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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matrix covariance an is matrix covariance a is D

error residual is to1 from ranges

dose ssubject' i theis

subject i for the timej theis

vectorparameter 1 a is

in nonlinear function scalar a is

subject i for the response j theis

th

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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

ii

i

iiiji

ijiiijij

RNBNb

baxg

dtfy

,0~,0~

),(

),,(

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.