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

2 Outline Introduction Purpose of PK/PD modeling The Model Modeling Procedure Example from literature: Bevacizumab

3 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

4 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)

5 C max T max AUC Figure 2 Time Concentration Concentration of Drug as a Function of Time Model for Extra-vascular Absorption

6 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

7 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

8 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

9 The Nonlinear Mixed Effects Model Pharmacokineticists use the term ”population” model when the model involves random effects.

10 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.

11 Input Elimination Central Peripheral VcVc VpVp k 10 k 12 k 21 Example: First-Order 2-Compartment Model (Intravenous Dose) Parameterized in terms of “Micro constants” A c = Amount of drug in central compartment A p = Amount of drug in peripheral compartment

12 Web Demonstration tionportfolio.phphttp://vam.anest.ufl.edu/simulations/simula tionportfolio.php

13 Input Elimination Central Peripheral VcVc VpVp k 10 k 12 k 21 Example: First-Order 2-Compartment Model (Intravenous Dose)

14 Input Elimination Central Peripheral VcVc VpVp k 10 k 12 k 21 Example: First-Order 2-Compartment Model (Intravenous Dose)

15 Input Elimination Central Peripheral VcVc VpVp k 10 k 12 k 21 Example: First-Order 2-Compartment Model (Intravenous Dose)

16 Input Elimination Central Peripheral VcVc VpVp k 10 k 12 k 21 Example: First-Order 2-Compartment Model (Intravenous Dose) Solution in terms of macro constants:

17 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

18 Nonlinear Mixed Effects Model With secondary structure for covariates: Often,  is a vector of log Cl, log V, and log k a

19 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)

20 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

21 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

22 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

23 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

24 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

25 Other Covariates Serum-asparate aminotransferase (SGPT) Serum-alanine aminotransferase (SGOT) Serum-alkaline phosphatase (ALK) Serum Serum-bilirubin Total protein Albumin Creatinine clearance

26 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

27 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

28 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)

29 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)

30 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.