Living up to expectations: Experimental tests of subjective life expectancy as reference point in time trade-off and standard gamble

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Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations:

Experimen-ContentslistsavailableatScienceDirect

Journal

of

Health

Economics

jo u rn al h om ep age :w w w . e l s e vi e r . c o m / l o c a t e / e c o n b a s e

Living

up

to

expectations:

Experimental

tests

of

subjective

life

expectancy

as

reference

point

in

time

trade-off

and

standard

gamble

Stefan

A. Lipman

a,∗

_,

_Werner

_B.F.

_Brouwer

a,b

_,

_Arthur

_E.

_Attema

a

a_Erasmus_School_of_Health_Policy_&_Management,_Erasmus_University_Rotterdam,_the_Netherlands b_Erasmus_School_of_Economics,_Erasmus_University_Rotterdam,_Rotterdam,_the_Netherlands

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received1March2019

Receivedinrevisedform13March2020 Accepted14March2020 Availableonlinexxx JELclassiﬁcation: I1 D9 Keywords: Timetrade-off Standardgamble QALYmodel Prospecttheory Subjectivelifeexpectancy Referencepoint

a

b

s

t

r

a

c

t

Earlierworksuggestedthatsubjectivelifeexpectancy(SLE)functionsasreferencepointin timetrade-off(TTO),buthasnottestedormodelledthisexplicitly.Inthispaperweconstruct amodelbasedonprospecttheorytoinvestigatethesepredictionsmorethoroughly.We reporttheﬁrstexperimentaltestofreference-dependencewithrespecttoSLEforTTOand extendthisapproachtostandardgamble(SG).Intwoexperiments,subjects’SLEswere usedtoconstructdifferentversionsof10-yearTTOandSGtasks,withthegaugeduration eitherdescribedasoccurringaboveorbelowlifeexpectation.Ouranalysessuggestthat bothTTOandSGweightswereaffectedbySLEaspredictedbyprospecttheorywithSLE asreferencepoint.SubjectsgaveupfeweryearsinTTOandwerelessrisk-tolerantinSG belowSLE,implyingthatweightsderivedfromthesehealthstatevaluationmethodsfor durationsbelowSLEwillbebiasedupwards.

1. Introduction

Time trade-off (TTO) and standard gamble (SG) are twopopularmethodstovaluehealthstates,i.e.toobtain utilityweightsrelevantfordeterminingqualityadjusted life-years(QALYs).1_Although_the_methods_share_a_similar purpose,theirframingandoutcomesdiffersubstantially (Bleichrodt and Johannesson, 1997; Bleichrodt, 2002), withSGweightstypicallybeinghigherthanTTOweights

∗ Correspondingauthorat:P.O.Box1738,3000DRRotterdam,the Netherlands.

E-mailaddress:lipman@eshpm.eur.nl(S.A.Lipman).

1_These_weights_are_sometimes_referred_to_as_{‘utilities’.}_We_will_use

thetermQALYweights,andTTOorSGweightstorefertoQALYweights elicitedbyTTOandSGrespectively.

(e.g.Readetal.,1984;Torrance,1976).Bleichrodt(2002) proposedthatthesedifferencescouldbeexplainedby dif-ferencesin the theoreticalassumptions underlyingTTO and SG. Both methods’ QALY weights are typically cal-culatedusing theoreticalmodels thathave beenshown tobeempiricallyinvalid,i.e.expectedutilitytheory(for violations, see: Llewellyn-Thomaset al., 1982; Starmer, 2000) and the linear QALY model (for violations, see: BleichrodtandPinto,2005;Abellan-Perpinanetal.,2006). Morespecifically,TTOandSGweightsarebiased, accord-ingtoBleichrodt(2002),becauseindividualsshowseveral empiricaldeviationsfromthesesimplifiedmodels, includ-inglossaversion,probabilityweighting,utilitycurvature andscalecompatibility.Thefirstthreeofthesedeviations canbemodelledthroughprospecttheory,andBleichrodt (2002)proposedthatsuchmodellingcouldreducethe

dif-https://doi.org/10.1016/j.jhealeco.2020.102318

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Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations: Experimen-ferencebetweenTTOandSG, forwhichsomeempirical

supportwasfoundbyLipmanetal.(2019b).

Prospecttheorywasoriginallydeveloped asan alter-nativetoexpectedutility(EU)theoryfordecisionmaking underriskanduncertainty(KahnemanandTversky,1979; TverskyandKahneman,1992).Mostimportantly,prospect theoryassumesreference-dependence,i.e.outcomesare notevaluatedinﬁnalterms,butaschangesrelativetoa referencepoint (RP).TheRPis a neutraloutcome, such asthestatusquo(i.e.currenthealth),butmany alterna-tivecomparatorshavebeenarguedtobeabletoserveas RP,suchas thelowestpossibleoutcome (Attemaetal., 2012; Bleichrodt et al., 2001), theguaranteed outcome inTTOorSG(vanOschandStiggelbout,2008;vanOsch et al., 2004), or the best outcome available (van Osch etal.,2006).Furthermore,theRPmaybe inﬂuencedor formed by aspirations, expectations, norms, and social comparisons(Tverskyand Kahneman,1991).It is, how-ever,paramounttodeterminetheexact location of the RP, as this ‘neutral outcome’ will divide all other out-comesintogainsandlosses.Withinprospecttheory,this isespeciallyrelevant,asitassumeslossaversion,i.e.losses (relativetotheRP)carrymoreweightthangainsofthe samesize.Furthermore,inprospecttheoryprobabilities canbetransformednon-linearlybymeansofaprobability weightingfunction,whichmayalsodifferbetweengains andlosses.

OftenitremainsunclearexactlyhowRPsareselected, andhowRPselectionshouldbemodelledwithinprospect theory(Wakker,2010).Twodifferentstreamsofliterature haveproducedinsightsontheroleofRPsinhealth-related decisionmaking,whichwetrytounifyinthispaper.First, inapplicationsofprospecttheorytohealthoutcomes, typ-ically some plausible assumption is made about which outcomecouldserveasRP.Thisapproach,wheretypically theRPisselectedfromtheoutcomesavailablewithinthe scenariospresented torespondents,allowsfor tractable modellingandtheformationofempiricalpredictionsbased ontheseassumptions. For example, earlierwork onRP locationforTTOandSGhassuggestedthatthecertain out-come,i.e.theimpairedhealthstate,willlikelyserveasRP inthesehealthstatevaluationexercises(vanOschetal., 2006).Usingsuchanapproach toRPselection,prospect theoryhasbeensuccessfullyappliedinthehealthdomain, forexample,earlierworkshowedthatthemaintenetsof prospecttheory(e.g.lossaversionandprobability weight-ing) apply to decisions about human lives (Kemel and Paraschiv,2018),lengthoflife(Attemaetal.,2013;Lipman etal.,2019b;Verhoefetal.,1994;TreadwellandLenert, 1999; Lipman et al., 2018), and quality of life (Attema etal.,2016).Second,aliteratureexistssuggestingthatRPs thatoriginate outsidethespeciﬁc decision taskathand mayalsobeselectedbyrespondents.Such studies typi-callyobservesomeeffectofthesereference-outcomeson decision-making orwell-being, and conjecturethat this effectmaybeduetoreference-dependence.Examplesof suchsuggestedreference-dependence areRPs based on expectationsforlength(vanNootenandBrouwer,2004; Van Nooten et al., 2009) and quality of life (Brouwer etal.,2005;Woutersetal.,2015),orsocialcomparisons (Wouters,2016).

Inthispaper,wefocusontheeffectsofindividuals’ sub-jectivelifeexpectancy(SLE),i.e.self-reportedanticipated lengthoflife,whichcouldserveasanRPasdeﬁnedwithin prospecttheoryinhealthstatevaluations.Itiswell-known thatmanyindividualsexpecttolivelongerthanactuarial lifeexpectancy(BrouwerandvanExel,2005;Pénteketal., 2014;Rappangeetal.,2016).GaugedurationsinTTO typ-icallydonotcoincidewiththeseexpectations;frequently, projectedlifespaninTTOisconsiderablyshorter.Although individualsmaynotbefullyawareofthisreduction dur-inghealthstatevaluation(vanNootenetal.,2014),earlier workonSLEhasconsistentlyfoundthatindividualswith higherSLEgaveupfeweryearsinTTO,andthusassociated QALYweightswerehigher.Wewillrefertothesechanges inQALYweightsfordurationsfurtherawayfrom expecta-tionsaboutlengthoflifeasthe‘SLEeffect’.ThisSLEeffect wasfoundfor10-yearTTOs(vanNootenetal.,2009),for patientsvaluingtheirownhealthstate(Heintzetal.,2013), andforTTOsusingalifetimetime-horizon(vanNootenand Brouwer,2004).Consideringthatinmostcaseslifeyears tradedoffinTTOfallshortofSLE,itmayseemplausible toassumethattheselifeyearsareperceivedasbeingin thelossdomainalready,andthusgivenupreluctantly(van NootenandBrouwer,2004;VanNootenetal.,2009).This earlierworkpostulatedthattheSLEeffectmayoccurasa resultoflossaversion,yieldingunwillingnessinTTO exer-cisestofurtherreducelifetimecomparedtoindividuals’ SLEwhichservesasRP.

However,thisexplanationoftheSLEeffecthasnever been modelled adequately or tested directly, as ear-lier work onthe SLE effect hasrelied oninvestigation of heterogeneity in SLE by means of an observational between-subjectsapproach,i.e.explainingdifferencesin TTOresponsesbydifferencesinSLE.Furthermore,ifthe SLEeffectappliestoTTOweightsasaresultof reference-dependence, one could also expect sucheffects on SG, as this method may also be affected by loss aversion (Bleichrodt, 2002).This hasnot yet beentested toour knowledge.Therefore,inthispaperweextendearlierwork onSLEeffectsinhealthstatevaluationby:

(i)Constructingamodelbasedonprospecttheorywith reference-dependencewithrespecttoSLE.

(ii)ReportinganelaboratetestoftheSLEeffectby exper-imentally varying thetradable life years above and belowSLEforbothTTOandSG.

More speciﬁcally, by developing a model based on prospecttheoryweareabletoconstructtractable predic-tionsabouttheSLEeffectforTTOandSGresponses,ifit indeedservesasRP.Wetestthesepredictionsbymeans ofwithin-subjectsexperimentalmethodologyinwhichwe constructdifferentversionsofTTOandSG,todirectly com-pareQALY weights forlife years both underand above SLEforeachindividual.Throughthisprocedurewetestif QALYweightsdifferfordurationsthatcanbeperceivedas eithergainsorlossescomparedtoSLEand,hence,whether SLEfunctionsasaformalreferencepoint.Thisapproachis appliedintwoexperiments(labelledStudy1andStudy2). Theremainderof thispaper isstructuredasfollows. In Section2 we deﬁne our theoreticalmodel based on

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Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations: Experimen-prospecttheoryand inSection3 wederivepredictions.

Section4(Study1)and5(Study2)reporttheexperiments usedtotestthesepredictionsusingdifferentversionsof TTOand SG.Study1 appliedtheexperimental method-ologywithaconveniencesampleofstudents.Theresults ofthisstudysuggestthatSLEindeedservesasRPforTTO andSG.InStudy2,theexternalvalidityofthesefindingsis testedbyrecruitingasampleofindividualsaged60years andolder,largelyconfirmingtheresultsfromStudy1.In thefinalsectionswediscusstheseresultsandconclude.

2. Theoreticalframework

2.1. Notation

TTOandSGaredenotedashealthprofilesdescribedas (Q,t),whereQrepresentshealthstatusandtdenotesthe ageatwhichtheprofileends(e.g.livinginawheelchair until age 85), withD and FH denoting thestates Dead andFullHealth,respectively.Subscripts(e.g.a,r,x,y)are usedtoindicatechronichealthprofilesfacedbya decision-makerwithageta,wheredurationisdefinedasTx=tx−ta.

Importantly,tacan,butneednot,bethedecisionmaker’s

current age (itcouldbe anyta>0). Riskyprospects are

deﬁnedas(Qx,Tx)p(Qy,Ty),i.e.healthproﬁle(Qx,Tx)with

probabilityp,andhealthproﬁle(Qy,Ty)withprobability

1−p.Preferencerelationsaredeﬁnedasusual,i.e.theyare weak-ordered(completeandtransitive),anddenotedby (strictpreference),(weakpreference),and (indiffer-ence).

TheTTOmethodasksforatimeequivalentinperfect healthwhichyieldsindifferencebetweenTxyearsinhealth

stateQ andTyyearsinFH.ThenumberofyearsinTy is

varieduntiltherespondentisindifferentbetweenthetwo options,i.e. (Qx,Tx)∼(FH,Ty).TheSG methodinvolvesa

choicebetweenanumberofyears(Tx)inhealthstateQx

forcertainand agamblewithtwooutcomes,whichare FHduringthesametimeperiod(Tx)andD.Probabilityp

isvarieduntiltherespondentisindifferentbetweenthe twoalternatives,i.e.(Qx,Tx)∼(FH,Tx)p(D).Typically,

pref-erencesinTTOand SGaremodelled withinthegeneral QALYmodel(MiyamotoandEraker,1989),whichassumes thatchronichealthproﬁles(Qx,Tx)canbeevaluatedbythe

utilityfunctionV (.):

V (Qx,Tx)=U(Qx)∗L(Tx), (1)

withU(Q )denotingutilityofhealthstatusandL(T ) denot-ingtheutilityofTlifeyears.

AssumingL(T )=T (i.e.thelinearQALYmodel2_),_with thecommonnormalisationsuchthatU(FH)=1,TTO indif-ferencescanbeevaluatedby:

U(Qx)=

Ty

Tx

. (2)

2_Note_that_this_framework_assumes_no_discounting_of_future_life_years,

i.e.linearutility.Thisframeworkhasbeengeneralizedtoinclude non-linearutilitybyMiyamotoandEraker(1989).

SGindifference,ontheotherhand,additionally assum-ingEUandV (D)=0,canbeevaluatedby:

U(Qx)=p. (3)

AlthoughEq.(2)andEq.(3)areonlyvalidunderthese strictassumptions(andmoregeneralderivationsforTTO andSGareavailable,seeforexample:Lipmanetal.,2019b), theseequationsareoftenusedinlargescalehealthstate valuations(Versteeghetal.,2016;Brazieretal.,2002).

2.2. Reference-dependencemodelforSGandTTO

Referencepointsplaynorolewithintheframeworks ofEUandthegeneralQALYmodel.Thus,inordertotest whetherSLEservesasRP,wewillsupplementthe gener-alizedQALYmodelwithprospecttheory,followingclosely themodeldevelopedinLipmanetal.(2019b).Thismeans thatweassumethatthegeneralQALYmodelholdswith theadditionalassumptionsoutlinedbelowincluded.

We assume separateevaluations of gainsand losses inlife durationcompared toanRP,denotedTr.ThisRP

is anexpectedhealth proﬁle,which is takentolast for Tr years,startingfromtheage(ta)ofthedecisionmaker

untiltheirSLE(tr),i.e.Tr=[ta,tr]=tr−ta.Throughoutwe

willdenotedurationsofhealthproﬁles(Qx,Tx)as

devi-ationswithrespecttothis RPasfollows:we willwrite (Qx,Tx∗) with Tx∗= Tx−Tr. For example, imagine a

50-yearold subject withSLEof living until 80. Thehealth proﬁle of living in a wheelchair until age 70 will be denotedas(living in wheelchair,Tx∗)withTx∗=(tx−ta)−

(tr−ta)=(70−50)−(80−50)=−10 (for more

exam-ples,seeOnlineSupplements). We restrictourprospect theorymodel to life duration, even thoughit has been suggestedthat reference-dependence mayalsoexistfor healthstatus(Woutersetal.,2015;Brouweretal.,2005). However,bothfromatheoreticalandfromanempirical pointofviewsuchreference-dependenceforQ ishardto approximate.Thatis,prospecttheoryistypicallyapplied tosingle-attributeoutcomes,suchasmoney,whilehealth proﬁles consist of both life duration and health status. Multi-attributecharacterizationsofprospecttheoryexist, but becausehealth status is a qualitative measure, loss aversionisnottheoreticallymeaningfulforthisattribute (BleichrodtandMiyamoto,2003).

Asasolution,weapplyanattribute-speciﬁcevaluation (Bleichrodtetal.,2009)bymakingthreemodiﬁcationsto thegeneralQALYmodel,toallowtesting for reference-dependencewithSLEasRP.First,wemodifyL(T )inthe generalQALYmodel to Li_(T∗_),_which_is _a_standard _ratio

scale utilityfunction, that candiffer betweengain out-comes(i.e.(Qx,Tx∗)withTx∗≥0,i=+)andlossoutcomes

(i.e.(Qx,Tx∗)with Tx∗<0, i=−), andis strictly

increas-ingandreal-valued.Second,lossaversionisincorporated intoourmodelbytakingL−(T∗)=Li_(T∗₎_for_T∗_<_0,_where

denotes a lossaversion index,with>1[=1,< 1]indicatinglossaversion[lossneutrality,gainseeking]. Third,weincorporateprobabilityweighting,by evaluat-ingprobabilitiesinriskyprospectsbyprobabilityweighing functionswi_,_i₌_+,_−,_that_assign_a_number_to_each

prob-ability, with wi₍₀₎₌₀ _and _wi₍₁₎₌_1. _These _probability

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Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations: Experimen-WedonotmodifyU(Q)ofthegeneralQALYmodel,but

we attempttocontrol for possibleeffects of reference-dependenceofhealthstatusbyapplyingourmodelonly tohealthproﬁleswherehealthstatusisbetterthanwhat isconsideredacceptableattheagesunderconsideration. If,asWoutersetal.(2015)suggested,suchacceptability servesasRPforhealth status,thisrestrictionto accept-ablehealthstatesmayavoidconfoundingeffectsaslosses willonlyoccurintermsofdurationwhilehealthstatuswill alwaysbeaboveexpectation.

Thus, as in Lipman et al. (2019b), references over risky prospects with both gain and loss outcomes, i.e. (Qx,Tx∗)p(Qy,Ty∗),withTx∗≥0>Ty∗areevaluatedby:

w+(p)U(Qx)L+(Tx∗)+w−(1−p)U(Qy)L−(Ty∗), (4)

whilepreferencesover riskyprospects (Qx,Tx∗)p(Qy,Ty∗)

foreithergainsorlossesareevaluatedby: wi_(p)U(Q

x)Li(Tx∗)+(1−wi(p))U(Qy)Li(Ty∗),i=+,− (5)

wherei=+[−]when T_x∗,T_y∗>[<]0,i.e.bothoutcomes are gains or losses. Lipman et al. (2019b) show that whenwi_(p)₌_p,₌_1,_and_no_distinction_is_made_between

gainsandlosses(i.e.noreference-dependence),thismodel reducestothegeneralQALYmodel.

3. Predictions

In this paper we consider two versions of TTO and SG.Typically,TTOandSGinvolve10-yeardurationsthat startatcurrentage.Instead,inthispaper,weletthe 10-year period in a reduced health state,which occurs in bothTTOandSG,a)startatSLE,i.e.ta=tr orb)endat

eachindividual’sSLE,i.e.ta=tr−10.IfSLEfunctionsas

RP,for a) the gauge duration occurs completely above SLEand thusalwaysinvolvesconsiderationsinthegain domain(because ta=tr givesTx∗,Ty∗>0).Similarly, for

b)thegaugeduration occurscompletelybelowSLEand thusinvolvestrade-offsinthelossdomain(because ta=

tr−10givesTx∗,Ty∗≤0).Therefore,welabelversionswith

gaugedurations completely above SLEas gain versions (i.e.TTO-gains andSG-gains),whilethose versionswith lifeyearsoccurringcompletelybelowSLEarelabelledas loss versions (i.e. TTO-losses and SG-losses). To distin-guishbetweenthestartingagesintheseversionsforgains and losses,we add superscriptsg and l, i.e. tag=tr and

tl

a=tr−10.As a ﬁnalnotational convention,given that

bothversionshavethesamedurationsTx(10years

start-ingatdifferentages),forclarity,wewilladdsuperscriptsto healthstatusforhealthproﬁles(Qx,Tx∗),suchthat(Q

g x,Tx∗)

and(Ql_x,T_x∗)refertoproﬁlesingain(startingatt_ag)orloss versions(startingattl

a),respectively.Forexample,consider

asubjectexpectingtoliveuntilage80(tr=80).Shewould

receivegainversionswitht_ag=80 andlossversionswith tl

a=70.IfSLEindeedservesasRP,thisshiftfromt g a to tla

allowsustotesttheSLEeffect,asitchangestheperception oflifeyearswithrespecttotheRP.

Intheremainderofthissection,we willemployour theoreticalmodelbasedonprospecttheorywithSLEas RPtoderivepredictionsabouttheSLEeffectonTTOand SG.We will obtainthesepredictions byillustrating the

Fig.1.Indifferencecurvesfortimetrade-offaboveandbelowSLE.

Fig.2. IndifferencecurvesforstandardgamblesaboveandbelowSLE (superscriptsrefertogainsandlosses).

implicationsofourprospecttheorymodelasopposedto areferencecase,inwhichlinearQALYsandEUhold(i.e. Eq.(2)andEq.(3)canbeapplied).Forthesakeofbrevity andclarity,wefocusonprovidinggraphicalillustrations ofthesepredictionsinFig.1andFig.2.Acomplete and formalproofofthesepredictionscanbefoundinOnline Supplements.

3.1. SLEeffectsforTTO

ForTTO,considerasreferencecase,asubjectwillingto giveup2yearswithreducedhealthstatus(Qx)toobtainfull

healthfor8moreyearsinthegainversion.Usingour nota-tionwithSLEasRP,thisyieldsthefollowingindifference: (Q_xg,10)∼(FHg_,_8)._That_is,_in_the_gain_version_the_subject_is

indifferentbetweengaining10yearsbeyondSLEinhealth stateQxandgaining8yearsinfullhealth.Wewillderive

predictionsfromourmodel astowhat thisindifference impliesfortheyearsgivenupinlossversions,i.e.predict Ty∗in(Qxl,0)∼(FHl,Ty∗).Weﬁrstconsiderthereferencecase,

withlinearutility(i.e.L−(T∗)=L+(T∗)=T∗)andnoloss aversion(=1),whichyieldsthefollowingindifferences: (Qxg,10)∼(FHg,8)and(Qxl,0)∼(FHl,−2)forgainandloss

versions,respectively(aseachyearhasthesamevalue).In Fig.1,wehaverepresentedsuchacombinationof

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indif-Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations: Experimen-ferencesmore generally.Initially forthereference case,

we observesymmetric indifferences: (Q_xg,T_x∗)∼(FHg_,_T_∗ y)

and(Ql

x,Tx∗)∼(FHl,Ty∗).Thatis,shiftingtga total,which in

ourexperimentswith10yeardurationsgives Tr=Tx∗for

losses, doesnot affectpreferences,as (Tx∗−Ty∗) isequal

betweengainsandlosses.Theseindifferencesindicatethat in bothscenarios eachyear givenupin Qx (i.e.Tx∗−Ty∗)

exactly offsetsan equal partof thevalueof thequality of life gained (U(FH)−U(Qx)). However,such a

com-binationofindifferencesdoesnottakeintoaccountany discrepanciesbetweengainsandlosses.InFig.1weprovide twoillustrationsofhowtheSLEeffectforTTOresponses due to:a)non-linearutilitycurvature,andb)loss aver-sion.

First,whereas TTOtypically isderivedassumingthat utilityoflifeduration islinear,i.e.L−(T∗)=L+(T∗)=T∗, earlier work on prospect theory has shown that this assumption is likely to be invalid for health outcomes (e.g. Attema et al., 2013; Kemel and Paraschiv, 2018; Lipmanetal.,2019b,2018)andmonetaryoutcomes(e.g. Abdellaoui, 2000; Abdellaoui et al., 2008, 2016; Bruhin etal.,2010).Instead,inprospecttheoryutilityforgains istypicallyconcave,andutilityforlossesisconvex–i.e. utilityforlifeduration isS-shaped.Thisinﬂection point in the utility curve may affect years given up in TTO-gainsand TTO-lossesversions,asit impliesdiminishing marginalsensitivityforadditionallifeyearsgainedorlost furtherawayfromTr,asopposedtothelinearityassumed

inthereferencecase.Hence,itbecomesimportantto con-siderwherethelifeyearsgivenupinQx,andtheyearsin

whichimprovedqualityoflife(U(FH)−U(Qx))is

real-ized, fallalong this S-shapedcurve(we illustratethese effectsinFig.1).ForTTO-gains,theyearsgivenupinQx

(e.g.between8and10)arefurtherawayfromTrthanthe

yearsinwhichimprovedqualityoflife(U(FH)−U(Qx))

is realized(e.g.between0and 8).Giventhat utilityfor gainsisconcave,incontrasttothereferencecasewhere eachyearisvaluedequally,weshouldﬁndthateachyear givenupinQxgetslessweightthaneachyearinwhich

improvedqualityoflife((U(FH)−U(Qx)))isexperienced.

Comparedtothelinearreference-case,thisyieldsa con-vex indifferencecurve,andtherespondent willgiveup more life years tooffsettheimprovement in quality of life((U(FH)−U(Qx)))andrestoreindifference.Hence,we

obtain((Qg_x,T_x∗)_∼(FHg_,_T∗

y’),withTy∗’<Ty∗.ForTTO-losses,

however,theyearsgivenupinQx(e.g.between0and−2)

occurclosertoTrthantheyearsinwhich(U(FH)−U(Qx))

isrealized(between−10and−2).Assuch,whenutilityfor lossesinlifeduration isconvex,each yearinwhichthe improvementinqualityoflifeisobtainedgetslessweight thaneachyeargivenup.Asaresult,ascomparedtothe reference case, this yieldsa concave indifferencecurve, andtherespondentshouldgiveupfeweryears tooffset theimprovementinqualityoflife(U(FH)−U(Qx))and

restoreindifference.Hence,weobtain(Ql

x,Tx∗)∼(FHl,Ty∗’),

withT_y∗’>T_y∗.

Second,wetakeintoaccountlossaversion,i.e.increased sensitivitytolossesrelativetoTr.Lossaversionyields

reluc-tancetogiveuplifeyears,andtoaccountforthiseffect each yeargiven upin Qx shouldoffseta largerpartof

thequalityoflifegained(U(FH)−U(Qx)).Thisyieldsthe

steeperindifferencecurveinFig.1,comparedtothe refer-encecasewherepeopleareequallysensitivetogainsand losses.Asaresult,ifoneislossaverseanddurationsinTTO occurbelowTr,feweryears(Ty∗’’) shouldbegivenupto

restoreindifference,yielding(Qlx,Tx∗)∼(FHl,Ty∗’’).Thus,we

predictthatlossaversionwithrespecttoSLEwilldecrease theyearsgivenupforTTO-lossesversionsascomparedto gainversions.Thisconclusionalsoholdswhentakinginto accountnon-linearityintheutilitycurveforlifeduration (seeFig.1).

3.2. SLEeffectsforSG

ForSG,considerasubjectwillingtoacceptatmosta 20% risk ofimmediate deathfor SG-gains. In our nota-tion, this yields the following indifferences for gains: (Qxg,10)∼(FHg,10)0.8(D).Wewillderivepredictionsfrom

ourmodelastowhatthisindifferenceimpliesfor proba-bilityofdeathacceptedinlossversions.Inthereference case,linearQALYsandEUhold,i.e.thesubjectwillalso accept at most a risk of 20% of immediate death for the lossversion, i.e. (Ql

x,0)∼(FHl,0)0.8(D). In Fig.2, we

haverepresentedsuchacombinationofpreferencesmore generally.Initiallyweobservethesameindifference,i.e. (Q_xg,T_x∗)∼(FHg_,_T_∗

x)pg(D) and (Q

l

x,Tx∗)∼(FHl,Tx∗)pl(D) with pg=pl. Thatis, shiftingtga to tal doesnot affect

prefer-ences,i.e.peoplearewillingtoriskthesameprobability of(D)forbothSG-gainsandSG-losses.Thiscombination ofindifferencesinthereferencecaseindicatesthatinboth scenariosthepossibilityofanimprovementinqualityof life(U(FH)−U(Qx))for Tx exactlyoffsetsthegenerally

smallchanceofdyingimmediately.Incasethedifference inqualityof lifeincreases,i.e.when ((U(FH)−U(Qx)))

increases,a largerchance of dyingimmediatelywill be accepted.However,justasforTTO,suchacombinationof indifferencesdoesnottakeintoaccountanydiscrepancies intheevaluationofgainsandlosses.

In Fig. 2 we provide two illustrations of how SG responsesare affectedwhen SLEservesas RP:a) prob-abilityweighting(whichmaybedifferentbetweengain and loss versions), and b) loss aversion. First, whereas in the reference case, probabilities are treated linearly (andthusalsoidenticallybetweengainsandlosses),our modelbasedonprospecttheoryallowsnon-linear prob-ability weighting. Importantly, it is typically observed thatprobability weightingis less pronouncedfor losses compared togains, that is probability weightingis less inverse-Sshaped,which hasbeenfoundfor health out-comes(e.g.Attemaetal.,2013,Attemaetal.,2016)and monetaryoutcomes(e.g.Kahneman andTversky, 1979; Tversky and Kahneman, 1992; Abdellaoui, 2000). This impliesthatifSLEservesasRP,thesame(small) probabil-ityofanextremeoutcomereceivesmoredecisionweight for SG-gains version compared to SG-losses versions. Inversely, when we observea gain version indifference (Qxg,Tx∗)∼(FHg,Tx∗)pg(D),then a higher probabilityof the extremeoutcome(D)maybeacceptedintheequivalent lossversion(Qlx,Tx∗)∼(FHl,Tx∗)pl(D).Forexample,imaginea subjectwithpg=20%,whichimpliesthatimmediatedeath

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Experimen-Table1

Healthstatesusedinexperiment.

Dimension(EQ-5D) Description Best(Q1):21211 Middle(Q2):31221 Worst(Q3):32331 Mobility Youhave...problemswithwalking Slight Moderate Moderate Self-care Youhave...problemswithwashinganddressingyourself No No Slight Usualactivities Youhave...problemswithyourusualactivities Slight Slight Moderate

Pain/discomfort Youhave... painordiscomfort No Slight Moderate

Anxiety/depression Youare...anxiousordepressed. Not Not Not

withdecisionweightw+(0.20)offsets3_the_possible_gain_of

qualityoflifefor(U(FH)−U(Qx))withdurationTx∗.When

wehavew+(pg)>w−(pl)forpg=pl,anincreaseinpltopl’

isrequiredtorestoreindifference,i.e.forthedisutilityof (D)tooffset(U(FH)−U(Qx)).

Second,we takeinto accountloss aversionbyagain assumingincreasedsensitivitytothepossibilityoflosing comparedtoSLE,i.e.todurationsbelowTr.Importantly,

theconsequenceofimmediatedeath(D)differsbetween gainandlossversions;intheSG-gainversion,entailsa20% chanceof livinguptoSLE,whileforlossversionsdying immediatelymeansliving10yearsshorterthanexpected (i.e.a loss).Hence,SG-gainversions,inourexperiment, involvednolossescomparedtoTr,andwerenotaffected

bylossaversion.Hence,iflossesareincurredmore reluc-tantly,smallerprobabilities(p_l <pg)ofalossareaccepted

forthesamedifferenceinqualityoflife((U(FH)−U(Qx))).

InFig.2weillustratethisbyasteeperindifferencecurve. Summarizing, for TTO our model predicts two SLE effects,bothdecreasingthelifeyearsgivenupforlosses, while for SG our model predicts SLE effects in oppo-sitedirections,wherethenetdirectionisdeterminedby thedegreeoflossaversionanddifferencesinprobability weightingforgainsand losses.Giventhatthese predic-tionsdifferbetweenTTOandSG,shiftinggaugeduration fromabovetobelowSLE(i.e.movingfromtagtotla)may

yielddifferentSLEeffectsbetweenthesetwomethods.We canderivenopredictionsaboutdifferencesinmagnitude oftheseSLEeffectsforTTOandSG,astheyareaffectedby differentcomponentsofprospecttheory.

4. Study1

Inthis ﬁrstexperiment, wetested ourpredictedSLE effectsforTTOandSGinalabexperimentwitha conve-niencesampleofstudents.

4.1. Methods

This lab experiment started with several questions regardingexpectationsaboutlengthandqualityoflife fol-lowedbyanelicitationofTTOandSG.Exampleinstructions andscreenshotscanbefoundinOnlineSupplements.The experimentuseda 2by2(method:TTOvs.SG,version:

3 _Typically,_in _applications_of_prospect_theory _outcomes_are

rank-ordered,whereinbinarygamblessuchasSG,probabilitypistakento reﬂecttheprobabilityoftheextremeoutcomeinthatdomain.Forthe sakeofclarity,intheseillustrationswedeviatedfromtheseconventions bytakingpgandpltorefertothechanceofimmediatedeathinboth

ver-sions.TheOnlineSupplementsshowhowtheconventionalnotationcan beappliedwithoutlossofgenerality.

lossesvs.gains)within-subjectsdesign,with randomiza-tionbymethod.Theexperiment wascompletedby102 BusinessAdministrationstudents,4 _recruited_in_the Eras-mus Behavioral Lab in Rotterdam. A total of 71 males participated, and mean age for our sample was 20.25 (SD=1.22).Allstudentswererewardedcoursecreditfor participationinthis30-minutestudy.

4.1.1. Measuresofexpectationsaboutlengthandquality oflife

Wemeasuredstudents’expectationsaboutlengthoflife withthefollowing questions(inthisorder):a)‘What is theminimumageyouwouldhopetobecome?’,b)‘What isthemaximumageyouwouldwanttobecome?’,andc) ‘Howolddoyouexpecttobecome?’.Thefirsttwomeasures wereobtainedtoexplorehowthetypicalestimatesforSLE fallinbetweenindividuals’aspiredminimumand maxi-mumage,whilequestionc)measuresSLE,usingasimilar phrasingasvanNootenetal.(2009).Studentsansweredall threequestionsusingadrop-downmenuwithanswersin fullyearsrangingfrom30to120.Tocheckifhealthstates wereconsideredacceptable,wealsoexploredexpectations aboutqualityoflifebyobtainingameasureof acceptabil-ityforthehealthstatesthatwereusedtoapplyTTOandSG (seeTable1).Thesequestionswereincludedasa manip-ulation check,to determine whetherour model, which pertainedtoacceptablehealth states,canbeapplied.To introducethisconcept,weusedthefollowinginstruction (adaptedfromWoutersetal.,2015):‘Inwhatfollowsyou willreceivequestionsregardinghealthatdifferentages. Generally,healthdeteriorateswhenwegetolder.Consider forexamplean80year-oldpersonwhoisnotabletowalk furtherthan1km.Youmightfindthisanacceptable con-ditionforsomeoneof80,butlessacceptablefor20year oldpersons.’Nextweaskedthemtorateallthreehealth states usinganidenticaldrop-downmenurangingfrom 30to120,usingthefollowingquestion:‘Couldyouplease indicatefromwhichageonwardsyoufindthefollowing threehealthstatesacceptable?’Studentscouldalsoanswer ‘Never’,iftheyfeltthatadeterioratedhealthstatewasnot acceptableatanyage.

4.1.2. OperationalizationofTTOandSG

AllversionsofTTOandSGfeaturedagaugedurationof 10yearsfollowedbyimmediatedeath,whichistypicalfor thistypeofvaluationexercises(VanNootenetal.,2009).

4_Power_analysis_for_paired_t-tests_with _n₌_102,_the_recommended

powerof0.8(Cohen,1988)andasigniﬁcancelevelof0.05indicatedthat itisadequatelypoweredtodetectdifferenceswitheffectsizesaslowas Cohen’sd=0.28,indicatingmediumtosmalleffectsizes(Cohen,1988).

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Medians,inter-quartilerange(ﬁrstquartile,thirdquartile),meansand standarddeviationsformeasuredhealthoutcomesforfullsample(n= 102).

Outcomes Median IQR Mean SD

SLE 85.0 (80.00, 90.00) 84.68 9.56 SLE-min 80.0 (70.00, 85.00) 77.20 11.42 SLE-max 100.0 (93.00, 105.00) 99.91 11.80 AcceptableageQ1 60.0 (55.00, 67.00) 59.55 11.23 AcceptableageQ2 70.0 (63.50, 75.00) 67.92 10.08 AcceptableageQ3 79.5 (70.00, 82.75) 76.35 9.71

Thesefourvaluationexercises(TTO-gains,TTO-losses,

SG-gainsandSG-losses)wereallcompletedforthreehealth

statesdescribedbymeansoftheEuroQolEQ-5D-5L

classi-ﬁcationsystem(seeTable1fortheselectedhealthstates).

TTOandSGwereoperationalisedbyusingtwo-stagechoice lists(seeOnlineSupplements),whichwerecomputerized viaQualtricstoprohibitmultipleswitchingandviolations of(stochastic)dominancewithineachchoicelist.ForTTO, afirstchoicelistidentifiedindifferenceinyears,and after-wards inmonthsin a secondchoicelist.For SG,choice listselicitedindifferencewithafirstchoicelistidentifying indifferenceatprobabilityintervalsof10%,andafterwards specifyingthisinpercentagepointsinasecondchoicelist.

4.2. Results

Table2reportsdescriptivestatisticsforourmeasuresof expectationsaboutlengthandqualityoflife.Onaverage, studentsexpectedtobecomecloseto85yearsold,while wishingtobecomeatleastaround77andatmostclose to100years.Aswerestrictedourtheoreticalanalysesto healthstatesconsideredacceptable,wedeterminedif stu-dentsdeemedhealthstatesQ1,Q2andQ3acceptableat allagesusedinimplementedTTOorSGversions. Over-all,healthstatesQ1andQ2wereconsideredacceptableby moststudents,forallagesconsideredinthisexperiment, with84%(Q1)and72%(Q2)ofoursampleindicatingthat suchahealthstatusisacceptablefromaloweragethan theagesconsideredinourexperiment.Themostsevere healthstate(Q3)wasnotconsideredacceptableatthe low-estageconsidered(i.e.tl

a),withonly34%ofoursample

consideringsuchhealthproblemsacceptableattheages presentedinthelossversionsofTTOandSG.Forgain ver-sions,thispercentagewasconsiderablyhigher,at80%.This

indicatesthatifreference-dependenceexistsforhealth sta-tus(asproposedbyWoutersetal.,2015),thisRPmayfallin betweentheagesconsideredinthegainandlossversionsof TTOandSGforhealthstateQ3.However,weﬁndrelatively littlenon-trading(i.e.QALYweightsof1),withratesof non-tradingfromaslowas2%to18%ofthesample.Hence,to seeifacceptabilityaffectedourmainresults,weranseveral teststoexplorewhetherthisviolationofthesimplifying assumptionsasdescribedinourtheoreticalmodelaffects TTOandSGresponses(seeOnlineSupplements).Wedid notobservesuchaneffectofacceptabilityofhealth sta-tusonTTOandSGresponses.Assuch,wereportourmain resultswithoutexcludingrespondentsfromthesample.

4.2.1. TestingpredictedSLEeffectsforTTO

First,wetestedourpredictionsaboutSLEeffectsinthe twoversionsofTTO(i.e.TTO-gainsandTTO-losses).Table3 showsaggregateresultsforTTOresponsesinbothversions. Inaccordancewithourpredictions,fewerlifeyearswere givenupinlossversionsofTTOcomparedtogainversions forallhealthstates(Wilcoxontests,allp’s<0.001). Accord-ingtoourmodel,thissuggeststhatstudentswouldeither belossaverseor showedless pronouncedutility curva-tureforlossesinlifeduration.Inversely,givingupfewer lifeyearsforlossversionswillyieldhigherTTOweights, i.e. higher QALY weights assigned to the same health state.Whenweanalysedourdataatwithin-subjects,we observedthatforQ1,Q2andQ3respectively,61,65,68% ofsamplegaveupfewerlifeyearsinloss-versions.Forall threehealth states,theseproportionsweresigniﬁcantly largerthanthepartofoursamplethatgaveupequallife yearsforbothversions,ormorelifeyearsforloss-versions (all2_’s_(2,_N₌₁₀₂₎_>_39.71,_all_p’s_<_0.001).

4.2.2. TestingSLEeffectsforSG

Next, we compared the probabilities of immediate deathriskedinSGbetweenthetwoversions(i.e.SG-gain andSG-losses).AscanbeseenfromTable3,lower probabil-itiesofimmediatedeathwereriskedforlossversionsofSG comparedtogainversions(Wilcoxontests,allp’s<0.001). Accordingtoourtheoreticalmodel,thisimpliesthatthe effectoflossaversionwasmorepronouncedthanthatof differencesinprobabilityweighting.Inversely,thisleads totheconclusionthatSGwithdurationsbelowSLEwill yieldhigherQALYweightsforthesamehealthstate.When

Table3

MedianyearsgivenupinTTOandprobabilityofdeathriskinSG,includingwithin-subjectdifferencesbetweengainandlossversions.

Gains Losses Diff.

TTO

Yearsgivenup Median IQR Median IQR Median IQR

Best(Q1) 4.00 (2.00, 5.50) 2.13 (0.17, 4.23) 1.08*** (0.00, 3.48)

Middle(Q2) 5.00 (2.94, 6.50) 3.17 (1.04, 5.00) 1.00*** (0.00, 3.00)

Worst(Q3) 6.00 (4.50, 8.00) 5.00 (3.00, 6.67) 1.23*** (0.00, 3.00)

SG

ProbabilityofD Median IQR Median IQR Median IQR

Best(Q1) 20.5 (5.75, 35.00) 14.50 (2.25, 30.00) 1.00*** (0.00, 9.75)

Middle(Q2) 25.00 (20.00, 40.00) 21.00 (10.00, 35.00) 0.00** (0.00, 10.00) Worst(Q3) 38.00 (24.00, 50.00) 31.50 (20.00, 45.75) 1.00*** (0.00, 11.00) Note:*,**,***indicatethatdifferencesbetweengainandlossversionweresigniﬁcantatp<0.05,p<0.01,andp<0.001,fortheWilcoxonsigned-ranktest.

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Experimen-Fig.3.MedianQALYweightsfordifferentversionsandhealthstates.

weanalysedourdatawithin-subjects,weobservedthat forQ1,Q2andQ3respectively,51,49,51%ofoursample waswillingtotakeasmallerriskofimmediatedeathin lossversions.Forallthreehealthstates,theseproportions weresigniﬁcantlylargerthanthepartofoursamplethat assignedequalprobabilitiestobothversions,orwaswilling toriskahigherchanceofimmediatedeathforlossversions (all2_’s_(2,_N₌₁₀₂₎_>_10.65,_all_p’s_<_0.005).

4.2.3. ComparingSLEeffectbetweenTTOandSGweights InordertocompareSLEeffectsbetweenTTOandSG weneededtonormaliseweightsobtainedbythesetwo healthstatevaluationmethodstoﬁtonthesamescale. Wewillachievethisnormalisationbyapplyingthe deriva-tion of TTO and SG weights under EU and the linear QALYframework(i.e.Eq.(2)andEq.(3).5_Although_this_is inconsistentwithourtheoreticalmodelbasedonprospect theory,it isinlinewithhowTTOandSG responsesare typicallytransformedintoQALYweights (seefor exam-ple:Versteegh et al.,2016; Brazieretal., 2002).Hence, thesecomparisonsmayalsoillustratethedirectionand magnitudeofreference-dependencewithrespecttoSLE whenTTOandSGweightsareobtainedwhenthisisnot accountedfor.

Fig.3illustratestheaggregateresultsforoursample. Withinversions(i.e.gainsorlosses),SGweightswere sig-nificantly higher than TTO weights (Wilcoxon tests, all p’s<0.037). Whencomparingwithin valuationmethods (i.e.TTOorSG),QALYweightsforhealthstatevaluation exercises involving losses produced significantly higher QALYweights,both for TTOandSG (Wilcoxontests, all p’s<0.002). For both methods, thedifferences between gainandlossversionswereofsimilarmagnitudeforQ1, Q2 and Q3 (not significantly different, Wilcoxon tests, p’s>0.52).Thesefindingsindicatethatshiftinggauge dura-tion below SLE resulted in an average increase in TTO weightsofbetween0.15and0.23.ForSG,asimilar pat-ternwasobserved,withsignificantdifferences between gainsandlossesvisible,wheremovinglifeyearsbelowSLE increasedSGweightsonaverageby0.02to0.12.TheseSLE effectsweresignificantlylargerthan0,andlargerforTTO

5 _Derivations_of_TTO_and_SG_weights_under_PT_are_available_(see_Lipman etal.,2018),butrequireassumptionsaboutormeasurementsofLi_{(T ),}

wi_(p)_and_._This_is_beyond_the_scope_of_this_paper.

weights comparedtoSGweights acrossallthree health states(Wilcoxontests,p’s<0.002).WevalidatedtheseSLE effectsusingamixedeffectsregression,whichalsoshowed thatourconclusionsappeartobeunaffectedby acceptabil-ityofthehealthstatesQ1,Q2andQ3orgender(seeOnline Supplements).Finally,wetestedwhetherthetypical dif-ferencebetweenTTOandSGweightsisaffectedbymoving thegaugedurationbelowSLE.Tothisend,foreachsubject, wecalculatedadifferencescorebetweenTTOandSGper healthstate,withdifferencescoresbeingobtainedwithin versions(e.g.TTO-gainsvs.SG-gains).ThisTTO-SG differ-encewassmallerforlossescomparedtogains(Wilcoxon tests,allp’s<0.02),butdifferencesremainedsigniﬁcantly larger than 0 (Wilcoxontests with=0, all p’s<0.04). Collectively,theseﬁndingssuggestthatmovingthegauge durationbelowSLEincreasesQALYweights,withthisSLE effectbeinglargerforTTOthanforSG.

4.3. Discussion

ThissectionbrieﬂydiscussestheresultsofStudy1and the main limitations of this experiment that are reme-diedinStudy2.Amoreelaboratediscussionoftheresults andlimitationscanbefoundinsection6(‘General Discus-sion’).

In accordance with our theoretical predictions, we observed a reduced willingness to giveup life years in theTTO-loss version comparedto theTTO-gain version (i.e.SLE-effectforTTO).ForSG,similartotheTTOresults, subjectswerereluctanttorisklosinglifeyearswhen decid-ing aboutlife years thatfell shortof theirexpectations (i.e.SLE-effectforSG).WhencomparingnormalisedTTO andSGweights(calculatedinthecommonway,basedon EUandthelinearQALYmodel),weobservedthatQALY weights increased when gauge durations were moved below SLE,albeitto alargerextentfor TTO.Hence,the differencebetweenTTOandSGwassmallerforloss ver-sions. However, the QALY weights elicited for Q1, Q2, andQ3werelow,especiallycomparedtoearlierworkon health statevaluation withgeneral populationsamples (Versteegh etal., 2016;Devlin et al.,2018).Theresults fromVersteeghetal.(2016)allowedcalculating aQALY weightforhealthstatesrepresentativeoftheDutch gen-eral public’svaluation (i.e.tariffs). For example,Q1, Q2 and Q3wereassignedvaluationsof0.88, 0.79and 0.68, respectively, which is considerably largerthan the val-uations in Study 1 (especially those elicited with gain versions).

ThelowQALYweightselicitedinStudy1suggestthat studentswerewillingtogiveuplargeproportionsoftheir remaininglifeoraccepthighrisksofimmediatedeath,just toavoidlivinginhealthstateswithrelativelyminor prob-lems.Atleasttworeasonscanbeprovidedtodoubtthe validityofsuchresponsestoTTOandSG.First,students were paidcoursecredits forparticipation inthis study. Generally,inbehaviouralexperimentsinhealthitis pre-ferredtouseﬁnancialincentivestomotivaterespondents tocarefullyconsidertheirresponses(GalizziandWiesen, 2018).Assuch,withoutanincentivetoprovideeffortinour modiﬁedversionsofTTOandSG,itcouldbehypothesized thatstudentsinvestedtoolittleeffortinconsideringthe

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Samplecharacteristicsforsampleolderrespondents(Study2).

Demographic Categories Frequency %

Age 60–65 202 61.6 66–70 81 24.7 70+ 41 12.5 Sex Male 127 38.7 Female 201 61.3

Haschronicdisease Yes_No 120₂₀₈ 36.6_63.4

Nationality UnitedKingdom 220 67.1 UnitedStates 84 24.4 Other 24 7.3 Relationshipstatus Married/inarelationship 187 57.0 Divorced/Separated/Single 58 17.7 Widowed 24 7.3

Highesteducationcompleted

Doctoratedegree(e.g.Ph.D.) 6 1.8

Graduatedegree(e.g.M.Sc.) 39 11.9

Undergraduatedegree(e.g.B.Sc.) 93 28.4

Technical/Communitycollege 45 13.7

Highschooldiploma 77 23.5

Noformaldiploma 6 1.8 Householdincome(GBP) £10,000-£29,999 127 38.7 £30,000-£49,999 68 20.7 £50,000-£69,999 34 10.4 £70,000-£99,999 13 4.0 £100,000ormore 12 3.7

consequencesoftheirchoices.Hence,toresolvethisissue,

in Study2 respondentswereprovidedwithamonetary

reward for participation.Second,this ﬁrstexperimental

explorationoftheprocessbywhichSLEaffectsvaluations

reliedonaconveniencesampleofstudents.Obviously,this

sampleissmallandnotrepresentativefortheDutch

popu-lationintermsofageandeducationlevel.Allstudentswere

requiredtoimaginebeingmucholderthantheircurrent

ageandlivinginhealthstatestheywereunlikelytohave

experienced. Thiscouldbeproblematic, as earlierwork

hasshownthatindividualsmayexperiencedifﬁculty

accu-ratelypredictingtheirfuturechoices(i.e.projectionbias,

see:Loewensteinetal.,2003).Furthermore,earlierwork hasfoundthatSLEisassociatedwithbothageand edu-cation level(Brouwerand vanExel,2005;Péntek etal., 2014;Rappangeetal.,2016),andTTOdependsonattitudes regardingageingandend-of-life(VanNootenetal.,2016), whichmayalsobedifferentforstudentscomparedtoolder populations.Hence,inStudy2weappliedourempirical testsinasampleofolderpersonstoinvestigatetheexternal validityofourﬁndings.

5. Study2

Inthesecondexperiment,totesttheexternalvalidityof ourﬁndings,weaimedtoreplicateourpredictedSLEeffects forTTOandSGinanonlineexperimentwithindividuals aged60yearsandolder.Themethodswerealmost iden-ticaltothatofStudy1,andassuchwewillonlyhighlight modiﬁcationstothemethodbelow.Furthermore,seeingas weappliedasimilaranalysisstrategy,wewillpresentthe resultsofStudy2withoutrepeatingthe(more)detailed descriptionsfoundinsection4.2.

5.1. Methods

Study2usedthesamemeasuresofexpectationsabout lengthandqualityoflife,healthstatesand operationalisa-tionsofTTOandSGaswereusedinStudy1.However,the experimentaltask(programmedinQualtrics)wasnow dis-tributedonlinetoasampleof328peopleaged60yearsand older.ThiswasdonethroughProliﬁc,aplatformforonline researchwithalargesampleofindividuals,whomostly liveintheUKandUS.Itallowsscreeningforawidearray ofdemographics,includingage.Whenthisexperimentwas run,Proliﬁchadaround2600usersthatwereeligible(i.e.60 yearsandolder)andactiveinthelast90days.Respondents wererewarded3£fortakingpartinthisexperiment.On averageittookrespondents24mintocompletethe exper-iment.Onlyasinglequestionwasaddedtotheoriginal setupinStudy1,i.e.aquestiontoinvestigateexperience withchronicillness.6_Demographic_{characteristics}_for_this sampleofolderpeoplecanbefoundinTable4.

5.2. Results

Table5 reports descriptive statistics onexpectations aboutlengthandqualityoflife.TheﬁndingsforSLEwere similartoStudy1withmedianSLEbeing85yearsold. Com-paredtothestudentsinStudy1,respondentswishedto becomesigniﬁcantlylessold(i.e.SLE-maxwassmaller)and consideredimpairedhealthstatesacceptablefromahigher ageonwards(Wilcoxtests,p’s<0.001).Consequently,only

6 _‘Do_you_have_a_health_condition_or_disease_with_long_lasting_effects

(i.e.achroniccondition)?Examplesofchronicconditionsare:arthritis, COPD,asthma,diabetes,hepatitis,AIDS,andcancer.’

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Medians,inter-quartilerange(ﬁrstquartile,thirdquartile),meansand standarddeviationsformeasuredhealthoutcomesforoldersample(n= 328).

Outcomes Median IQR Mean SD

SLE 85.00 (80.00, 90.00) 84.68 9.56 SLE-min 84.00 (80.00, 86.00) 82.43 7.30 SLE-max 95.00 (90.00, 100.00) 93.93 9.38 AcceptableageQ1 70.00 (65.00, 80.00) 70.21 11.23 AcceptableageQ2 75.00 (70.50, 82.00) 75.50 10.52 AcceptableageQ3 80.00 (75.00, 86.25) 80.79 9.79

53%(Q1),36%(Q2)and16%(Q3)oftherespondents

consid-eredthesehealthstatesacceptableatallagesconsidered

intheexperiment.Theseweresigniﬁcantlysmaller

propor-tionsthanobservedinStudy1(all2_’s_(2,_N₌₃₂₈₎_>_47.95,

allp’s<0.001).Ariskofhavingolderrespondents

complet-ingtheexperimentisthattl

a(i.e.theagetheyareaskedto

imaginetobeinthelossversionsofTTOandSG)islower

thantheircurrentage.Thiswasthecasefor32respondents

(10%ofthesample).However,excludingtheserespondents

didnotaffectourresults(seeOnlineSupplements).

Fur-thermore,comparedtoStudy1forallconditionsandhealth

stateswefoundlargeramountsofnon-tradingwithrates

ofnon-tradingrangingfrom12.5%to34%ofthesample(all

2_’s_(2,_N₌₃₂₈₎_>_3.93,_all_p’s_<_0.05)._As_for_Study_1,_several

analyseswereperformedtocheckifacceptabilityofhealth

statesaffectedQALYweightsorthemainconclusionsofour

study(seeOnlineSupplements).Wealsoincludedhaving

achronicdiseaseintheseanalyses.Acceptabilitydidnot

affectQALYweights,butexperiencewithchronicdisease

wasassociatedwithhigherQALYweights.However,our

mainresultsweresimilarforthosewithandwithout

expe-riencewithdisease(seeOnlineSupplements).Hence,we

reportonthefullsamplebelow.

5.2.1. TestingpredictedSLEeffectsforTTOandSG

Table 6 shows aggregate results for TTO and SG responsesinbothversions.AsinStudy1,fewerlifeyears weregivenupinthelossversionsofTTOcomparedtogain versionsforallhealthstates(Wilcoxontests,allp’s<0.001). WeobservedthatforQ1,Q2andQ3respectively50%,49%, and 41%of thesample gave up fewerlife years in loss versions(ratherthanmoreorthesame),whichwasa signif-icantmajority(all2_’s_(2,_N₌₃₂₈₎_>_36.67,_all_p’s_<_0.001).

AscanbeseenbycomparingTables3and6,theSLEeffect

Fig.4.MedianQALYweightsfordifferentversionsandhealthstatesfor oldersample(n=328).

forTTOappearssmallerforthisoldersample,butthis dif-ferencewasneversignificant(Wilcoxontest,allp’s>0.06). IncontrasttoStudy1,wefoundnoSLE-effectforSG,i.e. noevidence for lowerprobabilities of immediatedeath riskedforthelossversioncomparedtothegainversion. WeobservedthatforQ1,Q2andQ3respectively,35,30, 31% ofoursamplewaswillingtotakea smallerrisk of immediatedeathinlossversions(withsimilarproportions ofthesampletakinghigherrisksforlossversions).Ascan beseenbycomparingTables3and6,theSLEeffectfor SGwassmallerinStudy2,andthisdifferencewasindeed significantfor all threehealth states (Wilcoxontest, all p’s<0.002).Finally,weexploredwhetherexcluding non-tradingresponsesaffectedourfindingsforSLEeffectsfor TTOandSG.Althoughthisindeedincreasedeffectsizesfor TTO,theconclusionsremainedqualitativelysimilar(see OnlineSupplements).

5.2.2. ComparingSLEeffectbetweenTTOandSGweights Fig.4illustratestheaggregatenormalisedQALYweights foreachversion.Foreachcondition,QALYweightswere signiﬁcantlyhighercomparedtoStudy1(Wilcoxontests, p’s<0.04), except for SG losses for Q1 (Wilcoxon test, p=0.11).WealsocomparedourresultsagainsttheQALY weightscalculatedusingtheresultsbyDevlinetal.(2018), which representQALYweights forasample representa-tiveoftheUK(i.e.thecountryofresidencefor mostof

Table6

MedianyearsgivenupinTTOandprobabilityofdeathriskinSG,includingwithin-subjectdifferencesbetweengainandlossversions.

Gains Losses Diff.

TTO

Yearsgivenup Median IQR Median IQR Median IQR

Best(Q1) 2.92 (0.25, 5.31) 1.17 (0.00, 3.50) 0.00*** (0.00, 2.63)

Middle(Q2) 3.29 (1.00, 5.71) 2.00 (0.08, 4.40) 0.08*** (0.00, 2.00)

Worst(Q3) 4.92 (2.00, 6.65) 3.08 (0.92, 5.50) 0.08*** (0.00, 2.31a)

SG

ProbabilityofD Median IQR Median IQR Median IQR

Best(Q1) 10.00 (5.75, 35.00) 10.00 (2.25, 30.00) 0.00 (0.00, 5.00)

Middle(Q2) 13.00 (20.00, 40.00) 12.00 (1.00, 30.00) 0.00 (0.00, 2.00)

Worst(Q3) 22.00 (24.00, 50.00) 21.00 (3.00, 40.75) 0.00 (−1.00, 3.00)

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Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations: Experimen-our sample). We foundthat the QALY weights elicited

in Study2 weresignificantlyclosertotheestimates by Devlinetal.(2018)thanthoseelicitedinStudy1(Wilcoxon test, p’s<0.04), except for SG-losses for Q1 (Wilcoxon test, p= 0.11). Still, our olderpersons sample reported QALYweights that weresignificantlydifferentfromthe Devlinetal.(2018)estimatesforallconditions(Wilcoxon tests,p’s<0.01),exceptforSG-gainsandlossesforQ2and SG-gains for Q3(Wilcoxontests,p’s>0.16).Within ver-sions(i.e.gainsorlosses),SGweightsweresignificantly higherthanTTOweights(Wilcoxontests,allp’s<0.007). QALYweightsforhealthstatevaluationexercisesinvolving losses(comparedtogains)producedsignificantlyhigher QALYweightsforTTO(Wilcoxontests,allp’s<0.002),but not forSG(Wilcoxontests,allp’s>0.09).Shiftinggauge durationbelowSLEresultedinanaverageincreaseinTTO weightsofbetween0.10and0.11.ForSG,nosuchpattern wasobserved,wheremovinglifeyearsbelowSLEincreased SGweightsby0.001to0.02.AsinStudy1,theOnline Sup-plementsreportaqualificationofthesefindingsbymeans oflinearmixed-effectsregression.TheTTO-SGdifference wassmallerforlossescomparedtogains(Wilcoxontests, allp’s<0.001),butdifferencesremainedsignificantlylarger than0forallhealthstates(Wilcoxontestswith=0,all p’s<0.007).Collectively,thesefindingssuggestthat mov-inggaugedurationbelowSLEincreasesQALYweightsfor TTO,butnotforSG(whichleadstosmallerTTO-SG differ-encesforlossversions).

6. Generaldiscussion

Thegoalofthispaperwasto(further)exploreSLEeffects forTTOandSGbymeansofawithin-subjectsapproach. Weconstructedatheoreticalmodelbasedonprospect the-ory,whichallowedustotestitspredictionsusingdifferent versions for TTOand SG, witha gauge duration occur-ringeithercompletelybelow(i.e.losses)oraboveSLE(i.e. gains).AlthoughEUandtheQALYmodelgivenoreason toexpectdifferencesbetweentheseTTOandSGversions, prospecttheory,ontheotherhand,impliesthatifSLE func-tionsasRP,lossaversionandsign-dependentevaluation oflifeyearsandprobabilitiescangiveriseto discrepan-ciesbetweendifferentversions.Itwaspredictedthatfewer yearswouldbegivenupinTTOwhenelicitedbelowSLE,i.e. TTOweightswouldbehigher.Furthermore,forSGour pre-dictionsbasedonprospecttheorysuggestthat,depending ontheirlossaversionandprobabilityweightingfunctions, individualswouldbewillingtoeitherincreaseordecrease theirriskofimmediatedeath,i.e.theeffectonSGweights isambiguous.

Wetestedthesepredictionsintwostudieswitha stu-dent (Study1)and sampleof individuals aged60years andolder(Study2).WeﬁndSLEtobesimilartoestimates fromearlierwork(BrouwerandvanExel,2005;VanNooten etal.,2009;Pénteketal.,2014;Rappangeetal.,2016). Fur-thermore,SLEfallsinbetweenmaximumandminimum aspiredages,suggestingthatitcouldindeedbetakenas RPwithinprospecttheory,asthis istypically seenasa neutralposition(Wakker,2010).Inaccordancewithour theoreticalpredictions,iflifeyearsinTTOoccurredbelow SLE,weobservedlesswillingnesstogiveuplifeyearsin

bothStudy1andStudy2.Hence,ourresultsforTTO con-ﬁrmtheSLEeffectobservedinearlierwork(vanNooten andBrouwer,2004;VanNootenetal.,2009;Heintzetal., 2013;vanNootenetal.,2014)wheresimilarcomparisons weremadebetweenindividualsexpectingtolivelonger thanTTOgaugedurationorshorter.Furthermore,seeingas itoccursbothinstudentandsampleswitholder respon-dents,itappearstoberobusttoindividuals’currentage, whichprovidessomesupportfortheexternalvalidityof theeffectofSLEonTTO.Theseﬁndings(accordingtoour model)suggestthat:a)subjectsrefrainfromgivinguplife yearscomparedtoSLEasaresultoflossaversion(as sug-gestedbyVanNootenetal.,2009),and/orb)subjectsshow lessdiminishingmarginalutilityforlifedurationforlosses comparedtogainswithrespecttoSLE.

ForSG, theresultsfor Study1weresimilartothose forTTO,i.e.students weremorereluctanttorisklosing lifeyearswhendecidingaboutlifeyearsthatfallshortof theirexpectations.Thatis,whenthegaugedurationoccurs belowSLE,lowerchancesofimmediatedeathweretaken, whichis,toourknowledge,anovelfinding.However,these resultswerenotreplicatedforpeopleaged60yearsand olderinStudy2.Giventhatourmodelbasedonprospect theoryyieldsambiguouspredictionsforSG,itcanprovide anexplanationforthisnullresultinStudy2.ForStudy1, ourfindingssuggestthatlossaversiondecreased willing-nesstoriskimmediatedeathforgaugedurationsbelow SLE.Ourmodelpredictsthatprobabilityweightingforgains andlossesmayhaveoffsetpartoftheeffectduetoloss aver-sion,whichmayexplaintheweakereffectofSLEforSGin Study1,andperhapsthenullresultinStudy2.Toexplain thenon-significantSLEeffectforSGinStudy2individuals aged60yearsandoldershouldbelesslossaverseand/or hadlargerdifferences inprobability weightingbetween gainsandlossesthanthestudentsampleinStudy1had.

Although we derived predictions based on assump-tionsaboutlossaversion,utilitycurvature,andprobability weighting,wedidnotincludeanempiricalmeasurementof theseprospecttheoryparameters.Instead,ourpredictions werebasedonearlierworkonprospecttheoryforboth healthoutcomes(e.g.Attemaetal.,2013,2016; Attema et al., 2018; Kemel and Paraschiv, 2018; Lipmanet al., 2019b,2018)andmonetaryoutcomes(Abdellaoui etal., 2008; Bruhin et al., 2010; Kemel and Paraschiv, 2018), where substantial loss aversion and differences in cur-vature of probability weighting and/or utility functions betweengainsandlosseswereobserved.Assuch,ourstudy doesnotallowtodirectlytestourtheoreticalexplanations fortheSLEeffectforTTO,nortodeterminewhySLEeffects couldbeobservedinStudy1butnotinStudy2.Hence, combiningourexperimentalapproachwithmeasurement ofprospecttheoryparametersisapromisingavenuefor futureresearch.

However,existingworksuggeststhatolderindividuals aretypicallymorelossaverseandlossaversiondecreases with education level (Gächter et al., 2007; Arora and Kumari,2015),whichwouldleadustoexpectstrongerloss aversioninthesampleofStudy2.Forprobability weight-ingtheevidenceisinconclusive.Donkersetal.(2001)ﬁnd someevidencethatsuggestsmorepronouncedweighting ofprobabilitiesforhigherages,buttheydonotdifferentiate

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Pleasecitethisarticleinpressas:S.A.Lipman,W.B.F.BrouwerandA.E.Attema,Livinguptoexpectations: Experimen-betweengainsandlosses.Assuch,atleasttwoalternative

explanationsforthenullresultforSGinStudy2appear relevant.First,QALYweightsforhealthstatesQ1,Q2and Q3wereconsiderablyhigherinStudy2comparedtoStudy 1,withespeciallySGweightsforthesemildhealthstates nearing1.00.ItmaybepossiblethatnoSLEeffectforSGis observedduetoaceilingeffect,whichcouldbetestedby incorporatingmoreseverestatesinfuturework.Second, itis possiblethatthis nullresultis explainedby differ-encesbetweenthestudentandoldersamplesinhowthey perceivelife (anddeath) at theages considered in this experiment.Ourresultsprovidesomeindicationforthis, withstudentsindicatingtoﬁndhealthproblems accept-ablefrom younger ages than individuals aged 60 years andolder.Futureworkcouldexplore,forexampleusing qualitative interview techniques, theinﬂuence of these perceptionsontheeffectsofSLEonQALYweights.

BeforearrivingattheconclusionthatSLEservesasRP inTTOandSG,severalalternativeexplanations,notrelated toreference-dependencewithrespecttoSLE,and method-ologicallimitationsshouldbeconsidered.First,subjectsin bothstudieswereaskedtoimaginebeingolderthantheir currentage.Ifsubjectsdidnotadopttheinstructionsin ourexperiment, thegaugedurationsinthis experiment wouldbestronglydiscounted(vanderPolandRoux,2005; Attemaand Brouwer,2010).Giventhat lossversionsof TTOinvolved years below SLE,these would necessarily occurearlierintimethanyearsgivenupingainversions ifcurrentageisadoptedinsteadofSLE.Thus,compared totheircurrentage,lifeyearsingainversionsarelikely tobediscountedmorestrongly,andgivenupmore will-inglycompared tolifeyears for thelossversionof TTO (i.e.thiswouldpredicthigherQALYweightsforloss ver-sions).Similarly,ifsubjectsusedtheircurrentageinstead ofhypotheticalagesinourexperiment,thetimedimension mayexplainhigherutilityforSG-lossescomparedtogains, asfor monetaryoutcomes itis well-known (Abdellaoui etal.,2011;BaucellsandHeukamp,2012;Noussairand Wu,2006)thatrisk-seekingincreaseswhenlotteriesare resolved in the future. As such, SG-gains are resolved furtheraway in thefuture than lossversions,and thus higherrisk-seekingcouldexplainthehigherrisksofdeath acceptedforgainversionsofSG.Hence,althoughitisnot possibletomakesuresubjectsindeedadoptedour instruc-tions,intheOnlineSupplementsweshowthatifsubjects didnotadopttheagesinourexperimenttheeffectsof dis-countingwouldbenegligible.Hence,giventhatwedoﬁnd signiﬁcantSLEeffects,thisisnotlikelytoresultfromfailure toadopttagandtla.

Second, scale compatibility has been suggested to biasboth SG and TTO (Bleichrodt, 2002; vanOsch and Stiggelbout,2008).Ourmanipulation,i.e.shiftinglifeyears around SLE, may have caused subjects to focus onlife durationinTTOandSG.Giventhatlifedurationisﬁxed andequalinbothoptionsinSG,whileinTTOlife dura-tionis variedalong thechoicelist,thismayexplain the strongereffectofourmanipulationonTTO,especiallyas theRPwasalsooperationalisedonthescaleoflifeduration. Third,eventhoughweprovidedrespondentsinStudy2a monetaryincentivetodiligentlycompleteourexperiment, theirrewardswerenotcontingentontheirchoices(such

incentivecompatibilityistypicallypreferredineconomic experiments,GalizziandWiesen,2018).Althoughearlier workineconomicssuggeststhattheuseofhypothetical choicesasopposedtoincentive-compatiblechoiceshas lit-tletonoeffectonpreferences(HertwigandOrtmann,2001; Camerer and Hogarth, 1999), we encourage the explo-ration of incentive-compatiblechoices inthecontext of health.Fourth,alltheoreticalpredictionsinthisstudywere basedonprospecttheory,andhence,weexplicitlyassumed prospecttheorytoholdfordecisionsabouthealth.Several authorshavefoundviolationsofprospecttheory,mostly for monetaryoutcomes (Birnbaum, 2006; Payne, 2005; Batemanetal.,2007),butalsoforhealth(FeenyandEng, 2005).Assuch,futureworkcouldexploreifTTOandSGcan bemodelledinotherreference-dependentmodels(K ˝oszegi and Rabin, 2006).Finally, toaccommodateoursubjects andavoidconfusionorunnecessaryerrors,wemaintained aconsistentorderingthroughouttheexperiment.Future workcouldexplorewhetherthis lackof counterbalanc-ingbetween-subjectscouldhaveaffectedourconclusions, althoughotherauthorsﬁndnoeffectsoforderongain-loss framing(e.g.DeDreuetal.,1994).

7. Conclusion

Whereasitiswell-knownthatTTOandSGweightsare typicallydifferent(e.g.Readetal.,1984;Torrance,1976), earlier workon therole of SLEhas exclusivelyfocused onTTO.Ourworksuggeststhatdecision-makinginboth healthstatevaluationmethodsmaybeaffectedby subjec-tiveexpectationsaboutlengthoflife,withQALYweights being higher for TTOand (to a lesser extent) SG when gaugedurationsarebelowSLE;i.e.,SLEmayserveasRP in health state valuation.This SLEeffect could be rele-vantforthecurrentpracticeinhealthstatevaluation,as thistypicallyinvolvesshortgaugedurations,whichimply lossescomparedtotheirSLEforalargepartofthe sam-ple.Forexample,whenobtainingnationallyrepresentative TTOtariffsforEQ5D,EuroQoLtypicallyusesa10year dura-tionforhealthstatespreferredtodeath(Oppeetal.,2014), whichmustfallshortofSLEformanysubjects.Applying derivationsbasedonEUorlinearQALYswillthenyieldTTO orSGweightsthataretoohigh.

Although ﬁnding a solution for this biasing effect attributabletoSLEseemswarranted,asdiscussedbyHeintz etal.(2013),itcanbecomplextochooseanappropriate durationfor healthstatevaluation.DurationsbelowSLE mayinducereluctancetoloseanylifeyearsatall,while durationsaboveSLEmayyieldlowerQALYweightsas indi-vidualsaremorewillingtolosesomeofthese‘bonusyears’. To our knowledge, no compelling normative argument existstoprefereitherofthesescenarios,suggestingthatit maybenecessarytoacknowledgethesepossiblebiasesand derivehealthstateutilityinareference-dependentmodel (asdiscussed by: Abellan-Perpi ˜nanet al.,2009; Lipman etal.,2019a,b).Therefore,wehopethatourattemptto unifyearlierworkonreferencepointsinhealthstate valua-tionintoaformalmodelbasedonprospecttheoryprovides someinsightintotheconsequencesofnotbeingabletolive uptoexpectationsaboutlengthoflife.

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Experimen-Fundingsource

Thisresearchdidnot receiveanyspeciﬁcgrantfrom funding agencies in thepublic, commercial, or not-for-proﬁtsectors.

CRediTauthorshipcontributionstatement

Stefan A. Lipman: Conceptualization, Methodology, Software,Validation,Formalanalysis,Investigation,Data curation, Writing - original draft, Writing - review & editing,Visualization,Projectadministration.WernerB.F. Brouwer:Conceptualization,Writing-originaldraft, Writ-ing - review &editing, Supervision. ArthurE. Attema:

Conceptualization,Methodology,Validation,Investigation, Formalanalysis,Writing-originaldraft,Writing-review &editing,Supervision.

OnlineSupplements

Supplementarydataassociatedwiththisarticlecanbe found, in theonline version, at https://doi.org/10.1016/ j.jhealeco.2020.102318.

DeclarationofCompetingInterest

None.

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