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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