Testing Statistical Hypotheses of Equivalence and Noninferiority, Second Edition

Contents......Page 4
Preface......Page 9
1.1 Statistical meaning of the concepts of equivalence and noninferiority......Page 15
1.2 Demonstration of equivalence as a basic problem of applied statistics......Page 16
1.3.1 Comparative bioequivalence trials......Page 19
1.3.2 Clinical trials involving an active control......Page 21
1.4 Role of equivalence/noninferiority studies in current medical research......Page 22
1.5 Formulation of hypotheses......Page 24
1.6 Choosing the main distributional parameter......Page 27
1.7 Numerical specification of the limits of equivalence......Page 29
2.1.1 Paired observations......Page 32
2.1.2 Two independent samples......Page 35
2.1.3 Power and sample size calculation based on tests for noninferiority under location-shift models......Page 36
2.2 Methods of constructing exact optimal tests for settings beyond the location-shift model......Page 37
2.3 Large-sample solutions for problems inaccessible for exact constructions......Page 39
2.4 Objective Bayesian methods......Page 40
2.5 Improved nonrandomized tests for discrete distributions......Page 41
2.6 Relationship between tests for noninferiority and two-sided equivalence tests......Page 43
2.7 Halving alpha?......Page 44
3.1 The principle of confidence interval inclusion......Page 45
3.2 Bayesian tests for two-sided equivalence......Page 48
3.3 The classical approach to deriving optimal parametric tests for equivalence hypotheses......Page 52
3.4 Construction of asymptotic tests for equivalence......Page 57
4.1 The one-sample problem with normally distributed observations of known variance......Page 60
4.2 Test for equivalence of a hazard rate to some given reference value with exponentially distributed survival times......Page 66
4.3 Testing for equivalence of a single binomial proportion to a fixed reference success probability......Page 70
4.4 Confidence-interval inclusion rules as asymptotically UMP tests for equivalence......Page 75
4.5 Noninferiority analogues of the tests derived in this chapter......Page 79
5.1 Sign test for equivalence......Page 82
5.2 Equivalence tests for the McNemar setting......Page 87
5.2.1 Large-sample solution......Page 89
5.2.2 Corrected finite-sample version of the large-sample test......Page 92
5.2.3 Modifications for the noninferiority case......Page 96
5.3 Paired t-test for equivalence......Page 103
5.4 Signed rank test for equivalence......Page 110
5.5 A generalization of the signed rank test for equivalence for noncontinuous data......Page 119
6.1 Two-sample t-test for equivalence......Page 130
6.2 Mann-Whitney test for equivalence......Page 137
6.3 Two-sample equivalence tests based on linear rank statistics......Page 147
6.4 A distribution-free two-sample equivalence test allowing for arbitrary patterns of ties......Page 161
6.5 Testing for dispersion equivalence of two Gaussian distributions......Page 175
6.6.1 Exact Fisher type test for noninferiority with respect to the odds ratio......Page 183
6.6.2 Improved nonrandomized tests for noninferiority with respect to the odds ratio......Page 188
6.6.3 Tests for noninferiority using alternative parametrizations......Page 192
6.6.4 Exact test for two-sided equivalence with respect to the odds ratio......Page 197
6.6.5 An improved nonrandomized version of the UMPU test for two-sided equivalence......Page 204
6.6.6 Tests for two-sided equivalence with respect to the difference of success probabilities......Page 205
6.7 Log-rank test for equivalence of two survivor functions......Page 213
6.7.1 Rationale of the log-rank test for equivalence in the two-sided sense......Page 214
6.7.2 Power approximation and sample size calculation for the log-rank test for equivalence......Page 221
6.7.3 Log-rank test for noninferiority......Page 225
7.1 The intersection-union principle as a general solution to multisample equivalence problems......Page 230
7.2 F-test for equivalence of k normal distributions......Page 232
7.3 Modified studentized range test for equivalence......Page 236
7.4 Testing for dispersion equivalence of more than two Gaussian distributions......Page 238
7.5 A nonparametric k-sample test for equivalence......Page 242
8.1.1 Generalizing the paired t-test for equivalence by means of the T2-statistic......Page 246
8.1.2 A many-one equivalence test for dependent samples based on Euclidean distances......Page 252
8.1.3 Testing for equivalence with dependent samples and an indifference zone of rectangular shape......Page 259
8.1.4 Discussion......Page 263
8.2.1 A two-sample test for equivalence based on Hotelling's T2......Page 264
8.2.2 Behavior of the two-sample T2-test for equivalence under heteroskedasticity......Page 270
8.2.3 Multivariate two-sample tests for equivalence regions of rectangular shape......Page 273
9.1 Testing for equivalence of a single multinomial distribution with a fully specified reference distribution......Page 276
9.2 Testing for approximate collapsibility of multiway contingency tables......Page 281
9.3.1 An exact optimal test for negligibility of interactions in a two-way ANOVA layout......Page 289
9.3.2 Establishing negligibility of carryover effects in the analysis of two-period crossover trials......Page 295
9.4.1 Genetical background, measures of HW disequilibrium......Page 301
9.4.2 Exact conditional tests for absence of substantial disequilibrium......Page 304
9.4.3 Confidence-interval–based procedures for assessing HWE......Page 314
10.1 Introduction......Page 322
10.2.1 Equivalence with respect to nonstandardized mean bioavailabilities......Page 326
10.2.2 Testing for scaled average bioequivalence......Page 333
10.3.1 Introduction......Page 336
10.3.2 Distribution-free approach to testing for probability-based individual bioequivalence......Page 338
10.3.3 An improved parametric test for probability-based individual bioequivalence......Page 340
10.4.1 Introduction......Page 351
10.4.2 A testing procedure for establishing one-sided bioequivalence with respect to total variability......Page 353
10.4.3 Complete disaggregate testing procedure and illustrating example......Page 355
10.4.4 Some results on power and sample sizes......Page 356
10.4.5 Discussion......Page 358
10.5 Bioequivalence assessment as a problem of comparing bivariate distributions......Page 359
11.1 Introduction......Page 366
11.2 Exploiting the duality between testing for two-sided equivalence and existence of relevant differences......Page 367
11.3.1 One-sample problem with normally distributed data of known variance......Page 370
11.3.2 Two-sample t-test for relevant differences......Page 372
11.3.3 Exact Fisher type test for relevant differences between two binomial distributions......Page 375
A.1 UMP tests for equivalence problems in STP3 families......Page 380
A.2 UMPU equivalence tests in multiparameter exponential families......Page 386
A.3 A sufficient condition for the asymptotic validity of tests for equivalence......Page 387
Appendix B: List of special computer programs......Page 390
Appendix C: Frequently used special symbols and abbreviations......Page 394
References......Page 397