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PK/PD Modeling in Support of Drug Development. Alan Hartford, Ph.D. Associate Director Scientific Staff Clinical Pharmacology Statistics Merck Research Laboratories, Inc. alan_hartford@merck.com. Outline. Introduction Purpose of PK/PD modeling The Model Modeling Procedure
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PK/PD Modeling in Support of Drug Development Alan Hartford, Ph.D. Associate Director Scientific Staff Clinical Pharmacology Statistics Merck Research Laboratories, Inc. alan_hartford@merck.com
Outline • Introduction • Purpose of PK/PD modeling • The Model • Modeling Procedure • Example from literature: Bevacizumab
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
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)
Concentration of Drug as a Function of Time Model for Extra-vascular Absorption Cmax AUC Concentration Tmax Time Figure 2
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
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
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
The Nonlinear Mixed Effects Model Pharmacokineticists use the term ”population” model when the model involves random effects.
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.
Example: First-Order 2-CompartmentModel (Intravenous Dose) Input k12 Peripheral Central Parameterized in terms of “Micro constants” Vp Vc k21 Elimination Ac = Amount of drug in central compartment Ap = Amount of drug in peripheral compartment k10
Web Demonstration • http://vam.anest.ufl.edu/simulations/simulationportfolio.php
Example: First-Order 2-CompartmentModel (Intravenous Dose) Input k12 Peripheral Central Vp Vc k21 Elimination k10
Example: First-Order 2-CompartmentModel (Intravenous Dose) Input k12 Peripheral Central Vp Vc k21 Elimination k10
Example: First-Order 2-CompartmentModel (Intravenous Dose) Input k12 Peripheral Central Vp Vc k21 Elimination k10
Example: First-Order 2-CompartmentModel (Intravenous Dose) Input k12 Peripheral Central Vp Vc k21 Elimination k10 Solution in terms of macro constants:
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
Nonlinear Mixed Effects Model With secondary structure for covariates: Often, is a vector of log Cl, log V, and log ka
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)
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
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
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
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
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
Other Covariates • Serum-asparate aminotransferase (SGPT) • Serum-alanine aminotransferase (SGOT) • Serum-alkaline phosphatase (ALK) • Serum Serum-bilirubin • Total protein • Albumin • Creatinine clearance
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
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
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)
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)
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.