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Practical Guidance and Tools for Sensitivity to Unmeasured Confounding “Tipping Point” AnalysesLucy D’Agostino McGowan, MS
Robert Alan Greevy Jr., PhDDepartment of Biostatistics, Vanderbilt University
Background Methods Example• Strengthofevidenceprovidedbyepidemiologicalandobservational
studiesislimitedbythepotentialofunmeasuredconfounding• Areviewof90observationalstudieswithstatisticallysignificant
findingspublishedin2015inJAMA,NEJM,andAJErevealed• Lessthanhalf,41(45.6%),mentionedtheissueofunmeasured
confoundingasalimitation• Only4(4.4%)includedaquantitativesensitivityanalysis
• Thisdisparityrevealstheneedforpracticalguidanceandsimpletools• Tohelpthemedicalresearchcommunityincorporatesensitivity
analysesintotheirpapers• Toallowthereadersofmedicalresearchtoeasilyperformsuch
analyses whenapaperhasnotincludedone
BuildingonthemethodsputforthbyLinetal.(1998),weproposethefollowingtodeterminethesizeandprevalenceofanunmeasuredconfoundernecessarytochangethesignificanceofanobservedassociation:
Thiswouldallowinvestigatorstostate,
Hereishowtoeasilyincorporatethisintoyourstudy:
Statetheprimaryanalysisresults:Theprimaryanalysisyieldedagreaterriskofcongestiveheartfailure(CHF)withSulfonylureauseoverMetforminuse;HR(95%CI):1.40(1.30,1.50).
Stateasizeandprevalenceofahypothetical“tippingpoint”confounder:Ahypotheticalunobservedbinaryconfounderwitha10%prevalencedifferencebetweenthetherapieswouldneedtohaveanassociationwithCHFofHR=4.0totipthisanalysistononsignificance ata5%level.
Groundthisinanexamplefromyourstudy:Foracomparisonfromtheobservedconfounders,baselineCHFhistoryhadaprevalencedifferenceof5%inthepre-matchingcohortandanassociationwithCHFofHR=2.30;whichwouldhavebeeninsufficienttotipthisanalysishadwenotadjustedforit.
Conclusions• WefocusontheLinetal.approach,howevermanyotheruseful
methodsexistforawidevarietyofsettings.Ourobjectiveistopopularizetheuseofthesesensitivitymethodsingeneral.
• Ouruniversalfigurescanbeappliedtobothpastandfutureresearch,allowingreaderstounderstandthesensitivityofstudiesthatdonotincludesuchananalysis,andallowingfutureinvestigatorstoreadilyincludesuchananalysis.
TippingPointMethod• MainObjective:Reportthesizeandprevalenceofanunmeasured
confounderneededtochangethesignificanceofyourfindings.• Forexample,ifyouhaveafindingwithahazardratioof1.25anda95%
confidenceinterval(1.1,1.5),thiswouldnolongerbesignificantattheα=.05levelifadjustingforahypotheticalunmeasuredconfoundercausedthelower boundtocross1.
• The“tippingpoint”analysiswouldfindthesmallestpotentialunmeasuredconfounderthatwouldcausethistohappen.
• P isthethresholdprevalenceoftheunmeasuredconfounderinthetreatmentpopulation
• LB istheobservedlowerconfidencelimit• 𝚪 istheeffectsizeoftheunmeasuredconfounder
“’’
Inorderforourassociationtonolongerbesignificant,therewouldneedtoexistanunmeasuredconfounderofsize𝚪 thatisprevalentinPoftheexposedpopulation.UnmeasuredConfounder
Exposure Disease Figure1.Sensitivitythresholdstogivenunmeasuredconfoundersforobservedoddsratiolowerconfidenceboundsrangingfrom1to4.
P LB, Γ =LB − 1Γ − 1
for 1 < LB ≤ Γ1.
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