Group sequential methods with applications to clinical trials:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 390 S. graph. Darst. |
| ISBN: | 0849303168 |
Internformat
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| 245 | 1 | 0 | |a Group sequential methods with applications to clinical trials |c Christopher Jennison and Bruce W. Turnbull |
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| 650 | 4 | |a Clinical Trials as Topic |x methods | |
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Datensatz im Suchindex
| _version_ | 1804127557936742400 |
|---|---|
| adam_text | Contents
List of figures xj
List of tables xiii
Preface xvy
Glossary xjx
1 Introduction ]
1.1 About This Book 1
1.2 Why Sequential Methods 3
1.3 A Short History of Sequential and Group Sequential Methods 5
1.4 Some Examples 11
1.5 Chapter Organization: A Roadmap 15
1.6 Bibliography and Notes 18
2 Two Sided Tests: Introduction 21
2.1 Two Sided Tests for Comparing Two Treatments with Normal
Response of Known Variance 21
2.2 A Fixed Sample Test 22
2.3 Group Sequential Tests 23
2.4 Pocock s Test 24
2.5 O Brien Fleming s Test 29
2.6 Properties of Pocock and O Brien Fleming Tests 31
2.7 Other Tests 39
2.8 Conclusions 47
3 Two Sided Tests: General Applications 49
3.1 A Unified Formulation 49
3.2 Applying the Tests with Equal Group Sizes 53
3.3 Applying the Tests with Unequal Increments in Information 57
3.4 Normal Linear Models 62
3.5 Other Parametric Models 70
3.6 Binary Data: Group Sequential Tests for Proportions 74
3.7 The Group Sequential Log Rank Test for Survival Data 77
3.8 Group Sequential r Tests 79
viii CONTENTS
4 One Sided Tests 87
4.1 Introduction 87
4.2 The Power Family of One Sided Group Sequential Tests 89
4.3 Adapting Power Family Tests to Unequal Increments in
Information 96
4.4 Group Sequential One Sided r Tests 99
4.5 Whitehead s Triangular Test 105
5 Two Sided Tests with Early Stopping Under the Null Hypothesis 111
5.1 Introduction 111
5.2 The Power Family of Two Sided Inner Wedge Tests 112
5.3 Whitehead s Double Triangular Test 123
6 Equivalence Tests 129
6.1 Introduction 129
6.2 One Sided Tests of Equivalence 130
6.3 Two Sided Tests of Equivalence: Application to Comparative
Bioavailability Studies 130
6.4 Individual Bioequivalence: A One Sided Test for Proportions 141
6.5 Bibliography and Notes 143
7 Flexible Monitoring: The Error Spending Approach 145
7.1 Unpredictable Information Sequences 145
7.2 Two Sided Tests 146
7.3 One Sided Tests 161
7.4 Data Dependent Timing of Analyses 166
7.5 Computations for Error Spending Tests 169
8 Analysis Following a Sequential Test 171
8.1 Introduction 171
8.2 Distribution Theory 171
8.3 Point Estimation 175
8.4 P values 179
8.5 Confidence Intervals 181
9 Repeated Confidence Intervals 189
9.1 Introduction 189
9.2 Example: Difference of Normal Means 193
9.3 Derived Tests: Use of RCIs to Aid Early Stopping Decisions 194
9.4 Repeated P values 202
9.5 Discussion 202
10 Stochastic Curtailment 205
10.1 Introduction 205
10.2 The Conditional Power Approach 205
10.3 The Predictive Power Approach 210
CONTENTS ix
10.4 A Parameter Free Approach 213
10.5 A Case Study with Survival Data 215
10.6 Bibliography and Notes 219
11 General Group Sequential Distribution Theory 221
11.1 Introduction 221
11.2 A Standard Joint Distribution for Successive Estimates of a
Parameter Vector 221
11.3 Normal Linear Models 222
11.4 Normal Linear Models with Unknown Variance: Group
Sequential f Tests 224
11.5 Example: An Exact One Sample Group Sequential r Test 226
11.6 General Parametric Models: Generalized Linear Models 228
11.7 Bibliography and Notes 232
12 Binary Data 235
12.1 A Single Bernoulli Probability 235
12.2 Two Bernoulli Probabilities 244
12.3 The Odds Ratio and Multiple 2x2 Tables 251
12.4 Case Control and Matched Pair Analyses 254
12.5 Logistic Regression: Adjusting for Covariates 256
12.6 Connection with Survival Analysis 257
13 Survival Data 259
13.1 Introduction 259
13.2 The Log Rank Test 260
13.3 The Stratified Log Rank Test 261
13.4 Group Sequential Methods for Survival Data with Covariates 262
13.5 Repeated Confidence Intervals for a Hazard Ratio 265
13.6 Example: A Clinical Trial for Carcinoma of the Oropharynx 267
13.7 Survival Probabilities and Quantiles 274
13.8 Bibliography and Notes 276
14 Internal Pilot Studies: Sample Size Re estimation 279
14.1 The Role of an Internal Pilot Phase 279
14.2 Sample Size Re estimation for a Fixed Sample Test 281
14.3 Sample Size Re estimation in Group Sequential Tests 293
15 Multiple Endpoints 299
15.1 Introduction 299
15.2 The Bonferroni Procedure 300
15.3 A Group Sequential Hotelling Test 302
15.4 A Group Sequential Version of O Brien s Test 306
15.5 Tests Based on Other Global Statistics 310
15.6 Tests Based on Marginal Criteria 311
15.7 Bibliography and Notes 314
x CONTENTS
16 Multi Armed Trials 317
16.1 Introduction 317
16.2 Global Tests 317
16.3 Monitoring Pairwise Comparisons 321
16.4 Bibliography and Notes 324
17 Adaptive Treatment Assignment 327
17.1 A Multi Stage Adaptive Design 327
17.2 A Multi Stage Adaptive Design with Time Trends 331
17.3 Validity of Adaptive Multi stage Procedures 333
17.4 Bibliography and Notes 335
18 Bayesian Approaches 337
18.1 The Bayesian Paradigm 337
18.2 Stopping Rules 338
18.3 Choice of Prior Distribution 341
18.4 Discussion 343
19 Numerical Computations for Group Sequential Tests 345
19.1 Introduction 345
19.2 The Basic Calculation 346
19.3 Error Probabilities and Sample Size Distributions 351
19.4 Tests Defined by Error Spending Functions 353
19.5 Analysis Following a Group Sequential Test 355
19.6 Further Applications of Numerical Computation 357
19.7 Computer Software 360
References 363
Index 387
List of figures
2.1 A Pocock test for five groups of observations 28
2.2 An O Brien Fleming test for five groups of observations 32
2.3 Boundaries for Pocock, O Brien Fleming, Haybittle Peto, and
Wang Tsiatis tests 47
3.1 Pocock and O Brien Fleming tests for four groups of
observations expressed in terms of Z* and S* 73
4.1 Two power family one sided tests for four groups of observations 94
4.2 One sided test with four groups of observations 100
4.3 One sided triangular tests for four groups of observations 107
5.1 A power family inner wedge test for five groups of observations 117
5.2 Comparison of two inner wedge tests 126
8.1 Sub densities p(k, z; 9) when 9 = 0 for a four stage O Brien
Fleming test 174
8.2 Sub densities p(k, z; 9) when 9 = S for a four stage O Brien
Fleming test 175
8.3 Sampling densities of 9 when 9 = 0 for a four stage O Brien
Fleming test 176
8.4 Sampling densities of 9 when 9 = 1 for a four stage O Brien
Fleming test 177
8.5 Stopping boundaries where the consistency condition does and
does not hold for the MLE ordering 185
9.1 RCIs, parent test and derived tests 195
10.1 Conditional and unconditional power curves for a one sided test 208
10.2 Stopping boundary for a stochastically curtailed one sided test
using the conditional power approach 209
10.3 Stopping boundary for a stochastically curtailed two sided test
using the conditional power approach 2! 0
10.4 Stopping boundary for a stochastically curtailed one sided test
using the predictive power approach with a uniform prior 212
xii LIST OF FIGURES
10.5 Stopping boundary for a stochastically curtailed two sided test
using the predictive power approach 213
10.6 Stopping boundary for a stochastically curtailed two sided test
using the parameter free approach 215
10.7 Power and conditional power curves for the case study 217
List of tables
2.1 Pocock tests: constants Cp(K.a) 26
2.2 Pocock tests: constants Rp(K,a,P) 27
2.3 O Brien Fleming tests: constants CB(K, a) 29
2.4 O Brien Fleming tests: constants RB(K, a, P) 30
2.5 Pocock and O Brien Fleming tests: an example 33
2.6 Sample size distributions for Pocock and O Brien Fleming tests 34
2.7 Properties of Pocock tests 37
2.8 Properties of O Brien Fleming tests 38
2.9 Wang Tsiatis tests: constants Cwr(,K, a. A) 40
2.10 Wang Tsiatis tests: constants/?wr(K. a, P, A) 41
2.11 Properties of Wang Tsiatis tests for a = 0.05 and 1 p = 0.8 42
2.12 Properties of Wang Tsiatis tests for a = 0.05 and 1 P = 0.9 43
2.13 Haybittle Peto tests: constants CW/ (K. «) 45
2.14 Properties of Haybittle Peto tests 46
3.1 Properties of two sided tests for unequal group sizes 59
3.2 Properties of two sided tests for various information sequences 60
3.3 Properties of two sided group sequential f tests 82
4.1 Power family one sided tests: constants and properties for
a = 0.05 and 1 P = 0.8 90
4.2 Power family one sided tests: constants and properties for
a = 0.05 and 1 0=0.9 91
4.3 Power family one sided tests: constants and properties for
a = 0.05 and 1 P = 0.95 92
4.4 One sided tests: minimum expected sample sizes 95
4.5 Properties of power family one sided tests for various information
sequences
4.6 Properties of group sequential one sided t tests 103
4 7 Whitehead s triangular tests: constants RwhiK, a, ft) and
108
properties
4.8 Properties of Whitehead s triangular tests for various information
sequences
5.1 Power family two sided inner wedge tests: constants and
properties for a = 0.05 and 1 P = 0.8 114
xiv LIST OF TABLES
5.2 Power family two sided inner wedge tests: constants and
properties for a = 0.05 and 1 0 = 0.9 115
5.3 Power family two sided inner wedge tests: constants and i
properties for a = 0.05 and 1 0 = 0.95 116
5.4 Properties of power family inner wedge tests for various
information sequences 119
5.5 Properties of power family inner wedge r tests 121
5.6 Whitehead s double triangular tests: constants Rdt(K, a, fl) and
properties 125
6.1 Properties of power family equivalence tests for various
information sequences 136 ;
6.2 Properties of power family t tests for equivalence 139
6.3 AUC equivalence test data 140
7.1 Lan DeMets error spending tests: constants Rld(K, oe, P. p) 150
7.2 Properties of Lan DeMets error spending tests with a = 0.05
and 1 /5 = 0.8 151
7.3 Properties of Lan DeMets error spending tests with a = 0.05
and 1 /3 =0.9 152
7.4 Power attained by Lan DeMets error spending tests for various
information sequences 155
7.5 Power attained by Lan DeMets error spending tests when the
number of analyses differs from that planned 156
7.6 One sided error spending tests: constants Ros(K,«. /*.P) 164
7.7 Properties of one sided error spending tests with a = 0.05 and
1 0 = 0.8 165
7.8 Properties of one sided error spending tests with a = 0.05 and
1 P = 0.9 166
7.9 Properties of one sided error spending tests with a = 0.05 and
1 0 = 0.95 167
9.1 Simultaneous coverage probabilities for naive 95% confidence
intervals 190
9.2 Ratios of widths of 95% RCIs to unadjusted 95% confidence
intervals 193
9.3 Properties of one sided tests derived from RCIs 198
10.1 Interim mortality data for the case study 218
10.2 Additional person years under three possible scenarios for
continuing the case study 219
11.1 Repeated r tests: constants ZP(K, m, a) and ZB(K, m, a) 227
12.1 Selected two stage and three stage one sided binomial tests 238
12.2 90% confidence intervals following a three stage sampling plan 240
LIST OF TABLES xv
12.3 90% confidence intervals following a three stage sampling plan
(continued) 241
12.4 Continuation and acceptance regions for a three stage test of
Pa = Pb 247
12.5 Acceptance region of a modified three stage test of pA = pB 248
12.6 Hypothetical interim data for the Ille et Vilaine study 253
12.7 Interim results for the data of Table 12.6 254
12.8 Hypothetical interim data for the Leisure World study 255
12.9 Interim results for the data of Table 12.8 255
13.1 Summary data and critical values for a group sequential stratified
log rank test in a trial for carcinoma of the oropharynx 270
13.2 Repeated confidence intervals for the log hazard ratio for the
oropharynx trial data 271
13.3 Group sequential estimates of Cox model parameters for the
oropharynx trial data 272
13.4 Test statistics and critical values for a group sequential test based
on a Cox regression model for the oropharynx trial data 273
14.1 Properties of internal pilot tests for the difference of two binary
response probabilities using Herson Wittes approach 284
14.2 Properties of internal pilot tests for the difference of two binary
response probabilities using Gould s approach 285
14.3 Properties of internal pilot tests for the ratio of two binary
response probabilities 287
14.4 Properties of internal pilot tests of Wittes Brittain and of
Birkett Day for two normal distributions of unknown variance 289
14.5 Properties of internal pilot tests of Denne Jennison for two
normal distributions of unknown variance 292
15.1 Bonferroni procedures with p endpoints: constants CP(K,a) for
Pocock tests 301
15.2 Bonferroni procedures with p endpoints: constants CB(K, a) for
O Brien Fleming tests 302
15.3 Worksheet for a group sequential test using Hotelling s T2
statistic 305
15.4 Worksheet for a group sequential test using O Brien s GLS
statistic 310
16.1 Repeated x2 tests of homogeneity of J normal means: constants
CP(p, K, a) and CB(p,K,a) 319
17.1 Properties of power family one sided tests using adaptive
sampling
18.1 False positive rates for stopping rules based on Bayesian posterior
probabilities
|
| any_adam_object | 1 |
| author | Jennison, Christopher Turnbull, Bruce W. |
| author_facet | Jennison, Christopher Turnbull, Bruce W. |
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| dewey-full | 615/.19/0727 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 615 - Pharmacology and therapeutics |
| dewey-raw | 615/.19/0727 |
| dewey-search | 615/.19/0727 |
| dewey-sort | 3615 219 3727 |
| dewey-tens | 610 - Medicine and health |
| discipline | Mathematik Wirtschaftswissenschaften Medizin |
| format | Book |
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| id | DE-604.BV012873333 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:15Z |
| institution | BVB |
| isbn | 0849303168 |
| language | English |
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| physical | XVIII, 390 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Chapman & Hall |
| record_format | marc |
| spelling | Jennison, Christopher Verfasser aut Group sequential methods with applications to clinical trials Christopher Jennison and Bruce W. Turnbull Boca Raton [u.a.] Chapman & Hall 2000 XVIII, 390 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics cabt Ensaios clínicos (pesquisa e planejamento) larpcal Études cliniques - Méthodes statistiques Statistik Clinical Trials as Topic methods Clinical trials Statistical methods Decision Theory Models, Statistical Statistics as Topic methods Klinische Prüfung (DE-588)4031192-2 gnd rswk-swf Sequentialmethode (DE-588)4301567-0 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Medizinische Statistik (DE-588)4127563-9 gnd rswk-swf Medizinische Statistik (DE-588)4127563-9 s Klinische Prüfung (DE-588)4031192-2 s Datenanalyse (DE-588)4123037-1 s Sequentialmethode (DE-588)4301567-0 s DE-604 Turnbull, Bruce W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008761909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jennison, Christopher Turnbull, Bruce W. Group sequential methods with applications to clinical trials Statistics cabt Ensaios clínicos (pesquisa e planejamento) larpcal Études cliniques - Méthodes statistiques Statistik Clinical Trials as Topic methods Clinical trials Statistical methods Decision Theory Models, Statistical Statistics as Topic methods Klinische Prüfung (DE-588)4031192-2 gnd Sequentialmethode (DE-588)4301567-0 gnd Datenanalyse (DE-588)4123037-1 gnd Medizinische Statistik (DE-588)4127563-9 gnd |
| subject_GND | (DE-588)4031192-2 (DE-588)4301567-0 (DE-588)4123037-1 (DE-588)4127563-9 |
| title | Group sequential methods with applications to clinical trials |
| title_auth | Group sequential methods with applications to clinical trials |
| title_exact_search | Group sequential methods with applications to clinical trials |
| title_full | Group sequential methods with applications to clinical trials Christopher Jennison and Bruce W. Turnbull |
| title_fullStr | Group sequential methods with applications to clinical trials Christopher Jennison and Bruce W. Turnbull |
| title_full_unstemmed | Group sequential methods with applications to clinical trials Christopher Jennison and Bruce W. Turnbull |
| title_short | Group sequential methods with applications to clinical trials |
| title_sort | group sequential methods with applications to clinical trials |
| topic | Statistics cabt Ensaios clínicos (pesquisa e planejamento) larpcal Études cliniques - Méthodes statistiques Statistik Clinical Trials as Topic methods Clinical trials Statistical methods Decision Theory Models, Statistical Statistics as Topic methods Klinische Prüfung (DE-588)4031192-2 gnd Sequentialmethode (DE-588)4301567-0 gnd Datenanalyse (DE-588)4123037-1 gnd Medizinische Statistik (DE-588)4127563-9 gnd |
| topic_facet | Statistics Ensaios clínicos (pesquisa e planejamento) Études cliniques - Méthodes statistiques Statistik Clinical Trials as Topic methods Clinical trials Statistical methods Decision Theory Models, Statistical Statistics as Topic methods Klinische Prüfung Sequentialmethode Datenanalyse Medizinische Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008761909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jennisonchristopher groupsequentialmethodswithapplicationstoclinicaltrials AT turnbullbrucew groupsequentialmethodswithapplicationstoclinicaltrials |