc
AkAkdt
dA
AkkAkdt
dA
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
VAC
VAC
AkAkdt
dA
AkkAkdt
dA
c
ppp
ccc
pcp
cpc
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Input
Elimination
Central Peripheral
VcVp
k10
k12
k21
Example: First-Order 2-CompartmentModel (Intravenous Dose)
Dose Bolus0
/
/
2112
101221
tA
VAC
VAC
AkAkdt
dA
AkkAkdt
dA
c
ppp
ccc
pcp
cpc
)exp()exp( tBtAtCc Solution in terms of macro constants:
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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
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iiiji
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baxg
dtfy
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),(
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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.