Testing statistical hypotheses of equivalence and noninferiority:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2010
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 415 S. graph. Darst. |
| ISBN: | 9781439808184 |
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MARC
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| 100 | 1 | |a Wellek, Stefan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Testing statistical hypotheses of equivalence and noninferiority |c Stefan Wellek |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b Chapman & Hall/CRC |c 2010 | |
| 300 | |a XVI, 415 S. |b graph. Darst. | ||
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| adam_text | IMAGE 1
CONTENTS
PREFACE XI
1 INTRODUCTION 1
1.1 STATISTICAL MEANING OF THE CONCEPTS OF EQUIVALENCE AND IIONIN-
FERIORITY 1
1.2 DEMONSTRATION OF EQUIVALENCE AS A BASIC PROBLEM OF APPLIED
STATISTICS 2
1.3 MAJOR FIELDS OF APPLICATION OF EQUIVALENCE TESTS 5
1.3.1 COMPARATIVE BIOEQUIVALENCE TRIALS 5
1.3.2 CLINICAL TRIALS INVOLVING AN ACTIVE CONTROL 7
1.3.3 PRELIMINARY TESTS FOR CHECKING ASSUMPTIONS UNDERLYING OTHER
METHODS OF STATISTICAL INFERENCE 8
1.4 ROLE OF EQUIVALENCE/NONINFERIORITY STUDIES IN CURRENT MEDICAL
RESEARCH 8
1.5 FORMULATION OF HYPOTHESES 10
1.6 CHOOSING THE MAIN DISTRIBUTIONAL PARAMETER 13
1.7 NUMERICAL SPECIFICATION OF THE LIMITS OF EQUIVALENCE 15
2 GENERAL TECHNIQUES FOR DEALING WITH NONINFERIORITY PROBLEMS 19 2.1
STANDARD SOLUTION IN THE CASE OF LOCATION PARAMETER FAMILIES . 19 2.1.1
PAIRED OBSERVATIONS 19
2.1.2 TWO INDEPENDENT SAMPLES 22
2.1.3 POWER AND SAMPLE SIZE CALCULATION BASED ON TESTS FOR
NONINFERIORITY UNDER LOCATION-SHIFT MODELS 23
2.2 METHODS OF CONSTRUCTING EXACT OPTIMAL TESTS FOR SETTINGS BEYOND THE
LOCATION-SHIFT MODEL 24
2.3 LARGE-SAMPLE SOLUTIONS FOR PROBLEMS INACCESSIBLE FOR EXACT CON-
STRUCTIONS 26
2.4 OBJECTIVE BAYESIAN METHODS 27
2.5 IMPROVED NONRANDOMIZED TESTS FOR DISCRETE DISTRIBUTIONS . .. 28 2.6
RELATIONSHIP BETWEEN TESTS FOR NONINFERIORITY AND TWO-SIDED EQUIVALENCE
TESTS 30
2.7 HALVING ALPHA? 31
IMAGE 2
GENERAL APPROACHES TO THE CONSTRUCTION OF TESTS FOR EQUIVA-
LENCE IN THE STRICT SENSE 33
3. 1 THE PRINCIPLE OF CONFIDENCE INTERVAL INCLUSION 33
3.2 BAYESIAN TESTS FOR TWO-SIDED EQUIVALENCE 36
3.3 THE CLASSICAL APPROACH TO DERIVING OPTIMAL PARAMETRIC TESTS FOR
EQUIVALENCE HYPOTHESES 40
3.4 CONSTRUCTION OF ASYMPTOTIC TESTS FOR EQUIVALENCE 45
EQUIVALENCE TESTS FOR SELECTED ONE-PARAMETER PROBLEMS 49 4.1 THE
ONE-SAMPLE PROBLEM WITH NORMALLY DISTRIBUTED OBSERVA- TIONS OF KNOWN
VARIANCE 49
4.2 TEST FOR EQUIVALENCE OF A HAZARD RATE TO SOME GIVEN REFERENCE VALUE
WITH EXPONENTIALLY DISTRIBUTED SURVIVAL TIMES 55
4.3 TESTING FOR EQUIVALENCE OF A SINGLE BINOMIAL PROPORTION TO A FIXED
REFERENCE SUCCESS PROBABILITY 59
4.4 CONFIDENCE-INTERVAL INCLUSION RULES AS ASYMPTOTICALLY UMP TESTS FOR
EQUIVALENCE 64
4.5 NONINFERIORITY ANALOGUES OF THE TESTS DERIVED IN THIS CHAPTER . 68
EQUIVALENCE TESTS FOR DESIGNS WITH PAIRED OBSERVATIONS 71
5.1 SIGN TEST FOR EQUIVALENCE 71
5.2 EQUIVALENCE TESTS FOR THE MCNEMAR SETTING 76
5.2.1 LARGE-SAMPLE SOLUTION 78
5.2.2 CORRECTED FINITE-SAMPLE VERSION OF THE LARGE-SAMPLE TEST 81
5.2.3 MODIFICATIONS FOR THE NONINFERIORITY CASE 85
5.3 PAIRED F-TEST FOR EQUIVALENCE 92
5.4 SIGNED RANK TEST FOR EQUIVALENCE 99
5.5 A GENERALIZATION OF THE SIGNED RANK TEST FOR EQUIVALENCE FOR
LIONCONTINUOUS DATA 108
EQUIVALENCE TESTS FOR TWO UNRELATED SAMPLES 119
6.1 TWO-SAMPLE T-TEST FOR EQUIVALENCE 119
6.2 MANN-WHITNEY TEST FOR EQUIVALENCE 126
(5.3 TWO-SAMPLE EQUIVALENCE: TESTS BASED ON LINEAR RANK STATISTICS . 136
6.4 A DISTRIBUTION-FREE TWO-SAMPLE EQUIVALENCE TEST ALLOWING FOR
ARBITRARY PATTERNS OF TIES 150
6.5 TESTING FOR DISPERSION EQUIVALENCE OF TWO GAUSSIAN DISTRIBU- TIONS
164
6.6 EQUIVALENCE TESTS FOR TWO BINOMIAL SAMPLES 172
6.6.1 EXACT FISHER TYPE TEST FOR NONINFERIORITY WITH RESPECT TO THE ODDS
RATIO 172
6.6.2 IMPROVED NONRANDOMIZED TESTS FOR NONINFERIORITY WITH RESPECT TO
THE ODDS RATIO 177
IMAGE 3
6.6.3 TESTS FOR IIONINFERIORITY USING ALTERNATIVE PARAMETRIZA-
TIONS 181
6.6.4 EXACT TEST FOR TWO-SIDED EQUIVALENCE WITH RESPECT TO THE ODDS
RATIO 186
6.6.5 AN IMPROVED NONRANDOMIZED VERSION OF THE UMPU TEST FOR TWO-SIDED
EQUIVALENCE 193
6.6.6 TESTS FOR TWO-SIDED EQUIVALENCE WITH RESPECT TO THE DIF- FERENCE
OF SUCCESS PROBABILITIES 194
6.7 LOG-RANK TEST FOR EQUIVALENCE OF TWO SURVIVOR FUNCTIONS . . .. 202
6.7.1 RATIONALE OF THE LOG-RANK TEST FOR EQUIVALENCE IN THE TWO-SIDED
SENSE 203
6.7.2 POWER APPROXIMATION AND SAMPLE SIZE CALCULATION FOR THE LOG-RANK
TEST FOR EQUIVALENCE 210
6.7.3 LOG-RANK TEST FOR NONINFERIORITY 214
7 MULTISAMPLE TESTS FOR EQUIVALENCE 219
7.1 THE INTERSECTION-UNION PRINCIPLE AS A GENERAL SOLUTION TO NUIL-
TISAMPLE EQUIVALENCE PROBLEMS 219
7.2 F-TEST FOR EQUIVALENCE OF K NORMAL DISTRIBUTIONS 221
7.3 MODIFIED STUDENTIZED RANGE TEST FOR EQUIVALENCE 225
7.4 TESTING FOR DISPERSION EQUIVALENCE OF MORE THAN TWO GAUSSIAN
DISTRIBUTIONS 227
7.5 A NONPARAMETRIC FC-SAMPLE TEST FOR EQUIVALENCE 231
8 EQUIVALENCE TESTS FOR MULTIVARIATE DATA 235
8.1 EQUIVALENCE TESTS FOR SEVERAL DEPENDENT SAMPLES FROM NORMAL
DISTRIBUTIONS 235
8.1.1 GENERALIZING THE PAIRED I-TEST FOR EQUIVALENCE BY MEANS OF THE T 2
-STATISTIC 235
8.1.2 A MANY-ONE EQUIVALENCE TEST FOR DEPENDENT SAMPLES BASED ON
EUCLIDEAN DISTANCES 241
8.1.3 TESTING FOR EQUIVALENCE WITH DEPENDENT SAMPLES AND AN INDIFFERENCE
ZONE OF RECTANGULAR SHAPE 218
8.1.4 DISCUSSION 252
8.2 MULTIVARIATE TWO-SAMPLE TESTS FOR EQUIVALENCE 253
8.2.1 A TWO-SAMPLE TEST FOR EQUIVALENCE BASED ON HOTELLING S T 2 253
8.2.2 BEHAVIOR OF THE TWO-SAMPLE T 2 -TEST FOR EQUIVALENCE UN- DER
HETEROSKEDASTICITY 259
8.2.3 MULTIVARIATE TWO-SAMPLE TESTS FOR EQUIVALENCE REGIONS OF
RECTANGULAR SHAPE 262
9 TESTS FOR ESTABLISHING GOODNESS OF FIT 265
9.1 TESTING FOR EQUIVALENCE OF A SINGLE MULTINOMIAL DISTRIBUTION WITH A
FULLY SPECIFIED REFERENCE DISTRIBUTION 265
IMAGE 4
9.2 TESTING FOR APPROXIMATE COLLAPSIBILITY OF MULTIWAY CONTINGENCY
TABLES 270
9.3 ESTABLISHING GOODNESS OF FIT OF LINEAR MODELS FOR NORMALLY DIS-
TRIBUTED DATA 278
9.3.1 AN EXACT OPTIMAL TEST FOR NEGLIGIBILITY OF INTERACTIONS IN A
TWO-WAY ANOVA LAYOUT 278
9.3.2 ESTABLISHING NEGLIGIBILITY OF CARRYOVER EFFECTS IN THE ANALYSIS OF
TWO-PERIOD CROSSOVER TRIALS 284
9.4 TESTING FOR APPROXIMATE COMPATIBILITY OF A GENOTYPE DISTRIBU- TION
WITH THE HARDY-WEINBERG CONDITION 290
9.4.1 GENETICAL BACKGROUND, MEASURES OF HW DISEQUILIBRIUM 290 9.4.2
EXACT CONDITIONAL TESTS FOR ABSENCE OF SUBSTANTIAL DIS- EQUILIBRIUM 293
9.4.3 CONFIDENCE-INTERVAL-BASED PROCEDURES FOR ASSESSING HWE 303
10 THE ASSESSMENT OF BIOEQUIVALENCE 311
10.1 INTRODUCTION 311
10.2 METHODS OF TESTING FOR AVERAGE BIOEQUIVALENCE 315
10.2.1 EQUIVALENCE WITH RESPECT TO NONSTANDARDIZED MEAN BIO-
AVAILABILITIES 315
10.2.2 TESTING FOR SCALED AVERAGE BIOEQUIVALENCE 322 10.3 INDIVIDUAL
BIOEQUIVALENCE: CRITERIA AND TESTING PROCEDURES . . 325 10.3.1
INTRODUCTION 325
10.3.2 DISTRIBUTION-FREE APPROACH TO TESTING FOR PROBABILITY- BASED
INDIVIDUAL BIOEQUIVALENCE 327
10.3.3 AN IMPROVED PARAMETRIC TEST FOR PROBABILITY-BASED IN- DIVIDUAL
BIOEQUIVALENCE 329
10.4 APPROACHES TO DEFINING AND ESTABLISHING POPULATION BIOEQUI- VALENCE
340
10.4.1 INTRODUCTION 340
10.4.2 A TESTING PROCEDURE FOR ESTABLISHING ONE-SIDED BIOEQUI- VALENCE
WITH RESPECT TO TOTAL VARIABILITY 342
10.4.3 COMPLETE DISAGGREGATE TESTING PROCEDURE AND ILLUSTRAT- ING
EXAMPLE 344
10.4.4 SOME RESULTS ON POWER AND SAMPLE SIZES 345
10.4.5 DISCUSSION 347
10.5 BIOEQUIVALENCE ASSESSMENT AS A PROBLEM OF COMPARING BIVARI- ATE
DISTRIBUTIONS 348
11 TESTS FOR RELEVANT DIFFERENCES BETWEEN TREATMENTS 355 11.1
INTRODUCTION 355
11.2 EXPLOITING THE DUALITY BETWEEN TESTING FOR TWO-SIDED EQUIVA- LENCE
AND EXISTENCE OF RELEVANT DIFFERENCES 356
IMAGE 5
11.3 SOLUTIONS TO SOME SPECIAL PROBLEMS OF TESTING FOR RELEVANT DIF-
FERENCES 359
11.3.1 ONE-SAMPLE PROBLEM WITH NORMALLY DISTRIBUTED DATA OF KNOWN
VARIANCE 359
11.3.2 TWO-SAMPLE T-TEST FOR RELEVANT DIFFERENCES 361 11.3.3 EXACT
FISHER TYPE TEST FOR RELEVANT DIFFERENCES BETWEEN TWO BINOMIAL
DISTRIBUTIONS 364
APPENDIX A BASIC THEORETICAL RESULTS 369
A.I UMP TESTS FOR EQUIVALENCE PROBLEMS IN STPJJ FAMILIES 369 A.2 UMPU
EQUIVALENCE TESTS IN MULTIPARAMETER EXPONENTIAL FAMI- LIES 375
A.3 A SUFFICIENT CONDITION FOR THE ASYMPTOTIC VALIDITY OF TESTS FOR
EQUIVALENCE 376
APPENDIX B LIST OF SPECIAL COMPUTER PROGRAMS 379
APPENDIX C FREQUENTLY USED SPECIAL SYMBOLS AND
ABBREVIATIONS 383
REFERENCES 387
AUTHOR INDEX 403
SUBJECT INDEX 407
|
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| language | English |
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| spelling | Wellek, Stefan Verfasser aut Testing statistical hypotheses of equivalence and noninferiority Stefan Wellek 2. ed. Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2010 XVI, 415 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistical hypothesis testing Äquivalenz (DE-588)4141497-4 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistischer Test (DE-588)4077852-6 s Äquivalenz (DE-588)4141497-4 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022636379&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wellek, Stefan Testing statistical hypotheses of equivalence and noninferiority Statistical hypothesis testing Äquivalenz (DE-588)4141497-4 gnd Statistischer Test (DE-588)4077852-6 gnd |
| subject_GND | (DE-588)4141497-4 (DE-588)4077852-6 |
| title | Testing statistical hypotheses of equivalence and noninferiority |
| title_auth | Testing statistical hypotheses of equivalence and noninferiority |
| title_exact_search | Testing statistical hypotheses of equivalence and noninferiority |
| title_full | Testing statistical hypotheses of equivalence and noninferiority Stefan Wellek |
| title_fullStr | Testing statistical hypotheses of equivalence and noninferiority Stefan Wellek |
| title_full_unstemmed | Testing statistical hypotheses of equivalence and noninferiority Stefan Wellek |
| title_short | Testing statistical hypotheses of equivalence and noninferiority |
| title_sort | testing statistical hypotheses of equivalence and noninferiority |
| topic | Statistical hypothesis testing Äquivalenz (DE-588)4141497-4 gnd Statistischer Test (DE-588)4077852-6 gnd |
| topic_facet | Statistical hypothesis testing Äquivalenz Statistischer Test |
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