Table Of ContentStatistical Thinking for Non- Statisticians
in Drug Regulation
Statistical
Thinking for
Non- Statisticians
in Drug
Regulation
THIRD EDITION
Richard Kay, PhD
Statistical Consultant, RK Statistics Ltd
Honorary Visiting Professor, School of Pharmacy, Cardiff University, UK
This edition first published 2023
© 2023 John Wiley & Sons Ltd
Edition History
First edition John Wiley & Sons, Ltd. (2007); Second edition John Wiley & Sons, Ltd. (2015)
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Library of Congress Cataloging-i n- Publication Data
Names: Kay, Richard, 1949– author.
Title: Statistical thinking for non-statisticians in drug regulation /
Richard Kay.
Description: Third edition. | Hoboken, NJ : Wiley-Blackwell, 2023. |
Includes bibliographical references and index.
Identifiers: LCCN 2022032464 (print) | LCCN 2022032465 (ebook) | ISBN
9781119867388 (hardback) | ISBN 9781119867395 (adobe pdf) | ISBN
9781119867401 (epub)
Subjects: MESH: Clinical Trials as Topic–methods | Drug Approval |
Statistics as Topic | Drug Industry
Classification: LCC RM301.27 (print) | LCC RM301.27 (ebook) | NLM QV
771.4 | DDC 615.1072/4–dc23/eng/20220916
LC record available at https://lccn.loc.gov/2022032464
LC ebook record available at https://lccn.loc.gov/2022032465
Cover Design: Wiley
Cover Image: © WHYFRAME/Shutterstock
Set in 9.5/13pt MeridienLTStd by Straive, Pondicherry, India
Contents
Preface to the third edition, xv
Preface to the second edition, xvii
Preface to the first edition, xix
Abbreviations, xxiii
1 Basic ideas in clinical trial design, 1
1.1 Historical perspective, 1
1.2 Control groups, 2
1.3 Placebos and blinding, 3
1.4 Randomisation, 4
1.4.1 Unrestricted randomisation, 4
1.4.2 Block randomisation, 4
1.4.3 Unequal randomisation, 6
1.4.4 Stratified randomisation, 6
1.4.5 Central randomisation, 8
1.4.6 Dynamic allocation and minimisation, 9
1.4.7 Cluster randomisation, 10
1.5 Bias and precision, 10
1.6 Between- and within- patient designs, 12
1.7 Crossover trials, 13
1.8 Signal, noise and evidence, 14
1.8.1 Signal, 14
1.8.2 Noise, 15
1.8.3 Signal- to- noise ratio, 16
1.9 Confirmatory and exploratory trials, 16
1.10 Superiority, equivalence and non- inferiority trials, 17
1.11 Endpoint types, 18
1.12 Choice of endpoint, 20
1.12.1 Primary endpoints, 20
1.12.2 Secondary endpoints, 21
1.12.3 Surrogate endpoints, 21
1.12.4 Global assessment endpoints, 22
1.12.5 Composite endpoints, 23
1.12.6 Categorisation, 23
v
vi Contents
2 Sampling and inferential statistics, 25
2.1 Sample and population, 25
2.2 Sample statistics and population parameters, 26
2.2.1 Sample and population distribution, 26
2.2.2 Median and mean, 27
2.2.3 Standard deviation, 27
2.2.4 Notation, 28
2.2.5 Box plots, 29
2.3 The normal distribution, 30
2.4 Sampling and the standard error of the mean, 33
2.5 Standard errors more generally, 36
2.5.1 The standard error for the difference between two means, 38
2.5.2 Standard errors for proportions, 39
2.5.3 The general setting, 39
3 Confidence intervals and p- values, 40
3.1 Confidence intervals for a single mean, 40
3.1.1 The 95% confidence interval, 40
3.1.2 Changing the confidence coefficient, 42
3.1.3 Changing the multiplying constant, 42
3.1.4 The role of the standard error, 43
3.2 Confidence intervals for other parameters, 44
3.2.1 Difference between two means, 44
3.2.2 Confidence interval for proportions, 45
3.2.3 General case, 46
3.2.4 Bootstrap confidence interval, 47
3.3 Hypothesis testing, 47
3.3.1 Interpreting the p- value, 48
3.3.2 Calculating the p- value, 50
3.3.3 A common process, 53
3.3.4 The language of statistical significance, 56
3.3.5 One- sided and two- sided tests, 56
4 Tests for simple treatment comparisons, 58
4.1 The unpaired t- test, 58
4.2 The paired t- test, 59
4.3 Interpreting the t- tests, 62
4.4 The chi- square test for binary endpoints, 63
4.4.1 Pearson chi- square, 63
4.4.2 The link to a ratio of the signal to the standard error, 66
4.5 Measures of treatment benefit, 66
4.5.1 Odds ratio, 67
4.5.2 Relative risk, 67
4.5.3 Relative and absolute risk reduction, 68
4.5.4 Number needed to treat, 69
Contents vii
4.5.5 Confidence intervals, 69
4.5.6 Interpretation, 71
4.6 Fisher’s exact test, 72
4.7 Tests for categorical and ordered categorical endpoints, 73
4.7.1 Categorical endpoints, 73
4.7.2 Ordered categorical (ordinal) endpoints, 75
4.7.3 Measures of treatment benefit, 76
4.8 Count endpoints, 77
4.9 Extensions for multiple treatment groups, 77
4.9.1 Continuous endpoints, 77
4.9.2 Binary, categorical and ordered categorical endpoints, 78
4.9.3 Dose- ranging studies, 79
4.9.4 Further discussion, 79
5 Adjusting the analysis, 80
5.1 Objectives for adjusted analysis, 80
5.2 Comparing treatments for continuous endpoints, 80
5.3 Least squares means, 84
5.4 Evaluating the homogeneity of the treatment effect, 85
5.4.1 Treatment- by- factor interactions, 85
5.4.2 Quantitative and qualitative interactions, 87
5.5 Methods for binary and ordered categorical endpoints, 88
5.6 Multi- centre trials, 89
5.6.1 Adjusting for centre, 89
5.6.2 Significant treatment- by- centre interactions, 89
5.6.3 Combining centres, 90
6 Regression and analysis of covariance, 92
6.1 Adjusting for baseline factors, 92
6.2 Simple linear regression, 92
6.3 Multiple regression, 95
6.4 Logistic regression for binary endpoints, 97
6.4.1 Negative binomial regression for count endpoints, 97
6.5 Analysis of covariance for continuous outcomes, 98
6.5.1 Main effect of treatment, 98
6.5.2 Treatment- by- covariate interactions, 100
6.5.3 A single model, 102
6.5.4 Connection with adjusted analyses, 102
6.5.5 Advantages of ANCOVA, 103
6.5.6 Least squares means, 104
6.5.7 Random element, 105
6.6 Other endpoint types, 105
6.6.1 Binary endpoints and extensions, 105
6.6.2 Count endpoints, 108
6.7 Mixed models, 109
viii Contents
6.8 Regulatory aspects of the use of covariates, 110
6.9 Baseline testing, 113
6.10 Correlation and regression, 113
7 Intention- to- treat, analysis sets and missing data, 115
7.1 The principle of intention- to- treat, 115
7.2 The practice of intention- to- treat, 119
7.2.1 Full analysis set, 119
7.2.2 Per- protocol set, 120
7.2.3 Further aspects of ITT, 120
7.3 Missing data, 121
7.3.1 Introduction, 121
7.3.2 Complete cases analysis, 122
7.3.3 Last observation carried forward (LOCF), 123
7.3.4 Baseline observation carried forward (BOCF), 123
7.3.5 Success/failure classification, 123
7.3.6 Worst- case/best- case classification, 124
7.3.7 Sensitivity, 124
7.3.8 Avoidance of missing data, 125
7.3.9 Classification of missing data, 126
7.3.10 Multiple imputation, 127
7.4 Intention- to- treat and time- to- event data, 129
7.5 General questions and considerations, 131
8 Estimands, 134
8.1 ICH E9 (R1) 134
8.2 Attributes of an estimand, 134
8.2.1 Population, 135
8.2.2 Variable, 135
8.2.3 Intercurrent event (ICE), 136
8.2.4 Statistic for treatment effect, 136
8.3 Estimand strategies, 136
8.3.1 Five strategies, 136
8.3.2 Treatment policy, composite and hypothetical strategies, 137
8.3.3 While on treatment, 139
8.3.4 Principal stratification, 139
8.4 Sensitivity and supplementary analyses, 141
8.4.1 Main estimator, 141
8.4.2 Sensitivity analyses, 142
8.4.3 Supplementary analyses, 143
9 Power, sample size and clinical relevance, 144
9.1 Type I and type II errors, 144
9.2 Power, 145
9.3 Calculating sample size, 148
9.4 Impact of changing the parameters, 152
9.4.1 Standard deviation, 152
