Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction

646 Pages·2015·7.521 MB·English

by  Guido W. Imbens, Donald B. Rubin

CAUSAL INFERENCE
forStatistics, Social,and Biomedical Sciences
AnIntroduction
Mostquestionsinsocialandbiomedicalsciencesarecausalinnature:whatwould
happentoindividuals,ortogroups,ifpartoftheirenvironmentwerechanged?In
thisgroundbreakingtext,twoworld-renownedexpertspresentstatisticalmethods
forstudyingsuchquestions.
Thisbookstartswiththenotionofpotentialoutcomes, eachcorresponding to
theoutcomethatwouldberealizedifasubjectwereexposedtoaparticulartreat-
mentorregime.Inthisapproach,causaleffectsarecomparisonsofsuchpotential
outcomes. The fundamental problem of causal inference is that we can observe
only one of the potential outcomes for a particular subject. The authors discuss
how randomized experiments allow us to assess causal effects and then turn to
observational studies. They layout the assumptions needed for causal inference
anddescribetheleadinganalysismethods,includingmatching,propensity-score
methods, and instrumental variables. Many detailed applications are included,
withspecialfocusonpracticalaspectsfortheempiricalresearcher.
GuidoW.ImbensisAppliedEconometricsProfessorandProfessorofEconomics
attheGraduateSchoolofBusinessatStanfordUniversity.Hehasprevioulsyheld
tenuredpositionsattheUniversityofCaliforniaatLosAngeles,theUniversityof
CaliforniaatBerkeley,andHarvardUniversity.HeisaFellowoftheEconometric
Society and the American Academy of Arts and Sciences. He holds an hon-
orarydoctoratefromtheUniversityofSt.Gallen,Switzerland.Imbenshasdone
extensiveresearchineconometricsandstatistics,specializingincausalinference.
He has published widelyin leadingeconomics and statisticsjournals, including
the American Economic Review, Econometrica, the Review of Economic Stud-
ies, theJournal oftheAmericanStatisticalAssociation, theAnnals ofStatistics,
Biometrika,andtheJournaloftheRoyalStatisticalSociety,SeriesA.
Donald B. Rubin is John L. Loeb Professor of Statistics at Harvard University,
where he has been professor since 1983 and Department chair for 13 of those
years. He has been elected to be a Fellow/Member/Honorary Member of the
Woodrow Wilson Society, the Guggenheim Memorial Foundation, the Alexan-
dervonHumboldtFoundation,theAmericanStatisticalAssociation,theInstitute
of Mathematical Statistics, the International Statistical Institute, the American
AssociationfortheAdvancementofScience,theAmericanAcademyofArtsand
Sciences, the European Association of Methodology, the British Academy, and
theU.S.NationalAcademyofSciences.Asof2014,hehasauthored/coauthored
nearly400publications(includingtenbooks),hasfivejointpatents,andformany
yearshasbeenone of themost highlycitedauthors intheworld, withcurrently
over 150,000 citations (Google Scholar). He is also the recipient of honorary
doctorates from Otto Friedrich University, Bamberg, Germany; the University
of Ljubljana, Slovenia; and Universidad Santa To´mas, Bogota´, Colombia, and
hasbeennamedanhonoraryprofessoratfouruniversities.
AdvancePraiseforCausalInferenceforStatistics,Social,and
BiomedicalSciences
“Thisthoroughandcomprehensivebookusesthe‘potentialoutcomes’approachtocon-
nect the breadth of theory of causal inference to the real-world analyses that are the
foundation of evidence-based decision making in medicine, public policy, and many
otherfields. ImbensandRubinprovideunprecedentedguidancefor designingresearch
oncausalrelationships,andforinterpretingtheresultsofthatresearchappropriately.”
–Dr.MarkMcClellan,DirectoroftheHealthCareInnovation
andValueInitiative,theBrookingsInstitution
“Clarityofthinkingaboutcausalityisofcentralimportanceinfinancialdecisionmaking.
ImbensandRubinprovidearigorousfoundationallowingpractitionerstolearnfromthe
pioneersinthefield.”
–DrStephenBlyth,ManagingDirector,HeadofPublicMarkets,
HarvardManagementCompany
“A masterful account of the potential outcomes approach to causal inference from
observationalstudiesthatRubinhasbeendevelopingsincehepioneeredit40yearsago.”
–AdrianRaftery,Blumstein-JordanProfessorofStatisticsandSociology,
UniversityofWashington
“Correctlydrawingcausalinferencesiscriticalinmanyimportantapplications.Congrat-
ulationstoProfessorsImbensandRubin,whohavedrawnontheirdecadesofresearchin
thisarea,alongwiththeworkofseveralothers,toproducethisimpressivebookcovering
concepts, theory, methods, and applications. I especiallyappreciate their clear exposi-
tion of conceptual issues, which are important to understand in the context of either
a designed experiment or an observational study, and their use of real applications to
motivatethemethodsdescribed.”
–NathanielSchenker,FormerPresidentoftheAmericanStatisticalAssociation
CAUSAL INFERENCE
for Statistics, Social, and
Biomedical Sciences
An Introduction
Guido W. Imbens
StanfordUniversity
Donald B. Rubin
HarvardUniversity
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521885881
(cid:2)c GuidoW.ImbensandDonaldB.Rubin2015
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2015
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
Imbens,Guido.
Causalinferenceforstatistics,social,andbiomedicalsciences:
anintroduction/GuidoW.Imbens&DonaldB.Rubin.
pages cm
1. Socialsciences–Research. 2. Causation. 3. Inference. I. Rubin,DonaldB. II. Title.
H62.I5372014
(cid:2)
519.54–dc23 2014020988
ISBN978-0-521-88588-1Hardback
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URLsforexternalorthird-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain,
accurateorappropriate.
Tomyparents,AnnieImbens-FransenandGerardImbens,
foralltheirsupportandencouragementovertheyears;to
mychildren,Carleton,AnnaliseandSylvia,whohave
providedsomuchjoyinrecentyears;andtomywife
andbestfriend,SusanAthey.
GuidoW.Imbens
Tomyfamily,colleagues,andstudents
DonaldB.Rubin

Contents
Preface pagexvii
PART I INTRODUCTION
1 Causality:TheBasicFramework 3
1.1 Introduction 3
1.2 PotentialOutcomes 3
1.3 DefinitionofCausalEffects 5
1.4 CausalEffectsinCommonUsage 7
1.5 LearningaboutCausalEffects:MultipleUnits 8
1.6 TheStableUnitTreatmentValueAssumption 9
1.7 TheAssignmentMechanism:AnIntroduction 13
1.8 Attributes,Pre-TreatmentVariables,orCovariates 15
1.9 PotentialOutcomesandLord’sParadox 16
1.10 CausalEstimands 18
1.11 StructureoftheBook 20
1.12 Samples,Populations,andSuper-Populations 20
1.13 Conclusion 21
Notes 21
2 ABriefHistoryofthePotentialOutcomesApproachto
CausalInference 23
2.1 Introduction 23
2.2 PotentialOutcomesandtheAssignmentMechanism
beforeNeyman 24
2.3 Neyman’s(1923)PotentialOutcomeNotationinRandomized
Experiments 25
2.4 EarlierHintsforPhysicalRandomizing 26
2.5 Fisher’s(1925)ProposaltoRandomizeTreatmentstoUnits 26
2.6 TheObservedOutcomeNotationinObservationalStudiesfor
CausalEffects 27
2.7 EarlyUsesofPotentialOutcomesinObservationalStudiesin
SocialSciences 28
vii
viii Contents
2.8 PotentialOutcomesandtheAssignmentMechanismin
ObservationalStudies:Rubin(1974) 29
Notes 30
3 AClassificationofAssignmentMechanisms 31
3.1 Introduction 31
3.2 Notation 33
3.3 AssignmentProbabilities 34
3.4 RestrictionsontheAssignmentMechanism 37
3.5 AssignmentMechanismsandSuper-Populations 39
3.6 RandomizedExperiments 40
3.7 ObservationalStudies:RegularAssignmentMechanisms 41
3.8 ObservationalStudies:IrregularAssignmentMechanisms 42
3.9 Conclusion 43
Notes 43
PART II CLASSICAL RANDOMIZED EXPERIMENTS
4 ATaxonomyofClassicalRandomizedExperiments 47
4.1 Introduction 47
4.2 Notation 48
4.3 BernoulliTrials 48
4.4 CompletelyRandomizedExperiments 50
4.5 StratifiedRandomizedExperiments 51
4.6 PairedRandomizedExperiments 52
4.7 Discussion 53
4.8 Conclusion 55
Notes 56
5 Fisher’sExactP-ValuesforCompletelyRandomizedExperiments 57
5.1 Introduction 57
5.2 ThePauletal.HoneyExperimentData 59
5.3 ASimpleExamplewithSixUnits 59
5.4 TheChoiceofNullHypothesis 63
5.5 TheChoiceofStatistic 64
5.6 ASmallSimulationStudy 72
5.7 IntervalEstimatesBasedonFisherP-ValueCalculations 74
5.8 ComputationofP-Values 75
5.9 FisherExactP-ValueswithCovariates 78
5.10 FisherExactP-ValuesfortheHoneyData 80
5.11 Conclusion 81
Notes 81
6 Neyman’sRepeatedSamplingApproachtoCompletely
RandomizedExperiments 83
6.1 Introduction 83
6.2 TheDuflo-Hanna-RyanTeacher-IncentiveExperimentData 84
6.3 UnbiasedEstimationoftheAverageTreatmentEffect 85
Contents ix
6.4 TheSamplingVarianceoftheNeymanEstimator 87
6.5 EstimatingtheSamplingVariance 92
6.6 ConfidenceIntervalsandTesting 95
6.7 InferenceforPopulationAverageTreatmentEffects 98
6.8 Neyman’sApproachwithCovariates 101
6.9 ResultsfortheDuflo-Hanna-RyanTeacher-IncentiveData 102
6.10 Conclusion 104
Notes 104
AppendixASamplingVarianceCalculations 105
AppendixBRandomSamplingfromaSuper-Population 109
7 RegressionMethodsforCompletelyRandomizedExperiments 113
7.1 Introduction 113
7.2 TheLRC-CPPTCholesterolData 115
7.3 TheSuper-PopulationAverageTreatmentEffects 116
7.4 LinearRegressionwithNoCovariates 118
7.5 LinearRegressionwithAdditionalCovariates 122
7.6 LinearRegressionwithCovariatesandInteractions 125
7.7 TransformationsoftheOutcomeVariable 127
7.8 TheLimitsonIncreasesinPrecisionDuetoCovariates 128
7.9 TestingforthePresenceofTreatmentEffects 129
7.10 EstimatesforLRC-CPPTCholesterolData 131
7.11 Conclusion 133
Notes 134
Appendix 135
8 Model-BasedInferenceforCompletelyRandomizedExperiments 141
8.1 Introduction 141
8.2 TheLalondeNSWExperimentalJob-TrainingData 144
8.3 ASimpleExample:NaiveandMoreSophisticatedApproaches
toImputation 146
8.4 BayesianModel-BasedImputationintheAbsenceofCovariates 150
8.5 SimulationMethodsintheModel-BasedApproach 163
8.6 DependencebetweenPotentialOutcomes 165
8.7 Model-BasedImputationwithCovariates 169
8.8 Super-PopulationAverageTreatmentEffects 171
8.9 AFrequentistPerspective 172
8.10 Model-BasedEstimatesoftheEffectoftheNSWProgram 174
8.11 Conclusion 177
Notes 177
AppendixAPosteriorDistributionsforNormalModels 178
AppendixBAnalyticDerivationswithKnownCovariance
Matrix 181
9 StratifiedRandomizedExperiments 187
9.1 Introduction 187
9.2 TheTenneseeProjectStarData 188