PK/PD Modeling in Support of Drug Development Alan Hartford, Ph.D. Associate Director Scientific Staff Clinical Pharmacology Statistics Merck Research.

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

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

ii

i

ijiiijij

RN

DN

dtfy

,0~

,~

),,(

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

thth

thth

iii

ij

i

i

ij

ij

nnR

kk

nj

d

t

k

f

y

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

ii

i

iiiji

ijiiijij

RN

BNb

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.