Group Sequential Methods (Chapman & Hall CRC Interdisciplinary Statistics)

Contents......Page 5
List of figures......Page 9
List of tables......Page 11
Preface......Page 14
Glossary......Page 16
1.1 About This Book......Page 17
1.2 Why Sequential Methods......Page 19
1.3 A Short History of Sequential and Group Sequential Methods......Page 21
1.4 Some Examples......Page 27
1.5 Chapter Organization: A Roadmap......Page 31
1.6 Bibliography and Notes......Page 34
2.1 Two-Sided Tests for Comparing Two Treatments with Normal Response of Known Variance......Page 36
2.2 A Fixed Sample Test......Page 37
2.3 Group Sequential Tests......Page 38
2.4 Pocock’s Test......Page 39
2.5 O’Brien & Fleming’s Test......Page 44
2.6 Properties of Pocock and O’Brien & Fleming Tests......Page 46
2.7 Other Tests......Page 54
2.8 Conclusions......Page 62
3.1 A Unified Formulation......Page 64
3.2 Applying the Tests with Equal Group Sizes......Page 68
3.3 Applying the Tests with Unequal Increments in Information......Page 72
3.4 Normal Linear Models......Page 77
3.5 Other Parametric Models......Page 85
3.6 Binary Data: Group Sequential Tests for Proportions......Page 89
3.7 The Group Sequential Log-Rank Test for Survival Data......Page 92
3.8 Group Sequential t-Tests......Page 94
4.1 Introduction......Page 101
4.2 The Power Family of One-Sided Group Sequential Tests......Page 103
4.3 Adapting Power Family Tests to Unequal Increments in Information......Page 110
4.4 Group Sequential One-Sided t-Tests......Page 113
4.5 Whitehead’s Triangular Test......Page 119
5.1 Introduction......Page 125
5.2 The Power Family of Two-Sided Inner Wedge Tests......Page 126
5.3 Whitehead’s Double Triangular Test......Page 137
6.1 Introduction......Page 142
6.3 Two-Sided Tests of Equivalence: Application to Comparative Bioavailability Studies......Page 143
6.4 Individual Bioequivalence: A One-Sided Test for Proportions......Page 154
6.5 Bibliography and Notes......Page 156
7.1 Unpredictable Information Sequences......Page 158
7.2 Two-Sided Tests......Page 159
7.3 One-Sided Tests......Page 174
7.4 Data Dependent Timing of Analyses......Page 179
7.5 Computations for Error Spending Tests......Page 182
8.2 Distribution Theory......Page 184
8.3 Point Estimation......Page 188
8.4 P-values......Page 192
8.5 Confidence Intervals......Page 194
9.1 Introduction......Page 201
9.2 Example: Difference of Normal Means......Page 205
9.3 Derived Tests: Use of RCIs to Aid Early Stopping Decisions......Page 206
9.5 Discussion......Page 214
10.2 The Conditional Power Approach......Page 217
10.3 The Predictive Power Approach......Page 222
10.4 A Parameter-Free Approach......Page 225
10.5 A Case Study with Survival Data......Page 227
10.6 Bibliography and Notes......Page 231
11.2 A Standard Joint Distribution for Successive Estimates of a Parameter Vector......Page 233
11.3 Normal Linear Models......Page 234
11.4 Normal Linear Models with Unknown Variance: Group Sequential......Page 236
11.5 Example: An Exact One-Sample Group Sequential t-Test......Page 238
11.6 General Parametric Models: Generalized Linear Models......Page 240
11.7 Bibliography and Notes......Page 244
12.1 A Single Bernoulli Probability......Page 247
12.2 Two Bernoulli Probabilities......Page 256
12.3 The Odds Ratio and Multiple 2 × 2 Tables......Page 263
12.4 Case-Control and Matched Pair Analyses......Page 266
12.5 Logistic Regression: Adjusting for Covariates......Page 268
12.6 Connection with Survival Analysis......Page 269
13.1 Introduction......Page 270
13.2 The Log-Rank Test......Page 271
13.3 The Stratified Log-Rank Test......Page 272
13.4 Group Sequential Methods for Survival Data with Covariates......Page 273
13.5 Repeated Confidence Intervals for a Hazard Ratio......Page 276
13.6 Example: A Clinical Trial for Carcinoma of the Oropharynx......Page 278
13.7 Survival Probabilities and Quantiles......Page 285
13.8 Bibliography and Notes......Page 287
14.1 The Role of an Internal Pilot Phase......Page 289
14.2 Sample Size Re-estimation for a Fixed Sample Test......Page 291
14.3 Sample Size Re-estimation in Group Sequential Tests......Page 303
15.1 Introduction......Page 308
15.2 The Bonferroni Procedure......Page 309
15.3 A Group Sequential Hotelling Test......Page 311
15.4 A Group Sequential Version of O’Brien’s Test......Page 315
15.5 Tests Based on Other Global Statistics......Page 319
15.6 Tests Based on Marginal Criteria......Page 320
15.7 Bibliography and Notes......Page 323
16.2 Global Tests......Page 325
16.3 Monitoring Pairwise Comparisons......Page 329
16.4 Bibliography and Notes......Page 332
17.1 A Multi-Stage Adaptive Design......Page 334
17.2 A Multi-Stage Adaptive Design with Time Trends......Page 338
17.3 Validity of Adaptive Multi-stage Procedures......Page 340
17.4 Bibliography and Notes......Page 342
18.1 The Bayesian Paradigm......Page 344
18.2 Stopping Rules......Page 345
18.3 Choice of Prior Distribution......Page 348
18.4 Discussion......Page 350
19.1 Introduction......Page 352
19.2 The Basic Calculation......Page 353
19.3 Error Probabilities and Sample Size Distributions......Page 358
19.4 Tests Defined by Error Spending Functions......Page 360
19.5 Analysis Following a Group Sequential Test......Page 362
19.6 Further Applications of Numerical Computation......Page 364
19.7 Computer Software......Page 367
References......Page 369