Applied Statistics in the Pharmaceutical Industry978-1-4757-3466-9/1.pdf · Applied Statistics in...

Applied Statistics in the Pharmaceutical Industry

Springer Science+Business Media, LLC

Steven P. Millard Andreas Krause Editors

Applied Statistics in the Pharmaceutical Industry

With Case Studies Using S-PLUS

With 131 Illustrations

" Springer

Steven P. Millard Probability, Statistics & Information 7723 44th Avenue NE Seattle, WA 98115-5117 USA

Andreas Krause Novartis Pharma AG Biostatistics P.O. Box 4002 Basel Switzerland

Library of Congress Cataloging-in-Publication Data Applied statistics in the pharmaceutical industry : with case studies using S-PLus I editors, Steven P. Millard, Andreas Krause.

p. cm. Includes bibliographical references and index. ISBN 978-1-4419-3166-5 ISBN 978-1-4757-3466-9 (eBook) DOI 10.1007/978-1-4757-3466-9 1. Drugs-Research-Statistical methods. I. MilIard, Steven P. II. Krause, Andreas.

RS122 .A66S 2001 615'. 19'0727---dc21 00-053767

Printed on acid-free paper.

S-PLus is a registered trademark of Insightful Corporation. @ 2001 Springer Science+Business Media New York Originally published by Springer-Verlag New Y orle, Inc. in 2001 Softcover reprint ofthe hardcover Ist edition 2001

A1l rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieva1, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter deve10ped is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if The former are not especially identified, is not to be taken as a sign that such names, as understood By the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

Production managed by Timothy Taylor; manufacturing supervised by Jerome Basma. Camera-ready copy prepared from the authors' JnEX2e and Microsoft Word files.

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ISBN 978-1-4419-3166-5 SPIN 10716954

Preface Each year, hundreds of new drugs are approved for the marketplace. The ap­proval of a single new drug is the result of years of screening tens of thousands of compounds, performing preclinical research on their effects, and designing, implementing, and analyzing the results of clinical trials. Statisticians are in­volved in every phase of this process. Between the years 1960 and 2000, the number of statisticians working in the pharmaceutical industry grew from less than 100 to over 2500.

This book provides a general (but not exhaustive) guide to statistical meth­ods used in the pharmaceutical industry, and illustrates how to use S-PLUS to implement these methods. Specifically, each chapter in this book:

• Illustrates statistical applications in the pharmaceutical industry. • Illustrates how the statistical applications can be carried out using

S-PLUS (each chapter except the first contains an appendix with S-PLUS code).

• Illustrates why S-PLUS is a useful software package for carrying out these applications.

• Discusses the results and implications of a particular application.

The target audience for this book is very broad, including:

• Graduate students in biostatistics. • Statisticians who are involved in the industry as research scientists,

regulators, academics, and/or consultants who want to know more about how to use S-PLUS and learn about other subfields within the industry that they may not be familiar with.

• Statisticians in other fields who want to know more about statisti-cal applications in the pharmaceutical industry.

The data and code from each chapter are available on the following web site: http://www2.active.ch/-krause.aldoc/statistics-in-pharmal. (Due to confidenti­ality, the raw data are not available for some chapters.)

Part 1 of this book includes Chapter 1, which is an introductory chapter ex­plaining the history and current state of statistics in the drug development proc­ess. Following Chapter 1, this book is divided into six more sections that follow the sequence of the drug development process (see Figure 1.2). Part 2 encom­passes basic research and preclinical studies and Chapter 2 within this section discusses one-factor comparative studies. Part 3 covers preclinical safety as­sessment. Chapter 3 discusses analysis of animal carcinogenicity data, and Chapter 4 toxicokinetic and pharmacokinetic data. Part 4 involves Phase I studies. Chapter 5 discusses the analysis of pharmacokinetic data in humans, Chapter 6 illustrates graphical presentations of single patient results, Chapter 7 explains the design and analysis of Phase I oncology trials, Chapter 8 discusses

vi Preface

the analysis of analgesic trials, Chapter 9 points out problems with patient com­pliance and how this affects pharmacokinetic analysis, and Chapter 10 discusses the classic 2,2,2 crossover design. Part 5 includes chapters on Phase IT and ill clinical trials. Chapter 11 discusses power and sample size calculations, Chapter 12 compares how S-PLUS and SAS handle analysis of variance, Chapter 13 ex­plains a technique for sample size reestimation, Chapter 14 discusses permuta­tion tests for Phase ill clinical trials, Chapter 15 discusses comparing two treat­ments in a Phase ill clinical trial, and Chapter 16 covers meta-analysis of clini­cal trials. Part 6 covers Phase IV studies, and includes Chapter 17 on the analy­sis of health economic data. Finally, Part 7 encompasses manufacturing and production. Chapter 18 discusses the decimal reduction time of a sterilization process, and Chapter 19 covers acceptance sampling plans by attributes.

A Note about S-PLUS Versions The chapters in this book were written when the current versions of S-PLUS were Version 3.4 and then 5.1 for UNIX, and Version 4.5 and then 2000 for Windows. The Windows version of S-PWS includes a graphical user interface (GUI) with pull-down menus and buttons. By the time this book is published, both S-PWS 6.0 for UNIX and S-PWS 6.0 for Windows will be available, and both of these versions of S-PWS will have GUIs. All of the chapters in this book, however, illustrate how to use S-PLUS by writing S-PLUS commands and functions, rather than using pull-down menus.

Typographic Conventions Throughout this book, S-PWS commands and functions are displayed in a ftxed­width font, for example: summary (aov .psize). Within chapters, S-PLUS commands are preceded with> (the "greater than" sign), which is the default S-PWS prompt. Rather than use the S-PWS continuation prompt (+ by default) for continuation lines, we follow Venables and Ripley (1999) and use indenta­tion instead. Within appendices, S-PWS prompts are omitted.

Companion Web Site for This Book For more information about the authors, datasets, software, and related links, please refer to http://www2.active.ch/-krause.aldoc/statistics-in-pharmal.

Information on S-PLUS

For infonnation on S-PLUS, please contact Insightful Corporation:

Insightful Corporation 1700 Westlake Ave N, Suite 500 Seattle, W A 98lO9-3044 USA 800-569-0123 sales@insightful.com www.insightful.com

Insightful Corporation Knightway House Park Street Bagshot, Surrey GU195AQ United Kingdom +44 1276 452 299 sales@uk.insightful.com www.uk.insightful.com

Acknowledgments In the Spring of 1997, one of us (Steve) taught a course on using S-PLUS at two different branches of Merck Research Laboratories. The course was organized by Charles Liss and Thomas Bradstreet of Merck, and Charles (Chuck) Taylor of MathSoft, Inc. (now Insightful Corporation), and revolved around using S-PLUS to analyze three different data sets from the pharmaceutical industry. That course was the seed for this book.

Thomas Bradstreet put Steve in touch with several statisticians and provided early guidance on the scope and direction of this book. Andreas, who works in the pharmaceutical industry, had already published a book with Melvin Olson on using S-PLUS (The Basics of Sand S-PLUS), and therefore knew several people who became contributors to this book. Weare grateful to all of the authors who generously donated their time and efforts to writing chapters for this book. We would also like to thank John Kimmel for his help and guidance throughout the process of editing this book. Steve Millard would like to thank Aleksandr Aravkin, Sam Coskey, and Jeannine Silkey for their help in formatting many of the chapters. Finally, we would like to thank all of the statisticians in the phar­maceutical industry; you have devoted yourselves to improving the health of the world.

Contents Preface ........................................................................................................ v A Note About S-PLUS Versions ................................................................ vii Typographic Conventions ......................................................................... vii Companion Web Site for This Book ........................................................ vii Information on S-PLUS ............................................................................. ix Acknowledgments ..................................................................................... xi List of Contributors .................................................................................. xv

Part 1: Introduction .................................................................................... 1 1. Statistics and the Drug Development Process

Bruce Rodda, Steven P. Millard, and Andreas Krause ...................... 3

Part 2: Basic Research and Preclinical Studies ....................................... 15 2. One-Factor Comparative Studies

Bill Pikounis ..................................................................................... 17

Part 3: Pre-Clinical Safety Assessment .................................................... 41 3. Analysis of Animal Carcinogenicity Data

Hongshik Ahn and Ralph L. Kodell ................................................. 43 4. Analysis of Toxicokinetic and Pharmacokinetic Data from

Animal Studies Wherly P. Hoffman, Michael A. Heathman, James Z. Chou, and Darrel L. Allen ................................................ 75

Part 4: Phase I Studies ............................................................................ 107 5. Analysis ofPharmacokinetic Data

Ha Nguyen and Dhammika Amaratunga ....................................... 109 6. Graphical Presentation of Single Patient Results

Jiirgen Bock ................................................................................... 135 7. Graphical Insight and Data Analysis for the

2,2,2 Crossover Design Bill Pikounis, Thomas E. Bradstreet, and Steven P. Millard ......... 153

8. Design and Analysis of Phase I Trials in Clinical Oncology Axel Benner, Lutz Edler, and Gemot Hartung .............................. 189

9. Patient Compliance and its Impact on Steady State Pharmacokinetics Wenping Wang ............................................................................... 217

10. Analysis of Analgesic Trials Ene 1. Ette, Peter Lockwood, Raymond Miller, and Jaap Mandema ........................................................................ 237

xiv Contents

Part 5: Phase II and Phase III Clinical Trials ....................................... 267 11. Power and Sample Size Calculations

Jiirgen Bock ................................................................................... 269 12. Comparing Two Treatments in a Large Phase III Clinical Trial

Michaela Jahn ............................................................................... 299 13. Analysis of Variance: A Comparison Between SAS and S-Pws

Melvin Olson .................................................................................. 321 14. Permutation Tests for Phase III Clinical Trials

Vance Berger and Anastasia Ivanova ............................................ 349 15. Sample Size Reestimation

Wenping Wang and Andreas Krause ............................................. 375 16. Meta-Analysis of Clinical Trials

Keith O'Rourke, Beverley Shea, and George A. Wells .................. 397

Part 6: Phase IV Studies ......................................................................... 425 17. Analysis of Health Economic Data

John R. Cook, George W. Carides, and Erik J. Dasbach .............. 427

Part 7: Manufacturing and Production ................................................. 455 18. Evaluation of the Decimal Reduction Time ofa

Sterilization Process in Pharmaceutical Production Jeffrey Eisele, Mauro Gasparini, and Amy Racine ........................ 457

19. Acceptance Sampling Plans by Attributes Harry Yang and David Carlin ....................................................... 475

Index .......................................................................................................... 503

List of Contributors The following is a list of contact infonnation for chapter authors that was cur­rent at the time this book was published. Note that author affiliation may differ between what is listed here and what is listed at the beginning of a chapter. M­filiation listed at the beginning of a chapter reflects author affiliation at the time the chapter was written.

Hongshik Ahn Department of Applied Mathematics and Statistics

State University of New York Stony Brook, NY 11794-3600, USA hahn@ams.sunysb.edu

Darrel L. Allen Toxicology and Drug Disposition Research Laboratories

Lilly Research Laboratories 2001 West Main Street Indianapolis, IN 46140, USA allen_darreC/@lilly.com

Dhammika Amaratunga The R. W. Johnson Pharmaceutical Research Institute

OMPC Building, Room 2196, Route 202

P.D. Box 300 Raritan, NJ 08869-0602, USA damaratu@priusjnj.com

Axel Benner Biostatistics Unit German Cancer Research Center Heidelberg, Germany benner@dkfz-heidelberg.de

Vance Berger Biometry Research Group, DCP National Cancer Institute Executive Plaza North, Suite 344 Bethesda, MD 20892-7354, USA vance.berger@nih.gov

Jiirgen Bock F. Hoffmann-La Roche AG PDBS 74/0G-W, 4070 Basel, Switzerland juergen.bock@roche.com

Tom Bradstreet Department of Clinical

Pharmacology Statistics Merck Research Laboratories 10 Sentry Parkway, BL 3-2 Blue Bell, PA 19422, USA thomas_bradstreet@merck.com

George W. Carides Department of Health Economic

Statistics Merck Research Laboratories 10 Sentry Parkway, BL 2-3 Blue Bell, P A 19422, USA george_carides@merck.com

David Carlin MedImmune, Inc. 35 West Watkins Mill Road Gaithersburg, MD 20878, USA carlind@medimmune.com

James Z. Chou TAP Pharmaceutical Products Inc. 675 North Field Drive Lake Forest, IL 60045, USA james.chou@tap.com

xvi List of Contributors

JohnR. Cook Department of Health Economic

Statistics Merck Research Laboratories 10 Sentry Parkway, BL 2-3 Blue Bell, PA 19422, USA john300k@merck.com

Erik J. Dasbach Department of Health Economic

Statistics Merck Research Laboratories 10 Sentry Parkway, BL 2-3 Blue Bell, PA 19422, USA erik_dasbach@merck.com

Lutz Edler Biostatistics Unit German Cancer Research Center Heidelberg, Germany edler@dkft·de

Jeffrey Eisele Department of Biostatistics Novartis Pharma AG CH-4002 Basel, Switzerland jeffrey.eisele@Pharma.novartis.com

Ene I. Ette Clinical Pharmacology Vertex Pharmaceuticals, Inc. Cambridge, MA 02139, USA ette@vpharm.com

Mauro Gasparini Dipartimento di Matematica Politecnico di Torino 1-10129 Torino, Italy gasparin@calvino.polito.it

Gemot Hartung Oncological Center Mannheim Medical School Heidelberg, Germany gemot.hartung@med3.ma.uni-heidelberg.de

Michael A. Heathman Department of Pharmacokinetics and

Pharmacodynamics Lilly Research Laboratories 2001 West Main Street Indianapolis, IN 46140, USA heathman_michaeLa@lilly.com

Whedy P. Hoffman Division of Statistics and

Information Sciences Lilly Research Laboratories 2001 West Main Street Indianapolis, IN 46140, USA hoffman_wherly....P@lilly.com

Pulastasialvanova Department of Biostatistics School of Public Health, CB# 7400 University of North Carolina Chapel Hill, NC 27599-7400, USA aivanova@bios.unc.edu

Michaela Jahn F. Hoffmann-La Roche AG PDBS, Building 74, 4-W, 4070 Basel, Switzerland michaelajahn@roche.com

Ralph L. Kodell Division of Biometry and

Risk Assessment National Center for Toxicological Research

Food and Drug Administration Jefferson, AR 72079, USA rkodell@nctrjda.gov

Andreas Krause Novartis Pharma AG P.O. Box 4002 Basel Switzerland andreas.krause@pharma.novartis.com

Peter Lockwood Department of Pharmacokinetics, Dynamics and Metabolism

PfIZer Global Research and Development

2800 Plymouth Road Ann Arbor, MI48I05, USA peter.lockwood@pjizer.com

Jaap Mandema Pharsight Corporation 800 West El Camino Real, Suite 200 Mountain View, CA 94040, USA jaapm@pharsight.com

Steven P. Millard Probability, Statistics & Information 7723 44th Avenue NE Seattle, WA 98115-5117, USA smillard@probstatinfo.com

Raymond Miller Department of Pharmacokinetics,

Dynamics and Metabolism Pfizer Global Research and Development

2800 Plymouth Road Ann Arbor, MI48105, USA raymond.miller@pfizer.com

HaNguyen Global Medical Affairs Aventis Pharmaceuticals, Inc. P.o. Box 6800 Bridgewater, NJ 08807, USA ha.h.nguyen@aventis.com

Keith O'Rourke Clinical Epidemiology Unit and DepartmentofSurge~

Ottawa Hospital University of Ottawa Ottawa, Ontario K1 Y-4E9, Canada korourke@lri.ca

Melvin Olson Allergan, Inc. 2525 Dupont Drive Irvine, CA 92623-9534, USA olson_melvin@allergan.com

Bill Pikounis Biometrics Research Merck Research Laboratories 126 East Lincoln Avenue Mail Stop RY70-38 Rahway, NJ 07065-0900, USA v_bilCpikounis@merck.com

Amy Racine Department of Biostatistics Novartis Pharma AG CH-4002 Basel, Switzerland amy.racine@pharma.novartis.com

xvii

xviii List of Contributors

Bruce Rodda Health Services & Research Southwest Texas State University 601 University Drive San Marcos, TX 78666-4616, USA bruce]odda@msn.com

Beverley Shea Clinical Epidemiology Unit and Department of Medicine

Ottawa Hospital University of Ottawa Ottawa, Ontario Kl Y-4E9, Canada bshea@lri.ca

Wenping Wang Pharsight Corporation 5520 Dillard Drive, Suite 210 Cary, NC 27511, USA wwang@pharsight.com

George A. Wells Department of Epidemiology and

Community Medicine University of Ottawa Ottawa, Ontario Kl Y-4E9, Canada gwells@uottawa.ca

Harry Yang MedImmune, Inc. 35 West Watkins Mill Road Gaithersburg, MD 20878, USA yangh@medimmune.com