Testing statistical hypotheses of equivalence and noninferiority

A.1 UMP tests for equivalence problems in STP3 families......Page 1
A.2 UMPU equivalence tests in multiparameter exponential families......Page 7
A.3 A sufficient condition for the asymptotic validity of tests for equivalence......Page 8
Appendix B: List of special computer programs......Page 11
Appendix C: Frequently used special symbols and abbreviations......Page 15
References......Page 18
1.1 Statistical meaning of the concepts of equivalence and noninferiority......Page 33
1.2 Demonstration of equivalence as a basic problem of applied statistics......Page 34
1.3.1 Comparative bioequivalence trials......Page 37
1.3.2 Clinical trials involving an active control......Page 39
1.4 Role of equivalence/noninferiority studies in current medical research......Page 40
1.5 Formulation of hypotheses......Page 42
1.6 Choosing the main distributional parameter......Page 45
1.7 Numerical specification of the limits of equivalence......Page 47
2.1.1 Paired observations......Page 50
2.1.2 Two independent samples......Page 53
2.1.3 Power and sample size calculation based on tests for noninferiority under location-shift models......Page 54
2.2 Methods of constructing exact optimal tests for settings beyond the location-shift model......Page 55
2.3 Large-sample solutions for problems inaccessible for exact constructions......Page 57
2.4 Objective Bayesian methods......Page 58
2.5 Improved nonrandomized tests for discrete distributions......Page 59
2.6 Relationship between tests for noninferiority and two-sided equivalence tests......Page 61
2.7 Halving alpha?......Page 62
3.1 The principle of confidence interval inclusion......Page 63
3.2 Bayesian tests for two-sided equivalence......Page 66
3.3 The classical approach to deriving optimal parametric tests for equivalence hypotheses......Page 70
3.4 Construction of asymptotic tests for equivalence......Page 75
4.1 The one-sample problem with normally distributed observations of known variance......Page 78
4.2 Test for equivalence of a hazard rate to some given reference value with exponentially distributed survival times......Page 84
4.3 Testing for equivalence of a single binomial proportion to a fixed reference success probability......Page 88
4.4 Confidence-interval inclusion rules as asymptotically UMP tests for equivalence......Page 93
4.5 Noninferiority analogues of the tests derived in this chapter......Page 97
5.1 Sign test for equivalence......Page 100
5.2 Equivalence tests for the McNemar setting......Page 105
5.2.1 Large-sample solution......Page 107
5.2.2 Corrected finite-sample version of the large-sample test......Page 110
5.2.3 Modifications for the noninferiority case......Page 114
5.3 Paired t-test for equivalence......Page 121
5.4 Signed rank test for equivalence......Page 128
5.5 A generalization of the signed rank test for equivalence for noncontinuous data......Page 137
6.1 Two-sample t-test for equivalence......Page 148
6.2 Mann-Whitney test for equivalence......Page 155
6.3 Two-sample equivalence tests based on linear rank statistics......Page 165
6.4 A distribution-free two-sample equivalence test allowing for arbitrary patterns of ties......Page 179
6.5 Testing for dispersion equivalence of two Gaussian distributions......Page 193
6.6.1 Exact Fisher type test for noninferiority with respect to the odds ratio......Page 201
6.6.2 Improved nonrandomized tests for noninferiority with respect to the odds ratio......Page 206
6.6.3 Tests for noninferiority using alternative parametrizations......Page 210
6.6.4 Exact test for two-sided equivalence with respect to the odds ratio......Page 215
6.6.5 An improved nonrandomized version of the UMPU test for two-sided equivalence......Page 222
6.6.6 Tests for two-sided equivalence with respect to the difference of success probabilities......Page 223
6.7 Log-rank test for equivalence of two survivor functions......Page 231
6.7.1 Rationale of the log-rank test for equivalence in the two-sided sense......Page 232
6.7.2 Power approximation and sample size calculation for the log-rank test for equivalence......Page 239
6.7.3 Log-rank test for noninferiority......Page 243
7.1 The intersection-union principle as a general solution to multisample equivalence problems......Page 248
7.2 F-test for equivalence of k normal distributions......Page 250
7.3 Modified studentized range test for equivalence......Page 254
7.4 Testing for dispersion equivalence of more than two Gaussian distributions......Page 256
7.5 A nonparametric k-sample test for equivalence......Page 260
8.1.1 Generalizing the paired t-test for equivalence by means of the T2-statistic......Page 264
8.1.2 A many-one equivalence test for dependent samples based on Euclidean distances......Page 270
8.1.3 Testing for equivalence with dependent samples and an indifference zone of rectangular shape......Page 277
8.1.4 Discussion......Page 281
8.2.1 A two-sample test for equivalence based on Hotelling's T2......Page 282
8.2.2 Behavior of the two-sample T2-test for equivalence under heteroskedasticity......Page 288
8.2.3 Multivariate two-sample tests for equivalence regions of rectangular shape......Page 291
9.1 Testing for equivalence of a single multinomial distribution with a fully specified reference distribution......Page 294
9.2 Testing for approximate collapsibility of multiway contingency tables......Page 299
9.3.1 An exact optimal test for negligibility of interactions in a two-way ANOVA layout......Page 307
9.3.2 Establishing negligibility of carryover effects in the analysis of two-period crossover trials......Page 313
9.4.1 Genetical background, measures of HW disequilibrium......Page 319
9.4.2 Exact conditional tests for absence of substantial disequilibrium......Page 322
9.4.3 Confidence-interval–based procedures for assessing HWE......Page 332
10.1 Introduction......Page 340
10.2.1 Equivalence with respect to nonstandardized mean bioavailabilities......Page 344
10.2.2 Testing for scaled average bioequivalence......Page 351
10.3.1 Introduction......Page 354
10.3.2 Distribution-free approach to testing for probability-based individual bioequivalence......Page 356
10.3.3 An improved parametric test for probability-based individual bioequivalence......Page 358
10.4.1 Introduction......Page 369
10.4.2 A testing procedure for establishing one-sided bioequivalence with respect to total variability......Page 371
10.4.3 Complete disaggregate testing procedure and illustrating example......Page 373
10.4.4 Some results on power and sample sizes......Page 374
10.4.5 Discussion......Page 376
10.5 Bioequivalence assessment as a problem of comparing bivariate distributions......Page 377
11.1 Introduction......Page 384
11.2 Exploiting the duality between testing for two-sided equivalence and existence of relevant differences......Page 385
11.3.1 One-sample problem with normally distributed data of known variance......Page 388
11.3.2 Two-sample t-test for relevant differences......Page 390
11.3.3 Exact Fisher type test for relevant differences between two binomial distributions......Page 393
Contents......Page 401
Preface......Page 406