Causal Inference in Law: An Epidemiological Perspective

Abstract

Causal inference lies at the heart of many legal questions. Yet in the context of complicated disease litigation, in particular, the causal inquiry is beset with difficulties due to gaps in scientific knowledge concerning the precise biological processes underlying such diseases. Civil courts across the globe, faced with increased litigation on such matters, struggle to adhere to their judicial fact-finding and decision-making role in the face of such scientific uncertainty. An important difficulty in drawing evidentially sound causal inferences is the binary format of the traditional legal test for factual causation, being the ‘but for’ test, which is based on the condicio-sine-qua-non principle. To the question ‘would the damage have occurred in the absence of the defendant's wrongful behaviour’ the ‘but for’ test requires a simple yes or no answer. This is increasingly deemed unsatisfactory in cases in which, given the state of science, true causation cannot possibly be determined with certainty.

Full text

EJRR1|2016175 CausalInferenceinLaw:AnEpidemiologicalPerspective
CausalInferenceinLaw:AnEpidemiological
Perspective
BobSiegerink,WouterdenHollander,MauriceZeegersandRutgerMiddelburg*
I.Introduction
Causalinferenceliesattheheartofmanylegalques-
tions.Yetinthecontextofcomplicateddiseaseliti-
gation,inparticular,thecausalinquiryisbesetwith
difficultiesduetogapsinscientificknowledgecon-
cerningtheprecisebiologicalprocessesunderlying
suchdiseases.Civilcourtsacrosstheglobe,facedwith
increasedlitigationonsuchmatters,struggletoad-
heretotheirjudicialfact-findinganddecision-mak-
ingroleinthefaceofsuchscientificuncertainty .An
importantdifficultyindrawingevidentiallysound
causalinferencesisthebinaryformatofthetradi-
tionallegaltestforfactualcausation,beingthe‘but
for’test,whichisbasedonthecondicio-sine-qua-non
principle.1T othequestion‘wouldthedamagehave
occurredintheabsenceofthedefendant’swrongful
behaviour’the‘butfor’testrequiresasimpleyesor
noanswer.Thisisincreasinglydeemedunsatisfacto-
ryincasesinwhich,giventhestateofscience,true
causationcannotpossiblybedeterminedwithcer-
tainty.Giventhegeneralrulethattheburdenofproof
inprinciplelieswiththeclaimant,the‘butfor’test
passesontheuncertaintytotheclaimantentirely.
Suchisnotonlyfelttobeatoddswithfairness,but
isalsounsatisfactorilyfromanepidemiologicalper-
spective,giventhebinaryformatofthe‘butfor’test
ontheonehandandthefactthatmostdiseasesare
multi-causalandcannotbeascribedtoasinglefac-
toronlyontheotherhand.
Inthisarticle,wewillelaboratethisepidemiolog-
icalperspectiveandfromthatperspectivediscussthe
problemofcausalinferenceinlawingeneraland
scrutinizeonenewlegalconceptdealingwiththis
probleminparticular.Thisistheconceptoftheso-
calledproportionalliability,asacceptedbytheDutch
SupremeCourtintheNefalit-case.TheSupreme
Courtagreedwiththelowercourts,assumingliabil-
ityofemployerNefalit,inproportiontothereasoned
estimationofthechancethatthelungcancerKara-
mussufferedfromwascausedbyasbestosexposure
duringtheworkforhisemployerNefalit(55%).We
willarguethatalthoughsuchproportionalliability
adherestotheepidemiologicalconceptofmulti-
causality,andinthatrespect,isnotwithoutmerit,
epidemiologicalmeasurementsonapopulationlevel
shouldnotbetakentocalculatetheprobabilitythat
theemployers’wrongfulconducthasactuallycaused
thediseaseinanindividual.Weproposeadifferent
approachintwostages,makingproportionalliabili-
tymoretrulyproportionaltothedefendant’srelative
contributionintheknowncausalmechanismunder-
lyingthedamageinquestionand,bythat,morefair
forbothparties,eventhoughourapproachisnot
flawlesseither.
Wewillsetoutsomeimportantconceptsfromthe
fieldofepidemiologywithrespecttocausalinference
first.Athoroughunderstandingoftheseconcepts
willhelptofurtherstrengthenandinformlegalprin-
ciplesofcausation.Epidemiology ,whereprobabilis-
ticconceptsareappliedtoaddresscausalquestions
inindividuals,couldinparticularaidintheunder-
standingofmulti-causalityanditspossiblelinksto
proportionalliabilityasalegalconcept.Epidemiolo-
gystudiesthedistributionanddeterminantsofdis-
easefrequencyinhumanpopulations.Itcontrasts
withdailymedicalpracticewhichfocusesonindivid-
uals.Wewillelaboratethedifferenceinconceptsof
causalinferencebetweengroupsandindividuals,
withalinktothecondicio-sine-qua-nonprincipleand
theconceptofmulti-causality.W ewillthendiscuss
*BobSiegerink,Phd:CenterforStrokeResearch,Charité,Univeris-
titätsmedizinBerlin,Berlin,GermanyandDepartmentofClinical
Epidemiology,LeidenUniversityMedicalCenter,Leiden,the
Nehterlands;P .WouterHollander,LLMMA:InstituteforPrivate
Law,LeidenUniversity,Leiden,theNetherlands;MauriceP .
Zeegers,PhD:MaastrichtUniversity,SchoolofNutrition,Toxicol-
ogyandMetabolism&MaastrichtForensicInstitute,Maastricht,
theNetherlands;RutgerA.Middelburg,PhD:CenterforClinical
TransfusionResearch,SanquinResearch,Leiden,theNetherlands,
andDepartmentofClinicalEpidemiology,LeidenUniversity
MedicalCenter ,Leiden,theNetherlands.Theauthorswouldlike
toacknowledgeAGCastermansandRubendeGraaff(both
InstituteforPrivateLaw,LeidenUniversity)fortheirusefulcom-
ments.
1SeeforinstanceDeakin,S.,Johnston,A.,Markesinis,B.Markesi-
nisandDeakin’sT ortLaw(7thed.),Oxford:ClarendonPress
2013,pp.218-256.

EJRR1|2016 176CausalInferenceinLaw:AnEpidemiologicalPerspective
howcausationcanbequantifiedinasinglenumber
andhowthesenumberscomparetothelegalconcept
ofproportionalliabilityasacceptedintheNefalit-
case.Ultimately ,wewilltrytoreconciletheimpossi-
bilitytoknowtheexactcausalmechanismofadis-
easeinanindividualtothecondicio-sine-qua-non
principleandtheapplicationofproportionalliabili-
tytocometoafairreimbursementofdamagesin
complexdiseaselitigation.
II.CausalInferenceinMedicineand
Epidemiology
Inclinicalmedicine,doctorsareconfrontedwith
questionsofcausalityonadailybasis.Willthismed-
icaltreatmentcausethecureofapatient?Andwill
thebenefitsoutweightheside-effectscausedbythis
treatment?Forexample,whenapatientsuffersfrom
anischaemicstrokecausedbyabloodclotinthebrain
thatispreventingtheflowofoxygenatedblood,ade-
cisioncanbemadetostarttreatmenttargetedtore-
solvethebloodclotandrestorebloodflow .Thistreat-
mentiscalledthrombolysisandrestoresbloodflow
in43%oftreatedcases.2However,thrombolysisal-
socausesbleedings,whichinitselfcanalsobeacause
ofmorbidityandmortality.3Thrombolysiscanonly
beappliedinthefirst3-4,5hoursaftertheonsetof
symptoms,becauseonlyinthistimeperiodtheben-
efitsoftreatment,whichdeclinesovertime,out-
weighthenegativeconsequencesofthistreatment
onapopulationlevel.
Treatingapatientisnotrestrictedtoaddressing
theacutesymptomsofacertaincause,butalsoin-
cludestheremovalofpossiblecausestopreventa
possiblerecurrenceofthedisease.Forexample,the
physicianconfrontedwithapatientsufferingfrom
anischaemicstrokewillnotonlyapplythromboly-
sis,butwillalsotargetthesmokinghabitandthein-
creasedcholesterollevelsofthatparticularpatient
topreventanothercaseofischaemicstrokeinthe
longrun.Thedecisiontotargettheseriskfactorsis
basedonstudiesthatonapopulationlevelthesefac-
torsareacauseofthedisease.T argetingtheserisk
factorsinanindividualisthereforethoughttolow-
ertheriskofrecurrence.4,5Buthowcanthephysi-
cian,basedonepidemiologicalstudies,becertain
thatthesmokinghabitandhighcholesterollevels
werecausalinthemechanismleadingtotheis-
chaemicstrokeinthisparticularpatient?Theunset-
tlingansweristhatheisnotcertain,neithercanhe
everbe.
III.TheCounterfactualIdeal
Theoretically,wecanonlybecertainonthecausal
natureofariskfactorifweobservetheoutcomewhen
thepatientisexposedtothisriskfactorandcompare
thattothesituationwhenwegobackintime,and
seewhathappensifthepatientisunexposed,butall
otherfactorsarekeptconstant.6Becausethishypo-
theticalsituationiscontrarytofact,thisconceptis
sometimesreferredtoasthecounterfactualorpoten-
tialoutcomemodel.7,8Ifwecouldgobackintime,
andmanipulateonlyonecertainfactorwecouldde-
termineineachindividualpatientwhetheranindi-
vidualriskfactorwasindeedacauseoftheobserved
disease.
Thiscounterfactualmodeliscomparabletothe
condicio-sine-qua-non-testinlaw.Theriskthatde-
scribesthisrelationshipbetweenexposureanddis-
easeforoneindividualisbinary,being1(forthedis-
easeiscausedbytheexposure)or0(forthedisease
isnotcausedbytheexposure).However,sincethe
counterfactualoutcomecannotbeobserved,wecan-
notdeterminethecausalmechanisminanindivid-
ual.Thecounterfactualidealcanbeapproached,
though,inthecomparisonofdifferentpopulations
undercertainconditions.Forexample,iftwogroups
aresimilarexceptforthepresenceoftheriskfactor
ofinterest,adifferenceindiseasefrequencycanbe
ascribedtothesoledifferencebetweenthesegroups,
2Joung,H.Rha,&Saver,L.J.,‘TheImpactofRecanalizationon
IschaemicStrokeOutcome:aMeta-Analysis’,Stroke38(2007),
pp.967–73.
3Lansberg,M.G.etal.,‘ AntithromboticandThrombolyticTherapy
forIschaemicStroke:AntithromboticTherapyandPreventionof
Thrombosis,9thed:AmericanCollegeofChestPhysiciansEvi-
dence-BasedClinicalPracticeGuidelines’,Chest141(2012),
e601S–36S.
4GoyaWannamethee,S.etal.,‘SmokingCessationandtheRiskof
StrokeinMiddle-AgedMen’,JAMA274(1995),pp.155–60.
5Milionis,H.J.etal.,‘StatinTherapyafterFirstStrokeReduces10-
yearStrokeRecurrenceandImprovesSurvival’,Neurology72
(2009),pp.1816-22.
6Formorebackgroundreadingonthetheoryofcausation,please
referto:Pearl,J.,Causality:Models,Reasoning,andInference,
CambridgeUniversityPress,2000;2ndedition,2009.
7Rothman,K.J.etal.,‘CausationandCausalInferenceinEpidemi-
ology’,Am.J.PublicHealth95(2005)Suppl.1,pp.S144-50.
8Rothman,K.J.,Greenland,S.,Lash,T .L.,ModernEpidemiology
(thirdrevisededition),LippincottWilliams&Wilkins2008.

EJRR1|2016177 CausalInferenceinLaw:AnEpidemiologicalPerspective
beingtheriskfactorofinterest.Thiscomparisondoes
notallowtoestablishthecausalmechanismwithin
anindividual.However,thesegroupcomparisonsdo
allowustoestimatethecausalrelationshipbetween
theexposureandtheoutcometobequantifiedin
termsofprobability.
IV .FromOneCausetotheconceptof
Multi-causality
Beforewedescribehowcausalrelationshipscanbe
quantified,wefirsthavetofocusonthedefinitionof
acausalmechanism.Often,thecauseinacausal
mechanismisthoughttobeasinglefactorinacause-
consequencesequence.However,aconsequencecan
havemultiplecauses:severalfactors,asacombina-
tion,causeaneffect.Thisconceptisknownasmul-
ti-causalityandisimportantinepidemiological
thinkingoncausality ,foritprovidesawaytothink
aboutcausalmechanismsinsteadofsinglecause-con-
sequencesequences.Toavoidconfusion,multi-
causalityshouldbedistinguishedfromthesituation
inwhichasinglefactor,suchassmoking,cancause
differentdiseases.
Inepidemiologicaltheory ,theconceptofmulti-
causalityhasgainedgroundsinceitwasformalized
byK.J.Rothmanin1976.9Theconceptdistinguishes
anddescribestheimplicationsofnecessary,suffi-
cientandcomponentcausesandisfurtherexplained
withtheuseoffigure1.
Lettherebethreepossiblecausalmechanismsthat
leadtoacertaindisease.Figure1depictsthesethree
causalmechanismsasthreesufficientcauses,allcom-
prisingmultiplecomponentcauses.Inthisexample
weassumethatthesethreesufficientmechanisms
aretheonlythreepossiblecausalmechanismsthat
leadtoanevent,whichcanbeadisease,injuryor
anythingsimilar.Thefrequencyofthediseasenor-
mallyisadirectfunctionofthefrequencyof–acom-
binationof–thedifferentcomponentcauses.Weal-
soassumethatallcomponentcausesareequally
presentinthepopulationandthatthepresenceof
eachcomponentcauseisindependentfromtheoth-
ers(i.e.noconfoundingcauses,seebelow).
Importanttonoteisthatsometimescomponent
causesarepresentinallsufficientcauses,making
themnecessarycomponentcauses(Ainourexam-
ple).Intheory ,removalofanecessarycomponent
causefromthepopulationwillleadtocompleteerad-
icationofthedisease.Itisnotnecessaryforallsuf-
ficientcausestohaveanequalnumberofcomponent
causes,norisitneededtonameallcomponentcaus-
esindetail.Acomponentcausecanevenbeunknown
(oftendepictedas‘U’,asisdoneinthemiddlesuffi-
cientcauseinfigure1).
Acomponentcausecanbepresentlongbeforethe
sufficientcauseiscompleted.Forexample,agenet-
icvariationinacertaingeneispresentfrombefore
birth,butothercomponentcausesareneededtocom-
pleteasufficientcause.Thecompletionofasuffi-
cientcauseequalsthebiologiconsetofthedisease,
whichisnotnecessarilythetimeofdiagnosis.These
conceptsareillustratedinanexamplewheregenet-
icvariationsarepartofthecausalmechanismlead-
ingtoischaemicstroke:geneticvariationsinthe
APOEgeneareknowntocausebloodcholesterollev-
elstorise.Thesegeneticvariationsarepresentfrom
beforebirth,butthissmallincreaseinbloodcholes-
terolaloneisinitselfinsufficientandadditionalcar-
9Rothman,K.J.,‘Causes’,Am.J.Epidemiol104(1976),pp,
587-92.
Figure1-Threesufficientcauses

EJRR1|2016 178CausalInferenceinLaw:AnEpidemiologicalPerspective
diovascularriskfactorsareneededinordertocause
anischaemicstroke.Togetherwithsuchfactors(e.g.
smoking),increasedbloodcholesterolmightresult
inanatheroscleroticplaque.Sometimes,these
plaquesruptureandathrombusisformed,which
subsequentlyblockstheflowofbloodtothebrain.
Also,themomentofdiagnosisoftheischaemicstroke
oreventhefirstsymptomscanbehourslaterthan
theactualblockageofthecerebralartery.
Sincecomponentcausesaccumulateovertime,the
incidenceofmanydiseasesrisessharplywithage.
Thetimebetweenthefirstpresenceofacomponent
causeandthecompletionofthesufficientcauseis
referredtoastheinductiontime.Inourexample,the
alphabeticalorderofthecomponentsreferstothe
orderinwhichtheyoccur.Itisimportanttonotethat
thelengthoftheinductiondoesnotnecessarilyre-
ducetheimportanceofaparticularcomponentcause.
Thecomponentcausethatcompletesthesufficient
causehasaninductiontimeofzeroandistherefore
easilyidentifiedasacause.Componentcauseswith
littletonoinductiontimeareinlayman’stermsfor
thatreasonsometimeserroneouslyreferredtoasthe
causeofthedisease.
Nonetheless,theorderofcomponentcausesisof
importance:apersonwhoisonlyexposedtocompo-
nentcausesAandBhasnosufficientcause.Subse-
quentexposuretothetwocomponentscausesCand
Dwillcompleteasufficientcause.Whenthisperson
isnotexposedtoCorD,hewillnotdevelopthedis-
easeatthatparticularpointintime.However,when
thissamepersonatalatermomentisexposedtocom-
ponentcauseF,asufficientcausehasformedandthe
personstilldevelopsthedisease,albeitsomewhatlat-
erintime.
Thesufficientcausemodeladherestothecounter-
factualideal.Whenweconsiderthesufficientcause
1depictedinfigure1,wecanseethatA,B,CandD
arethecomponentcausesforthisparticularsuffi-
cientcause.Ifwethinkofthecounterfactualsitua-
tionthatthisparticularindividualwasnotexposed
tocomponentcauseAandallotherthingsequal,this
diseasewouldnothaveoccurred.Thesamegoesfor
thecommoncausesB,CandD.Wecanevenbroad-
enourviewandseewhathappenswiththewhole
population:ifnecessarycomponentcauseAwereto
beeliminatedfromthepopulation,100%ofallsuf-
ficientcausescannotbeformedanymoreandthedis-
easewouldhavebeeneradicatedfromthepopula-
tion.
Wecanalsoseethat2/3ofthesufficientcauses
comprisecomponentcauseD.RemovingDfromour
populationwouldhowevernotnecessarilyreduce
thenumberofdiseasedinourpopulationbythis
samenumber.Afterall,personswithsufficientcause
1arenowonlyexposedtocomponentcauseA,Band
Candthereforestillatriskofdevelopingthedisease
forexamplewhenexposedtocomponentcauseFlat-
erintime.Ifintheextremecaseeachindividualex-
posedtocomponentcauseDisalso,atsomelater
time,exposedtocomponentcauseF,sufficientcause
threewouldbeformedinhalfofthepeopleforwhom
thesufficientcauseotherwiseincludedD(halfsince
halfofthosepeople–sufficientcause2–isnotex-
posedtocomponentcauseB).Inthisexamplewe
canseethatonly1/3ofthediseasedcanbeattrib-
utedtocomponentcauseD(knownastheattribut-
ablefraction),eventhoughitispresentin2/3suffi-
cientcauses(knownastheaetiologicfraction).
Pleasenoticethatthisobservationcanbeatodds
withtheinterpretationofthecondicio-sine-qua-non-
testthatisappliedindifferentjudicialsystems,for
thisprincipledoesnotnecessarilyprovidetheright
mind-settohandlethepossibilitythatadifferent
causalmechanismleadingtothesameconsequence
couldarise.
Althoughneitherthecounterfactualnorthesuffi-
cientcauseofanindividualcanbeobserved,thiscon-
ceptualframeworkdoesprovideusefulinsightinthe
ideaofcausationandmulti-causality.
V .StudyDesigns
Thecounterfactualidealcanbeapproachedinsev-
eralstudydesigns,aslongasseveralassumptions
aremade.Althoughuncommon,sometimesthe
counterfactualisundisputedanddirectcausalinfer-
encescanbemade.Forexample,certainformsof
braininjurycaninducemassiveswellingofthebrain
whichleadstoincreasedintracranialpressureand
subsequentlythedeathofalmostallpatientswith
thiscondition.10Anyinterventionthatreducesthe
intracranialpressureandpreventsdeathinallpa-
tients,forexamplebydrillingaholeintheskullso
thattheswollenbraincanextentoutward,willbere-
10Zuurbier ,S.M.etal.,‘DecompressiveHemicraniectomyin
SevereCerebralVenousThrombosis:aProspectiveCaseSeries’,
Journalof.Neurology259(2012),pp.1099-105.

EJRR1|2016179 CausalInferenceinLaw:AnEpidemiologicalPerspective
gardedascausalinthepreventionofdeathofthese
patients.
Therewillhardlybeanydiscussionaboutthe
causalclaimmadeinsuchascenario,sowewillnot
focusonthistypeofstudies.Wewillfocusonsce-
narioswhicharemuchmoreunclear.Sincemost,if
notall,diseasescanberegardedasmulti-causal,the
compositionofsufficientcauseofindividualpatients
cannotbeknown,makingitimpossibletodetermine
causalmechanismsinindividuals.Wecanonlyquan-
tifytheeffectofcomponentcausesinprobabilistic
terms.11Oftenthisisdonebycomparingtheriskof
thosewhoareexposedtothefactorofinteresttothe
riskofthosewhoarenotexposed,forexampleby
theratiooftherespectiveprobabilitiesofdisease.
Thisratioisalsoknownastherelativerisk.
Thestudydesignthatapproachesthecounterfac-
tualidealascloseaspossibleisthecrossovertrial.
Inthisdesignpatientsareassignedtotwosubse-
quenttreatmentstrategies,ofwhichonecanbea
placebotreatment,andtheoutcomeofthepatient
(e.g.bloodpressure)ismeasureddirectlyaftereach
treatment(e.g.antihypertensivemedicationvs.
placebo).Thiswaythesamepatientisobservedboth
withandwithouttheexposure,asprescribedbythe
counterfactualideal.Itisimportantthatthepatient
hastoreturntohis‘originalstate’frombeforehis
firsttreatment,beforereceivinghissecondtreat-
ment.Otherwisesuchacomparisonwillnotresult
incorrectcausalinference.Thisproblemcanbe
counteredbytweakingtheexperimentaldesign,for
exampleintroducingawash-outperiodbetweenthe
twotreatmentperiods,butalsoseverelylimitsthe
applicabilityofthisdesign.12Anotherstudydesign
thatapproachesthecounterfactualidealisthecase-
crossoverdesign.Inthisdesigntheexposurestatus
ofapatientisdeterminedontwomoments:acutely
beforetheonsetofthediseaseandinacontrolperi-
odsometimebeforetheonsetofthedisease.Ifthe
exposureofinterestisindeedacauseofthedisease
itislikelytobemorepresentjustbeforetheacute
onsetofthediseasethaninthecontrolperiod.This
canonlybedonewhentheinformationneededto
determineexposurestatuscanbereliablyobtained
afterthepatientsareidentified.Anotherdisadvan-
tageofthisdesignisthatitcanonlyinvestigatetrig-
gersofdiseaseswithanacuteonset,whicharethe
componentcauseswithnoorlittleinductiontime.
Anexampleofthisstudydesignisastudythatin-
vestigatedpotentialtriggersofsubarachnoidbleed-
ing,whichshowedthatshortbutdistinctiveexpo-
suressuchascoffeeconsumptionandsexualinter-
coursecanindeedbethetriggerofthistypeofhaem-
orrhagicstroke.13,14
Althoughthesetwostudydesignsapproachthe
counterfactualideal,thesecanonlybeappliedtosit-
uationsinwhichanexposureisvariablewithinone
personandtheeffectiseitheracuteorreversible.
Manyresearchquestionsdonotadheretothesecon-
ditions(e.g.geneticexposuresarenotvariablewith-
inaperson,cancerhasnoacuteonsetanddeathis
notreversible)thusleavingoneorbothofthese
crossoverdesignsinappropriate.Otherstudydesigns
donotsufferfromtheserestrictions,butneedmore
assumptionstojustifycausalinferences.Random-
izedtrialscanbeusedtostudytheeffectofdifferent
treatmentstrategiesbyapplyingthetreatmentsto
differentgroupsofpersonsandobservewhether
thereisadifferenceinthefrequencyoftheoutcome
ofinterest.Thisstudydesignreliesheavilyontheas-
sumptionthatthetwogroupswouldhaveasimilar
riskoftheoutcomeifthesewereleftuntreated,asit-
uationinwhichthecounterfactualidealclearlyres-
onates.Thissituationiscreatedbytherandomiza-
tionprinciple:thelikelihoodofreceivingacertain
treatmentisindependentfromothercausesofthe
outcome.Randomizedtrialsareapowerfultoolin
thediscoveryofintendedeffectsofmodifiableexpo-
sures,beingtreatmentstargetedatreducingtherisk
oftheoutcome,asisthecaseinaclinicaltrialthat
comparestwotreatmentstopreventcardiovascular
disease.Also,datafromrandomizedtrialscanpro-
videmoreinsightinthesideeffectsofnewdrugs.
However,theuseofrandomizedtrialstoidentify
causesofadiseaseisinmanycasesethicallyunde-
sirable.Additionally ,manyexposurescannotbe
modified(e.g.geneticvariations)andthereforea
largeproportionofcausalquestionscannotbean-
sweredbyexperimentalstudies.Insuchcasesobser-
vationalstudiesmustbeappliedtoestimatethe
causalrelationshipbetweentheexposureandthe
11Rothman,K.J.,Greenland,S.,Lash,T.L.,ModernEpidemiology
(thirdrevisededition),LippincottWilliams&Wilkins2008.
12Senn,S.,Crossover-trialsinclinicalresearch,Wiley1993.
13Maclure,M.etal,‘Shouldweuseacase-crossoverdesign?’,
AnnualReviewofPublicHealth(2000),pp.193-221.
14Vlak,M.H.M.etal.,‘TriggerFactorsandTheirAttributableRisk
forRuptureofIntracranialAneurysms:aCase-crossoverStudy’,
Stroke42(2011),pp.1878–82.

EJRR1|2016 180CausalInferenceinLaw:AnEpidemiologicalPerspective
outcomeofinterest.Theobservationalstudydesigns
canbecategorisedintwogroups,beingthecohort
studiesandthecase-controlstudy,eachwiththeir
ownmerits.Likeexperimentalstudydesigns,obser-
vationalstudydesignsrelyoncertainassumptions
toallowestimationofthecausaleffect.Thesede-
signs,theirmeritsandpitfallsaswellastheassump-
tionsneededforcausalinferencearetoocomplexto
describehereindetailandarediscussedatgreat
lengthinseveraltextbooksandwelimitourselvesto
ageneraldescriptionoftheconceptofbias.15
VI.Bias
Onemajorassumptionincausalinferencefromepi-
demiologicalstudiesistheabsenceofbias,whichin-
troducesanincomparabilityintothestudy.W ewill
discussthreemajorformsofbiaswithregardtothe
causalrelationshipbetweensmokingandlungcan-
cer.Thefirstisinformationbiasinwhichdataare
collectedincorrectlyandbiastheresultinaparticu-
lardirection.Forexamplewhendataaboutsmoking
habitsarecollectedinadifferentfashion(forexam-
plemorerigorouslyorthroughdifferenttypesof
questionnaires)inlungcancerpatientsthanin
healthysubjects.Acomparisonofthosedatawould
notonlyreflecttheeffectofsmokingontheriskof
developinglungcancer,butundesirablyalsoreflects
thedifferencesindatacollection.Anotherformof
biasisselectionbiasinwhichstudyparticipationis
dependentontheexposureand/ortheoutcome.For
example,whenlungcancerpatientsarecomparedto
agroupofhealthyvolunteerswhoarenotreflective
ofthepopulationfromwhichthelungcancerpa-
tientsarose,butareinstead(indirectly)selectedfor
beingnon-smokers,resultsofthecomparisonof
thesegroupswouldnotreflecttheeffectofsmoking
ontheriskofdevelopinglungcancer.Itwillunde-
sirablybereflectiveofthedifferencesbetweenthe
twoseparatepopulationsfromwhichthepatients
andcontrolgroupweresampled.Athirdformofbias
isconfoundingbiasinwhichtheincreaseinriskof
theexposureofinterestismixedwiththeriskofan-
othercauseofthediseaseofinterest.Thishappens
whentheexposureofinterestsharesacommoncause
withtheoutcomeofinterest,asisdiscussedinfig-
ure2.
15Rothman,K.J.,Greenland,S.,Lash,T.L.,ModernEpidemiology
(thirdrevisededition),LippincottWilliams&Wilkins2008.
Figure2

EJRR1|2016181 CausalInferenceinLaw:AnEpidemiologicalPerspective
Thisfigurecontainsfourgraphsthatdescribethe
causalrelationshipbetweensmokingandlungcan-
cer,butalsoincludeathirdfactor.Thesegraphsare
examplesoffourdifferentclassesoffactorsthatare
statisticallyassociatedtotheriskoflungcancer,
whichcouldimpedecausalinference.Itisimportant
todifferentiatebetweentheseclassesbecausethena-
tureofsuchavariabledetermineswhetheritshould
betakenintoaccounttoensurevalidestimationof
thecausaleffectbetweensmokingandlungcancer
development.
A|Acommoncauseoftheexposureandoutcome
isconsideredaconfounder.Thisexampleshowsthat
menaremorelikelytosmoke,butalsothatmenin-
trinsicallyhaveahigherriskoflungcancer.The
smoking-lungcancerassociationissaidtobecon-
foundedand‘malesex’needstobetakenintoaccount
inordertoensurevalidcausalinference.Confound-
ingcanbeasourceoffallacious‘posthocergopropter
hoc’conclusions.
B|Anothercauseoflungcancer,e.g.ageneticpre-
disposition,whichisindependentofsmokingisnot
consideredaconfounder.Therefore,theadditional
riskofsomeindividualswillnotconfoundthesmok-
ing-lungcancerassociation.
C|Causesoftheexposurewhicharenotacauseof
theoutcomeotherthanviatheexposureofinterest
arenotconfounders.Inthisexample,anaddiction
pronepersonalityisacausalfactorinthedevelop-
mentofasmokinghabit.However,itisnotacause
oflungcancerbyitself.Thesecausesarepartofthe
causalmechanismoflungcancer,butdonotcon-
foundthesmoking-lungcancerassociation.
D|Adirectconsequenceoftheexposurewhichul-
timatelyleadstotheoutcomeofinterestisnotcon-
sideredtobeaconfounder.Inthisexample,smok-
ingincreasestheriskoflungcancerbecauseitcaus-
esdamagetolungtissue.Thisintermediatecauseis
saidtolie‘inthecausalpathway’.Therefore,thereis
noconfoundingpresent.
Thepresenceofconfoundingcanleadtoafalla-
cious‘posthocergopropterhoc’conclusion:even
whenanexposureofinterestisnotacauseofthedis-
ease,itisstillpossiblethatexposedindividualsare
morelikelytodevelopthedisease.Thisincreasein
risk,whichisinfactaspuriousrelationship,canthen
beexplainedbyothercausesofdiseasethatarefound
moreoftenamongstexposedindividualsleadingto
confoundingbias.Whenconfoundingisnottakenin-
toaccountthediseasedevelopsmoreofteninthose
withacertainexposure,itseemsasiftheexposure
isinfactthecause.Ifsourcesofconfoundingare
identifiedbeforethestartofthestudy ,confounding
canbeaddressedandaccountedforinthestudyde-
signorstatisticalanalyses.16However,whencon-
foundingisnotsufficientlyaddressed,itspresence
mayleadtoerroneouscausalstatements.
Allstudydesignsaresubjecttobias,butdifferent
studydesignssufferfromdifferentformsofbiasand
toadifferentextent.Therearesomeclassifications
thatcategorisestudiesaccordingtotheir‘levelofev-
idence’.17Thispracticecanbeuseful,aslongasthis
practicedoesnotprecludecriticalthinking.Forex-
ample,manyresearchersbelievethattherandomized
clinicaltrialistheonlystudydesigninwhichcausal
relationshipscanbestudied.Thisishoweveranout-
datedpointofview,sinceobservationalstudiescan
beascredibleasrandomizedtrialsundercertaincon-
ditions.18Therandomizedcontrolledtrialstudyde-
signremainshowevertheunbeatablegoldenstan-
dardifonewantstostudythebeneficialeffectsofa
newdrug.Therandomizationprocedurebreaksthe
linkbetweentheprescriptionofthenewdrugand
theprobabilityoftheoutcome.Observationalstud-
iesdonotbreakthislink,whichcouldseverelybias
theresults(i.e.confoundingbyindication).Howev-
er,thesebiasesarelessseverewhenonewantsto
studydrugsideeffectsoridentifycausesofadisease.
Thismakesobservationalstudiessuitabletoinvesti-
gatecausalmechanisms,incasebiasescanbeac-
countedfor.
VII.CausalInference:MorethanOne
Study
Socanwedrawdefiniteconclusionsontheproba-
bilisticrelationshipofacauseanditsconsequence
basedonasinglestudy?Itisadvisabletousemulti-
plestudiesforseveralreasons.First,itispossiblethat
16Formorebackgroundinformationonthestatisticalapproaches
thatcanbeappliedtoinvestigatecausalrelationships,please
refertoBerzuini,C.,Dawid,S.,Bernadinell,L.,(editors),‘Causali-
ty:StatisticalPerspectivesandApplications ’ ,(Wiley,2012)
17SeeforexamplethewebsiteoftheCentreforevidencebased
medicinewiththetitle‘Levelsofevidence’,<http://www .cebm
.net/index.aspx?o=1025>(21July2014).
18Vandenbroucke,J.P.,‘Whenareobservationalstudiesascredible
asrandomisedtrials?’,Lancet363(2004),pp.1728–31.

EJRR1|2016 182CausalInferenceinLaw:AnEpidemiologicalPerspective
justbychancetheeffectestimatefromasinglestudy
isverydifferentfromthetrueeffect.Bycombining
theresultofmultiplestudiesintoaso-called‘meta-
analysis’thestatisticalpowerincreasesandtheef-
fectestimateismoreprecise.Second,allstudiesare
subjecttobiasandsomestudiesaremoreproneto
particularformsofbias.Therefore,alotcanbe
learnedfromcomparingtheresultsofstudieswith
differentstudydesigns.Butevenintheunlikelysce-
nariothatbiasisthoughttobecompletelyabsentand
thattheeffectofthepresumedcauseismeasured
withsufficientstatisticalpower,moreinformationis
neededtodrawfirminferencesonthecausalrela-
tionshipbetweentheexposureandoutcomeofinter-
est.Thisknowledgemustfocusontheplausibilityof
theproposedcausalclaim.Areotherplausiblefac-
torspresentthatcouldexplainourresults?Isthepro-
posedmechanisminlinewithourcurrentknowl-
edge?
Therefore,partofcausalinferenceinmedicinelies
outsidethereachofasinglestudyorevenoutside
therealmofepidemiology.Thisconceptisinline
withthecrosswordanalogyofsciencephilosopher
SusanHaack.19,20Severalfactorsareofimportance
whenfillingoutacrossword:theclue,thealready
enteredanswers,thepossibilityofalternativean-
swers,andthelevelofcompletionofthecrossword.
Anewanswercannotbeatoddswithalreadyexist-
ingentrieswithoutrethinkingpreviousanswers.
Causalinferencecanberegardedinasimilarfash-
ion:onesingleresultisnotlikelytojustifycausal
claims.Butseveralresults,fromvariousresearch
groups,backedbypreviousknowledge,notlikelyto
beexplainedbyalternativescenariossuchasbiasor
chancecouldjustifycautiouscausalclaimsaboutthe
quantificationofthecauseandeffectestimateofin-
terest.
Somehavetriedtocodifyallaspectsthatneedto
beconsideredbeforearelationcanberegardedas
causal.Forexample,SirAustinBradfordHillnoted
nineaspectsofcausalitythatmightbeconsidered
whentalkingaboutcausalityinepidemiology .21Hill
notedinhisoriginaladdresstotheRoyalSocietythat
thesefactorsarenottobeconsideredascriteria.On-
lyone,‘temporality’,isatruecriterion,thatisthat
thecausemustbepresentoractbeforeitseffect.The
othereightaspectsarenotcriteriaandcanberegard-
edasaspectsthatmightbediscussedwhenonewants
tocometoacausaljudgement.However,despitethe
warningsbyHillandothers,someresearchershave
misusedthesenineconditionsasachecklistfor
causalclaims.Suchpracticeprohibitsacriticalap-
praisalofallevidenceandshouldbeabandoned.Un-
fortunately,thisnotthecase.22,23
VIII.CausalClaimsinLaw
Itiseasytoseethatitisnotstraightforwardtotrans-
ferepidemiologicalknowledgeobtainedfrompopu-
lationstoindividuallegalclaims.Wewilldiscuss
thesedifficultiesbydiscussingtheDutchNefalit-
case.24Inthiscase,Karamusattributedhisdisease
tohislong-termexposuretoasbestos,sufferedinthe
factorywhereheworked,forwhichheheldhisfor-
meremployerNefalitliable.Nefalithadfailedtotake
thenecessaryprecautionarymeasuresandwasthere-
fore,intheviewofKaramus,tocompensatealldam-
agesrelatedtohisdisease.Nefalitresponded,how-
ever,thatthelungcancercouldalsohavebeencaused
byKaramus’longtimesmokinghabit,byotherfac-
torsoracombinationofthese.Itisindeedknown
fromepidemiologicalevidenceaswellaslaboratory
studiesthatbothexposuresareknowntoincrease
theriskofthisparticulartypeoflungcancer,often
incombinationwithotherscauses.Thereforeitis
notpossible,giventhestateofscienceandtheidea
ofmulti-causality,todeterminethesinglecauseof
Karamus’diseaseandhisdamages.Lowercourts,
withtheconsentoftheDutchSupremeCourt,ac-
knowledgedthatapplyingthecondicio-sine-qua-non-
testwouldmeanpassingonthisuncertaintytoKara-
musentirely,ashisclaimwouldhavetobedismissed
onthegroundthatcausationcouldnotbeestab-
19Haack,S.,ManifestoofaPassionateModerate,Chicago:Univer-
sityofChicagoPress1998.
20Vandenbroucke,J.P.,‘ AlternativeMedicine:A“MirrorImage”for
ScientificReasoninginConventionalMedicine’,AnnalsofInter-
nalMedicine135(2001),pp.507-511.
21Hillreferstotheseninepointsas‘aspectsof…(an)association’
thatshouldbeconsideredbeforedecidingontheinterpretationof
causation.Thesepointsare:strength,consistency,specificity,
temporality,biologicalgradient,plausibility,coherence,experi-
mentandanalogy.SeealsoHill,A.B.,‘TheEnvironmentand
Disease:AssociationorCausation?’,ProceedingsoftheRoyal
SocietyofMedicine(1965),pp.295-300.
22Morabia,A.,‘OntheOriginofHill’ sCausalCriteria’,Epidemiolo-
gy2(1991),pp.367-369.
23Phillips,C.V .etal.,‘TheMissedLessonsofSirAustinBradford
Hill’,EpidemiologyPerspectivesandInnovations1(2004),p.3.
24HogeRaad31March2006,ECLI:NL:HR:2006:AU6092,reach-
ablethrough<http://uitspraken.rechtspraak.nl/#ljn/AU6092>(in
Dutch;9December2014).

EJRR1|2016183 CausalInferenceinLaw:AnEpidemiologicalPerspective
lished.Thereforethesecourtsappliedtheconceptof
so-calledproportionalliability,rulingthatNefalit
wasliableforonlyaproportionofKaramus’dam-
ages,basedonexperttestimonyandepidemiologi-
calpublicationsaboutthechancesthathislungcan-
cerwasindeedcausedbytheasbestosexposure
(55%).25
Itwasamatteroffairness,theSupremeCourtin-
dicated,nottopassonthisuncertaintytothe
claimantentirely ,bydismissingKaramus’claimal-
together,giventhatinthiscasethechancethatthe
lungcancerwasindeedcausedbyasbestos,wasnei-
therverysmallnorverylarge.Insuchcases,courts
areallowedtomakeareasonedestimate,ifnecessary
onthebasisofexperttestimony .Itisimportantto
notethattheSupremeCourtjustifiedtheapplication
ofthisso-called‘proportionalliability’inpartbystat-
ingthattherewasuncertaintywhetheritwastheas-
bestosexposure,theclaimant’ssmokinghabits,ge-
neticsorotheradditionalexternalfactorsthatcaused
thelungcancer,aloneorincombination.
Wewilldiscusslaterwhetherthe55%-rulingis
justifiedinlightofthismotivationgivenbytheDutch
SupremeCourt.First,itisimportanttounderstand
howthe55%cameabout.Thisnumberwasobtained
bycalculatingtheattributablefraction,asdiscussed
insectionIV ,whichisdefinedasthefractionofcas-
esinwhichtheexposureofinterestisacomponent
causeofthesufficientcauseleadingtothedisease.
Asecondrelatedmeasureistheprobabilityofcausa-
tion,whichisadirectfunctionofanotherfraction:
theaetiologicalfraction.Thisfractiondescribesthe
probabilitythatthefactorofinterestisacomponent
causeinasufficientcause,inacaserandomlydrawn
fromapatientpopulation.Intheory ,theseconcepts
canbeveryhelpfulinliabilitycases,becausethey
provideawaytolinkapopulationmeasuretoasin-
glecase.However,wehavealreadyarguedthatthe
aetiologicalfractioncannotbeobserveddirectlyor
calculatedwithoutstrongadditionalassumptions,
whichcannotbeempiricallyverified.
However,theattributablefraction,thefractionof
thediseasesamongtheexposedthatcanbeascribed
totheexposureofinterest,onthecontrarycanbe
calculatedinacohortstudyas(seeEquation1),where
therelativeriskistheriskoftheoutcomeamongst
theexposeddividedbytheriskintheunexposed.
Oncecalculatedtheattributablefractionshoulddi-
rectlybeinterpretedastheaetiologicalfraction:the
aetiologicfractionisalwayssimilarorhigher,but
neverlowerthantheattributablefraction.26
Somepointshavetobeemphasizedtoensurecor-
rectinterpretationofthesenumbers.Boththeaetio-
logicandattributablefractionarecalculatedforcom-
ponentcauses,whichimpliesthatthesumofallfrac-
tionsdonotnecessarilyequal,butislikelytobehigh-
erthan100%,duetothemulti-causalnatureofcom-
plexdiseases.Infact,thesumofthesefractionscould
bebothhigherorlower,andbasicallydependslarge-
lyonthenumberofcausesthathavebeenidentified
foraspecificdisease.Therefore,thesefractions
shouldneverbeinterpretedastheprobabilitythata
certainfactorofinterestisthesinglecauseofthedis-
easeinaparticularcase,sincethereisnosuchthing
asasinglecause.Somehaveproposedthiswrongde-
finitioninordertousetheeffectsizeasameasure
ofcausality .Inlinewiththiswrongnotionarelative
riskgreaterthan2,whichequalsanattributablefrac-
tionof>50%(AF=(2-1)/2),hassometimeseven
beenabusedascutoffpointfor‘causality-provenvs.
25HogeRaad31maart2006,ECLI:NL:HR:2006:AU6092.See
also,morerecently,HogeRaad14december2012,
ECLI:NL:HR:2012:BX8349.Onthesecases,seeCastermans,A.G.
&Hollander ,P.W.den,‘Omgaanmetonzekerheid.Proportionele
aansprakelijkheid,artikel6:101BWendeleervandekanss-
chade’,NTBR2013,pp.185-195(inDutch).
26Thesituationunderwhichtheattributablefractioncanbeinter -
pretedastheaetiologicalfractionaredescribedinKennethJ.
Rothman,SanderGreenland,T imothyL.Lash.ModernEpidemi-
ology,thirdrevisededition,(LippincottWilliams&Wilkins,
2008)

EJRR1|2016 184CausalInferenceinLaw:AnEpidemiologicalPerspective
causalitynotproven’.27Thismisuseoftheattribut-
ablefractionprecludesanyformofcriticalthinking
aboutthecausalmechanismunderlyingeventsand
shouldbeabandoned.
Anotherpossiblemisinterpretationofboththeae-
tiologicandattributablefractionliesinthedirect
translationoftheattributablefractiontothepropor-
tionoftheclaimsthatshouldbereimbursed,with
theideathatonaverageboththeplaintiffaswellas
thedefendantsaretreatedsatisfactorily.However ,by
couplingtheattributablefractiontotheproportion
thatshouldbereimbursed,thecourtforgetsacrucial
characteristicoftheattributablerisk,whichagainis
thatthesumoftheattributablefractioncanexceed
100%.Incontrast,thesharesinproportionalliabili-
tyinoneparticularcaseshouldnot.Consideragain
ourexampleinfigure1,inwhich100%ofcases(3/3)
was‘causedbyA’and66%ofallcases(2/3)was
‘causedbyB’.Ifaclaimantwiththisparticulardis-
easewouldtheoreticallyholdboth‘ A’and‘B’liable
inseparatelawsuits,thisapproachwouldyieldato-
talof166%oftheclaimedsum,whichdoesnotad-
heretothefairnessprinciple.Themisconceptionthat
theaetiologicorattributablefractioncandirectlybe
appliedasanallocationinstrumentforproportional
liabilityasalegalconceptthusliesinerroneouslyap-
plyingapopulationmeasuretoanindividualproba-
bilityestimation.Thiscanalsobeappreciatedwhen
wecomparetheformulafortheaetiologicalfraction
(seeEquation2)totheconceptthatusesproportion-
alliabilitytoadheretothefairnessprinciple(see
Equation3).
Sowhattothinkthenoftheuseofproportional
liabilityinthecaseofNefalitandKaramus?During
thehearings,anexpertmotivatedthattherewasa
125%increaseinriskduetoasbestosexposure,which
correspondstoarelativeriskof2.25andanattribut-
ablefractionof55%(theAF=(2.25-1)/2.25=55.56%,
thelowercourtmentions55%initsruling).The
DutchSupremeCourtmotivatedtheuseofpropor-
tionalliability ,includingthisfigure,andtherebyim-
plicitlytheuseoftheattributablefractioninitsrul-
ingwiththeobservationthattherewasuncertainty
whetherasbestoswasindeedthecause.However,the
courtwentfurtherbycouplingthisnumberasthe
fractionofthedamagesthatemployerNefalitshould
reimburseasamatteroffairness.Atfirstglance,the
motivationoftheSupremeCourtsoundsfair,butwe
havealreadyshowedinourexampleabovethatlink-
ingtheattributablefractiontothefractionthat
shouldbereimbursedbythedefendantdoesnotal-
waysadheretothematteroffairness.Therefore,the
rulingbytheSupremeCourtcouldleadtounfairre-
imbursementsand,perhapsunknowinglyandun-
wantedly,setsaprecedentwithpossiblyunwanted
consequences.
WewillcontinuewiththeNefalit-casetoillustrate
this.Letsaythatbesidessmokingandasbestosexpo-
suretheclaimantwasalsosubjectedtoanotherrisk
factor‘X’duetonegligenceofanotheremployer.
Again,itisuncertainwhetherindeeditwas‘X’that
wasthecauseofhisdisease.Letusstatethat‘X’in-
creasestheriskoflungcancerby178%andtherefore
hasanattributablefractionof64%(i.e.arelativerisk
=2.78andAF=(2.78-1)/2.78).Followingthesame
lineofreasoningasthecourtdidwhenitcametoas-
bestosexposure(i.e.thereisuncertaintyaboutthe
causalclaimandthereforeonlyapartoftheclaim
shouldbereimbursed),intheory64%oftheclaim
27Greenland,S.,‘RelationofProbabilityofCausationtoRelative
RiskandDoublingDose:aMethodologicErrorThatHasBecome
aSocialProblem’,AmericanJournalofPublicHealth89(1999),
pp.1166–9.

EJRR1|2016185 CausalInferenceinLaw:AnEpidemiologicalPerspective
shouldbereimbursedbythesecondemployer.This
makesthereceivedamounttotheoreticallysuper-
sedetheoriginalclaim.
Whenacourtwantstodirectlycoupletheaetio-
logicalfactiontoa‘fair’distributionofthedamages
thecourthastoknowthetrueunderlyingcausal
mechanismofeachindividualliabilityclaim.Ina
sense,thecourthastobecertainaboutallthecom-
ponentcausesthatmakeupthesufficientcausein
thisparticularindividual.However,theexactsuffi-
cientcausecannotbeobservedinanindividualcase,
anuncertaintythattheSupremeCourtusedtomo-
tivateitsruling.So,whenacourtiswillingtoassume
proportionalliability ,itshouldbewellmotivated.
Evenmore,whenacourtisuncertainwhetherthe
defendantisindeedresponsibleforoneofthecom-
ponentcausesinthisparticularcase,itisevenmore
difficulttounderstandhowitcanbejustifiedtolink
theproportionalliabilitytotheaetiologicalfraction,
itsderivativesandapproximations.
Basedonthesepoints,itisalreadyhighlyques-
tionablewhetherproportionalliabilityshouldbedi-
rectlylinkedtoepidemiologicalpopulationmeasures
suchastheunobservableaetiologicalfractionorthe
attributablefractionasitsderivative.Butthemost
importantobjectionofthisdirectcouplingisthefact
thatthesumofthesenumbersarenotrestrictedto,
andisevenverylikelytosupersede,100%.Wedosee
themeritofproportionalliability ,especiallygiven
themulti-causalnatureofmostdiseases,andwe
wouldthereforeliketoproposeadifferentapproach
thatlinksthesetwoconceptswithouttheaforemen-
tionedproblems.Forthis,wewillusethecomponent
causeconceptincombinationwiththecondicio-sine-
qua-non-principleinatwo-stagesapproach.
IX.ProportionalLiabilityinTwoStages
Theapproachwewouldliketoproposeisatwo-
stages-approach,linkingtheconceptsofproportion-
alliabilityandmulti-causality .Thisapproachmakes
useofthecondicio-sine-qua-non-testandthuspro-
videsequalweightstoallpossiblecauses.Thisisin
linewiththenotionofboththesufficientcausemod-
elandthecounterfactualmodel.
Duringthefirststageofthisapproach,thecourt
hastodecidewhetherthedefendant’swrongfulbe-
haviourindeedplayedaroleinthecausalmecha-
nism.Thecourtshouldmotivateitsdecisiononevi-
denceandexpertwitnesses.Oncedecidedwhether
thedefendantindeedplayedaroleinthecausalmech-
anism(i.e.isresponsibleforoneormorecomponent
causesofthesufficientcause),thedefendantcanad-
vocateproportionalliabilityinthesecondstage.The
defendantdoessobyprovidingalistofpossibleoth-
ercomponentcausestothecourt,ofwhichithasto
determinewhetherthesealsoplayedaroleinthis
particularcase.Thisway ,thecourtcandeterminethe
fractionofcomponentcausespartofthepresumed
sufficientcause,thataretheresponsibilityofthede-
fendant.Thisfractioncouldbeusedtodetermine
proportionalliability(cf.equation2).Forexample,
whentherearesixpossiblecauses,ofwhichfour
mightplayaroleinthecaseathandandoneofthese
fourcanbeattributedtothedefendant,thedefen-
dantwouldhavetocompensate25%oftheclaim.
Thistwo-stages-approachisnotflawless,forit
couldoverestimatethenumberofcomponentcaus-
esthatplayaroleinthesufficientcauseandthere-
byunderestimatetheliabilityofthedefendant.Al-
so,newcomponentcausescouldbeidentifiedafter
thecourthasdecided.Ifthiswouldleadtoanewli-
abilityclaimwithanewdefendant,ourexample
couldbesummarisedasfollows.Withthediscovery
ofanewcausethatisrelevanttoourcase,thereare
nowsevencomponentcausesofwhichfiveareap-
plicabletothecaseathand.Ifoneofthosecompo-
nentcausescanbeattributedtotheseconddefen-
dant,thenhewouldhavetopay20%oftheoriginal
claim.Thisway ,thetotalsumofallclaims,40%in
ourexample,willneversupersede100%oftheorig-
inalclaim,butapproachesthisnumberasymptoti-
cally.Receivingthis20%oftheseconddefendant
shouldbeconditionalonthereimbursementofthe
excess5%thatwaspaidbythefirstdefendant.
Anotherproblematicaspectofthistwo-stage-
methodisthatallpossiblecomponentcausesarecon-
sideredequallyimportantandaregiventhesame
weightinthisapproach.Althoughthisisinlinewith
thecomponentcausemodel,itdoesresultinsome
practicalproblems.Forexample,therecanbenumer-
ouscomponentcauseswhichmightbelistedthatin-
deedarecomponentcausesinthemoststrictdefin-
ition,butlackrelevancewhenitcomestoproportion-
alliability(e.g.onehastohavelungsinordertode-
veloplungcancer).Also,evidencemightsuggestthat
somecomponentcausescannotbediscarded,butare
certainlylessrelevanttothecaseinquestionthen
others.Inthatcase,aweightedapproachcouldbe

EJRR1|2016 186CausalInferenceinLaw:AnEpidemiologicalPerspective
considered.Allinall,itisuptothecourt,withthe
aidofexpertsandscientists,torulewhichpossible
componentcausesarerelevanttothequestionofli-
ability.
X.Conclusion
Causalityresearchinepidemiologyislargelyembed-
dedintheconceptofthecounterfactualmodel,which
resemblesthelegalcondicio-sine-qua-non-test.Byde-
finition,thecounterfactualcannotbeobservedand
thesufficientcauseinasinglepersoncannotbe
known.Therefore,itisnotpossibletoknowtheex-
actcausalmechanismleadingtothediseaseinanin-
dividualperson.However,epidemiologicalstudies
canbeusedtostudytheeffectofapresumedcause
ontheriskofdiseaseatthepopulationlevel.Results
frommultipleandreliablestudies,consideringmul-
ti-causality,combinedwithpriorbiologicalknowl-
edgecanresultincautiouscausalclaims.Although
theaetiologicfractioncanneverbeknown,theat-
tributablefractioncanbecalculatedandgivesinsight
intherelationbetweencauseandeffectonagroup
level.
Thispopulationmeasurecannotdirectlybeap-
pliedtoindividualcaseswithoutrelyingon
untestableassumptions(seeBox1).
Linkingtheconceptofproportionalliabilitytothe
attributablefractionisthuswrong.Inaddition,the
sumoftheattributableaetiologicalfractionsislike-
lytoexceed100%,whichcouldleadtounfairreim-
bursements.Wehavethereforeproposedatwo-stage-
approachforacourttoapplytheconceptofpropor-
tionalliability ,byfirstdecidingonliabilityandthen
ontheproportion.Thislinksproportionalliabilityto
theconceptofmulti-causality ,whilealsoandfirstly
adheringtothecondicio-sine-qua-non-test.Inthis
process,thecourtshouldconsultscientistandex-
perts,butultimately,thedecisionremainsanorma-
tivejudgmentforthecourtitselftomake.
Box1-Takehomemessages
-Causalclaimsshouldalwaysbeconsideredinthelightofmulti-causality:thereisneverthe
cause,butasetofcomponentcausesthatmakeupasufficientcause.
-Causalityinepidemiologyreliesonmorethanjustonestudy:differentstudies,theeffectof
possiblebiasesandadditionalevidence,evenoutsidetherealmofepidemiology,shouldall
betakenintoaccountbeforecautiousclaimscanbemade.
-Theaetiologicalfractionandtheprobabilityofcausationasitsderivativearebothepidemio-
logicalmeasureswhichcannotbecalculated.Theycanonlybeapproached,undercertainas-
sumptions,bycalculatingtheattributablefraction.
-Linkingtheconceptofproportionalliabilitytotheattributablefractioniswrong,especially
becausethesumofallattributablefractionsislikelytoexceed100%.