Sample Size Determination and Power

378 Pages·2013·1.876 MB·English

by  Thomas P. Ryan(auth.)

Sample Size Determination
and Power
WILEYSERIESINPROBABILITYANDSTATISTICS
EstablishedbyWALTERA.SHEWHARTandSAMUELS.WILKS
Editors:DavidJ.Balding,NoelA.C.Cressie,GarrettM.Fitzmaurice,
HarveyGoldstein,IainM.Johnstone,GeertMolenberghs,DavidW.Scott,
AdrianF.M.Smith,RueyS.Tsay,SanfordWeisberg
EditorsEmeriti:VicBarnett,J.StuartHunter,JosephB.Kadane,JozefL.Teugels
Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume.
Sample Size Determination
and Power
THOMASP.RYAN
InstituteforStatisticsEducation,Arlington,Virginiaand
NorthwesternUniversity,Evanston,Illinois
Coverdesign:JohnWiley&Sons,Inc.
Coverimage:(cid:2)C ThomasP.Ryan
Copyright(cid:2)C 2013byJohnWiley&Sons,Inc.Allrightsreserved.
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.
PublishedsimultaneouslyinCanada.
Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformor
byanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptas
permittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteithertheprior
writtenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeeto
theCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,[phone],
fax[phone],oronthewebatwww.copyright.com.RequeststothePublisherforpermission
shouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,
NJ07030,[phone],fax[phone],oronlineathttp://www.wiley.com/go/permission.
LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin
preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyor
completenessofthecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesof
merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysales
representativesorwrittensalesmaterials.Theadviceandstrategiescontainedhereinmaynotbesuitable
foryoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernor
authorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedto
special,incidental,consequential,orotherdamages.
Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactour
CustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat
[phone]orfax(317)572-4002.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay
notbeavailableinelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteat
www.wiley.com.
LibraryofCongressCataloging-in-PublicationData:
Ryan,ThomasP.,1945–
Samplesizedeterminationandpower/ThomasP.Ryan.
p.;cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-118-43760-5(cloth)
I.Title.
[DNLM:1.SampleSize. 2.ClinicalTrialsasTopic. 3.MathematicalComputing. 4.Regression
Analysis. 5.SamplingStudies.WA950]
615.5072(cid:3)4–dc23
2013000329
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
Contents
Preface xv
1 BriefReviewofHypothesisTestingConcepts/Issuesand
ConfidenceIntervals 1
1.1 BasicConceptsofHypothesisTesting, 1
1.2 ReviewofConfidenceIntervalsandTheirRelationshipto
HypothesisTests, 5
1.3 SportsApplications, 9
1.4 ObservedPower,RetrospectivePower,ConditionalPower,
andPredictivePower, 9
1.5 TestingforEquality,Equivalence,Noninferiority,
orSuperiority, 10
1.5.1 Software, 11
References, 12
Exercises, 14
2 MethodsofDeterminingSampleSizes 17
2.1 InternalPilotStudyVersusExternalPilotStudy, 20
2.2 Examples:FrequentistandBayesian, 24
2.2.1 BayesianApproaches, 30
2.2.2 ProbabilityAssessmentApproach, 31
2.2.3 ReproducibilityProbabilityApproach, 32
2.2.4 CompetingProbabilityApproach, 32
2.2.5 EvidentialApproach, 32
2.3 FinitePopulations, 32
v
vi CONTENTS
2.4 SampleSizesforConfidenceIntervals, 33
2.4.1 UsingtheFinitePopulationCorrectionFactor, 36
2.4.1.1 EstimatingPopulationTotals, 38
2.5 ConfidenceIntervalsonSampleSizeandPower, 39
2.6 SpecificationofPower, 39
2.7 CostofSampling, 40
2.8 EthicalConsiderations, 40
2.9 StandardizationandSpecificationofEffectSizes, 42
2.10 EquivalenceTests, 43
2.11 SoftwareandApplets, 45
2.12 Summary, 47
References, 47
Exercises, 53
3 MeansandVariances 57
3.1 OneMean,Normality,andKnownStandardDeviation, 58
3.1.1 UsingtheCoefficientofVariation, 65
3.2 OneMean,StandardDeviationUnknown,Normality
Assumed, 66
3.3 ConfidenceIntervalsonPowerand/orSampleSize, 67
3.4 OneMean,StandardDeviationUnknown,Nonnormality
Assumed, 70
3.5 OneMean,ExponentialDistribution, 71
3.6 TwoMeans,KnownStandardDeviations—Independent
Samples, 71
3.6.1 UnequalSampleSizes, 74
3.7 TwoMeans,UnknownbutEqualStandard
Deviations—IndependentSamples, 74
3.7.1 UnequalSampleSizes, 76
3.8 TwoMeans,UnequalVariancesandSample
Sizes—IndependentSamples, 77
3.9 TwoMeans,UnknownandUnequalStandard
Deviations—IndependentSamples, 77
3.10 TwoMeans,KnownandUnknownStandard
Deviations—DependentSamples, 78
3.11 BayesianMethodsforComparingMeans, 81
3.12 OneVarianceorStandardDeviation, 81
3.13 TwoVariances, 83
3.14 MoreThanTwoVariances, 84
CONTENTS vii
3.15 ConfidenceIntervals, 84
3.15.1 AdaptiveConfidenceIntervals, 85
3.15.2 OneMean,StandardDeviationUnknown—With
ToleranceProbability, 85
3.15.3 DifferenceBetweenTwoIndependentMeans,
StandardDeviationsKnownandUnknown—Withand
WithoutToleranceProbability, 88
3.15.4 DifferenceBetweenTwoPairedMeans, 90
3.15.5 OneVariance, 91
3.15.6 One-SidedConfidenceBounds, 92
3.16 RelativePrecision, 93
3.17 ComputingAids, 94
3.18 Software, 94
3.19 Summary, 95
Appendix, 95
References, 96
Exercises, 99
4 ProportionsandRates 103
4.1 OneProportion, 103
4.1.1 OneProportion—WithContinuityCorrection, 107
4.1.2 SoftwareDisagreementandRectification, 108
4.1.3 EquivalenceTestsandNoninferiorityTests
forOneProportion, 109
4.1.4 ConfidenceIntervalandErrorofEstimation, 110
4.1.5 OneProportion—ExactApproach, 113
4.1.6 BayesianApproaches, 115
4.2 TwoProportions, 115
4.2.1 TwoProportions—WithContinuityCorrection, 119
4.2.2 TwoProportions—Fisher’sExactTest, 121
4.2.3 WhatApproachIsRecommended?, 122
4.2.4 CorrelatedProportions, 123
4.2.5 EquivalenceTestsforTwoProportions, 124
4.2.6 NoninferiorityTestsforTwoProportions, 125
4.2.7 NeedforPilotStudy?, 125
4.2.8 LinearTrendinProportions, 125
4.2.9 BayesianMethodforEstimatingtheDifference
ofTwoBinomialProportions, 126
4.3 MultipleProportions, 126
viii CONTENTS
4.4 MultinomialProbabilitiesandDistributions, 129
4.5 OneRate, 130
4.5.1 PilotStudyNeeded?, 132
4.6 TwoRates, 132
4.7 BayesianSampleSizeDeterminationMethodsforRates, 135
4.8 Software, 135
4.9 Summary, 136
Appendix, 136
References, 140
Exercises, 144
5 RegressionMethodsandCorrelation 145
5.1 LinearRegression, 145
5.1.1 SimpleLinearRegression, 146
5.1.2 MultipleLinearRegression, 150
5.1.2.1 Application:PredictingCollegeFreshman
GradePointAverage, 155
5.2 LogisticRegression, 155
5.2.1 SimpleLogisticRegression, 156
5.2.1.1 NormallyDistributedCovariate, 158
5.2.1.2 BinaryCovariate, 162
5.2.2 MultipleLogisticRegression, 163
5.2.2.1 MeasurementError, 165
5.2.3 PolytomousLogisticRegression, 165
5.2.4 OrdinalLogisticRegression, 166
5.2.5 ExactLogisticRegression, 167
5.3 CoxRegression, 167
5.4 PoissonRegression, 169
5.5 NonlinearRegression, 172
5.6 OtherTypesofRegressionModels, 172
5.7 Correlation, 172
5.7.1 ConfidenceIntervals, 174
5.7.2 IntraclassCorrelation, 175
5.7.3 TwoCorrelations, 175
5.8 Software, 176
5.9 Summary, 177
References, 177
Exercises, 180
CONTENTS ix
6 ExperimentalDesigns 183
6.1 OneFactor—TwoFixedLevels, 184
6.1.1 UnequalSampleSizes, 186
6.2 OneFactor—MoreThanTwoFixedLevels, 187
6.2.1 MultipleComparisonsandDunnett’sTest, 192
6.2.2 AnalysisofMeans(ANOM), 193
6.2.3 UnequalSampleSizes, 195
6.2.4 AnalysisofCovariance, 196
6.2.5 RandomizedCompleteBlockDesigns, 197
6.2.6 IncompleteBlockDesigns, 198
6.2.7 LatinSquareDesigns, 199
6.2.7.1 Graeco-LatinSquareDesigns, 202
6.3 TwoFactors, 203
6.4 2k Designs, 205
6.4.1 22 DesignwithEqualandUnequalVariances, 206
6.4.2 Unreplicated2k Designs, 206
6.4.3 Softwarefor2k Designs, 208
6.5 2k−p Designs, 209
6.6 DetectingConditionalEffects, 210
6.7 GeneralFactorialDesigns, 211
6.8 RepeatedMeasuresDesigns, 212
6.8.1 CrossoverDesigns, 215
6.8.1.1 Software, 217
6.9 ResponseSurfaceDesigns, 218
6.10 MicroarrayExperiments, 219
6.10.1 Software, 220
6.11 OtherDesigns, 220
6.11.1 Plackett–BurmanDesigns, 220
6.11.2 Split-PlotandStrip-PlotDesigns, 222
6.11.3 NestedDesigns, 224
6.11.4 Raydesigns, 225
6.12 DesignsforNonnormalResponses, 225
6.13 DesignswithRandomFactors, 227
6.14 ZeroPatientDesign, 228
6.15 ComputerExperiments, 228
6.16 NoninferiorityandEquivalenceDesigns, 229
6.17 PharmacokineticExperiments, 229
6.18 BayesianExperimentalDesign, 229
x CONTENTS
6.19 Software, 230
6.20 Summary, 232
Appendix, 233
References, 234
Exercises, 239
7 ClinicalTrials 243
7.1 ClinicalTrials, 245
7.1.1 ClusterRandomizedTrials, 247
7.1.2 PhaseIITrials, 247
7.1.2.1 PhaseIICancerTrials, 247
7.1.3 PhaseIIITrials, 247
7.1.4 LongitudinalClinicalTrials, 248
7.1.5 FixedVersusAdaptiveClinicalTrials, 248
7.1.6 NoninferiorityTrials, 249
7.1.7 RepeatedMeasurements, 249
7.1.8 MultipleTests, 250
7.1.9 UseofInternalPilotStudiesforClinical
Trials, 250
7.1.10 UsingHistoricalControls, 250
7.1.11 TrialswithCombinationTreatments, 251
7.1.12 GroupSequentialTrials, 251
7.1.13 VaccineEfficacyStudies, 251
7.2 BioequivalenceStudies, 251
7.3 EthicalConsiderations, 252
7.4 TheUseofPowerinClinicalStudies, 252
7.5 PreclinicalExperimentation, 253
7.6 Pharmacodynamic,Pharmacokinetic,andPharmacogenetic
Experiments, 253
7.7 MethodofCompetingProbability, 254
7.8 BayesianMethods, 255
7.9 CostandOtherSampleSizeDeterminationMethods
forClinicalTrials, 256
7.10 Meta-AnalysesofClinicalTrials, 256
7.11 Miscellaneous, 257
7.12 SurveyResultsofPublishedArticles, 259
7.13 Software, 260
7.14 Summary, 263