Statistical Thinking for Non-Statisticians in Drug Regulation

Preface to the second edition xv
Preface to the first edition xvii
Abbreviations xxi
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 3
1.5 Bias and precision 9
1.6 Between- and within-patient designs 11
1.7 Crossover trials 12
1.8 Signal noise and evidence 13
1.9 Confirmatory and exploratory trials 15
1.10 Superiority equivalence and non-inferiority trials 16
1.11 Data and endpoint types 17
1.12 Choice of endpoint 18
2 Sampling and inferential statistics 23
2.1 Sample and population 23
2.2 Sample statistics and population parameters 24
2.3 The normal distribution 28
2.4 Sampling and the standard error of the mean 31
2.5 Standard errors more generally 34
3 Confidence intervals and p-values 38
3.1 Confidence intervals for a single mean 38
3.2 Confidence interval for other parameters 42
3.3 Hypothesis testing 45
4 Tests for simple treatment comparisons 56
4.1 The unpaired t-test 56
4.2 The paired t-test 57
4.3 Interpreting the t-tests 60
4.4 The chi-square test for binary data 61
4.5 Measures of treatment benefit 64
4.6 Fisher's exact test 69
4.7 Tests for categorical and ordinal data 71
4.8 Extensions for multiple treatment groups 75
5 Adjusting the analysis 78
5.1 Objectives for adjusted analysis 78
5.2 Comparing treatments for continuous data 78
5.3 Least squares means 82
5.4 Evaluating the homogeneity of the treatment effect 83
5.5 Methods for binary categorical and ordinal data 86
5.6 Multi-centre trials 87
6 Regression and analysis of covariance 89
6.1 Adjusting for baseline factors 89
6.2 Simple linear regression 89
6.3 Multiple regression 91
6.4 Logistic regression 94
6.5 Analysis of covariance for continuous data 94
6.6 Binary categorical and ordinal data 101
6.7 Regulatory aspects of the use of covariates 103
6.8 Baseline testing 105
7 Intention-to-treat and analysis sets 107
7.1 The principle of intention-to-treat 107
7.2 The practice of intention-to-treat 110
7.3 Missing data 113
7.4 Intention-to-treat and time-to-event data 118
7.5 General questions and considerations 120
8 Power and sample size 123
8.1 Type I and type II errors 123
8.2 Power 124
8.3 Calculating sample size 127
8.4 Impact of changing the parameters 130
8.5 Regulatory aspects 132
8.6 Reporting the sample size calculation 134
9 Statistical significance and clinical importance 136
9.1 Link between p-values and Confidence intervals 136
9.2 Confidence intervals for clinical importance 137
9.3 Misinterpretation of the p-value 139
9.4 Single pivotal trial and 0.05 140
10 Multiple testing 142
10.1 Inflation of the type I error 142
10.2 How does multiplicity arise? 143
10.3 Regulatory view 144
10.4 Multiple primary endpoints 145
10.5 Methods for adjustment 149
10.6 Multiple comparisons 152
10.7 Repeated evaluation over time 153
10.8 Subgroup testing 154
10.9 Other areas for multiplicity 156
11 Non-parametric and related methods 158
11.1 Assumptions underlying the t-tests and their extensions 158
11.2 Homogeneity of variance 158
11.3 The assumption of normality 159
11.4 Non-normality and transformations 161
11.5 Non-parametric tests 164
11.6 Advantages and disadvantages of non-parametric methods 168
11.7 Outliers 169
12 Equivalence and non-inferiority 170
12.1 Demonstrating similarity 170
12.2 Confidence intervals for equivalence 172
12.3 Confidence intervals for non-inferiority 173
12.4 A p-value approach 174
12.5 Assay sensitivity 176
12.6 Analysis sets 178
12.7 The choice of " 179
12.8 Biocreep and constancy 184
12.9 Sample size calculations 184
12.10 Switching between non-inferiority and superiority 186
13 The analysis of survival data 189
13.1 Time-to-event data and censoring 189
13.2 Kaplan-Meier curves 190
13.3 Treatment comparisons 193
13.4 The hazard ratio 196
13.5 Adjusted analyses 199
13.6 Independent censoring 202
13.7 Sample size calculations 203
14 Interim analysis and data monitoring committees 205
14.1 Stopping rules for interim analysis 205
14.2 Stopping for efficacy and futility 206
14.3 Monitoring safety 210
14.4 Data monitoring committees 211
15 Bayesian statistics 215
15.1 Introduction 215
15.2 Prior and posterior distributions 215
15.3 Bayesian inference 219
15.4 Case study 221
15.5 History and regulatory acceptance 222
15.6 Discussion 224
16 Adaptive designs 225
16.1 What are adaptive designs? 225
16.2 Minimising bias 228
16.3 Unblinded sample size re-estimation 232
16.4 Seamless phase II/III studies 234
16.5 Other types of adaptation 236
16.6 Further regulatory considerations 238
17 Observational studies 241
17.1 Introduction 241
17.2 Guidance on design conduct and analysis 247
17.3 Evaluating and adjusting for selection bias 249
17.4 Case-control studies 257
18 Meta-analysis 261
18.1 Definition 261
18.2 Objectives 263
18.3 Statistical methodology 264
18.4 Case study 270
18.5 Ensuring scientific validity 271
18.6 Further regulatory aspects 275
19 Methods for the safety analysis and safety monitoring 277
19.1 Introduction 277
19.2 Routine evaluation in clinical studies 279
19.3 Data monitoring committees 289
19.4 Assessing benefit-risk 290
19.5 Pharmacovigilance 299
20 Diagnosis 304
20.1 Introduction 304
20.2 Measures of diagnostic performance 304
20.3 Receiver operating characteristic curves 308
20.4 Diagnostic performance using regression models 310
20.5 Aspects of trial design for diagnostic agents 312
20.6 Assessing agreement 313
21 The role of statistics and statisticians 316
21.1 The importance of statistical thinking at the design stage 316
21.2 Regulatory guidelines 317
21.3 The statistics process 321
21.4 The regulatory submission 327
21.5 Publications and presentations 328
References 331
Index 339