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Case-ControlStudies
Thecase-controlapproachisapowerfulmethodforinvestigatingfactorsthatmay
explainaparticularevent.Itisextensivelyusedinepidemiologytostudydisease
incidence,oneofthebest-knownexamplesbeingtheinvestigationbyBradfordHill
andDollofthepossibleconnectionbetweencigarettesmokingandlungcancer.More
recently,case-controlstudieshavebeenincreasinglyusedinotherfields,including
sociologyandeconometrics.
Withaparticularfocusonstatisticalanalysis,thisbookisidealforappliedand
theoreticalstatisticianswantinganup-to-dateintroductiontothefield.Itcoversthe
fundamentalsofcase-controlstudydesignandanalysisaswellasmorerecent
developments,includingtwo-stagestudies,case-onlystudiesandmethodsfor
case-controlsamplingintime.Thelatterhaveimportantapplicationsinlarge
prospectivecohortsthatrequirecase-controlsamplingdesignstomakeefficientuseof
resources.Moretheoreticalbackgroundisprovidedinanappendixforthosenewto
thefield.
ruth h. keoghisaLecturerintheDepartmentofMedicalStatisticsattheLondon
SchoolofHygieneandTropicalMedicine.
d. r. coxisoneoftheworld’spre-eminentstatisticians.Hisworkontheproportional
hazardsregressionmodelisoneofthemost-citedandmostinfluentialpapersin
modernstatistics.In2010hewontheCopleyMedaloftheRoyalSociety‘forhis
seminalcontributionstothetheoryandapplicationofstatistics’.Heiscurrentlyan
HonoraryFellowatNuffieldCollege,Oxford.
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INSTITUTE OF MATHEMATICAL STATISTICS
MONOGRAPHS
EditorialBoard
D.R.Cox(UniversityofOxford)
A.Agresti(UniversityofFlorida)
B.Hambly(UniversityofOxford)
S.Holmes(StanfordUniversity)
X.-L.Meng(HarvardUniversity)
IMSMonographsareconciseresearchmonographsofhighqualityonanybranchof
statistics or probability of sufficient interest to warrant publication as books. Some
concern relatively traditional topics in need of up-to-date assessment. Others are on
emergingthemes.Inallcasestheobjectiveistoprovideabalancedviewofthefield.
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Case-Control Studies
RUTH H. KEOGH
LondonSchoolofHygiene
andTropicalMedicine
D. R. COX
UniversityofOxford
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CUUK2556-FM CUUK2556-Keogh 9781107019560 October7,2013 14:40
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
CambridgeUniversityPressisapartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learningandresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107019560
(cid:2)C RuthH.KeoghandD.R.Cox2014
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2014
PrintedintheUnitedKingdombyMPGPrintgroupLtd,Cambridge
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloguinginPublicationdata
ISBN978-1-107-01956-0Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
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Contents
Preface ix
Preamble 1
Notes 7
1 Introductiontocase-controlstudies 8
1.1 Definingacase-controlstudy 8
1.2 Measuringassociation:theoddsratio 12
1.3 Methodsforcontrollingconfounding 13
1.4 Temporalaspects 16
1.5 Furtherdetailsonthesamplingofcasesandcontrols 20
1.6 Biasincase-controlstudies 23
1.7 Useofcase-controlstudies 26
Notes 29
2 Thesimplestsituation 31
2.1 Preliminaries 31
2.2 Measuringassociation 34
2.3 Statisticalanalysis 36
2.4 Modelformulation 42
2.5 Designimplicationsfornumbersofcasesandcontrols 44
2.6 Logisticdependence 45
2.7 Explanatoryvariablewithmorethantwolevels 47
2.8 Conditionaloddsratios:combiningestimates 48
2.9 Aspecialfeatureofoddsratios 51
2.10 Introducingtime 54
2.11 Causalityandcase-controlstudies 57
Notes 59
3 Matchedcase-controlstudies 62
3.1 Preliminaries 62
3.2 Choiceofmatchedcontrols 63
v
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vi Contents
3.3 Analysisofmatcheddata 65
3.4 Discussion 70
3.5 Alternativeanalysesofmatcheddata 71
3.6 Overmatching 73
3.7 Furthertheoreticalpoints 75
3.8 Generalizations:severalcontrolspercase 76
3.9 Logisticdependence 78
3.10 Introducingtime 80
Notes 81
4 Ageneralformulation 83
4.1 Preliminaries 83
4.2 Logisticregressionforcase-controlstudies 84
4.3 Extensions 89
4.4 Moreonnon-collapsibility 93
4.5 Non-logisticmodels 97
4.6 Statisticalefficiency 99
4.7 Estimatingotherquantities 102
4.8 Useofthedistributionofexposure 104
4.9 Beyondcase-controlstudies:amoregeneralview 105
Notes 108
5 Case-controlstudieswithmorethantwooutcomes 111
5.1 Preliminaries 111
5.2 Polychotomouscase-controlstudies 111
5.3 Polychotomousstudieswithmatching 117
5.4 Morethanonecontrolgroup 119
5.5 Orderedoutcomegroups 120
5.6 Case-onlystudies 122
Notes 130
6 Specialsamplingdesigns 132
6.1 Preliminaries 132
6.2 Two-stagesamplingdesign 133
6.3 Likelihoodanalysesfortwo-stagestudies 143
6.4 Discussion 148
6.5 Specialsamplinginmatchedcase-controlstudies 150
6.6 Case-controlstudiesusingfamilymembers 152
6.7 Augmentingcase-controldatausingfamilymembers 155
Notes 157
7 Nestedcase-controlstudies 160
7.1 Preliminaries 160
7.2 Thenestedcase-controldesign 162
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Contents vii
7.3 Analysisofnestedcase-controlstudies 165
7.4 Furthercommentsonanalysis 167
7.5 Someextensions 169
7.6 Moreelaboratesamplingprocedures 170
7.7 Furthercommentsonthesamplingofcontrols 175
7.8 Somealternativemodels 176
7.9 Extendeduseofcontrols 180
7.10 Estimatingabsoluterisk 182
7.11 Usingfull-cohortinformation 184
Notes 186
8 Case-subcohortstudies 191
8.1 Preliminaries 191
8.2 Essentialoutlineofthecase-subcohortdesign 193
8.3 Analysisdisregardingtime 194
8.4 Case-subcohortstudyusingeventtimes 198
8.5 Sizeofthesubcohort 202
8.6 Stratifiedcase-subcohortstudies 204
8.7 Somefurtherapproaches 207
8.8 Comparisonbetweennestedcase-controland
case-subcohortstudies 208
Notes 209
9 Misclassificationandmeasurementerror 212
9.1 Preliminaries 212
9.2 Misclassificationinanexposurevariable 214
9.3 Misclassificationofcasesandcontrols 218
9.4 Misclassificationinmatchedcase-controlstudies 220
9.5 Errorincontinuousexposures 221
9.6 Correctingforerrorinacontinuousexposure 228
Notes 236
10 Synthesisofstudies 240
10.1 Preliminaries 240
10.2 Somelarge-samplemethods 241
10.3 Graphicalrepresentation 243
10.4 Studyhomogeneity 244
10.5 Anexactanalysis 248
10.6 Combiningstudiesofdifferenttype 250
Notes 250
Appendix Atheoreticaldiversion 252
A.1 Preliminaries 252
A.2 Multidimensionalparameter 253
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viii Contents
A.3 Themaximum-likelihoodestimate 254
A.4 Significancetests 256
A.5 Moredetailedtheory 256
A.6 Pseudo-likelihood 256
A.7 Weightedestimation 258
A.8 Bayesiananalysis 258
Notes 261
References 262
Index 281
