Marginal Structural Models - University of Connecticut

MarginalStructuralModelsforEs3ma3ngtheEffectsof

ChronicCommunityViolenceExposureonAggression&Depression

TraciM.Kennedy,PhDTheUniversityofPi0sburgh,DepartmentofPsychiatry

EdwardH.Kennedy,PhDCarnegieMellonUniversity,DepartmentofSta>s>cs

ModernModelingMethodsConferenceMay23,2017

Today’sTalk

1.  Communityviolenceexposure

2.  Causalinference&marginalstructuralmodels(MSM)

3.  ApplicaDon

4.  Results

5.  Discussion

6.  Resources

CommunityViolenceExposure&YouthMentalHealth

•  High prevalence of youth CVE in U.S. cities •  Range of outcomes

•  Internalizing symptoms •  Depression, anxiety, PTSD

•  Externalizing symptoms •  Aggression, delinquency


•  CumulaDveeffectsmodel– Dose-response– Linear– Supportedinliterature

•  ButMOSTstudiestestonlylineareffects




CVE

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•  DesensiDzaDonmodel:curvilinear–  IsolatedCVE!internalizing– ChronicCVE!externalizing

CVE

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•  DesensiDzaDonmodel:curvilinear–  IsolatedCVE!internalizing– ChronicCVE!externalizing

CVE

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CVEW

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•  DesensiDzaDonmodel:curvilinear–  IsolatedCVE!internalizing– ChronicCVE!externalizing– “pathologicadaptaDon”

CVE

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CVEW

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CommunityViolenceExposure&CausalInference

•  AssociaDons–  CVE!symptoms

–  ObservaDonal–  CorrelaDon≠CausaDon


•  PossibleexplanaDons


•  PossibleexplanaDons–  Violenceexposurecausesincreasedaggression



A!Y





–  Aggressioncausesincreasedviolenceexposure




Y1!A1




Y1!A1!Y2






–  Aggressioncausesincreasedviolenceexposure–  Violenceexposurecausesaggression,which

causesmoreviolenceexposure,etc.





A1!Y1!A2!Y2









–  Somethingelse(SES,neighborhood)causesboth





–  Somethingelse(SES,neighborhood)causesboth

L

A1!Y1!A2!Y2


•  PotenDaloutcomes(Ya)–  Wewanttocomparewhatwouldhavehappenedunder

noexposure(“treatment”)towhatactuallyhappenedtosomeonewhowasexposed(“treated”)

•  E(Y1–Y0)




•  E(Y1–Y0)




•  E(Y1–Y0)

Whatactuallyhappened:




•  E(Y1–Y0)

Whatactuallyhappened: Whatwouldhavehappened:




•  E(Y1–Y0)

–  Violenceexposure




•  E(Y1–Y0)


Exposed Unexposed




•  E(Y1–Y0)


Exposedalot UnexposedExposedali_le




•  E(Y1–Y0)


Exposedalot UnexposedExposedali_le


•  PotenDaloutcomes(Ya)–  Weonlygettoobservewhatactuallyhappened



•  e.g.,exposedtoaspecificlevelofviolence

Exposedalot




–  Butmaybedifferentfrominmanyways…




–  …whichmayinstead/alsoexplainwhytheydifferontheoutcome(e.g.,mentalhealth)




–  Weonlyknowwhatanindividual’smentalhealthlookslikeunderwhichmaybethesameordifferentunder


•  RandomizaDon


•  RandomizaDon–  Everyoneisassignedalevelofviolenceexposure

randomly



randomly–  Equalchanceofexposure,regardlessofallother

characterisDcs(e.g.,race,age,neighborhood)



randomly–  Equalchanceofexposure,regardlessofallother

characterisDcs(e.g.,race,age,neighborhood)–  Onaverage,everyoneidenDcalexceptexposure


•  RandomizaDon–  Notfeasible/ethical


•  HowweusuallytrytoapproximatecausaleffectsinobservaDonalstudies

–  Longitudinaldata•  Measure“baseline”levelsofoutcomes

–  E.g.,aggression

•  Adjustforcovariatesinregression–  E.g.,baselineaggression,SES,age,neighborhood

•  Problem:ExposureandoutcomevaryoverDme–  AdjusDngforbaselineaggressionmay“adjustaway”true

effectofviolenceexposurealongthecausalpathway


Y1!A2!Y2Aggression AggressionViolence

Exposure



Exposure



Exposure

MarginalStructuralModels(MSM)

•  SimulatetheactualandpotenDaloutcomes(counterfactural)usingobservaDonaldata


•  Suppose:


•  Suppose:–  kidsalwaysnonaggressive(exposureirrelevant)



–  kidshave25%chanceofbeingnonaggressiveifexposedtoviolence,&50%ifunexposed



–  kidshave25%chanceofbeingnonaggressiveifexposedtoviolence,&50%ifunexposed

–  (binaryexposurefornow,forsimplicity)


•  SupposepopulaDonlookslike:

Exposed:

Unexposed:



Exposed:

Unexposed:

•  Exposureisclearlyharmful



Exposed:

Unexposed:

•  Exposureisclearlyharmful–  IfALLwereexposed,(6/10)0.25=15%wouldbenonaggressive



Exposed:

Unexposed:

•  Exposureisclearlyharmful–  IfALLwereexposed,(6/10)0.25=15%wouldbenonaggressive

–  IfNONEwereexposed,(6/10)0.5=30%wouldbenonaggressive


•  PopulaDon:

Exposed:

Unexposed:

•  However,inourobserveddata,4/5(.25)=20%ofexposed&2/5(.5)=20%ofunexposedbecomenonaggressive


•  PopulaDon:

Exposed:

Unexposed:

•  However,inourobserveddata,4/5(.25)=20%ofexposed&2/5(.5)=20%ofunexposedbecomenonaggressive

–  Lookslikeexposurehasnoeffect!


•  PopulaDon:

Exposed:

Unexposed:

pr(exposed|=4/6

pr(exposed|=1/4

pr(exposed|=4/6

pr(exposed|=1/4


•  PopulaDon:

Exposed:

Unexposed:pr(unexposed|=2/6

pr(unexposed|=3/4

pr(exposed|=4/6

pr(exposed|=1/4


•  PopulaDon:

Exposed:

Unexposed:

Nowwecancreateapseudo-popula3onbyweighDngeachkidbytheinverseprobabilityofreceivingtheirobservedtreatment(Robinsetal.,2000)

pr(unexposed|=2/6

pr(unexposed|=3/4


•  Pseudo-populaDon:

Exposed*:

Unexposed*:



Exposed*:

Unexposed*:

Downweightthosewhoareover-representedinpopulaDon,&upweighttheunder-represented



Exposed*:

Unexposed*:

Inthepseudo-populaDon:–  6/10(.25)=15%ofexposedwerenonaggressive

–  6/10(.5)=30%ofunexposedwerenonaggressive



Exposed*:

Unexposed*:

•  Matchesthecounterfactualnumbers!



Exposed*:

Unexposed*:

•  Matchesthecounterfactualnumbers!•  SameasrandomizaDon


•  WeighDng=creaDngapseudo-populaDonwhere:


•  WeighDng=creaDngapseudo-populaDonwhere:–  ThecovariatedistribuDonisthesameasinthe

populaDon



populaDon

–  ThereisnoassociaDonbetweentreatment&covariates



populaDon



Exposure



populaDon


A2!Y2AggressionViolence

Exposure



populaDon


–  Thus,noconfounding•  CausaleffectscanbeesDmatedwithoutaddiDonaladjustment

A2!Y2AggressionViolence

Exposure


•  Time-varyingextensionofpropensityscoreweighDng

HowtoApplyMSM

1.  Fitpropensityscoremodelofprobabilityofexposure

2.  Doaweightedregression(usingtheIPWs)

Assump3ons

1.  Consistency:Y=YawhenA=a–  Weobservetheoutcomethatagivenlevelofexposure

causeswhenweobservethatexposure

2.  PosiDvity:pr(A=a|L=l)>0–  TheremustexistaposiDveprobabilityofallexposure

levelsforallstrataofcovariates

–  Noonemayhave0probabilityofexposure

3.  Ignorability:Nounmeasuredconfounding

Results

•  DoescommunityviolenceexposuredifferenDallyaffectyouths’mentalhealth?

Results

•  DoescommunityviolenceexposuredifferenDallyaffectyouths’mentalhealth?

–  DesensiDzaDonhypothesis:•  QuadraDceffectoninternalizingsymptoms

•  Lineareffectonexternalizingsymptoms

CVE

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Results

•  Data–  ProjectonHumanDevelopmentinChicago

Neighborhoods(PHDCN)

(Earls,Brooks-Gunn,Raudenbush,&Sampson,1994-2002)

–  LongitudinalCohortStudy–  Youth&primarycaregiver–  StraDfiedprobabilitysample:N=4,149–  Waves2&3–  CohortagesatWave2:6,9,12,15,18–  RepresentaDvesample

Results

•  Measures–  Baselinedemographiccovariates

•  Age,sex,race,income,SES

–  Communityviolenceexposure(CVE)•  MyExposuretoViolence•  PastyearCVEfrequencyon20items

•  Witnessing&vicDmizaDon

–  Mentalhealth•  CBCLInternalizing&Externalizing

–  ControlledforpriorlevelsinGEEmodels

Results

•  GEE&MSM•  CVE2!agg2&CVE3!agg3•  Baselinecovariates&prioraggression

•  CondiDonaldensi>esinsteadofprobabiliDesforconDnuousexposure(CVE)

Results:GEE

Results:GEEInternalizing

Results:GEEExternalizing

Results:MSM

Results:MSM

0 5 10 15

52.0

52.5

53.0

53.5

54.0

54.5

55.0

55.5

Violence Exposure

Inte

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0 5 10 15

6.5

7.0

7.5

8.0

8.5

9.0

Violence Exposure

Exte

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izin

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Internalizing Externalizing

Conclusions

•  DesensiDzaDoneffectofCVE–  PathologicadaptaDon?

•  Similar,butslightlyweakereffectsusingMSM–  SomeDmeseffectdisappears,orreversesdirecDon

•  MoreaccuratecausaleffectofCVE•  IntervenDonimplicaDons

–  Everyoneexposedvseveryoneunexposed

•  (InteracDonswerens)

Limita3ons

•  ModelspecificaDon–  Moreflexibility(splines)probablyneeded

•  CVEmeasurement–  RetrospecDvereport–  Ordinalcoding–  Timebetweenassessments

Limita3ons

•  MSMassumpDons–  Likelyunmeasuredconfounding

•  E.g.,parenDng,schoola_endance,etc.

–  PosiDvity•  MaybeyouthwithzeroprobabilityofCVE

MSMTips

•  SpecifyquesDonpreciselytooperaDonalize&isolatecausaleffectofinterest

–  RCTframework•  E.g.:

–  Whoexactlyarethesubjects?–  Whatexactlyisthetreatment?

–  Forexactlyhowlongaretheytreated?

MSMTips

•  Avoidunmeasuredconfounding–  Measureallpossibleconfounders

•  FancystaDsDcscannotfixbaddesigns

–  SensiDvityanalysis•  VanderWeele(2010)BiasformulasforsensiDvityanalysisfordirectand

indirecteffects,Epidemiology,21,540-551•  Brumbacketal(2004)SensiDvityanalysesforunmeasuredconfounding

assumingamarginalstructuralmodelforrepeatedmeasures,Sta>s>csinMedicine,23(5),749-767

MSMTips

•  Usestabilizedweights–  InverseprobabiliDesbecomeunwieldy

–  Incorporatebaselinecovariatestostabilize–  Robinsetal(2000)Marginalstructuralmodelsandcausalinferenceinepidemiology,

Epidemiology,11,550-560

MSMExtensions

•  AlthoughMSMsovenuseIPW,otherapproachestoesDmateMSMparameters:

–  Regression-basedg-computaDon–  DoublyrobustesDmaDngequaDons–  Targetedmaximumlikelihood(TMLE)

MSMExtensions

•  MLM,growthcurvemodeling,SEM,etc.–  SimplyapplyIPWweights

•  MediaDon(e.g.,Coffman&Zhong,2012;VanderWeele)

•  AddiDonalDmepoints•  CompoundedeffectsoverDme

–  E.g.,effectsofCVE2&CVE3onagg3

•  Effectofremovingvsaddingexposure•  IncrementalintervenDons(Kennedy,underreview)

–  MorerealisDcintervenDonimplicaDons

Applica3ons

•  Typicallymedicine&epidemiology–  E.g.,HIVtreatment

•  Expandtopsychology&socialsciences–  Time-dependentconfounding&reciprocaleffects–  E.g.:

•  Mentalhealthtreatment

•  Bullying

•  ADHDsDmulantmedicaDons•  RCTswithnoncompliance

ConcludingThoughts

•  UseMSMs!•  R,SAS,&Stata

References&Resources

•  Conceptual–  Robins&Hernánbookdrav:

h_ps://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/

–  Robinsetal(2000)–Epidemiology

–  Robins&Hernán(2009)–Chapter1inLongitudinalDataAnalysis

–  Faries&Kadziolachapter:AnalysisoflongitudinalobservaDonaldatausingmarginalstructuralmodels

–  VanderWeele(2009)–Epidemiology•  MediaDon

–  Kennedy(underreview)NonparametriccausaleffectsbasedonincrementalpropensityscoreintervenDons

h_ps://arxiv.org/abs/1704.00211

References&Resources

•  Applied–  Bacak&Kennedy(2015)–J.ofMarriageandFamily

•  Marriage&recidivism–  Hernánetal(2002)–Sta>s>csinMedicine

•  HIVtreatmenteffecDveness–  Pateletal(2008)–ClinicalInfec>ousDiseases

•  PediatricHIVtreatmenteffecDveness–  VanderWeeleetal(2011)–JCCP

•  Loneliness&depression–  VanderWeeleetal(2016)–SocPsychiatry&Psychiatr

Epidem•  Religion&mentalhealth

References&Resources•  SoUware

–  R•  Bacak&Kennedy(2015)–J.ofMarriageandFamily•  Coffman&Zhong(2012)–PsychologicalMethods•  Moerkerkeetal(2015)–PsychologicalMethods

–  MediaDon

–  SAS•  Faries&Kadziolachapter:Analysisoflongitudinal

observaDonaldatausingmarginalstructuralmodels•  Crowsonetal(2013)Thebasicsofpropensityscoringand

marginalstructuralmodels

–  SAS,Stata,&R•  Robins&Hernánbookdrav

Conferences&Workshops•  PennCausalInference&BigDataSummerInsDtute

July24-27,2017–EdwardKennedyh_p://www.med.upenn.edu/cbd/

•  CausalInferenceMethodsforPCORusingObservaDonalData(CIMPOD)–NIHh_p://cimpod2017.org/

•  AtlanDcCausalInferenceConferenceMay2018–CarnegieMellonUniversityh_p://causal.unc.edu/acic2017/

•  StaDsDcalHorizons–CausalMediaDonAnalysisOctober13-14,2017–TylerVanderweeleh_ps://staDsDcalhorizons.com/seminars/public-seminars

Acknowledgments•  RosarioCeballo&JimCranford

•  MarshallJoffe&DylanSmall

•  BrookeMolina

•  AndreaHoward

•  KunjalPatel

Currentresearchsupport:DA039881;AA011873;HD083404(PI:BrookeS.G.Molina)

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