Pharmacometrics E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 2015

Veröffentlichungsjahr: 2013

Beschreibung

Pharmacometrics is the science of interpreting and describing pharmacology in a quantitative fashion. The pharmaceutical industry is integrating pharmacometrics into its drug development program, but there is a lack of and need for experienced pharmacometricians since fewer and fewer academic programs exist to train them. Pharmacometrics: The Science of Quantitative Pharmacology lays out the science of pharmacometrics and its application to drug development, evaluation, and patient pharmacotherapy, providing a comprehensive set of tools for the training and development of pharmacometricians. Edited and written by key leaders in the field, this flagship text on pharmacometrics: * Integrates theory and practice to let the reader apply principles and concepts. * Provides a comprehensive set of tools for training and developing expertise in the pharmacometric field. * Is unique in including computer code information with the examples. This volume is an invaluable resource for all pharmacometricians, statisticians, teachers, graduate and undergraduate students in academia, industry, and regulatory agencies.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Contributors

Preface

Acknowledgments

Chapter 1: Pharmacometrics: Impacting Drug Development and Pharmacotherapy

1.1 Introduction

1.2 Pharmacometrics Defined

1.3 History of Pharmacometrics

1.4 Pivotal Role of Pharmacometrics in Drug Development

1.5 Pharmacometrics and Regulatory Agencies

1.6 Summary

References

Part I: General Principles

Chapter 2: General Principles of Programming: Computer and Statistical

2.1 Introduction

2.2 Pharmacometric Programming Tasks

2.3 Overview of Scientific Programming Methodology

2.4 Good Programming Practices: Basic Syntax, Coding Conventions, and Constructs

2.5 Good Programming Practices: Relevant Mathematical Concepts

2.6 Good Programming Practices: Reducing Programming Errors

2.7 Good Programming Practices: Basics of Script and Program Design

2.8 Good Programming Practices: Modular Code Design for Functions

2.9 Good Programming Practices: Writing Extensible and Noninteractive Programs

2.10 Good Practices: Relevant Software Engineering Concepts

2.11 Summary

Acknowledgments

References

Chapter 3: Validation of Software for Pharmacometric Analysis

3.1 Introduction

3.2 Software Development and Implementation: Background

3.3 Methods

3.4 Validation Process

3.5 Informative Examples

3.6 Summary

References

Appendix 3.1 Sample Installation Qualification

Appendix 3.2 Sample Operation Qualification

Appendix 3.3 Sample Performance Qualification

Chapter 4: Linear, Generalized Linear, and Nonlinear Mixed Effects Models

4.1 Introduction

4.2 Pharmacokinetic Dose Proportionality Problem

4.3 Pharmacokinetic-Pharmacodynamic (Pk-Pd) Model

4.4 Repeated Binary Measure: Glmm Fit

4.5 Model Uncertainty: Simulation

4.6 Summary

References

Appendix 4.1 S-Plus Code

Chapter 5: Bayesian Hierarchical Modeling with Markov Chain Monte Carlo Methods

5.1 Introduction

5.2 Specification of Priors

5.3 Model Selection

5.4 Summary

References

Chapter 6: Estimating the Dynamics of Drug Regimen Compliance

6.1 Introduction

6.2 Measurement of Compliance

6.3 Compliance Indices

6.4 Probability Basis of Compliance

6.5 Noncompliance and Steady-State Pharmacokinetics

6.6 Application

6.7 Summary

References

Chapter 7: Graphical Displays for Modeling Population Data

7.1 Introduction

7.2 Characteristics of Informative Displays of Population Data

7.3 Before Analysis

7.4 During Analysis

7.5 After Analysis

7.6 Summary

References

Appendix 7.1 Obtaining Individual Predictions and Residuals

Appendix 7.2 Obtaining Standard Errors for η

Appendix 7.3 Confidence and Prediction Intervals

Chapter 8: The Epistemology of Pharmacometrics

8.1 Introduction

8.2 Definitions

8.3 Model Appropriateness

8.4 Model Identification

8.5 Parameter Identifiability

8.6 Approaches to Model Evaluation

8.7 Model Validation

8.8 Application Example

8.9 Summary

References

Chapter 9: Data Imputation

9.1 Introduction

9.2 Data Imputation

9.3 Description of Incomplete Data Types

9.4 Approaches for Handling Data Incompleteness

9.5 Multiple Imputations

9.6 The Mi Paradigm

9.7 A Simulation Study to Evaluate Some Bql Imputation Techniques

9.8 Software for Mi

9.9 Summary

References

Appendix 9.1 S-Plus Code for Implementation of the Cmi and Fcsi Examples

Part II: Population Pharmacokinetic Basis of Pharmacometrics

Chapter 10: Population Pharmacokinetic Estimation Methods

10.1 Introduction

10.2 Statistical Framework for Estimating Population Pharmacokinetics

10.3 Methods Applied to Population Pharmacokinetic Modeling

10.4 Summary

References

Chapter 11: Timing and Efficiency in Population Pharmacokinetic / Pharmacodynamic Data Analysis Projects

11.1 Introduction

11.2 Saving Time in a Population Modeling Project

11.3 The Population Modeling Project

11.4 Revised Time Plan

11.5 Summary

References

Chapter 12: Designing Population Pharmacokinetic Studies for Efficient Parameter Estimation

12.1 Introduction

12.2 Issues in the Design of Ppk Studies

12.3 Importance of Simulation in Evaluating Study Designs

12.4 Information Theory and Sampling Design/Sample Location

12.5 Number of Samples Per Subject

12.6 Sample Size and Study Power

12.7 Study Execution and Impact on Parameter Estimation Efficiency

12.8 Summary

References

Appendix 12.1 Adapt Ii Fortran Code Specifying a 1-Compartment 1St-Order Absorption Model

Appendix 12.2 S-Plus Script to Create Nonmem Dataset Templates

Appendix 12.3 Nonmem Control File

Appendix 12.4 Unix Shell Script to Create Multiple Simulation Files

Appendix 12.5 Nonmem Control File

Appendix 12.6 Unix Shell Script to Create Multiple Estimation Files

Appendix 12.7 Perl Code to Extract Parameters Estimates From Nonmem Output Files

Appendix 12.8 S-Plus Code to Analyze and Compare Nonmem Estimation Results

Chapter 13: Population Models for Drug Absorption and Enterohepatic Recycling

13.1 Introduction

13.2 General Considerations

13.3 Drug Absorption Models

13.4 Enterohepatic Recycling Model

13.5 Summary

References

Appendix 13.1 First-Order Absorption

Appendix 13.2 Zero-Order Absorption

Appendix 13.3 Two Parallel First-Order Absorptions

Appendix 13.4 Mixture of First-Order and Zero-Order Absorption

Appendix 13.5 Weibull-Type Absorption

Appendix 13.6 Enterohepatic Recycling Model

Chapter 14: Pharmacometric Knowledge Discovery From Clinical Trial Data Sets

14.1 Introduction

14.2 Pharmacometric Knowledge Discovery Process

14.3 Some Techniques Employed in Pmkd

14.4 Some Challenges in Pmkd

14.5 Application Example

14.6 Summary

References

Chapter 15: Resampling Techniques and Their Application to Pharmacometrics

15.1 Introduction

15.2 Resampling and the Plug-In Principle

15.3 Descriptive Summaries of Resampling Methods

15.4 Bias Correction

15.5 Example of Model Evaluation and Validation

15.6 Summary

References

Chapter 16: Population Modeling Approach in Bioequivalence Assessment

16.1 Introduction

16.2 Bioequivalence Overview

16.3 Methods for Assessing Pk Bioequivalence with Presence of Sparsely Sampled Subjects

16.4 Methodology

16.5 Application Example

16.6 Pharmacodynamic Endpoint Bioequivalence

16.7 Application Examples

16.8 Summary

References

Appendix 16.1

Part III: Pharmacokineticsi Pharmacodynamics Relationship: Biomarkers and Pharmacogenomics, Pk/Pd Models for Continuous Data, and Pk/Pd Models for Outcomes Data

Chapter 17: Biomarkers in Drug Development and Pharmacometric Modeling

17.1 Introduction

17.2 Vocabulary

17.3 Biomarker Validation

17.4 Analytical Integrity

17.5 Technologies for Biomarkers

17.6 Modeling and Biomarkers

17.7 Estimation of Biomarker Models

17.8 Example of Biomarker Estimation and Application

17.9 Summary

References

Chapter 18: Analysis of Gene Expression Data

18.1 Introduction

18.2 Microarray Data Analysis

18.3 Summary

Acknowledgment

References

Chapter 19: Pharmacogenomics and Pharmacokinetic/Pharmacodynamic Modeling

19.1 Introduction

19.2 Modeling of Selective Genomic Markers

19.3 Modeling of Microarray Profiles

19.4 Modeling Methodology

19.5 Summary

Acknowledgments

References

Appendix 19.1

Chapter 20: Empirical Pharmacokinetic/Pharmacodynamic Models

20.1 Introduction

20.2 Direct Empirical Models

20.3 Pharmacokinetic/Pharmacodynamic Link Models

20.4 Examples of Complex Dynamic Behavior Using Empirical/Direct Models

20.5 Summary

References

Chapter 21: Developing Models of Disease Progression

21.1 Introduction

21.2 Data

21.3 Models

21.4 Summary

References

Appendix 21.1 Example for the Simple Linear Disease Progression Model

Chapter 22: Mechanistic Pharmacokinetic/Pharmacodynamic Models I

22.1 Introduction

22.2 Indirect Response Models

22.3 Viral Dynamic Models

22.4 Summary

References

Appendix 22.1 Implementation of Models in Winnonlin/Nonmem

Chapter 23: Mechanistic Pharmacokinetic/Pharmacodynamic Models Ii

23.1 Introduction

23.2 Irreversible Pharmacological Effects

23.3 Nonlinear and Time-Dependent Transduction Processes

23.4 Tolerance and Rebound Phenomena

23.5 Complex Pharmacodynamic Models

Acknowledgments

References

Appendix 23.1

Chapter 24: Pk/Pd Analysis of Binary (Logistic) Outcome Data

24.1 Introduction and Application of Logistic Regression in Nonlinear Mixed Effects Modeling

24.2 Statistical Basis for Logistic Regression Models

24.3 An Example Utilizing Simulated Clinical Trial Data

24.4 Model Building

24.5 Model Extensions

24.6 Summary

References

Appendix 24.1 Nonmem Code for Base Model Example

Appendix 24.2 Nonmem Code for Final Model Example

Appendix 24.3 Nonmem Report File for Final Model Example

Chapter 25: Population Pharmacokinetic/Pharmacodynamic Modeling of Ordered Categorical Longitudinal Data

25.1 Introduction

25.2 Survival Data

25.3 Nonlinear Mixed Effects Modeling Approach to the Analysis of Nonrandomly Censored Ordered Categorical Longitudinal Data From Analgesic Trials

25.4 Application

25.5 Other Methods for Analyzing Ordered Categorical Data

25.6 Summary

References

Appendix 25.1 S-Plus Code to Generate Nonmem Data Set

Appendix 25.2 Nonmem Code to Simulate Clinical Trial

Appendix 25.3 S-Plus Code to Process Simulated Nonmem Data Set

Appendix 25.4 S-Plus Code Created Barplots of Pain Relief Scores Versus Time By Dose

Appendix 25.5 Nonmem Control File to Estimate Pain and Remedication Model Parameters

Appendix 25.6 S-Plus Code Created Plots of Probability/Proportion Pain Relief Versus Time By Pain Relief and Dose

Chapter 26: Transition Models in Pharmacodynamics

26.1 Introduction

26.2 Overview of Markov Models

26.3 Discrete Time Markov Chain

26.4 The Markovian Assumption

26.5 Mixed Effects Transition Models

26.6 Hybrid Markov Mixed Effects and Proportional Odds Model

26.7 Summary

References

Chapter 27: Mixed Effects Modeling Analysis of Count Data

27.1 Introduction

27.2 Motivating Example: Neonatal Apnea

27.3 Theory on the Analysis of Count Data

27.4 Application of Poisson-Based Population Analysis to Apneic Episode Data

27.5 Summary

References

Appendix 27.1

Chapter 28: Mixture Modeling with Nonmem V

28.1 Introduction/Motivating Examples

28.2 History

28.3 Submodel Parameterizations

28.4 Probability Parameterizations

28.5 Hypothesis Testing

28.6 Dynamic Mixtures

28.7 Multiple Mixtures

28.8 Graphic Considerations

28.9 Simulation with Mixtures

28.10 Summary

References

Part IV: Clinical Trial Designs

Chapter 29: Designs for First-Time-In-Human Studies in Nononcology Indications

29.1 Introduction

29.2 Dose-Escalation Scheme

29.3 First-Time-In-Human Study Designs

29.4 Cohort Size in Ftih Studies

29.5 Adverse Events in Ftih Studies

29.6 Determination of the Efficiency of Ftih Designs in Healthy Volunteers

29.7 Study Outcome

29.8 Discussion

29.9 Summary

References

Appendix 29.1 Code for Exposure-Ae Relationship Figure

Appendix 29.2 Function Code for Pk Profile

Appendix 29.3 Code of Pk Simulation

Chapter 30: Design of Phase 1 Studies in Oncology

30.1 Introduction

30.2 Objectives for Phase 1 Studies

30.3 Subject Enrollment for Phase 1 Studies

30.4 Treatment Plan for Phase 1 Studies

30.5 Data Collection

30.6 Phase 1 Studies for a Combination of Two Drugs

30.7 Summary

Acknowledgments

References

Appendix 30.1 Nonmem Code for Allometric Scaling

Chapter 31: Design and Analysis of Clinical Exposure: Response Trials

31.1 Introduction and Motivation

31.2 Exposure–Response Strategy and Objectives

31.3 Regulatory Guidances on Exposure–Response

31.4 Exposure-Response Trial Designs and Analysis Strategies

31.5 Summary

References

Part V: Pharmacometric Knowledge Creation

Chapter 32: Pharmacokinetic/Pharmacodynamic Knowledge Creation: Toward Characterizing an Unexplored Region of the Response Surface

32.1 Introduction

32.2 Types of Pk/Pd Knowledge Creation

32.3 General Steps in the Pk/Pd Knowledge Creation Process

32.4 Data Supplementation

32.5 Structure-Based Multiple Supplementation: A Motivating Example

32.6 Implications of the Use of Multiple Data Supplementation for the Characterization of an Unexplored Region of the Response

References

Appendix 32.1 Code for Auc Simulation Based on Population Pk Model

Appendix 32.2 Code for Density Plot—Observed Versus Simulated

Appendix 32.3 Sample Code for Pd Data Supplementation

Chapter 33: Clinical Trial Simulation: Theory

33.1 Introduction

33.2 Modeling Versus Simulation

33.3 Elements of Simulation

33.4 Random Numbers

33.5 Simulating Continuous Random Variables

33.6 Simulating Discrete Random Variables

33.7 Software

33.8 Application of M&S in Drug Development and Regulatory Review

33.9 Summary

References

Chapter 34: Modeling and Simulation: Planning and Execution

34.1 Introduction

34.2 Execution of the Simulation Exercise

34.3 Miscellaneous Points to Consider

34.4 Summary

References

Chapter 35: Clinical Trial Simulation: Efficacy Trials

35.1 Introduction

35.2 Simulation Planning

35.3 Simulation Execution and Interpretation

35.4 Efficacy Trial Simulation Example

35.5 Summary

Acknowledgment

References

Appendix 35.1 Nonmem Code for Efficacy Trial Simulation

Part VI: Pharmacometric Service and Communication

Chapter 36: Engineering a Pharmacometrics Enterprise

36.1 Introduction

36.2 Enterprise of Pharmacometric Analysis

36.3 Process of Pharmacometric Analysis

36.4 Pharmacometrics Enterprise Design

36.5 Summary

Acknowledgments

References

Chapter 37: Communicating Pharmacometric Analysis Outcome

37.1 Introduction

37.2 Graphics in Pharmacometrics Communication

37.3 Information/Knowledge Integration

37.4 Summary

References

Part VII: Specific Application Examples

Chapter 38: Pharmacometrics Applications in Population Exposure–Response Data for New Drug Development and Evaluation

38.1 Introduction

38.2 Drug Enhibitor

38.3 Drug Botani

38.4 Drug Amicid

38.5 Discussion

38.6 Summary

References

Appendix 38.1

Chapter 39: Pharmacometrics in Pharmacotherapy and Drug Development: Pediatric Application

39.1 Introduction

39.2 Regulatory Climate

39.3 Obstacles of Pm Research in Pediatrics

39.4 Differences Between Adult and Pediatric Patients

39.5 Covariate Impact in Pediatric Pharmacometrics

39.6 Population Modeling in Pediatrics

39.7 Clinical Trial Simulation

39.8 An Informative Example

39.9 Summary

References

Chapter 40: Pharmacometric Methods for Assessing Drug-Induced Qt and Qtc Prolongations for Non-Antiarrhythmic Drugs

40.1 Introduction

40.2 Correction of the Qt Interval for Heart Rate

40.3 Data Analysis Considerations in Study Design

40.4 Summary

References

Chapter 41: Using Pharmacometrics in the Development of Therapeutic Biological Agents

41.1 Pharmacokinetics of Therapeutic Proteins

41.2 Evaluating Pharmacokinetics Using Model-Based Analysis

41.3 Pharmacodynamics of Therapeutic Proteins: Background

41.4 Specific Proteins

41.5 Covariates for Pharmacodynamic Response

41.6 Evaluating Pharmacodynamics Using Model-Based Analysis

41.7 Summary

Abbreviations

References

Chapter 42: Analysis of Quantic Pharmacokinetic Study: Robust Estimation of Tissue-To-Plasma Ratio

42.1 Introduction

42.2 Estimation of Tissue-To-Plasma Ratio

42.3 Comparison of Ppbb and Rs Approaches

42.4 Overall Assessment of Tissue-To-Plasma Ratio Estimation

42.5 Summary

References

Appendix 42.1 Code for Naive Data Averaging Approach

Appendix 42.2 Code for Random Sampling Approach

Appendix 42.3 Code for Pseudoprofile-Based Bootstrap

Appendix 42.4 Code for Convergence

Appendix 42.5 Code for Outlier Effect

Appendix 42.6 Code for Other Subroutines

Chapter 43: Physiologically Based Pharmacokinetic Modeling: Inhalation, Ingestion, and Dermal Absorption

43.1 Introduction

43.2 Overview of Pbpk Modeling

43.3 Steps in Formulating a Pbpk Model

43.4 Steps in Model Implementation, Evaluation, and Refinement of Pbpk Models

43.5 Application Example: A Pbpk Model for Chloroform

43.6 Summary

Acknowledgment

References

Appendix 43.1 Code Listing 1

Appendix 43.2 Code Listing 2

Appendix 43.3 Code Listing 3

Appendix 43.4 Code Listing 4

Appendix 43.5 Code Listing 5

Appendix 43.6 Code Listing 6

Chapter 44: Modeling of Metabolite Pharmacokinetics in a Large Pharmacokinetic Data Set: An Application

44.1 Introduction

44.2 The Nelfinavir Example

44.3 Summary

References

Appendix 44.1 Coding 1

Appendix 44.2 Coding 2

Appendix 44.3 Coding 3

Appendix 44.4 Coding 4

Chapter 45: Characterizing Nonlinear Pharmacokinetics: An Example Scenario for a Therapeutic Protein

45.1 Introduction

45.2 An Example

45.3 Discussion

45.4 Summary

References

Appendix 45.1 Model 1 Nonmem Control Code

Appendix 45.2 Model 2 Nonmem Control Code

Chapter 46: Development, Evaluation, and Applications of in Vitro/In Vivo Correlations: A Regulatory Perspective

46.1 Introduction

46.2 Levels of Correlation

46.3 Development of Level a Correlation

46.4 Evaluation of the Predictability of the Ivivc

46.5 Approaches to the Evaluation of Predictability

46.6 Applications of Ivivc

46.7 Case Study

46.8 Summary

References

Chapter 47: The Confluence of Pharmacometric Knowledge Discovery and Creation in the Characterization of Drug Safety

47.1 Introduction

47.2 Pharmacometric Knowledge Discovery Techniques

47.3 The Confluence of Pharmacometric Knowledge Discovery and Creation

47.4 Application

47.5 Summary

References

Appendix 47.1 Code for Percentile Division Approach

Appendix 47.2 Code for the New Metric Calculation

Appendix 47.3 Data Processing Code

Appendix 47.5 Tree Based Model

Appendix 47.6 2-D Bubble Plot

Appendix 47.7 An Example Code for Logistic Regression

Appendix 47.8 Auc Plot

Index

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Library of Congress Cataloging-in-Publication Data:

Pharmacometrics : the science of quantitative pharmacology / [edited by] Ene I. Ette, Paul J. Williams.p. ; cm.Includes bibliographical references.ISBN 978-0-471-67783-31. Pharmacology. 2. Pharmacokinetics. I. Ette, Ene I. II. Williams, Paul J. [DNLM: 1. Chemistry, Pharmaceutical-methods. 2. Drug Evaluation-methods. 3. Models, Theoretical. 4. Pharmacoepidemiology–methods. 5. Pharmacokinetics. 6. Technology, pharmaceutical–methods. 7. Drug Development. 8. Pharmacometrics. QV 744 P5363 2006]RS187.P4553 2006615’. 1–dc222006016629

To my wife, Esther, who supports, comforts, and inspires and is always there for me.E. I. E.

To my wife, Debbie, who supports, comforts, and inspires.P. J. W.

CONTRIBUTORS

Alaa Ahmad, Clinical Pharmacology, Vertex Pharmaceuticals, 130 Waverly St., Cambridge, MA 02139 [[email protected]]

Peter L. Bonate, Genzyme Corporation, Pharmacokinetics, 4545 Horizon Hill Blvd., San Antonio, TX 78229 [[email protected]]

Daniel Brazeau, Department of Pharmaceutical Sciences, 517 Cooke Hall, State University of New York at Buffalo, Buffalo, NY 14260 [[email protected]]

René Bruno, Pharsight Corporation, 84 Chemin des Grives, 13013 Marseille, France [[email protected]]

Edmund V. Capparelli, Pediatric Pharmacology Research Unit, School of Medicine, University of California—San Diego, 4094 4th Avenue, San Diego, CA 92103 and Trials by Design, 1918 Verdi Ct., Stockton, CA 95207 [[email protected]]

Hui-May Chu, Clinical Pharmacology, Vertex Pharmaceuticals, 130 Waverly St., Cambridge, MA 02139 [[email protected]]

Valérie Cosson, Clinical Pharmacokinetics Modeling and Simulation, Psychiatry, GSK Spa, Via Fleming 4, 37135 Verona, Italy [[email protected]] and Hoffman—La Roche Ltd., PDMP, 663/2130, CH-4070 Basel, Switzerland [[email protected]]

Charles W. Dement, 260 Jacobs Management Center, University at Buffalo–SUNY, Buffalo, NY 14260

Chantaratsamon Dansirikul, School of Pharmacy, University of Queensland, Brisbane 4072, Australia [[email protected]] and Department of Pharmaceutical Biosciences, Uppsala University, Box 591, SE-751 24 Uppsala, Sweden

Stephen B. Duffull, School of Pharmacy, University of Queensland, Brisbane 4072, Australia [[email protected]] and School of Pharmacy, University of Otago, PO Box 913, Dunedin, New Zealand [[email protected]]

Ene I. Ette, Clinical Pharmacology, Vertex Pharmaceuticals, 130 Waverly St., Cambridge, MA 02139 and Anoixis Corp., 214 N. Main St., Natick, MA 01760 [[email protected]]

Wayne Ewy, Pfizer, PGR&D, 2800 Plymouth Road, Ann Arbor, MI 48105 [[email protected]]

Farkad Ezzet, Pharsight Corporation, 87 Lisa Drive, Chatham, NJ 07928

Emmanuel O. Fadiran, Division of Clinical Pharmacology 2, OCP, FDA, 10903 New Hampshire Avenue, Building 21, Silver Springs, MD 20993-0002 [[email protected]]

Jill Fiedler-Kelly, Cognigen Corporation, 395 S Youngs Rd., Williamsville, NY 14221 [[email protected]]

Bill Frame, C.R.T., 5216 Pratt Rd., Ann Arbor, MI 48103 [[email protected]]

Gilles Freyer, Ciblage Thérapeutique en Oncologie, Service Oncologie Médicale, EA 3738, CH Lyon-Sud, 69495 Pierre-Bénite Cedex, France [[email protected]]

Lena E. Friberg, School of Pharmacy, University of Queensland, Brisbane 4072, Australia [[email protected]] and Department of Pharmaceutical Biosciences, Uppsala University, Box 591, SE-751 24 Uppsala, Sweden

Stuart Friedrich, Global PK/PD and Trial Simulations, Eli Lilly Canada Inc., 3650 Danforth Ave., Toronto, ON, MIN 2E8 Canada [[email protected]]

Eliane Fuseau, EMF Consulting, Aix en Provence Cedex 4, France [[email protected]]

Varun Garg, Clinical Pharmacology, Vertex Pharmaceuticals, 130 Waverly St., Cambridge, MA 02139 [[email protected]]

Marc R. Gastonguay, Metrum Research Group LLC, 2 Tunxis Road, Suite 112, Tariffville, CT 06081 [[email protected]]

Panos G. Georgopoulos, Computational Chemodynamics Laboratory, Environmental and Occupational Health Sciences Institute, 70 Frelinghuysen Road, Piscataway, NJ 08854 [[email protected]]

Christopher J. Godfrey, Clinical Pharmacology, Vertex Pharmaceuticals, 130 Waverly St., Cambridge, MA 02139 and Anoixis Corp., 214 N. Main St., Natick, MA 01760 [[email protected]]

Thaddeus H. Grasela, Cognigen Corporation, 395 S Youngs Rd, Williamsville, NY 14221 [[email protected]]

David Hermann, deCODE Genetics, 1032 Karl Greimel Drive, Brighton, MI 48116 [[email protected]]

Chuanpu Hu, Biostatistics, Sanofi-Aventis, 9 Great Valley Parkway, Malvern, PA 19355-1304 [[email protected]]

Matthew Hutmacher, Pfizer, PGR&D, 2800 Plymouth Road, Ann Arbor, MI 48105 [[email protected]]

Sastry S. Isukapalli, Computational Chemodynamics Laboratory, Environmental and Occupational Health Sciences Institute, 70 Frelinghuysen Road, Piscataway, NJ 08854 [[email protected]]

Jin Y. Jin, Department of Pharmaceutical Sciences, School of Pharmacy, 519 Hochstetter Hall, State University of New York at Buffalo, Buffalo, NY 14260

Siv Jönsson, Clinical Pharmacology, AstraZeneca R&D Södertälje, SE-151 85 Södertälje, Sweden [[email protected]]

E. Niclas Jonsson, Hoffmann-La Roche Ltd., PDMP Modelling and Simulation, Grenzacherstr 124, Bldg. 15/1.052, CH-4070 Basel, Switzerland [[email protected]]

Karin Jorga, Hoffmann-La Roche Ltd., PDMP Clinical Pharmacology, Grenzacherstrasse 124, Bldg. 15/1.081A, CH-4070 Basel, Switzerland [[email protected]]

William J. Jusko, Department of Pharmaceutical Sciences, School of Pharmacy, 519 Hochstetter Hall, State University of New York at Buffalo, Buffalo, NY 14260 [[email protected]]

Mats O. Karlsson, Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Uppsala University, Box 591, SE-751 24 Uppsala, Sweden [[email protected]]

Ariya Khunvichai, Clinical Pharmacology, Vertex Pharmaceuticals, 130 Waverly St., Cambridge, MA 02139 [[email protected]]

Yong Ho Kim, Clinical Pharmacokinetics, Five Moore Drive, Sanders Bldg. 17.2245 PO Box 13398, Research Triangle Park, NC 27709 [[email protected]] and Clinical Pharmacokinetics, GlaxoSmithKline, Raleigh, NC [[email protected]]

Kenneth Kowalski, Pfizer, PGR&D, 2800 Plymouth Road, Ann Arbor, MI 48105 [[email protected]]

James R. Lane, Department of Pharmacy, Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California San Diego, 200 West Arbor Drive, San Diego, CA 92103-8765 [[email protected]]

Donald E. Mager Department of Pharmaceutical Sciences, School of Pharmacy, 519 Hochstetter Hall, State University of New York at Buffalo, Buffalo, NY 14260 [[email protected]]

Mathilde Marchland, EMF Consulting, 425 rue Rene Descartes, BP 02, 13545 Aix-en-Provence Cedex 4, France [[email protected]]

Patrick J. Marroum, Office of Clinical Pharmacology, CDER, FDA, 10903 New Hampshire Avenue, Building 21, Silver Spring, MD 20993 [[email protected]]

Raymond Miller, Pfizer, PGR&D, 2800 Plymouth Road, Ann Arbor, MI 48105 [[email protected]]

Peter A. Milligan, Pfizer, Ramsgate Road, Sandwich, Kent, CT13 9NJ, UK [[email protected]]

Diane R. Mould, Projections Research, Inc., 535 Springview Lane, Phoenixville, PA 19460 [[email protected]]

Partha Nandy, Johnson & Johnson Pharmaceutical Research and Development, 1125 Trenton-Hourborton Road, Titusville, NJ 08560 [[email protected]]

Leonard C. Onyiah, Engineering and Computer Center, Department of Statistics and Computer Networking, St. Cloud State University, 720 4th Avenue South, St. Cloud, MN 56301 [[email protected]]

Olivier Pétricoul, EMF Consulting, 425 rue Rene Descartes, BP 02, 13545 Aix-en-Provence Cedex 4, France [[email protected]]

José Pinheiro, Biostatistics, Novartis Pharmaceuticals Corporation, One Health Plaza, 419/2115, East Hanover, NJ 07936 [[email protected]]

Murali Ramanathan, Pharmaceutical Sciences and Neurology, 543 Cooke Hall, State University of New York, Buffalo, NY 14260

Amit Roy, Strategic Modeling and Simulation, Bristol-Myers Squibb, Route 206 and Provinceline Road, Princeton, NJ 08540 [[email protected]]

Matthew M. Riggs, Metrum Research Group LLC, 2 Tunxis Road, Suite 112, Tariffville, CT 06081 [[email protected]]

Mark E. Sale, Next Level Solutions LLC, 1013 Dickinson Circle, Raleigh, NC 27614 [[email protected], [email protected]]

He Sun, SunTech Research Institute, 1 Research Court, Suite 450-54, Rockville, MD 20850 [[email protected], [email protected]]

Brigitte Tranchand, Ciblage Thérapeutique en Oncologie, Faculté de Médecine, EA3738, Lyon-Sud, BP12, 69921 Oullins Cedex, France [[email protected]]

James A. Uchizono, Department of Pharmaceutics and Medicinal Chemistry, Thomas J. Long School of Pharmacy, University of the Pacific, Stockton, CA 95211 [[email protected]]

Paul J. Williams, Thomas J. Long School of Pharmacy and Health Sciences, University of the Pacific, Stockton, CA 95211 and Anoixis Corp., 1918 Verdi Ct., Stockton CA 95207 [[email protected], [email protected]]

Gary L. Wolk, 1215 South Kihei Rd., Kihei, HI 96753 [[email protected]]

Jiuhong Zha, Biopharmacentical Sciences, Astellas Pharma, US Inc., Chicago [[email protected]]

PREFACE

The subspecialty of population pharmacokinetics was introduced into clinical pharmacology / pharmacy in the late 1970s as a method for analyzing observational data collected during patient drug therapy in order to estimate patient-based pharmacokinetic parameters. It later became the basis for dosage individualization and rational pharmacotherapy. The population pharmacokinetics method (i.e., the population approach) was later extended to the characterization of the relationship between pharmacokinetics and pharmacodynamics, and into the discipline of pharmacometrics. Pharmacometrics is the science of interpreting and describing pharmacology in a quantitative fashion. Vast amounts of data are generated during clinical trials and patient care, and it is the responsibility of the pharmacometrician to extract the knowledge embedded in the data for rational drug development and pharmacotherapy. He/she is also responsible for providing that knowledge for decision making in patient care and the drug development process.

With the publication of the Guidance for Industry: Population Pharmacokinetics by the Food and Drug Administration (the advent of population pharmacokinetics/pharmacodynamics-based clinical trial simulation) and recently the FDA Critical Path Initiative—The Critical Path to New Medical Products, the assimilation of pharmacometrics as an applied science in drug development and evaluation is increasing. Although a great deal has been written in the journal literature on population pharmacokinetics, population pharmacokinetics/pharmacodynamics, and pharmacometrics in general, there is no major reference textbook that pulls all these facets of knowledge together in one volume for pharmacometricians in academia, regulatory agencies, or industry and graduate students/postdoctoral fellows who work/research in this subject area. It is for this purpose that this book is written.

Although no book can be complete in itself, what we have endeavored to assemble are contributors and an array of topics that we believe provide the reader with the knowledge base necessary to perform pharmacometric analysis, to interpret the results of the analysis, and to be able to communicate the same effectively to impact mission-critical decision making. The book is divided into seven sections—general principles, population pharmacokinetic basis of pharmacometrics, pharmacokinetics/pharmacodynamics relationship, clinical trial designs, pharmacometric knowledge creation, pharmacometric service and communication, and specific application examples. In the introductory chapter, the history of the development of pharmacometrics is traced and its application to drug development, evaluation, and pharmacotherapy is delineated. This is followed by Part I on general principles that addresses topics such as the general principles of programming, which is a must for every pharmacometrician, pharmacometric analysis software validation—a subject that has become prominent in last few years, linear and nonlinear mixed effects modeling to provide the reader with the background knowledge on these topics and thus setting the pace for the remainder of the book, estimation of the dynamics of compliance, which is important for having a complete picture of a study outcome, graphical display of population data—a sine qua non for informative pharmacometric data analysis, the epistemology of pharmacometrics, which provides a pathway for performing a pharmacometric analysis, and data imputation. Data analysis without the proper handling of missing data may result in biased parameter estimates. The chapter on data imputation covers the various aspects of “missingness” and includes an example of how to handle left censored data—a challenge with most pharmacokinetic data sets.

In Part II of the book various aspects of population pharmacokinetics, pharmacometric knowledge discovery, and resampling techniques used in pharmacometric data analysis are covered. Thus, various aspects of the informative design and analysis of population pharmacokinetic studies are addressed together with population pharmacokinetics estimation methods. The chapter on pharmacometric knowledge discovery deals with the integrated approach for discovering knowledge from clinical trial data sets and communicating the same for optimal pharmacotherapy and knowledge/model-based drug development.

Part III, which is on the pharmacokinetics–pharmacodynamics relationship, deals with biomarkers and surrogates in drug development, gene expression analysis, integration of pharmacogenomics into pharmacokinetics/pharmacodynamics, empirical and mechanistic PK/PD models, outcome models, and disease progression models that are needed for understanding disease progression as the basis for building models that can be used in clinical trial simulation.

Part IV builds on the knowledge gained from the previous sections to provide the basis for designing clinical trials. The section opens with a chapter on the design of first-time-in-human (FTIH) studies for nononcology indications. The literature is filled with a discussion of the design of FTIH oncology studies, but very little has been written on the design of FTIH studies for nononcology indications. A comprehensive overview of different FTIH study designs is provided with an evaluation of the designs that provide the reader with the knowledge needed for choosing an appropriate study design. A comprehensive coverage of the design of Phase 1 and phase 2a oncology studies is provided in another chapter; the section closes with a chapter on the design of dose − response studies.

Part V addresses pharmacometric knowledge creation, which entails the application of pharmacometric methodologies to the characterization of an unexplored region of the response surface. It is the process of building upon current understanding of data that is already acquired by generating more data (information) that can be translated into knowledge. Thus, the section opens with a chapter on knowledge creation, followed by the theory of clinical trial simulation and the basics of clinical trial simulation, and ends with a chapter on the simulation of efficacy trials.

Parts VI and VII discuss what a pharmacometric service is all about, how to communicate the results of a pharmacometric analysis, and specific examples ranging from applications in a regulatory setting, characterization of QT interval prolongation, pharmacometrics in biologics development, pharmacometrics in pediatric pharmacotherapy, application of pharmacometric principles to the analysis of preclinical data, physiologically based pharmacokinetic modeling, characterizing metabolic and nonlinear pharmacokinetics, in vitro in vivo correlation, and the application of pharmacometric knowledge discovery and creation to the characterization of drug safety.

What makes this book unique is not just the presentation of theory in an easy to comprehend fashion, but the fact that for a majority of the chapters there are application examples with codes in NONMEM, S-Plus, WinNonlin, or Matlab. The majority of the codes are for NONMEM and S-Plus. Thus, the reader is able to reproduce the examples in his/her spare time and gain an understanding of both the theory and principles of pharmacometrics covered in a particular chapter. A reader friendly approach was taken in the writing of this book. Although there are many contributors to the book, we have tried as much as possible to unify the style of presentation to aid the reader’s understanding of the subject matter covered in each chapter. Emphasis has been placed on drug development because of the need to apply pharmacometrics in drug development to increase productivity. Examples have been provided for the application of pharmacometrics in pharmacotherapy and drug evaluation to show how pharmacometric principles have been applied in these areas with great benefit.

In the writing of this text, the reader’s knowledge of pharmacokinetics, pharmacodynamics, and statistics is assumed. If not, the reader is referred to Applied Pharmacokinetics by Shargel and Yu, Pharmacokinetics by Gibaldi and Perrier, Pharmacokinetics and Pharmacodynamics by Gabrielson and Weiner, and statistics from standard textbooks.

Finally, this book is written for the graduate students or postdoctoral fellows who want to specialize in pharmacometrics; and for pharmaceutical scientists, clinical pharmacologists/pharmacists, and statisticians in academia, regulatory bodies, and the pharmaceutical industry who are in pharmacometrics or are interested in developing their skill set in the subject.

ENE I. ETTEPAUL J. WILLIAMS

Text documents and data sets that accompany this book can be found at: ftp://ftp.wiley.com/public/sci_tech_med/pharmacometrics/

ACKNOWLEDGMENTS

This book is the result of many hands and minds. None of us is as smart as all of us; therefore we acknowledge the contributions of the chapter authors who withstood bullyragging as this work was put together. Furthermore, the contributions of our parents over the long haul of our lives must be recognized. We thank Esther and the children, and Debbie, who have been patient not only through the process of writing and editing this work but for a lifetime. In addition, we are thankful to Jonathan Rose, Wiley commissioning editor for pharmaceutical sciences books, and Rosalyn Farkas, production editor at Wiley, for their patience and cooperation. Finally and most importantly, we recognize the work of the Father, Son, and Holy Spirit who gave us the idea and provided the energy to complete this work and to whom we are eternally indebted.

E. I. E.P. J. W.

CHAPTER 1

Pharmacometrics: Impacting Drug Development and Pharmacotherapy

PAUL J. WILLIAMS and ENE I. ETTE

1.1 INTRODUCTION

Drug development continues to be expensive, time consuming, and inefficient, while pharmacotherapy is often practiced at suboptimal levels of performance (1–3). This trend has not waned despite the fact that massive amounts of drug data are obtained each year. Within these massive amounts of data, knowledge that would improve drug development and pharmacotherapy lays hidden and undiscovered. The application of pharmacometric (PM) principles and models to drug development and pharmacotherapy will significantly improve both (4,5). Furthermore, with drug utilization review, generic competition, managed care organization bidding, and therapeutic substitution, there is increasing pressure for the drug development industry to deliver high-value therapeutic agents.

The Food and Drug Administration (FDA) has expressed its concern about the rising cost and stagnation of drug development in the white paper Challenge and Opportunity on the Critical Path to New Products published in March of 2004 (3). In this document the FDA states: “Not enough applied scientific work has been done to create new tools to get fundamentally better answers about how the safety and effectiveness of new products can be demonstrated in faster time frames, with more certainty, and at lower costs…. A new product development toolkit—containing powerful new scientific and technical methods such as animal or computer-based predictive models, biomarkers for safety and effectiveness, and new clinical evaluation techniques—is urgently needed to improve predictability and efficiency along the critical path from laboratory concept to commercial product. We need superior product development science to address these challenges.” In the critical path document, the FDA states that the three main areas of the path that need to be addressed are tools for assessing safety, tools for demonstrating medical utility, and lastly tools for characterization and manufacturing. Pharmacometrics can be applied to and can impact the first two areas, thus positively impacting the critical path.

For impacting safety, the FDA has noted opportunities to better define the importance of the QT interval, for improved extrapolation of in vitro and animal data to humans, and for use of extant clinical data to help construct models to screen candidates early in drug development (e.g., liver toxicity). Pharmacometrics can have a role in developing better links for all of these models.

For demonstrating medical utility, the FDA has highlighted the importance of model-based drug development in which pharmacostatistical models of drug efficacy and safety are developed from preclinical and available clinical data. The FDA goes on to say that “Systematic application of this concept to drug development has the potential to significantly improve it. FDA scientists use and are collaborating with others in the refinement of quantitative clinical trial modeling using simulation software to improve trial design and to predict outcomes.” The pivotal role of pharmacometrics on the critical path is obvious.

Drug development could be improved by planning to develop and apply PM models along with novel pathways to approval, improved project management, and improved program development. Recent advances in computational speed, novel models, stochastic simulation methods, real-time data collection, and novel biomarkers all portend improvements in drug development.

Dosing strategy and patient selection continue to be the most easily manipulated parts of a patient’s therapy. Optimal dosing often depends on patient size, sex, and renal function or liver function. All too often, the impact of these covariates on a PM parameter is unstudied and therefore cannot be incorporated into any therapeutic strategy. PM model development and application will improve both drug development and support rational pharmacotherapy.

1.2 PHARMACOMETRICS DEFINED

Pharmacometrics is the science of developing and applying mathematical and statistical methods to characterize, understand, and predict a drug’s pharmacokinetic, pharmacodynamic, and biomarker–outcomes behavior (6). Pharmacometrics lives at the intersection of pharmacokinetic (PK) models, pharmacodynamic (PD) models, pharmacodynamic-biomarker–outcomes link models, data visualization (often by employing informative modern graphical methods), statistics, stochastic simulation, and computer programming. Through pharmacometrics one can quantify the uncertainty of information about model behavior and rationalize knowledge-driven decision making in the drug development process. Pharmacometrics is dependent on knowledge discovery, the application of informative graphics, understanding of biomarkers/surrogate endpoints, and knowledge creation (7–10). When applied to drug development, pharmacometrics often involves the development or estimation of pharmacokinetic, pharmacodynamic, pharmcodynamic-outcomes linking, and disease progression models. These models can be linked and applied to competing study designs to aid in understanding the impact of varying dosing strategies, patient selection criteria, differing statistical methods, and different study endpoints. In the realm of pharmacotherapy, pharmacometrics can be employed to customize patient drug therapy through therapeutic drug monitoring and improved population dosing strategies. To contextualize the role of pharmacometrics in drug development and pharmacotherapy, it is important to examine the history of pharmacometrics. The growth of pharmacometrics informs much on its content and utility.

1.3 HISTORY OF PHARMACOMETRICS

1.3.1 Pharmacokinetics

Pharmacometrics begins with pharmacokinetics. As far back as 1847, Buchanan understood that the brain content of anesthetics determined the depth of narcosis and depended on the arterial concentration, which in turn was related to the strength of the inhaled mixture (11). Interestingly, Buchanan pointed out that rate of recovery was related to the distribution of ether in the body. Though there was pharmacokinetic (PK) work done earlier, the term pharmacokinetics was first introduced by F. H. Dost in 1953 in his text, Der Blutspeigel-Kinetic der Knozen-trationsablaufe in der Kreislauffussigkeit (12). The first use in the English language occurred in 1961 when Nelson published his “Kinetics of Drug Absorption, Distribution, Metabolism, and Excretion” (13). The exact word pharmacokinetics was not used in this publication.

In their classic work, the German scientists Michaelis and Menton published their equation describing enzyme kinetics in 1913 (14). This equation is still used today to describe the kinetics of drugs such as phenytoin. Widmark and Tandberg (15) published the equations for the one-compartment model in 1924 and in that same year Haggard (16) published his work on the uptake, distribution, and elimination of diethyl ether. In 1934 Dominguez and Pomerene (17) introduced the concept of volume of distribution, which was defined as “the hypothetical volume of body fluid dissolving the substance at the same concentration as the plasma. In 1937 Teorrel (18) published a seminal paper that is now considered the foundation of modern pharmacokinetics. This paper was the first physiologically based PK model, which included a five-compartment model. Bioavailability was introduced as a term in 1945 by Oser and colleagues (19), while Lapp (20) in France was working on excretions kinetics.

Polyexponential curve fitting was introduced by Perl in 1960 (21). The use of analog computers for curve fitting and simulation was introduced in 1960 by two groups of researchers (22, 23).

The great growth period for pharmacokinetics was from 1961 to 1972, starting with the landmark works of Wagner and Nelson (24). In 1962 the first symposium with the title pharmacokinetics, “Pharmacokinetik und Arzniemitteldosireung,” was held.

Clinical pharmacokinetics began to be recognized in the 1970s, especially in two papers by Gibaldi and Levy, “Pharmacokinetics in Clinical Practice,” in the Journal of the American Medical Association in 1976 (25). Of further importance that same year was a paper by Koup et al. (26) on a system for the monitoring and dosing of theophylline based on pharmacokinetic principles.

Rational drug therapy is based on the assumption of a causal relationship between exposure and response. There pharmacokinetics has great utility when linked to pharmacodynamics and the examination of pharmacodynamics is of paramount importance.

1.3.2 Pharmacodynamics

In 1848 Dungilson (27) stated that pharmacodynamics was “a division of pharmacology which considers the effects and uses of medicines.” This definition has been refined and restricted over the centuries to a more useful definition, where “pharmacokinetics is what the body does to the drug; pharmacodynamics is what the drug does to the body” (28, 29). More specifically, pharmacodynamics was best defined by Derendorf et al. (28) as “a broad term that is intended to include all of the pharmacological actions, pathophysiological effects and therapeutic responses both beneficial or adverse of active drug ingredient, therapeutic moiety, and/or its metabolite(s) on various systems of the body from subcellular effects to clinical outcomes.” Pharmacodynamics most often involves mathematical models, which relate some concentration (serum, blood, urine) to a physiologic effect (blood pressure, liver function tests) and clinical outcome (survival, adverse effect). The pharmacodynamic (PD) models have been described as fixed, linear, log-linear, Emax, sigmoid Emax, and indirect PD response (29–31).

The indirect PD response model has been a particularly significant contribution to PD modeling (30, 31). It has great utility because it is more mechanistic than the other models, does not assume symmetry of the onset and offset, and incorporates the impact of time in addition to drug concentration, thus accounting for a delay in onset and offset of the effect. For these models the maximum response occurs later than the time of occurrence of the maximum plasma concentration because the drug causes incremental inhibition or stimulation as long as the concentration is “high enough.” After the response reaches the maximum, the return to baseline is a function of the dynamic model parameters and drug elimination. Thus, there is a response that lasts beyond the presence of effective drug levels because of the time needed for the system to regain equilibrium. Whenever possible, these mechanistic models should be employed for PD modeling and several dose levels should be employed for accurate determination of the PD parameters, taking into consideration the resolution in exposure between doses.

The dependent variables in these PD models are either biomarkers, surrogate endpoints, or clinical endpoints. It is important to differentiate between these and to understand their relative importance and utility.

1.3.3 Biomarkers

The importance of biomarkers has been noted in recent years and is evidenced by the formation of The Biomarkers Definitions Working Group (BDWG) (32). According to the BDWG, a biomarker is a “characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic process or pharmacologic responses to a therapeutic intervention.” Biomarkers cannot serve as penultimate clinical endpoints in confirming clinical trials; however, there is usually considered to be some link between a biomarker based on prior therapeutic experience, well understood physiology or pathophysiology, along with knowledge of the drug mechanism. Biomarkers often have the advantage of changing in drug therapy prior to the clinical endpoint that will ultimately be employed to determine drug effect, thus providing evidence early in clinical drug development of potential efficacy or safety.

A surrogate endpoint is “a biomarker that is intended to substitute for a clinical endpoint. A surrogate endpoint is expected to predict clinical benefit, harm, lack of benefit, or lack of harm based on epidemiologic, therapeutic, pathophysiologic or other scientific evidence” (32). Surrogate endpoints are a subset of biomarkers such as viral load or blood pressure. All surrogate endpoints are biomarkers. However, few biomarkers will ever become surrogate endpoints. Biomarkers are reclassified as surrogate endpoints when a preponderance of evidence indicates that changes in the biomarker correlate strongly with the desired clinical endpoint.

A clinical endpoint is “a characteristic or variable that reflects how a patient feels, functions or survives. It is a distinct measurement or analysis of disease characteristics observed in a study or a clinical trial that reflect the effect of a therapeutic intervention. Clinical endpoints are the most credible characteristics used in the assessment of the benefits and risks of a therapeutic intervention in randomized clinical trials.” There can be problems with using clinical endpoints as the final measure of patient response because a large patient sample size may be needed to determine drug effect or the modification in the clinical endpoint for a drug may not be detectable for several years after the initiation of therapy.

There are several ways in which the discovery and utilization of biomarkers can provide insight into the drug development process and patient care. Biomarkers can identify patients at risk for a disease, predict patient response, predict the occurrence of toxicity, and predict exposure to the drug. Given these uses, biomarkers can also provide a basis for selecting lead compounds for development and can contribute knowledge about clinical pharmacology. Therefore, biomarkers have the potential to be one of the pivotal factors in drug development—from drug target discovery through preclinical development to clinical development to regulatory approval and labeling information, by way of pharmacokinetic/pharmacodynamic–outcomes modeling with clinical trial simulations.

1.3.4 PK/PD Link Modeling

PK/PD modeling provides the seamless integration of PK and PD models to arrive at an enlightened understanding of the dose–exposure–response relationship. PK/PD modeling can be done either sequentially or simultaneously (33, 34). Sequential models estimate the pharmacokinetics first and fix the PK parameters, generating concentrations corresponding to some PD measurement. Thus, the pharmacodynamics is conditioned on the PK data or on the estimates of the PK parameters. Simultaneous PK/PD modeling fits all the PK and PD data at once and the PK and PD parameters are considered to be jointly distributed. When simultaneous modeling is done, the flow of information is bidirectional. Both of these approaches appear to provide similar results (33, 35). However, it is important to note that PD measurements are usually less precise than PK measurements and using sequential PK and PD modeling may be the preferred approach in most instances.

PK and PD can be linked directly through a measured concentration that is directly linked to an effect site. The direct link model does not work well when there is a temporal relationship between a measured concentration and effect, as when hysteresis is present. When this is the case, an indirect link between the measured concentration and effect must be accounted for in the model. This has been done in general by the construction of an effect compartment, where a hypothetical effect compartment is linked to a PK compartment. Here the effect compartment is very small and thus has negligible impact on mass balance with a concentration time course in the effect compartment. The effect is related to the concentration in the effect compartment, which has a different time course than the compartment where drug concentrations are actually measured. In addition to the effect compartment approach to account for temporal concentration–effect relationships, the indirect response concept has found great utility.

PK and PD have been linked by many models, sometimes mechanistic and at other times empirical. These models are especially useful in better understanding the dose strategy and response, especially when applied by stochastic simulation. The population approach can be applied to multiple types of data—for example, both intensely and sparsely sampled data and preclinical to Phase 4 clinical data—and therefore has found great utility when applied to PK/PD modeling.

1.3.5 Emergence of Pharmacometrics

The term pharmacometrics first appeared in the literature in 1982 in the Journal of Pharmacokinetics and Biopharmaceutics (36). At that time, the journal made a commitment to a regular column dealing with the emerging discipline of pharmacometrics, which was defined as “the design, modeling, and analysis of experiments involving complex dynamic systems in the field of pharmacokinetics and biopharmaceutics … concerning primarily data analysis problems with such models.” They went on to say that problems with study design, determination of model identifiability, estimation, and hypothesis testing would be addressed along with identifying the importance of graphical methods. Since this time, the importance of pharmacometrics in optimizing pharmacotherapy and drug development has been recognized, and several graduate programs have been established that emphasize pharmacometrics (37). Pharmacometrics is therefore the science of developing and applying mathematical and statistical methods to (a) characterize, understand, and predict a drug’s pharmacokinetic and pharmacodynamic behavior; (b) quantify uncertainty of information about that behavior; and (c) rationalize data-driven decision making in the drug development process and pharmacotherapy. In effect, pharmacometrics is the science of quantitative pharmacology.

1.3.6 Population Modeling

A major development in pharmacometrics was the application of population methods to the estimation of PM parameters (38). With the advent of population approaches, one could now obtain estimates of PM parameters from sparse data from large databases and also obtain improved estimates of the random effects (variances) in the parameters of interest. These models first found great applicability by taking massive amounts of data obtained during therapeutic drug monitoring (TDM) from which typical values and variability of PK parameters were obtained. The parameters once estimated were applied to TDM to estimate initial doses and, using Bayesian algorithms, to estimate a patient’s individual PK parameters to optimize dosing strategies. Population methods have become widely accepted to the extent that a Guidance for Industry has been issued by the United States Food and Drug Administration (FDA) on population pharmacokinetics. Population methods are applied to pharmacokinetics, pharmacodynamics, and models linking biomarkers to clinical outcomes (39).

1.3.7 Stochastic Simulation

Stochastic simulation was another step forward in the arena of pharmacometrics. Simulation had been widely used in the aerospace industry, engineering, and econometrics prior to its application in pharmacometrics. Simulation of clinical trials first appeared in the clinical pharmacology literature in 1971 (40) but has only recently gained momentum as a useful tool for examining the power, efficiency, robustness, and informativeness of complex clinical trial structure (41).

A major impetus promoting the use of clinical trial simulation was presented in a publication by Hale et al. (41), who demonstrated the utility of simulating a clinical trial on the construction of a pivotal study targeting regulatory approval. The FDA has shown interest in clinical trial simulation to the extent that it has said: “Simulation is a useful tool to provide convincing objective evidence of the merits of a proposed study design and analysis. Simulating a planned study offers a potentially useful tool for evaluating and understanding the consequences of different study designs” (39). While we often think of clinical trial simulation as a way for the drug sponsor to determine optimal study structure, it is also a way for the FDA to determine the acceptability of a proposed study protocol. Simulation serves as a tool not only to evaluate the value of a study structure but also to communicate the logical implications of a PM model, such as the logical implication of competing dosing strategies for labeling.

The use and role of a simulated Phase 3 safety and efficacy study is still under discussion as confirmatory evidence at the FDA; however, a simulation of this type can serve as supportive evidence for regulatory review (4, 5). It is likely that at some time in the future knowledge of a disease’s pathophysiology plus knowledge of drug behavior and action will be applied to a group of virtual patients as the pivotal Phase 3 study for approval by a clinical trial simulation. Stochastic simulation should result in more powerful, efficient, robust, and informative clinical trials; therefore, more can be learned, and confirming efficacy will be more certain as stochastic simulation is applied to the drug development process.

1.3.8 Learn–Confirm–Learn Process

Drug development has traditionally been empirical and proceeded sequentially from preclinical through clinical Phases 1 to 3. Sheiner (42) first proposed a major paradigm shift in drug development away from an empirical approach to the learn–confirm approach based on Box’s inductive versus deductive cycles (43). Williams et al. (6, 44) and Ette et al. (45) have since revised this process to the learn–confirm–learn approach because of their emphasis on the fact that learning continues throughout the entire drug development process. The learn–confirm–learn process contends that drug development ought to consist of alternate cycles of learning from experience and then confirming what has been learned but that one never proposes a protocol where learning ceases.

In the past, Phases 1 and 2a have been considered the learning phases of drug development because the primary objectives are to determine the tolerated doses and the doses producing the desired therapeutic effect. Phase 2 has targeted how to use the drug in the target patient population, determining the dose strategy and proof of concept. Phase 3 has focused on confirming efficacy and demonstrating a low incidence of adverse events, where if the ratio of benefit to risk is acceptable then the drug is approved. An encouraging outcome in these early cycles results in investment in the costly Phase 2b and 3 studies. However, even in the confirming stages of drug development, one ought to continue to be interested in learning even though confirming is the primary objective of a study; that is, all studies should incorporate an opportunity for learning in the protocol. Therefore, the process has been renamed “learn–confirm–learn”.

Learning and confirming have quite different goals in the process of drug development. When a trial structure optimizes confirming, it most often imposes some restrictions on learning; for example, patient enrollment criteria are limited, thus limiting one’s ability to learn about the agent in a variety of populations. For example, many protocols limit enrollment to patients with creatinine clearances above a certain number (e.g., 50 mL/min). If this is done, one cannot learn how to use such a drug in patients with compromised renal function. Empirical commercial drug development has in general focused on confirming because it provides the necessary knowledge for regulatory approval, addressing the primary issue of efficacy. The downside of the focus on confirming is that it has led to a lack of learning, which can result in a dysfunctional drug development process and less than optimal pharmacotherapy postapproval.

PM modeling focuses on learning, where the focus is on building a model that relates dosing strategy, exposure, patient type, prognostic variables, and more to outcomes. Here the three-dimensional response surface is built (42) (see Section 1.3.9.2). PM models are built to define the response surface to increase the signal-to-noise ratio, which will be discussed shortly. The entire drug development process is an exercise of the learn–confirm–learn paradigm.

1.3.9 Exposure–Response Relationship

The importance of elucidating the exposure–response relationship must be emphasized. When the term exposure is used, one is usually referring to dose or variables related to concentration such as area under the concentration–time curve (AUC), maximum concentration (Cmax), minimum concentration (Cmin), or average concentration (Cave) in some biological specimen such as serum, urine, cerebral spinal fluid, or sputum. It is worth noting that dose is a very weak surrogate of exposure, especially where there is no proportionality between dose and AUC or Cmax. Response is a measure of the effect of a drug either therapeutic or adverse, such as blood pressure, cardiac index, blood sugar, survival, liver function, or renal function.

1.3.9.1 Regulatory Perspective

The FDA document, Guidance for Industry: Exposure–Response Relationships—Study Design, Data Analysis, and Regulatory Applications, has commented extensively on the exposure–response relationship (46). It states: “Exposure–response information is at the heart of any determination of the safety and effectiveness of drugs…. In most cases, however, it is important to develop information on the population exposure–response relationships for favorable and unfavorable effects and information on how, and whether, exposure can be adjusted for various subsets of the population.” The FDA recognizes the value of exposure–response knowledge to support the drug development process and to support the determination of safety and efficacy. In this document it stated that “dose–response studies can, in some cases, be particularly convincing and can include elements of consistency that, depending on the size of the study and outcome, can allow reliance on a single clinical efficacy study as evidence of effectiveness.” The exposure–response relationship was further refined in the defining of the response surface.

1.3.9.2 Response Surface

A significant development of the exposure–response concept was the proposing of the response surface. Sheiner (42) first proposed the pharmacological response surface as a philosophical framework for development of PM models. The response surface can be thought of as three dimensional: on one axis are the input variables (dose, concurrent therapies, etc.); on the second axis are the important ways that patients can differ from one another that affect the benefit to toxicity ratio; and the final axis represents the benefit to toxicity ratio. Sheiner stated: “the real surface is neither static, nor is all the information about the patient conveyed by his/her initial prognostic status, nor are exact predictions possible. A realistically useful response … must include the elements of variability, uncertainty and time …” Thus, the primary goal of the response model is to define the complex relationship between the input profile and dose magnitude when comparing beneficial and harmful pharmacological effects and how this relationship varies between patients. For rational drug use and drug development, the response surface must be mapped. PM models, once developed and validated, allow extrapolation beyond the immediate study subjects to allow application to other patients from whom the model was not derived. These predictive models permit the evaluation of outcomes of competing dosing strategies in patients who have not received the drug and therefore aid in constructing future pivotal studies. One important aspect of PM models employed in mapping the response surface is that they increase the signal-to-noise ratio in a data set because they translate some of the noise into signal. This is important because when we are converting information (data) into knowledge, the knowledge is proportional to the signal-to-noise ratio.

1.3.10 PM Knowledge Discovery

It is our experience that most drug development programs are data rich and knowledge poor. This occurs when data are collected but all of the knowledge hidden in the data set is not extracted. In reality, huge amounts of data are generated from modern clinical trials, observational studies, and clinical practice, but at the same time there is an acute widening gap between data collection, knowledge, and comprehension. PM knowledge discovery applies 13 comprehensive and interwoven steps to PM model development and communication and relies heavily on modern statistical techniques, modern informative graphical applications, and population modeling (8, 9) (see Chapter 14). The more that is known about a drug the better will be its application to direct patient care, and the more powerful and efficient will be the development program. To this end, PM knowledge discovery is the best approach to extracting knowledge from data and has been defined and applied to PM model development.

1.3.11 PM Knowledge Creation

Most often, knowledge discovery provides the foundation for knowledge creation and is simply the initial step in the application of PM knowledge (10). The discovered knowledge can be used to synthesize new data or knowledge, or to supplement existing data. PM knowledge creation has something in common with knowledge discovery its intent to understand and better define the response surface. Data supplementation deals with the use of models on available data to generate supplemental data that would be used to characterize a targeted unexplored segment of the response surface (47).

1.3.12 Model Appropriateness

Model appropriateness brought a new epistemology to PM model estimation and development (48) (see Chapter 8). The pivotal event in establishing model appropriateness is stating the intended use of the model. The entire process requires the stating of the intended use of the model, classifying the model as either descriptive or predictive, evaluating the model, and validating the model if the model is to be used for predictive purposes. Descriptive models are not intended to be applied to any external population—that is, their sole purpose is to gain knowledge about the drug in the population studied. Predictive models are intended to be applied to subjects from whom the model was not derived or estimated. Predictive models require a higher degree of correspondence to the external universe than descriptive models and therefore require validation.