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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Statistics in Practice
- Sprache: Englisch
Statistical Issues in Drug Development
The revised third edition of Statistical Issues in Drug Development delivers an insightful treatment of the intersection between statistics and the life sciences. The book offers readers new discussions of crucial topics, including cluster randomization, historical controls, responder analysis, studies in children, post-hoc tests, estimands, publication bias, the replication crisis, and many more.
This work presents the major statistical issues in drug development in a way that is accessible and comprehensible to life scientists working in the field, and takes pains not to gloss over significant disagreements in the field of statistics, while encouraging communication between the statistical and life sciences disciplines. In addition to new material on topics like invalid inversion, severity, random effects in network meta-analysis, and explained variation, readers will benefit from the inclusion of:
- A thorough introduction to basic topics in drug development and statistics, including the role played by statistics in drug development
- An exploration of the four views of statistics in drug development, including the historical, methodological, technical, and professional
- An examination of debatable and controversial topics in drug development, including the allocation of treatments to patients in clinical trials, baselines and covariate information, and the measurement of treatment effects
Perfect for life scientists and other professionals working in the field of drug development, Statistical Issues in Drug Development is the ideal resource for anyone seeking a one-stop reference to enhance their understanding of the use of statistics during drug development.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Series Page
Title Page
Copyright Page
Dedication Page
Preface to the Third Edition
References
Preface to the Second Edition
References
Preface to the First Edition
Acknowledgements
1 Introduction
1.1 DRUG DEVELOPMENT
1.2 THE ROLE OF STATISTICS IN DRUG DEVELOPMENT
1.3 THE OBJECT OF THIS BOOK
1.4 THE AUTHOR'S KNOWLEDGE OF STATISTICS IN DRUG DEVELOPMENT
1.5 THE READER AND HER OR HIS KNOWLEDGE OF STATISTICS
1.6 HOW TO USE THE BOOK
References
Part 1: Four Views of Statistics in Drug Development
2 A Brief and Superficial History of Statistics for Drug Developers
2.1 INTRODUCTION
2.2 EARLY PROBABILISTS
2.3 JAMES BERNOULLI (1654–1705)
2.4 JOHN ARBUTHNOTT (1667–1753)
2.5 THE MATHEMATICS OF PROBABILITY IN THE LATE SEVENTEENTH, THE EIGHTEENTH, AND EARLY NINETEENTH CENTURIES
2.6 THOMAS BAYES (1701–1761)
2.7 ADOLPHE QUETELET (1796–1874)
2.8 GEORGE BIDDELL AIRY (1801–1892)
2.9 FRANCIS GALTON (1822–1911)
2.10 KARL PEARSON (1857–1936)
2.11 ‘STUDENT’ (1876–1937)
2.12 R.A. FISHER (1890–1962)
2.13 MODERN MATHEMATICAL STATISTICS
2.14 MEDICAL STATISTICS
2.15 STATISTICS IN CLINICAL TRIALS TODAY
2.16 THE CURRENT DEBATE
2.17 A LIVING SCIENCE
2.18 FURTHER READING
References
3 Design and Interpretation of Clinical Trials as Seen by a Statistician
3.1 PREFATORY WARNING
3.2 INTRODUCTION
3.3 DEFINING EFFECTS
3.4 PRACTICAL PROBLEMS IN USING THE COUNTERFACTUAL ARGUMENT
3.5 REGRESSION TO THE MEAN
3.6 CONTROL IN CLINICAL TRIALS
3.7 RANDOMIZATION
3.8 BLINDING
3.9 USING CONCOMITANT OBSERVATIONS
3.10 MEASURING TREATMENT EFFECTS
3.11 DATA GENERATION MODELS
3.12 IN CONCLUSION
3.13 FURTHER READING
References
4 Probability, Bayes, P‐values, Tests of Hypotheses and Confidence Intervals
4.1 INTRODUCTION
4.2 AN EXAMPLE
4.3 ODDS AND SODS
4.4 THE BAYESIAN SOLUTION TO THE EXAMPLE
4.5 WHY DON'T WE REGULARLY USE THE BAYESIAN APPROACH IN CLINICAL TRIALS?
4.6 A FREQUENTIST APPROACH
4.7 HYPOTHESIS TESTING IN CONTROLLED CLINICAL TRIALS
4.8 SIGNIFICANCE TESTS AND P‐VALUES
4.9 CONFIDENCE INTERVALS AND LIMITS AND CREDIBLE INTERVALS
4.10 SOME BAYESIAN CRITICISM OF THE FREQUENTIST APPROACH
4.11 DECISION THEORY
4.12 CONCLUSION
4.13 FURTHER READING
References
5 The Work of the Pharmaceutical Statistician
5.1 PREFATORY REMARKS
5.2 INTRODUCTION
5.3 IN THE BEGINNING
5.4 THE TRIAL PROTOCOL
5.5 THE STATISTICIAN'S ROLE IN PLANNING THE PROTOCOL
5.6 SAMPLE SIZE DETERMINATION
5.7 OTHER IMPORTANT DESIGN ISSUES
5.8 RANDOMIZATION
5.9 DATA COLLECTION PREVIEW
5.10 PERFORMING THE TRIAL
5.11 DATA ANALYSIS PREVIEW
5.12 ANALYSIS AND REPORTING
5.13 OTHER ACTIVITIES
5.14 STATISTICAL RESEARCH
5.15 FURTHER READING
References
Part 2: Statistical Issues
6 Allocating Treatments to Patients in Clinical Trials
6.1 BACKGROUND
6.2 ISSUES
References
6.A Appendix
7 Baselines and Covariate Information
7.1 BACKGROUND
7.2 ISSUES
References
7.A Appendix
8 The Measurement of Treatment Effects
8.1 BACKGROUND
8.2 ISSUES
References
8.A Appendix
9 Demographic Subgroups :
9.1 BACKGROUND
9.2 ISSUES
References
9.A Appendix
10 Multiplicity
10.1 BACKGROUND
10.2 ISSUES
References
10.A Appendix
11 Intention‐to‐Treat, Missing Data and Related Matters
11.1 BACKGROUND
11.2 ISSUES
References
11.A Appendix
12 One‐Sided and Two‐Sided Tests and Other Issues to Do with Significance and P‐values
12.1 BACKGROUND
12.2 ISSUES
References
13 Determining the Sample Size
13.1 BACKGROUND
13.2 ISSUES
References
14 Multicentre Trials
14.1 BACKGROUND
14.2 ISSUES
References
14.A TECHNICAL APPENDIX
15 Active Control Equivalence Studies
15.1 BACKGROUND
15.2 ISSUES
References
15.A TECHNICAL APPENDIX
16 Meta‐Analysis
16.1 BACKGROUND
16.2 ISSUES
References
16.A TECHNICAL APPENDIX
17 Cross‐Over Trials
17.1 BACKGROUND
17.2 ISSUES
References
18 n‐of‐1 Trials
18.1 BACKGROUND
18.2 ISSUES
References
19 Sequential and Flexible Trials
19.1 BACKGROUND
19.2 ISSUES
References
20 Dose‐Finding
20.1 BACKGROUND
20.2 ISSUES
References
21 Concerning Pharmacokinetics and Pharmacodynamics
21.1 BACKGROUND
21.2 ISSUES
References
22 Bioequivalence Studies
22.1 BACKGROUND
22.2 ISSUES
References
23 Safety Data, Harms, Drug Monitoring and Pharmaco‐Epidemiology
23.1 BACKGROUND
23.2 ISSUES
References
24 Pharmaco‐economics and Portfolio Management
24.1 BACKGROUND
24.2 ISSUES
References
25 Concerning Pharmacogenetics, Pharmacogenomics and Personalized Medicine
25.1 BACKGROUND
25.2 ISSUES
References
25.A TECHNICAL APPENDIX
Glossary
INTRODUCTION
References
Index
Wiley Series in Statistics in Practice
End User License Agreement
List of Tables
Chapter 3
Table 3.1 Road sites in Lothian region cross‐classified by number of accident...
Table 3.2 Distribution of patients by sex and treatment in a clinical trial i...
Table 3.3 Distribution of patients by sex and treatment in a second clinical ...
Chapter 4
Table 4.1 Prior probabilities and likelihoods for the CD player example.
Chapter 6
Table 6.1 Randomized blocks for a trial with two treatments and block sizes o...
Table 6.2 Completely randomized trial with two groups, 10 patients. Possible ...
Table 6.3 Example 6.1: Disposition of patients in a clinical trial of asthma ...
Table 6.4 Minimization scores for four types of patient who might be recruite...
Table 6.5 Number of patients allocated to the inferior treatment by trial des...
Table 6.6 A possible schedule for a trial with double dummy loading.
Chapter 7
Table 7.1 Numbers of patients in a clinical trial of asthma cross‐classified ...
Chapter 8
Table 8.1 Effect of a bronchodilator on absolute and log FEV
1
.
Chapter 9
Table 9.1 Numbers surviving and dying by treatment and disease severity toget...
Table 9.2 Numbers of patients in a clinical trial cross‐classified by treatme...
Chapter 10
Table 10.1 Null hypothesis cross‐classified by status (true or false) and dec...
Table 10.2 Possible frequencies for a two by two contingency table with margi...
Table 10.3 Possible outcome, probabilities, and one‐sided P‐values for contin...
Chapter 11
Table 11.1 Cross‐classification of two methods of analysis of 202 contrasts f...
Chapter 12
Table 12.1 Hypothetical 2 × 2 contingency table based on Yates (1984).
Chapter 14
Table 14.1 Summary of results for a binary outcome for a trial with two treat...
Chapter 15
Table 15.1 Possible 2 × 2 table giving patients by treatment and outcome for ...
Table 15.2 Possible 2 × 2 table giving patients by treatment and outcome for ...
Chapter 16
Table 16.1 Estimated treatment effects and differences in the effects of trea...
Table 16.2 Prediction (log‐odds scale) for all four possible cross‐classifica...
Chapter 17
Table 17.1 FEV
1
readings in ml for patients in a cross‐over trial.
Table 17.2 FEV
1
readings in ml for patients in a cross‐over trial. The case w...
Table 17.3 FEV
1
readings in ml for patients in a cross‐over trial. The case w...
Table 17.4 FEV
1
readings in ml for patients in a cross‐over trial. The case w...
Table 17.5 Weights for an AABB/BBAA cross‐over.
Table 17.6 Optimal weights and the variance inflation factor (q) for four mod...
Chapter 18
Table 18.1 Number of pairs of periodsY in which patients preferred amitriptyl...
Chapter 19
Table 19.1 Allocation of subjects in a smoking cessation trial.
Chapter 20
Table 20.1 Two possible designs for a first‐in‐man study using 40 subjects an...
Chapter 21
Table 21.1 Models and degrees of freedom for dose‐proportionality example of ...
Table 21.2 Trough‐to‐peak (T : P) ratios for felodipine for systolic blood pr...
Table 21.3 Models for dealing with values below the limit of quantitation con...
Chapter 23
Table 23.1 Survival times in months for 44 patients on a placebo‐controlled t...
Table 23.2 Illustration of
treatment emergent signs and symptoms
(
TESS
). In th...
Chapter 24
Table 24.1 Naive Summary of two games.
Table 24.2 Calculation of expected value for game 1.
Table 24.3 Calculation of expected value for game 2.
Table 24.4 Variances of treatment contrasts as a ratio of the variance for a ...
Chapter 25
Table 25.1 Patients in two cross‐over trials: case 1.
Table 25.2 Patients in two cross‐over trials: case 2.
Table 25.3 Patients in one cross‐over trial: case 1 or 2.
Table 25.4 Sources of variation in clinical trials.
Table 25.5 Identifiability and clinical trials.
Table 25.6 Possible contrasts for comparing genotypes.
Table 25.7 Percentage of patients by indication for whom treatment is ineffec...
List of Illustrations
Preface to the Third Edition
Figure P3.1 Words per chapters for the second and third editions.
Figure P3.2 Additional length of third edition compared to the second.
Preface to the Second Edition
Figure P.1 Comparison of the first and second editions in length.
Figure P.2 Additional length (in thousand of words) of the second edition co...
Chapter 2
Figure 2.1 Pascal's triangle.
Figure 2.2 Family tree of the Bernoullis (based on Boyer 1991). Nicholas sen...
Figure 2.3 Arbuthnott's figures for male and female christenings.
Figure 2.4 The sex ratio (male to females) for Arbuthnott's figures for chri...
Chapter 3
Figure 3.1 Mean accident rates in Lothian region in 1981–1982 classified by ...
Figure 3.2 Mean accident rates in Lothian region in 1979–1980 classified by ...
Figure 3.3 Bivariate distribution of accidents per site in Lothian region.
Figure 3.4 Simulated bivariate distribution of diastolic blood pressure in m...
Figure 3.5 Bivariate values for the members of the population defined as ‘hy...
Chapter 6
Figure 6.1 Efficiency of a randomized trial compared with a perfectly balanc...
Figure 6.2 Possible allocations as a function of the number of patients in e...
Figure 6.3 Schematic representation of a cut‐off design.
Figure 6.4 Variance of a symmetric cut‐off design as a function of the rando...
Chapter 7
Figure 7.1 Baselines and outcomes for FEV
1
in ml for a two‐parallel‐group tr...
Figure 7.2 200 simulated unadjusted confidence intervals for the treatment e...
Figure 7.3 200 simulated adjusted (by analysis of covariance) confidence int...
Figure 7.4 Variance of three estimators as a function of the correlation coe...
Figure 7.5 Time course of FEV
1
for a provocation test in asthma comparing a ...
Figure 7.6 The results from the experiment shown in 7.5 expressed as percent...
Chapter 8
Figure 8.1 Difference and proportionate difference in probability of success...
Figure 8.2 Proportion of patients showing an apparent mean bronchodilation o...
Figure 8.3 Pitman efficiency of a dichotomy compared to the original measure...
Figure 8.4 Response region (solid) for a common definition of response in hy...
Figure 8.5 Probability of response given a common definition of response in ...
Figure 8.6 A satisfactory surrogate endpoint. The difference between experim...
Figure 8.7 An unsatisfactory surrogate endpoint. Treatment improves the surr...
Figure 8.8 Theoretical and simulated probability of ‘response’ for headache ...
Figure 8.9 A simulated experiment with counterfactuals. The left‐hand panel ...
Chapter 9
Figure 9.1 Recruitment times of type II and type III discriminatory trials r...
Figure 9.2 Mean square error for two estimates of the treatment effect for w...
Figure 9.3 Mean square error for three estimators of the true treatment effe...
Figure 9.4 P‐values in each of two sub‐groups as a function of the proportio...
Figure 9.5 An equivalent plot to Figure 9.4 but with the overall P‐value now...
Chapter 10
Figure 10.1 Power of individual tests given the Bonferroni correction, as a ...
Figure 10.2 Disjunctive power (probability of at least one significant resul...
Figure 10.3 Conditional size of significance tests comparing five doses of a...
Figure 10.4 Possible P‐values for 2 × 2 tables with few good outcomes. There...
Figure 10.5 Possible P‐values for 2 × 2 tables with few bad outcomes. There ...
Chapter 11
Figure 11.1 Model for publication success. Positive studies are assumed to h...
Figure 11.2 Model for publication success. Positive studies are assumed to h...
Chapter 12
Figure 12.1 Illustration of the two‐trials rule and the pooled‐trials rule....
Chapter 13
Figure 13.1 Power as a function of clinically relevant difference for a two‐...
Figure 13.2 Scaled likelihood for null and alternative hypotheses for trials...
Figure 13.3 Scaled likelihood for null and alternative hypotheses for (a) 10...
Figure 13.4 Severity for various possible hypothesized treatment effects. Th...
Figure 13.5 The severity plot of Figure 13.4 with the corresponding 95% conf...
Figure 13.6 The confidence plot corresponding to Figure 13.4.
Chapter 14
Figure 14.1 Type III efficiency in a two‐centre trial. The number of patient...
Figure 14.2 Probability of at least one effect reversal as a function of the...
Figure 14.3 Power of a multi‐centre trial as a function of the number of cen...
Chapter 15
Figure 15.1 Possible point estimates and confidence intervals arising from a...
Figure 15.2 Illustration of hypotheses for proving equivalence.
Chapter 16
Figure 16.1 Probability that a patient chosen at random from the experimenta...
Figure 16.2 Distribution of FEV
1
measurements for two treatment groups.
Figure 16.3 Illustration of the sequential meta‐analysis paradox. Box 1 repr...
Figure 16.4 Estimates, standard errors and Wald statistics as a function of ...
Chapter 17
Figure 17.1 The two‐stage procedure.
Chapter 18
Figure 18.1 Distribution of a one‐sided P‐value given as a function of power...
Figure 18.2 Raw and shrunk probabilities of preferring treatment to placebo ...
Figure 18.3 The probability that the ratio of the largest variance to the sm...
Chapter 19
Figure 19.1 Continuous framework for a triangular test.
Figure 19.2 Nominal significance level at each look for three group sequenti...
Figure 19.3 Alpha‐spending functions for Pocock and O'Brien–Fleming approach...
Figure 19.4 Simulations of 10, 100, 1000 and 10 000 values from a normal dis...
Chapter 20
Figure 20.1 Fitted response surface showing predicted change from baseline i...
Figure 20.2 Efficacy, harm and net benefit as a function of dose.
Figure 20.3 A family of possible dose–response models that might be consider...
Figure 20.4 Stages of the MCP‐Mod approach.
Figure 20.5 Comparison of two designs in terms of variances of the contrast ...
Chapter 21
Figure 21.1 Concentration–time profile for a single dose of an oral formulat...
Figure 21.2 Illustration of the superposition principle.
Figure 21.3 Illustration of iteration towards steady‐state pharmacokinetics....
Figure 21.4 Pharmacodynamic response as a function of concentration for vari...
Figure 21.5 Pharmacodynamic time profiles as a function of dose.
Figure 21.6 Log‐likelihood contours as a function of mean μ and standar...
Chapter 22
Figure 22.1 Schematic representation of relationship between drug dosage D a...
Figure 22.2 Concentration–time profiles for a test and reference product.
Figure 22.3 Lower value and sum of values as a function of the upper value f...
Figure 22.4 Kirkwood, Westlake and Shuirmann (TOST) critical boundaries for ...
Figure 22.5 Schuirmann (TOST), Lindley and Neyman–Pearson critical values fo...
Figure 22.6 f
2
as a function of the root mean square difference in dissolut...
Chapter 23
Figure 23.1 Kaplan–Meier plots for survival in months in chronic active hepa...
Figure 23.2 Various functions plotted against time for the case of a constan...
Figure 23.3 Various functions plotted against time for the case of an increa...
Figure 23.4 Various probability functions for two subgroups with constant ha...
Figure 23.5 ‘The rule of three’ approximation and the exact value for the 95...
Chapter 24
Figure 24.1 Plot of the cost‐effectiveness for a trial comparing an experime...
Figure 24.2 Diagrammatic representation of a three‐stage project.
Figure 24.3 Probability of progressing to the next stage in a drug developme...
Figure 24.4 Probability of progressing in a drug development programmeCo...
Figure 24.5 Candidates for a portfolio.
Figure 24.6 Illustration of the value of genotyping patients. See text for e...
Chapter 25
Figure 25.1 Phenotypic response to genotypic score.
Figure 25.2 Illustration of Hardy–Weinberg equilibrium. Probability for each...
Figure 25.3 Observed response under two treatments in terms of percent incre...
Figure 25.4 Two cross‐over trials in 200 patients with asthma, with differen...
Figure 25.5 Comparison of single one‐degree‐of‐freedom t‐test and single two...
Figure 25.6 Illustration of two approaches to testing, each using two degree...
Figure 25.7 Multipliers for the three genotypic groups where a linear contra...
Figure 25.8 Variances of four possible estimators of phenotypic response. Th...
Figure 25.9 NNTs for the ten best selling drugs in the USA at the time.
Guide
Cover Page
Series Page
Title Page
Copyright Page
Dedication Page
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgements
Table of Contents
Begin Reading
Glossary
Index
Wiley Series in Statistics in Practice
Wiley End User License Agreement
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Statistics in Practice
Advisory Editor
Stephen SennEdinburgh, UK
Founding Editor
Vic BarnettNottingham Trent University, UK
Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study.
With sound motivation and many worked practical examples, the books show in down‐to‐earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title’s special topic area.
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A complete list of titles in this series appears at the end of the volume.
Statistical Issues in Drug Development
Third Edition
Stephen Senn
Consultant Statistician,Edinburgh, UK
This edition first published 2021© 2021 John Wiley & Sons Ltd
Edition HistoryJohn Wiley & Sons Ltd. (1e 1997, 2e 2007)
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Library of Congress Cataloging‐in‐Publication Data
Names: Senn, Stephen, author.Title: Statistical issues in drug development / Stephen Senn.Other titles: Statistics in practice.Description: Third edition. | Hoboken, NJ, USA : John Wiley and Sons, Ltd., 2021. | Series: Statistics in practice | Includes bibliographical references and index.Identifiers: LCCN 2020040719 (print) | LCCN 2020040720 (ebook) | ISBN 9781119238577 (hardback) | ISBN 9781119238607 (ePDF) | ISBN 9781119238591 (ePUB) | ISBN 9781119238614 (oBook)Subjects: MESH: Clinical Trials as Topic | Drug Design | Statistics as Topic–methodsClassification: LCC RM301.25 (print) | LCC RM301.25 (ebook) | NLM QV 771.4 | DDC 615/.190727–dc23LC record available at https://lccn.loc.gov/2020040719LC ebook record available at https://lccn.loc.gov/2020040720
Cover Design: WileyCover Image: © No System images/Getty Images
To Victoria, Helen and Mark
Preface to the Third Edition
I have a special affection for The Statistics in Practice series. My first book, Cross‐over Trials in Clinical Research was the first to be published in the series and I vividly remember travelling from Switzerland to Harpenden to see Vic Barnett (then at Rothamsted) and get advice on writing the book. This was my first visit to Harpenden. By the time the first edition of Statistical Issues in Drug Development was published, I myself was living in Harpenden and commuting to University College London (UCL) and in a period of several years that followed, during which I was on the council of the Royal Statistical Society, had frequent contact with Vic who was the treasurer. By the time the second edition was published, I was proud to have become one of the editors who took over from Vic and mentioned it in the preface. Sadly, Vic died in 2014. He continues to be missed. I am pleased to acknowledge my debt to him in helping to get me started in writing monographs and in founding the series that made it possible.
New books continue to appear in the series and these are now too numerous to merit a separate mention in the preface but many are referenced in the text. I am delighted also, that Geert Molenberghs, himself a contributor to the series, has now taken over from me as a series editor. I am sure the series is in safe hands and wish him and future authors every success.
Concerning Statistical Issues in Drug Development itself, as with the second edition, and following my motto that, ‘statistics is not just for Christmas but for life’, I have decided to give a statistical impression of what additions there have been to the book. Again, there are two figures. The first, shows Fig P3.1 the number of words by chapter and edition and the second, Fig P3.2 the difference in words by chapter. In both cases the division of the book into the minor first section (Chapters 1–5), which give a basic coverage of the subject in terms of various perspectives and the major part, consisting of 20 in‐depth chapters on issues grouped by theme, is marked. This is a good point to mention one further change. In the first two editions all the figures were produced in Mathcad®, long a favourite package of mine and one I used to help me in various theoretical investigations I undertook. Using the same package for both made it easy to produce the figures. However, although Mathcad has excellent default settings in graphics, it has limited flexibility and I took the decision to replace all the figures using Gentstat®, also long a favourite package of mine. The number of figures has also been increased from 66 to 98 (excluding the two in the preface), in some cases to better illustrate old topics but in many cases to accompany new ones.
As regards new topics covered, they include cluster randomization, historical controls, responder analysis, studies in children, post‐hoc tests, estimands, publication bias, the ‘replication crisis’, invalid inversion, severity, random effects in network meta‐analysis, explained variation, meta‐analysis of sequential trials, individual patient data meta‐analysis, cross‐over trials for absorbing binary endpoints, contralateral studies, Dawid's selection paradox, the MCP‐mod approach to dose‐finding, limits of quantitation, dissolution studies, biosimilars, collapsibility of measures, zero frequencies in meta‐analysis of binary data, drug–drug interactions, choice of comparators and studies in network meta‐analysis and using heteroscedasticity to identify variation in response.
Figure P3.1 Words per chapters for the second and third editions.
Figure P3.2 Additional length of third edition compared to the second.
I received help from many people, to all of whom I owe thanks. New co‐authors I have acquired since the second edition and whose work is cited include Olivier Collignon, Susi Schmitz and Anna Schritz from my group at the Luxembourg Institute of Health, PhD and MSc students Artur Araujo, Andisheh Bakhshi, Boikanyo Makubate, Edith Jude‐Eze and Jim Weir and other collaborators Vlad Anisimov, Val Fedorov, Philip Dawid, Hans Hockey, Nick Holford, Roger Lewis and Alan Philips and I am also grateful for continued collaboration with Rosemary Bailey, Sheila Bird, Carl‐Fredrik Burman, Andy Grieve and Steven Julious. Others who kindly involved me in multi‐author projects they led were Jordi Cortes, Carole Gamble, Jen Gewandter, Sander Greenland, Dennis Lendrem and Christine McNamee. Although we did not publish together, I have used and cited Nicola Greenlaw's MSc and Emmanuel Baah’s PhD theses with me and am grateful to them for their work. I have a particular thankyou to give to Dieter Hilgers, who led the IDeAl project (Hilgers, R.D. et al. 2018), in which I was involved, and to the EU FP7 programme which funded the work under grant 602552. Some work on the Simplicity Complexity and Modelling (SCAM) project (Christie, M. et al. 2011), for which I was the lead investigator is also used and I am grateful to the EPSRC for funding. Other funding from ICON and Boehringer‐Ingelheim for work in which I was involved is also gratefully acknowledged.
I also thank my many colleagues in both IDeAl and SCAM for their collaboration and members of my group at the Luxembourg Institute of Health for stimulating conversations over the seven years of my time there (2011–2018), in particular my deputy Michel Vaillant. I thank the following persons who gave generous help on particular chapters or provided me with suggestions or relevant papers: Fiona Baines, John Belmont, Tanja Berger, Björn Bornkamp, Frank Bretz, Olivier Collignon, George Davey Smith, Stephen Evans, Val Fedorov, Tim Friede, Georgi Giorgiev, Björn Holzhauer, Mats Karlsson, Simon Kirby, Huw Llewelyn, Mohammad Mansournia, Peter McCullagh, Kathrin Möllenhoff, David Norris, Sabine Preussler, Richard Riley, Patrick Royston, Claudia Schmoor, Julia Singer, Harry Southworth, Theo Stijnen, Alex Thompson, Peter Westfall, John Whittaker and Christina Yap.
A particular thanks is due to philosopher of science Deborah Mayo. She suggested some years ago that I contribute occasional blogs to her website. I have continued to do this for many years now, with many of the topics covered having relevance to this book. I am also grateful to Jean Miller, who works with Deborah, for her expert help in putting these up. Thanks to Deborah and Jean, all I have had to do is write! An index of my blogs is kept here http://www.senns.uk/Blogs.html and the reader may find that these contain additional relevant material. Deborah has also made me re‐think about frequentist statistics in a more positive way. The reader who wishes to know more should consult (Mayo, D. 2018).
I am grateful to Carl‐Frederik (Caffe) Burman, a frequent collaborator, for pointing out that I need to issue a warning. The warning was already (thanks to him) in the second edition but who reads previous prefaces? Thus, I shall give it again. Steven Piantadosi's excellent book on clinical trials (Piantadosi, S. 2017), for example, has much by the way of positive advice for trialists with section headings such as Increase the sample size for non‐adherence or Prevent methodologic errors, with sound discussion as to what needs to be done. On the other hand, in this book, the reader will occasionally encounter headings such as It is essential that the noninferiority margin be prespecificed or You cannot pool different studies or Small trials are unethical. These are usually an indication that I am not in 100% agreement with such statements but take issue with them, as indeed is appropriate in a book with this title.
The objective of the book remains to aid dialogue between statisticians and life‐scientists and others working in drug development. Statistics, and in particular pharmaceutical statistics, is a subject that has given me great pleasure. I hope that the reader can share some of this. The reader who finds bite‐size statistics interesting can follow me on Twitter at @stephensenn.
References
Christie, M., Cliffe, A., Dawid, A.P., and Senn, S. (eds.) (2011).
Simplicity, Complexity and Modelling
. Chichester: Wiley.
Hilgers, R.D., Bogdan, M., Burman, C.F. et al. (2018). Lessons learned from IDeAl – 33 recommendations from the IDeAl‐net about design and analysis of small population clinical trials.
Orphanet Journal of Rare Diseases
13 (1): 77.
Mayo, D. (2018).
Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars
. Cambridge: Cambridge University Press.
Piantadosi, S. (2017).
Clinical Trials: A Methodologic Perspective
, 3e. New York: Wiley.
Preface to the Second Edition
There have been many developments since the first edition of this book and it was high time for a second. My own period working in the pharmaceutical industry is now a distant memory but the 10 years working as an academic since the first edition has had its compensations. I have been fortunate enough to be able to consult for many pharmaceutical companies during this time and this has certainly widened my appreciation of the work that statisticians do within the industry and the problems they face.
Alas, this appreciation is not shared by all. Many take it as almost axiomatic that statistical analysis carried out within the pharmaceutical industry is necessarily inferior to that carried out elsewhere. Indeed, one medical journal has even gone so far as to make it a requirement for publication that analyses from the pharmaceutical industry should be confirmed by an academic statistician, a policy which is as impractical as it is illogical.
Two related developments since the first edition, one of which is personal, are highly relevant. The first is that I have been honoured to succeed Vic Barnett as an editor for Wiley's Statistics in Practice series, in which this book appears. The second is that the series itself, so ably founded by Vic and Helen Ramsey, has been growing steadily and since the first edition now has attracted a number of further volumes that are highly relevant to this one. The chapters that have particularly benefited are listed with the relevant references as follows.
Chapter 6
Allocating treatments to patients in clinical trials (Berger
2005
)
Chapter 7
Baselines and covariate information (Berger
2005
)
Chapter 11
Intention to treat, missing data and related matters (Molenberghs and Kenward
2007
)
Chapter 16
Meta‐analysis (Whitehead
2002
)
Chapter 19
Sequential trials (Ellenberg et al.
2003
)
Chapter 20
Dose‐finding (Chevret
2006
)
Chapter 22
Bioequivalence studies (Hauschke et al.
2007
)
Chapter 23
Safety data, harms, drug‐monitoring and pharmacoepidemiology (Lui
2004
)
Chapter 24
Pharmacoeconomics and portfolio management (Parmigiani
2002
; Willan and Briggs
2006
)
Also extremely useful are two books on Bayesian methods (O'Hagan et al. 2006; Spiegelhalter et al. 2003) and Brown and Prescott's book on mixed models (Brown and Prescott 2006), which is already in a second edition. The books on survival analysis and sequential analysis by Marubini and Valsecchi (1995) and Whitehead (1997) remain highly relevant, of course, as does my own on cross‐over trials, (Senn 2002), also now in a second edition.
All chapters have been brought up to date in the new edition and in particular, there is extensive reference to various guidelines of the International Conference of Harmonization that have been issued since the first edition, in particular ICH E9, Statistical Principles for Clinical Trials. A new chapter on pharmaco‐genetics has been added. For the reader in possession of a first edition who wishes to know whether to splash out on a second, Figure P.1 may be helpful. (This is partly so that I can underline the fact that nothing in life, not even an author's preface, should be exempt from statistics!) This compares the two editions chapter by chapter in terms of their length in thousands of words.
The major division of the book occurs after Chapter 5, when material introducing statistics in drug development from historical, philosophical, technical and professional perspectives is succeeded by single‐issue chapters. Figure P.2 shows even more clearly that much of the additional material has gone into chapters in Part 2. Apart from the wholly new chapter on pharmacogenetics in particular, chapters on baselines, measuring effects, intention to treat and missing data, equivalence, meta‐analysis, sequential analysis, dose‐finding, pharmaco‐epidemiology and pharmaco‐economics have had extensive additions.
Figure P.1 Comparison of the first and second editions in length.
Figure P.2 Additional length (in thousand of words) of the second edition compared to the first. The mean increase (excluding Chapter 25) is 2000 words.
It is appropriate for me to repeat a general warning about the book that Carl‐Fredrik Burman has drawn to my attention. A number of the section headings contain statements of position. For example, Chapter 7 has a section, ‘The propensity score is a superior alternative to adjusting for confounders than analysis of covariance’. You will get a very misleading impression of the message of the book if you take these as being my position. This is a book about issues and where such statements are made it is nearly always because, as is the case with this one, I wish to take issue with them.
I am grateful to Frank Bretz, Diane Elbourne, Paul Gallo, Oliver Keene, Dieter Hauschke, Nick Holford, Paul Johnson, Vincent Macaulay, Helmut Schütz, Helen Senn and John Sorkin for comments, and to Mateo Aboy, Nick Holford, Jerry Nedelman, Luis Pereira and Michael Talias for providing copies of their papers. Since the first edition, I have acquired several new co‐authors whose work is reflected in this edition: my PhD students Dimitris Lambrou and Sally Lee and also, Pina D'Angelo, Frank Bretz, Carl‐Fredrik Burman, Angelika Caputo, Farkad Ezzett, Erika Graf, Emmanuel Lesaffre, Frank Harrell, Hans van Houwelingen, William Mezanotte, Christopher Miller, Diane Potvin, Peter Regan and Nicoletta Rosati, whom I thank. I am also extremely grateful to Andy Grieve, for continued collaboration and to my PhD students Steven Julious, Andy Garrett for their work. I thank Kathryn Sharples, Susan Barclay, Beth Dufour and Simon Lightfoot at Wiley and also Len Cegielka and Cherline Daniel for work on preparing the book.
I continue to hope, of course, that this book will aid dialogue between statisticians and life‐scientists within the pharmaceutical industry but also hope that it will contribute to a wider appreciation of the interesting challenges that statisticians within the pharmaceutical industry face and the seriousness with which they are met. I hope that the reader finds both stimulation and enjoyment in encountering these challenges.
References
Berger, V.W. (2005).
Selection Bias and Covariate Imbalances in Randomized Clinical Trials
. Chichester: Wiley.
Brown, H. and Prescott, R. (2006).
Applied Mixed Models in Medicine
. Chichester: Wiley.
Chevret, S. (ed.) (2006).
Statistical Methods for Dose‐Finding Experiments
. Chichester: Wiley.
Ellenberg, S., Fleming, T., and DeMets, D. (2003).
Data Monitoring Committees in Clinical Trials: A Practical Perspective
. Chichester: Wiley.
Hauschke, D., Steinijans, V., and Pigeot, I. (2007).
Bioequivalence Studies in Drug Development: Methods and Applications
. Chichester: Wiley.
Lui, K.‐J. (2004).
Statistical Estimation of Epidemiological Risk
. Hoboken: Wiley.
Marubini, E. and Valsecchi, M.G. (1995).
Analysing Survival Data from Clinical Trials and Observational Studies
. Chichester: Wiley.
Molenberghs, G. and Kenward, M.G. (2007).
Missing Data in Clinical Studies
. Chichester: Wiley.
O'Hagan, A., Buck, C.E., Daneshkah, A. et al. (2006).
Uncertain Judgements
. Chichester: Wiley.
Parmigiani, G. (2002).
Modeling in Medical Decision Making: A Bayesian Approach
. Chichester: Wiley.
Senn, S.J. (2002).
Cross‐Over Trials in Clinical Research
, 2e. Chichester: Wiley.
Spiegelhalter, D.J., Abrams, K.R., and Myles, J.P. (2003).
Bayesian Approaches to Clinical Trials and Health‐Care Evaluation
. Chichester: Wiley.
Whitehead, J. (1997).
The Design and Analysis of Sequential Trials
, Revised 2nd ed. Chichester: Wiley.
Whitehead, A. (2002).
Meta‐Analysis of Controlled Clinical Trials
. Chichester: Wiley.
Willan, A.R. and Briggs, A.H. (2006).
Statistical Analysis of Cost‐Effectiveness Data
. Chichester: Wiley.
Preface to the First Edition
The conscientious mathematician acts in this respect like the lady who is a conscientious shopper. Wishing to satisfy herself of the quality of a fabric, she wants to see it and to touch it. Intuitive insight and formal proof are two different ways of perceiving the truth, comparable to the perception of a material object through two different senses, sight and touch.
Polya, How to Solve It
When I first started work in the Swiss pharmaceutical industry in 1987, I had already been working as a statistician for 12 : 3 years in the National Health Service in England and then 9 years lecturing in Scotland. What struck me then was how much I still had to learn, not only about medicine, pharmacology and drug development in general, but also about my own subject, statistics. Working with other professionals, many of them experts in fields of which I knew nothing, called for a different approach to statistics in at least four ways. First, I had to examine what I ‘knew’ in order to establish what was useful and what was not. Second, I had to supplement it with knowledge of many fields of statistical theory which were new to me (design and analysis of cross‐over trials was an example). Third, I had to pay attention to the scientific fields of my colleagues, in particular pharmacology, and try to work out the implications in statistical terms. Fourth, I had to repay my colleagues' willingness to explain their sciences to me by making my statistical points in terms that were clear to them.
In doing the latter, it became clear to me that there were many things which I myself had taken for granted which were debatable. I also came to the conclusion that many of the difficulties with statistical ideas lie deeper than statistics itself (an example would be notions of causality). Furthermore, I became convinced that statisticians pay their non‐statistical colleagues a disservice if they try to gloss over genuine disagreements. This book is an attempt to present many of the statistical issues in drug development in a way which is comprehensible to life scientists working in drug development whilst avoiding false consensus. The emphasis will be on the intuition which Polya, although himself a distinguished mathematician, valued so highly. Although addressed to the life‐scientist it is my hope that many statisticians, in particular those studying medical statistics or embarking on a career in drug development, will also find it useful. Above all I hope that it will help communication between the disciplines: a process by which the statistician stands to benefit as much as any other professional in drug development. I cannot pretend, however, to be objective on all issues and am not even sure of what such objectivity might consist. In my defence, however, I think that I may justly claim, that if all viewpoints are not given equal care and consideration, the reader will at least come away with a wider awareness that other views exist, than would have been the case in a more conventional approach.
The book is in two sections. The first, and by far the shorter section, is based on a statistics appreciation course which I gave a number of times to my colleagues at Ciba‐Geigy. In addition to a brief introduction it consists of four chapters, each of which takes a different view, of statistics in drug development: historical, ‘philosophical’, technical and professional. I recommend that every reader will either read these chapters or satisfy her or himself that the material is familiar. The second and larger section is loosely based on a course (but less technical than that course) which I give to students on the Postgraduate Diploma in Statistics at Neuchatel University and consists of 19 chapters of varying length which may be read in almost any order and consulted as considered desirable. Each chapter consists of a brief background statement and then a second section split into a number of issues. These are sometimes presented as true open issues and sometimes as positions which one might take on an issue. (Where the latter is the case, the reader should be warned that I usually disagree with the position taken.) At the end of each chapter are a number of references. Sometimes these will have been referred to explicitly but in some cases they are merely listed because they are useful additional reading.
When it comes to handling statistics, the life‐scientist in drug development has two particular advantages over his or her colleagues elsewhere. First, (s)he will, through the nature of the work, come into frequent contact with statistical problems. Consequently, a basic familiarity with some essential concepts will be obtained. Second, technical statistical matters will be handled as a matter of course by the statisticians assigned to the various drug development projects. Life scientists working elsewhere will not always be so fortunate as to have resident experts whom they may consult. This provides a further justification for my decision to concentrate on issues rather than technicalities.
I find the subject matter fascinating, of course, but am aware that the reader will not always share my enthusiasm. I have tried to leaven the mix by adding chapter quotations and even the occasional joke or anecdote, ignoring Sterne's warning that: Tis no extravagant arithmetic to say, that for every ten jokes, − thou has got an hundred enemies; and till thou hast gone on, and raised a swarm of wasps about thine ears, and art half stung to death by them, thou wilt never be convinced it is so.
This book would have been impossible to write without the help of many statisticians and life scientists from whom I received my education at Ciba‐Geigy (now merged with Sandoz to form Novartis). In particular, amongst statisticians, I have to thank my former colleagues Farkad Ezzet, Hans‐Peter Graf, Andy Grieve, Walter Kremers, Gunther Mehring, Amy Racine and Jakob Schenker for many helpful discussions during my time at Ciba‐Geigy, as well as the various members of my own group, Bernhard Bablok, Nathalie Ezzet, Friedhelm Hornig, Rolf Meinert, Erhard Quebe‐Fehling, Peter Sacares, Denise Till, Elizabeth Wehrle and Albert Widmer for shared work over the years, and also others in Switzerland, the USA and elsewhere, too numerous to mention. I also learned a great deal from the life scientists with whom I collaborated and I would particularly like to thank Reto Brambilla, Giovanni Della Cioppa, Brigitte Franke, Francesco Patalano and Bill Richardson for sharing the joys and pains of drug development with me. I also owe a particular thank you to William Jenkins who, in introducing me to the problem of portfolio management, led me to a wider appreciation of the role of statistics in drug development, and to Anders Hove, Keith Widdowson, Marc Cohen, Bill Huebner, Ronald Steele of CIBA‐Geigy and Peter Regan, formerly of Strategic Decisions Group for working on this problem with me. My UCL colleagues, Vern Farewell and Rebecca Hardy made helpful comments on various chapters as did Leon Aarons, Peter Bauer, Michael Budde, Stephen Evans, Farkad Ezzet, Dieter Hauschke, Oliver Keene, Walter Kremers, John Lewis, Bill Richardson, Joachim Röhmel, Mark Sculpher and John Whitehead. I thank Lew Sheiner for permission to reproduce figure 22.1 from one of his papers. I am also grateful to Peter Bauer, Roger Berger, Michael Dewey, Farkad Ezzet, Nancy Geller, Andy Grieve, Miranda Mugford and Wendy Ungar for giving me access to (as yet) unpublished work of theirs and to Yadolah Dodge, professor of statistics at the University of Neuchatel and the students on the postgraduate diploma there for the opportunity to expound this subject. Thanks are also due to Guernsey McPearson for contributing quotations and other material.
Acknowledgements
With thanks to the following copyright holders for their kind permission to reproduce quotations from their publications:
Chapter 1
Brazzaville Beach, by William Boyd, published by Sinclair‐Stevenson. Reprinted by permission of HarperCollins Publishers.
Chapter 6
The Lottery in Babylon, by Jorge Luis Borges, Translated by John M. Fein from LABYRINTHS, copyright © 1962, 1964, by New Directions Publishing Corp. Reprinted by permission of New Directions Publishing Corp.
Chapter 22
Enderby Outside, by Anthony Burgess. © Estate of Anthony Burgess from Enderby Outside (1968), reproduced with permission of Penguin.
Chapter 24
The Bear, Wodwo (1967), by Ted Hughes. Reproduced with permission from Faber & Faber.
1 Introduction
Ye maun understand I found my remarks on figures, whilk … is the only true demonstrable root of human knowledge.
Sir Walter Scott, Rob Roy
Statisticians know that words are important to statistics, yet surely their importance is not fully recognized.
William Kruskal
Opinions are made to be changed – or how is truth to be got at? We don't arrive at it by standing on one leg.
Lord Byron, letter to Murray
1.1 DRUG DEVELOPMENT
Drug development is the process not only of finding and producing therapeutically useful pharmaceuticals and turning them into high‐quality formulations of usable, effective and safe medicines, but also of delivering valuable, reliable, and trustworthy information about appropriate doses and dosing intervals and about likely effects and side‐effects of these treatments. Drug development is a process carried out by sponsors (mainly pharmaceutical companies) and its acceptability is ultimately judged by regulators. It is an extremely complex business and the risks are high, but the potential rewards are also considerable.
It takes many years for a project to reach development. First, basic research must be undertaken to validate concepts and mechanisms. Assessments of commercial potential for diseases and therapies are also needed and these will continue throughout the life of a project. Next, a lead compound must be identified for a particular indication. This will then be subjected to a battery of screening tests to assess its potential in terms of therapeutic activity. Back‐up compounds will also be investigated. If a compound looks promising, it will also be evaluated from both safety and practical points of view. Will it be easy to formulate? How many steps are involved in the synthesis? How difficult will it be to manufacture in large‐scale quantities? Before a treatment can go into development, not only must satisfactory answers have been obtained to all these questions but a viable pharmaceutical formulation permitting further study must be available. This can be an extremely delicate matter, involving work to develop suitable solutions, pills, patches or aerosols, as the case may be.
If and when a molecule is accepted into development, animal studies will be undertaken in order to check safety and to establish a dose at which studies in humans may be undertaken. Once basic toxicological work has been undertaken, ‘phase I’ may begin and the first such studies may start. These will be single‐dose studies in which lower doses are tried first and cautiously increased until a maximum tolerated dose may be established. In many indications such studies are carried out on healthy volunteers, but where the treatment is highly aggressive (and hence intended for serious diseases) patients will be used instead. In the meantime, longer‐scale toxicological studies with animals will have been completed. Pharmacokinetic studies in humans will be undertaken in which the concentration–time profile of the drug in blood will be measured at frequent intervals in order to establish the rate at which the drug is absorbed and eliminated. These studies together, if successful, will permit multiple‐dose studies to be undertaken.
Once maximum tolerated doses have been established, phase II begins and dose finding studies in patients are started. This is usually an extremely difficult phase of development but, if the drug proves acceptable, the object is that preliminary indications of efficacy should be available and that a firm recommendation for doses and dose schedules should emerge. Once these studies have been completed, the pivotal phase III studies can begin. These have the object of proving efficacy to a sceptical regulator and also of obtaining information on the safety and tolerability of the treatment.
A successfully completed development programme results in a dossier – an enormous collection of clinical trial and other reports, as well as expert summaries covering not only the clinical studies as regards efficacy and safety but also pre‐clinical studies and other technical reports as well as details of the manufacturing process. If successful, the package leads to registration, but even during the review process, phase IV studies may have been initiated in order to discover more about the effect of the treatment in specialist subpopulations, or perhaps with the object of providing data to cover price negotiations with reimbursers.
Regulatory dossier: A mountain of documents which takes a forest of trees to obscure the wood.
Once a drug has been launched on the market, the process of monitoring and ‘pharmacovigilance’ begins in earnest, since the drug will now be used by far more persons than was ever the case in the clinical trials in phases I to III, and rare side‐effects, which could not be detected earlier, may now appear. Some further phase IV postmarketing studies may be initiated and further work extending indications or preparing new formulations may be undertaken.
1.2 THE ROLE OF STATISTICS IN DRUG DEVELOPMENT
There is no aspect of drug development in which statistics cannot intrude: from screening chemicals for activity to forecasting sales. Because the efficacy and safety of treatments has to be judged against a background of considerable biological variability, all of the judgements
