Statistical Thinking for Non-Statisticians in Drug Regulation

Statistical Thinking for Non-Statisticians in Drug Regulation......Page 3
Contents......Page 9
Preface......Page 15
Abbreviations......Page 19
1.1 Historical perspective......Page 21
1.2 Control groups......Page 22
1.3 Placebos and blinding......Page 23
1.4 Randomisation......Page 24
1.4.2 Block randomisation......Page 25
1.4.3 Unequal randomisation......Page 26
1.4.4 Stratified randomisation......Page 27
1.4.5 Central randomisation......Page 28
1.4.6 Dynamic allocation and minimisation......Page 29
1.4.7 Cluster randomisation......Page 30
1.5 Bias and precision......Page 31
1.6 Between- and within-patient designs......Page 32
1.7 Cross-over trials......Page 34
1.8.3 Signal-to-noise ratio......Page 35
1.9 Confirmatory and exploratory trials......Page 36
1.10 Superiority, equivalence and non-inferiority trials......Page 37
1.11 Data types......Page 38
1.12.1 Primary variables......Page 40
1.12.3 Surrogate variables......Page 41
1.12.4 Global assessment variables......Page 42
1.12.6 Categorisation......Page 43
2.1 Sample and population......Page 45
2.2.1 Sample and population distribution......Page 46
2.2.2 Median and mean......Page 47
2.2.3 Standard deviation......Page 48
2.3 The normal distribution......Page 49
2.4 Sampling and the standard error of the mean......Page 52
2.5.1 The standard error for the difference between two means......Page 55
2.5.3 The general setting......Page 58
3.1.1 The 95 per cent confidence interval......Page 59
3.1.3 Changing the multiplying constant......Page 61
3.1.4 The role of the standard error......Page 63
3.2.1 Difference between two means......Page 64
3.2.2 Confidence intervals for proportions......Page 65
3.2.3 General case......Page 66
3.3.1 Interpreting the p-value......Page 67
3.3.2 Calculating the p-value......Page 69
3.3.3 A common process......Page 72
3.3.5 One-tailed and two-tailed tests......Page 75
4.1 The unpaired t-test......Page 77
4.2 The paired t-test......Page 78
4.3 Interpreting the t-tests......Page 81
4.4.1 Pearson chi-square......Page 83
4.4.2 The link to a signal-to-noise ratio......Page 86
4.5.1 Odds ratio (OR)......Page 87
4.5.2 Relative risk (RR)......Page 88
4.5.4 Number needed to treat (NNT)......Page 89
4.5.5 Confidence intervals......Page 90
4.6 Fisher’s exact test......Page 91
4.7.1 Categorical data......Page 93
4.7.2 Ordered categorical (ordinal) data......Page 95
4.7.3 Measures of treatment benefit for categorical and ordinal data......Page 96
4.8.1 Between-patient designs and continuous data......Page 97
4.8.2 Within-patient designs and continuous data......Page 98
4.8.4 Dose ranging studies......Page 99
4.8.5 Further discussion......Page 100
5.1 Rationale for multi-centre trials......Page 101
5.2 Comparing treatments for continuous data......Page 102
5.3.1 Treatment-by-centre interactions......Page 104
5.3.2 Quantitative and qualitative interactions......Page 107
5.5 Combining centres......Page 108
6.1 Adjusting for baseline factors......Page 111
6.2 Simple linear regression......Page 112
∗6.3 Multiple regression......Page 114
6.4 Logistic regression......Page 116
6.5.1 Main effect of treatment......Page 117
6.5.2 Treatment-by-covariate interactions......Page 119
∗6.5.3 A single model......Page 121
6.5.5 Advantages of analysis of covariance......Page 122
6.6 Binary, categorical and ordinal data......Page 124
6.7 Regulatory aspects of the use of covariates......Page 126
6.9 Baseline testing......Page 129
7.1 The principle of intention-to-treat......Page 131
7.2.1 Full analysis set......Page 135
7.2.3 Sensitivity......Page 137
7.3.1 Introduction......Page 138
7.3.3 Last observation carried forward (LOCF)......Page 139
7.3.5 Worst case/best case imputation......Page 140
7.3.7 Avoidance of missing data......Page 141
7.4 Intention-to-treat and time-to-event data......Page 142
7.5 General questions and considerations......Page 144
8.1 Type I and type II errors......Page 147
8.2 Power......Page 148
8.3 Calculating sample size......Page 151
8.4.1 Standard deviation......Page 154
8.4.3 Clinically relevant difference......Page 155
8.5.1 Power > 80 per cent......Page 156
8.5.3 Sample size adjustment......Page 157
8.6 Reporting the sample size calculation......Page 158
9.1 Link between p-values and confidence intervals......Page 161
9.2 Confidence intervals for clinical importance......Page 163
9.3.1 Conclusions of similarity......Page 164
9.3.2 The problem with 0.05......Page 165
10.1 Inflation of the type I error......Page 167
10.3 Regulatory view......Page 168
10.4.2 Significance needed on all endpoints......Page 169
10.4.4 Variables ranked according to clinical importance......Page 170
10.5 Methods for adjustment......Page 172
10.6 Multiple comparisons......Page 173
10.7 Repeated evaluation over time......Page 174
10.8 Subgroup testing......Page 175
10.9.1 Using different statistical tests......Page 177
10.9.2 Different analysis sets......Page 178
11.1 Assumptions underlying the t-tests and their extensions......Page 179
11.3 The assumption of normality......Page 180
11.4 Transformations......Page 183
11.5.1 The Mann–Whitney U-test......Page 186
11.5.2 The Wilcoxon signed rank test......Page 188
11.6 Advantages and disadvantages of non-parametric methods......Page 189
11.7 Outliers......Page 190
12.1 Demonstrating similarity......Page 193
12.2 Confidence intervals for equivalence......Page 195
12.3 Confidence intervals for non-inferiority......Page 196
12.4 A p-value approach......Page 198
12.5 Assay sensitivity......Page 200
12.7 The choice of Δ......Page 202
12.7.2 Therapeutic equivalence......Page 203
12.7.3 Non-inferiority......Page 204
12.7.4 The 10 per cent rule for cure rates......Page 205
12.7.5 Biocreep and constancy......Page 206
12.8 Sample size calculations......Page 207
12.9 Switching between non-inferiority and superiority......Page 209
13.1 Time-to-event data and censoring......Page 213
13.2.1 Plotting KM curves......Page 215
13.2.3 Median event times......Page 216
13.3 Treatment comparisons......Page 217
13.4.1 The hazard rate......Page 220
13.4.3 Non-constant hazard ratio......Page 221
13.4.4 Link to survival curves......Page 222
∗13.4.5 Calculating KM curves......Page 223
13.5.2 Proportional hazards regression......Page 224
13.5.3 Accelerated failure time model......Page 227
13.6 Independent censoring......Page 228
13.7 Sample size calculations......Page 229
14.1 Stopping rules for interim analysis......Page 233
14.2.1 Efficacy......Page 234
14.2.2 Futility and conditional power......Page 235
14.2.3 Some practical issues......Page 236
14.2.4 Analyses following completion of recruitment......Page 237
14.3 Monitoring safety......Page 238
14.4.1 Introduction and responsibilities......Page 239
14.4.2 Structure......Page 240
14.4.3 Meetings and recommendations......Page 242
14.5.1 Sample size re-evaluation......Page 243
14.5.2 Flexible designs......Page 244
15.1 Definition......Page 249
15.2 Objectives......Page 251
15.3.1 Methods for combination......Page 252
15.3.2 Confidence Intervals......Page 253
15.3.4 Graphical methods......Page 254
15.3.6 Robustness......Page 256
15.4.1 Planning......Page 257
15.4.2 Publication bias and funnel plots......Page 258
15.5.1 Retrospective analyses......Page 260
15.5.2 One pivotal study......Page 261
16.1 The importance of statistical thinking at the design stage......Page 265
16.2 Regulatory guidelines......Page 267
16.3 The statistics process......Page 269
16.3.2 The statistical analysis plan......Page 270
16.3.4 The blind review......Page 271
16.3.6 Reporting the analysis......Page 272
16.3.7 Pre-planning......Page 273
16.3.8 Sensitivity and robustness......Page 275
16.4 The regulatory submission......Page 276
16.5 Publications and presentations......Page 277
References......Page 281
Index......Page 287