2PietdeJongTableIGlossaryofmainsymbolsandde12nitions symboldescriptionrange vhealthbene12tof1kmofaccidentfreecyclingv210 mprelawunhelmetedkmcyclingofthebehaviorchanginggroupmx00000 pbeh ID: 937684
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Electronic copy available at: http://ssrn.com/abstract=1368064 2PietdeJongTableI.Glossaryofmainsymbolsanddenitions symboldescriptionrange vhealthbenetof1kmofaccidentfreecyclingv0 mpre{lawunhelmetedkmcy-clingofthebehaviorchanginggroupm�0 pbehavioralresponseparame-ter:probabilityacyclingkmisnotmaintainedpost{law0p1 p 1�poddsacyclingkmisnotmain-tained0 c,cexpectedinjurycostsperac-cident,withandwithoutahelmetc�c0 rateofaccidentsperkm�0 cexpectedhealthcostperkmunhelmetedcyclingc�0 v�cexpectedhealthbenetperkmofunhelmetedcyclingv�c�0 v�c cbenet{to{costratioofunhel-metedcycling�0 ehelmete ectiveness:propor-tionalreductioninheadinjurycostswhenwearingahelmet0e1 qheadinjurycostsasfractionoftotalinjurycostsinunhel-metedcycling0q1 eq=c�c chelmetpreventablefractionofaccidentcosts0eq1 thelawworehelmets.Furtheristheratioofhealthbenettohealthcostinunhelmetedcycling:agureof20isoftenquotedforarepresentativeriderindicatinghealthbenetsoutweighhealthcostsbyafactorof20.Finallyistheoddsaunitofcyclingisnotmaintainedwhenahelmetlawcomesintoe ect.Asthenotationin(1)indicates,thepreventablefractioneqistheproductoftwoproportions:0e1,measuringthee ectivenessofthehelmetsand0q1,indicatingtheproportionofinjurycostsduetoheadinjuriesinunhelmetedcycling.Denitionsandestimatesfor,,eandqaregiveninTableIandx3.Thesizeofeachofthefourquantitiesin(1)areuncertain.Thisisanissueexceptthatoverawiderangeofplausibleestimates,theinequality(1)fails.Forexample,sinceeq1theinequalityfailswhenever�1.Inparticular(1)failsif=20and=0:1,evenifhelmetsare100%e ectiveandallhealthcostsareheadinjurycosts.Henceevenwithveryoptimisticassumptionsastotheecacyofhelmets,relativelyminorreductionsincyclingonaccountofahelmetlawaresucienttocancelout,inpopulationaverageterms,allheadinjuryhealthbenets3.Therelationshipbetweentheamountofcyclingandmandataryhelmetlawsissubjecttocontroversy.Theliteratureisreviewedinx3togetherwiththeliteratureonthehealthbenetsofcycling.Thisarticledoesnotpresentnewevidenceontheamountbywhichhelmetlawsreducecycling,orthehealthbenetofcycling,orthee ectivenessofhelmetsinreducingheadinjuries.Howeverwedousewidelycitedestimatesasinputsintoourmodeltoarriveatthenetimpliedbenet.Theseinputscanbedisputedandvaried.Howeverifoneacceptsthepremissesofthemodelthenonemustacceptitsimplications.Beforeproceeding,itisusefultoaddressanumberofissues.First,theanalysisinthisarticleassumesthataproperlyttedhelmethas,onaverage,ahealthbenetinaccidentsinvolvingthehead,thatise�0.Thuseveniftheanalysissuggeststhereisnonetsocietalhealthbenettoamandatorybicyclehelmetlaw,thisdoesnotarguethatanindividualisnotbenetedbywearingahelmet.Toemphasize,thisarticledealswithwhetheramandatorybicyclehelmetlawisgoodpublicpolicy,notwhetheritis
advantageousforanindividualtowearahelmet.Second,areductionincyclingdoesnotneces-sarilyimplyanequalreductioninexercise,sincecyclingmaybe\substituted."Thisviewofcyclingasasubstitutableexercisesportmaybecorrectinsomejurisdiction{manypartsofNorthAmericaspringtomind.Howeverthisarticledealswithcyclingasamodeoftransport,withhealthbenets.Thisisthenormaldailycyclingcarriedoutbymanymillionsofcyclistsaroundtheworld.Forexample,relativelyfewDutchorChinese,whobicycleaspartoftheirdailyroutine,wouldincreasegymvisitsortakeupotherexerciseactivitiesif,asaresultofamandatorybicyclehelmetlaw,theywerediscouragedfromcycling.Relatedisthatformanypeople,3Thepresentarticlerelatestothewiderliteratureonriskorhealthtradeo s.(10,11)Apertinentquote(11)is:\Thecountervailingrisksofwell{intendedactionstoreduceatargetriskarenotalwaysanalyzedoropenlydiscussedinpublicpolicydebates.Becauseadvocacygroups,electedocials,andbureaucraciesmaybenetfromanexclusivefocusontargetrisk,theymaychoosetoignore{orevensuppressdiscussionof{thecountervailingrisksofproposedpolicies." TheHealthImpactofMandatoryBicycleHelmetLaws3exerciseisonlysustainableifitisintegratedintodailyroutinesuchasshoppingerrandsortravelingtoandfromwork.Inanycase,intheanalysisbelow,substitutione ectscanbeaccommodatedbyloweringtheassumedhealthbenetofeachkmofcycling.Third,thehealthimpactscalculatedbelowdonotre ectthepossiblynegativehealthoreconomicimpactsassociatedwithshiftstoothermodesoftransportationsuchascars.Fourth,thediscussionbelowisintermsofstatisticalaveragesandsetso gainsandlossesacrossdi erentindividuals.Theanalysisisbasedona\representative"bicyclistanddoesnotdistinguishbetweendi erentgroupsofbicycleriders.Di erentgroupsmayhavedi erentparametersandatargetedhelmetlawmaybewarranted.Further,groupsofridersmayhavedi erentparametercongurationsmakingforamisleading\average"analysis.Thisisfurtherdiscussedinx6.Relation(1)isbasedonassumptionsdetailed,discussedandanalyzedinsubsequentsections.Thenextsectionpresentsthekeyexpressionsforevalu-atingthenethealthimpactofahelmetlaw.Thekeyparametersandtheirvaluesintheseexpressionsarediscussedinx3.Section4usesguresfromEuropeancountriesandtheUStocomputepotentialnethealthimpacts.Section5displaysfurthersensitivitycalculations.Substitutionandenvironmentale ectsareconsideredinx6.Conclusionsarepresentedinx7.2.THENETHEALTHIMPACTOFAHELMETLAWThissectionshows(1)isanecessaryconditionfortheretobeanethealthbenettoamandatorybicyclehelmetlaw.Theargumentisbasedona\representative"cyclistmodel.Thecyclistaccruesagrosshealthbenetvfromeachaccidentfreekmofcycling.Thegrosshealthbenetvisdenominatedinanappropriateunitsuchasdollars,increasedlifeexpectancy,reducedmortalityrisk,orother.Representativeridersareassumedtosu erbicyclingaccidentsaccordingtoaPoissonprocesswithexpectedaccidentrateofperkm.(12)Ifthereisanaccident,theexpectedhealthcostifnohelmetiswornisc,reducingtocifahelmetisworn.Accidentcostsaredenominatedinthesameunitsashealthv.Hereandbelowquantitieswithanasteriski
ndicatevalueswhenahelmetisworn.Thusv�cistheexpectedhealthbenetof1kmofhelmetlesscyclingandv�cistheexpectedhealthbenetofcycling1kmwithahelmet.Amandatoryhelmetlawe ectsonlycyclistswhodonotwearhelmetbeforethelawandwhoeitherstartwearingahelmetorchoosetogiveupcycling.Thisgroupiscalledthebehaviorchanginggroup.Thussupposethosewhoalreadywearahelmetpriortothelawandthoseunhelmetedriderswhochoosetoignorethelawdonotchangebehavior4.Supposetherearemkmriddenbythebehaviorchanginggroupbeforethelawofwhichproportionpisgivenupasaresultofthelaw.Thenthehealthbenetofcyclingforthegroupism(v�c)beforethelaw,and(1�p)m(v�c)after.Thenethealthimpactofthelaw,expressedasafractionofhelmetpreventablehealthcostsis nethealthimpactofhelmetlaw helmetpreventablehealthcost(2)=(1�p)m(v�c)�m(v�c) m(c�c)=(1�p)(c�c)�p(v�c) (c�c)=(1�p)1� eq(3)=(1�p)�p eq;(4)wheretheequalitiesfollowfromdirectmanipulationandthefactthathelmetsareonlyusefulinpreventingheadinjuries:c�c c=qc�(1�e)qc c=eq:Theadvantageoftheexpressionsin(3)or(4)isthat isstatedintermsoftestableandreadilyestimated,intelligibleconstructsanddoesnotexplicitlyinvolvetheunitsofmeasurementofv.Note 1with �0indicatingbenetsexceedcostswhile 0indicatesanunintendednethealthcost.Further &#x]TJ/;ø 9;&#x.962; Tf;&#x 12.; ;� Td;&#x [00;0ifandonlyifeq&#x]TJ/;ø 9;&#x.962; Tf;&#x 12.; ;� Td;&#x [00;asin(1).Theratio eq=pm(v�c) (1�p)m(c�c);(5)isthecost{to{benetratioofahelmetlawwithp=0implyingthecostiszeroandthehelmetlawe ectiveness =1.4Thenumberofriderswhoignorethelawandhencethesizeofthebehaviorchanginggroupwilldependonthedegreetowhichthelawisenforced. 4PietdeJongThedenition in(2)isbasedonan\average"or\representative"riderand,v,candcareaveragevaluesacrossriders.Inpracticeridersareheterogenous.Itisassumedthatthosechangingtheirbicyclingasaresultofthelawareaveragewithrespecttoaccidentrates,injurycostsandhealthbenets.Thisisfurtherdiscussedinx6.Furtheritisassumedtheaccidentrateandbenetvareuna ectedbywearingahelmet.Finallyifmanycyclistsalreadywearhelmetsormanyridersignorethelawthen measureshealthimpactofalimitedgroup.Asanexample,Australiandata(13),suggestspreandpostlegislationhelmetwearingratesof35%and84%,respectively.Supposethelawledtoanoverall10%reductionincycling.Thendirectcalculationsshow,assumingalldropsincyclingoccurredamongsttheunhelmetedgroup,proportionp=0:22ofcyclingintheunhelmetedgroupis\lost"asaresultofthelawand=p=(1�p)=0:28.Hence(1)holdsifeq=0:28.If1=0:28=3:51thereisanethealthcostevenifhelmetsare100%e ectiveandallinjuriesareheadinjuries.Equation(2)canbeusedtoevaluatethehealthimpactofcampaignsaimedatincreasingvoluntarybicyclinghelmetwearing.Theinterventioninthiscaseisacampaign,stressingtheheadinjuriesthatmaybeavoidedifwearingahelmet.Whilethecampaig
nmayinducehelmetusage,itmayalsofrightenpeopleo cycling.(14)Supposeonlyunhelmetedridersarepossiblyfrightenedo riding.Writemasthekmcycledbyunhelmetedridersbeforethecampaign,reducingto(1�p)mafterthecampaignofwhichsayproportion ishelmeted.Similarto(2),thenethealthimpactofthecampaign,expressedasafractionofthehelmetpreventablehealthcost,is = (1�p)m(c�c)�pm(v�c) m(c�c)=(1�p) � eq:Thecampaignhasanethealthbenetif �=(eq).Evenifthecampaignis100%successful, =1,thereisanethealthcostif�1.3.PARAMETERESTIMATESThissectionreviewstheliteratureonthehealthbenetofcycling(),thee ectivenessofhelmets(eandq),andthee ectofbicyclehelmetlawsontheamountofbicycling(por).Theliteratureisusedindicatethelikelysizeofeachoftheseparameters.Theseestimatesareusedinx4tothrowlightonthelikelymagnitudeof .3.1ThehealthbenetofcyclingRegulardailyexercisehassubstantialhealthbenets(15)andbicyclingisanexcellentformofexercise.(16)Exerciseisespeciallysustainablewheningrainedaspartofdailyroutine.(17)Hencebicycling,asadailymodeoftransport,isanexcellentformofsustainableexercise.Itissafe,especiallyforadults.(6)Itislesssafewhenmixedinwithapreponderanceofmotorizedtrac.TheHillman(18,19)reportfortheBritishMedicalAssociation,comparestheexercisebenetofcyclingtoaccidentrisks.Actuarialdataisexaminedtodeterminelifeyearsgainedbypeopleengagedinexercisewhichiscomparedtoyearslostthroughcyclingaccidents.Hillman(19)concludes\...eveninthecurrenthostiletracenvironment,thebenetsgainedfromregularcyclingoutweighthelossoflifeyearsincyclingfatalitiesbyafactorofaround20to1."The20to1ratioisanestimateofin(1).Theestimatemustbeinterpretedwithcare.Itisanaveragewithlikelyvariationsdependinglocality,age,experienceandevenindividualrider.Transportpoliciesareinstrumentalindeterminingthevalueof,byshapingthebicyclingenvironment.TheexpressionforinTableIindicatesisthebenet{costratioofcyclingwithoutahelmet.Givenc=(1�eq)c,adetailedcalculationshowsthatthebenet{costratioofcyclingwithahelmetis(+eq)=(1�eq).Henceifislow,helmetsdolittletoimproveunlesseqisnear1.Ifishigh,thenmandatoryhelmetlegislationislikelytobecounterproductivesinceevensmallreductionsincyclingarelikelytoswampthedirecthealthbenets.3.2Thee ectivenessofhelmetsHelmetscanreduceheadinjuriesinaccidentsinoneofthreeways:byreducingtheprobabilityofaheadinjury,byreducingthemagnitudeofaheadinjuryifthereisanaccidentinvolvingthehead,orboth.Toformalizethesituationwriteastheprobabilityofaheadinjuryinanaccident,hastheexpectedcostofaheadinjuryinanunhelmetedaccidentinvolvingthehead,andbastheexpectedcostofa\body"ornon{headinjurygiventhereis TheHealthImpactofMandatoryBicycleHelmetLaws5anaccident.Thenintermsofthenotationofx2q=h h+b;e=h�(h) h=1�(h) h;where(h)denotestheexpectedcostofheadinjuriesinahelmetedbicyclingaccident.Usingthisnotat
ionsuggeststhreepossibilitiesformodelingtheprotectivee ectofahelmet.First,ahelmetmayreducetheprobabilityofanaccidentinvolvingtheheadbutleavehunchanged.Inthiscase(h)=hande=1�=.Second,ahelmetmayreducetheexpectedseverityofaheadinjurybutleavetheprobabilityunchanged.Inthiscase(h)=hande=1�h=h.Thusineithercase0e1isinterpretedasthe"eciency"ofahelmet.Athirdpossibilityiswherehelmetsmayprotectagainstproportioneofheadinjuriesbelowthreshold ,say,andforthoseexceeding thecostoftheheadinjuryisreducedby .UsingaParetoseveritydistribution(20)forheadinjuriesitmaybeshownthatinthissituation(c�c)=ceq.Inthefurtherdiscussionbelow,tokeepthediscussionalignedwithpreviousliterature,itisassumede=1�=.Thompsonet.al.(21)review,referenceanddiscussthee ectivenessofhelmetsinpreventingheadinjuries{seealsoAttewell(22)andRobin-son(13).Theirsummaryndingis\...wearingahelmetreducedtheriskofheadorbraininjurybyapproximatelytwo-thirdsormore..."indicatinge=1�=2=3.Inthereviewedstudies,therelativerisk=isestimatedfromtheobservedoddsratioofhelmetwearingcomparingheadinjuredtononheadinjuredbicyclists.Thompsonet.al.(21)poolestimatesoftheoddsratioderivedfromavarietyofstudiesyieldinganoddsratioestimateof0:310:05wherethelimitsindicate95%errorbounds.Attewell(22)ndsthe\consensus"estimateoftheoddsratiohigherdependingonthenatureofheadinjury.Hencefromthisliteratureitappearssafetoassumee0:69.Whiletherelativerisk=isthesubjectofmuchstudy,thereismuchlessliteratureonthepreventablefractioneq.IntheNetherlands,wherebicyclehelmetsarerare,27:5%ofbicyclistsadmittedtohospitalhaveheadinjuries(23)suggesting=0:275providingisdenedastheprobabilityofaheadinjuryinanaccidentnecessitatingahospitalvisit.ThisestimateofisbroadlyconsistentwithAustraliandataofbicycleaccidentvictimswhopresentthemselvestotheemergencydepartmentataSydneyhospital.(24)InSydney 1andbasedonhospitaldataabout2/3ofpatientshaveminorbumpsandscratchesandgohomeafteradressingorpatch.Theremaining1/3arerecordedinthetraumaregistryandduring2008{2010atotalof287patientswerecompletelyrecorded.Ofthese25%hadheadinjuries,respectivelyindicating25%oftraumaregisteredadmissionshadheadinjuries.Hence=0:275appearsreasonable.Writingb=b1+(1�)b2whereb1andb2aretheaveragenon{headinjurycostofaheadinjuredandnonheadinjuredbicyclistthen1�q q=b1+(1�)b2 h=b1 h+1� b2 h:If=0:275then(1�)==2:64whileb1=0andh=b2implyq=0:275.Toarriveatq=0:75,equivalenttoalefthandsideoddsof1/3requires,ifb1=0,thath=32:64b8b2.Thisseemsextreme.Thusq=0:75appearsextreme.Ife=0:67andtheproportionofinjurycostsduetoheadinjuriesisq=0:75theneq=0:5,whichappears,giventheabovediscussion,anoptimisticestimateofthehelmetpreventablefractionofinjurycosts.3.3HelmetlawsandtheamountofbicyclingManymotorcyclistsdislikehelmets.(21)Itissafetoassumethesameistrueforbicyclists.Thusamandatorybi
cyclehelmetlawwill,ifanything,reducecycling.Dropsincyclingmayalsoresultfromhelmetsandhelmetlawsinstillinganexageratedperceptionoftherisksofcycling.Manywesterncountrieshaveexperiencedlargereductionsinpercapitacyclingsincethe1940'saswellasevenmoresubstantialreductionsinbicycles'modalshareoftransport.Theseculardownwardtrendnecessitatesacarefulanalysistodetecta\helmetlaw"e ectinthosejurisdictionswherealawhasbeenpassed.Themainstatisticalstudies(2,4,13)attemptingtoquantifytheimpactofhelmetlawsonbicyclingusebeforeandafterdatafromAustralianstateswhichhaveenactedandenforcedmandatoryhelmetlegislation.Thesedatasuggestthatthee ectoflegislationistoreducebicycleridingby20%to40%.Thepermanenceofanyreductionsissubjecttodebate.Aneventualreturntopreviouslevelsbegsthequestionofwhatcyclinglevelswouldhavebeenintheabsenceofthelaw. 6PietdeJong4.NETHEALTHIMPACTSFORSELECTEDCOUNTRIESThissectionestimatesthenethealthbenetofmandatorycyclehelmetlawsforthedi erentcountrieslistedinTableII.Thecountriesspanarangeofcyclingcultures.(25)Crosscountrycomparisonsareusedthrowlightonthelikelysizeofthebenet{costratioofbicyclingindi erentjurisdictionsandinturnthelikelyvaluesofthestandardizedhealthimpact .Thelikelysizeofindi erentcountriesisestablishedusingtworeferencepoints:thecountryspecicperkmdeathratefrombicyclinginjuriesandthereferencevalue=20suggestedinHillmanreporttotheBritishMedicalAssociation.(18)Valuesforthebicyclingdeathratediperkmofbicyclinfordi erentcountriesiaredisplayedinTableII.Supposetheaccidentrateincountryiisproportionaltothebicyclingdeathratediperkm:i=diwhereisaconstant,independentofthecountry.Thenifthegrosshealthbenetvandexpectedcostcperaccidentarethesameforallcountriesiv�ic ic=v dic�1= di�1;(6)where v=(c)doesnotdependoni.Equation(6)canbeusedtodetermine fromthedeathratediandiforaparticularcountry.Given andthedeathratespermitsthedeterminationofiforallothercountries.Hillman(18)suggestsi=20fortheUK,anotparticularlysafebicyclingcountryasindicatedbythebicyclingmortalityratesdiinTableII.Assumei=20appliestotheNetherlands,thesafestbicyclingnationlistedinTableII.Thisisclearlyapessimisticviewofthebenet{costratioofcycling.Givendi=1:6fortheNetherlandsthen =di(1+i)=1:621=33:6.Hence25 50appearsapessimisticrangefor .Thetwoextremevaluesfor yield,whensubstitutedinto(6),thetwoivaluesforeachcountrylistedinTableII.Theresultingivaluesrangefromalowof1inItaly,toahighof30intheNetherlands.TheresultingivaluesforGreatBritainare3and7,verypessimisticgiventheassessmentofHillman(18).Theoverallrangeofpessimisticivaluesfordi erentcountriesigivesareasonablerangewhichmaybeusedinavarietyofotherjurisdictions{sayAustin,TexasorMelbourne,VictoriaorKyoto,Japan.TheiforeachcountryiinTableIIiscombinedwithtworeductionsincycling:p=0:10andp=0:20.Theserelativelymodestreductionsshouldbecomparedtotherange20%to40%reportedinthestudiescitedinx3.3.Inallcas
esitisassumedthepreventablefractioneq=0:5correspondingtoanoptimisticviewofhelmete ectiveness,achievedforexamplewithe=0:67andq=0:75.The guresgiveninTableIIhaveamaximumof1.Theguresarepositivewhenevereq&#x]TJ/;ø 9;&#x.962; Tf;&#x 30.;! 0;&#x Td ;&#x[000;iori1=(2),equalto5and2.5,ifp=0:1andp=0:2,respectively.Thatis,foranethealthbenet,cyclingmustbeverydangerousasoccursforexampleinItalyforbothscenariosorGreatBritainfortheworsescenario.Withp=0:2andthemoreoptimisticscenario,onlyItalydisplaysanethealthbenet.Ifahelmetlawisstrictlyenforcedthenallpre{lawunhelmetedcyclingissensitivetoahelmetlawinthesensethateitheritis\lost"orconvertedtoahelmetedkm.Theannualpercapitanethealthimpactofastrictlyenforcedmandatoryhelmetlawinunitsvisthus(1� )m(c�c) nv =(1� )meq n(1+) ;(7)wherenisthepopulationofthecountryand(1� )mistheannualpercapitarateofunhelmetedbicycling.Dailycyclingratesm=(365n)andhelmetwearingrates fordi erentcountriesaredisplayedinTableIItogetherwithresultingestimatesfor.ForexamplefortheUSA,with=5:7andp=0:1then=�1,indicatingapercapitaperannumhealthcostequivalenttothehealthbenetof1kmofaccidentfreecycling.ForGreatBritainusing=7:3andp=0:20,thenethealthcostofamandatoryhelmetlawis3:6vperpersonperannum.Forcountrieswherecyclingisverysafeandpopular,suchastheNetherlands,DenmarkandSweden,thenethealthcostsofamandatorybicyclehelmetlawarelarge.TableIIshowsthatformostcountries,underassumptionsfavorabletothehelmetlegislationcase,theunintendedhealthcostscanceloutthedirecthealthbenet.Notethesearenotcoststo\solvetheheadinjuryproblem"butguresshowingtheextenttowhichtheproblemiscompounded.TheratesinTableIIprovideevidenceontherelationshipbetweenthebicyclingdeathratedi,thebicyclingratebiandhelmetusage i.Inparticularsupposelndi +lnbi+ i.Thenmodelsthe\safetyinnumbers"e ect.(26)Further,1�e isthereductionintherelativeriskofdeathduetohelmets.Leastsquaresestimationleadstoestimates TheHealthImpactofMandatoryBicycleHelmetLaws7ofand of-0.54and-0.40,respectively.Theestimateishighlysignicant(p{value0.01)whilethehelmete ectisinsignicant(p{value0.76).Hencethereductionindeathriskonaccountofhelmetsisestimatedas1�e�0:40=0:33withawidemarginoferror.Incomparisontheestimatesuggestsahalvingincyclingincreasesthedeathratebyabout1�(0:5)�0:54=0:31.Withabehavioralresponseofp,anenforcedhelmetlawreducesbicyclingfrombito ibi+(1�p)(1� i)bi=bif1�p(1� i)g.Thenete ectofastrictlyenforcedhelmetlawisthustoreducethedeathratebyproportion1�e (1� i)+lnf1�p(1� i)g(1� i)(p� ):Usingtheestimates,theproportionatereduction� =0:40is,onaccountof\safetyinnumbers",modiedto0:40�0:54p,whichinturnismultipliedbythefractionofunhelmetedridersbeforethelaw.Withp=0:10orp=0:20,asusedinTableII,themodicationhasamarginale ect.5.SENSITIVITYANALYSISFigure1plots versuspr
eventablefractioneqforavarietyofparametercombinations.Ineachpanelitisassumednohelmetsarewornprehelmetlawandthereisproper100%post{lawcompliance.Di erentpanelscorrespondtodi erentvaluesofp.Noteifhelmetsare67%e ectiveand75%ofinjurycostsareduetoheadinjuriestheneq=0:50.Di erentcorrespondtothedi erentlines.Figure1indicatesanethealthbenetsisdiculttoachieveexceptinextremecircumstances:asmallbehavioralresponse(porissmall),helmetshighlye ective(eqnear1),andalowhealthbenetofcycling(small),indicatingeitherminimalexercisebenetsoradangerousbicyclingenvironment.6.NONHEALTHCOSTS,SUBSTITUTIONANDGROUPINGTheanalysisoftheprevioussectionsfocusessolelyonhealthcosts.Thisisinappropriateinanoverallappraisalofamandatorybicyclehelmetlaw,giventhatbicyclingisoftensubstitutedforbymorecostlyandlessenvironmentallybenignmodesoftransport.Bicycles,onaverage,posesmallriskstoothers,especiallywhencomparedtosaycars.Supposereducingcyclingby1kmleadsto,onaverage,anincreaseinenvironmentalcostsof(v�c).Hencetheenvironmentalcostisdenominatedintermsoftheexpectedhealthbenetof1kmofcycling.Thenthestandardizedhealthimpactcombinedwiththeenvironmentalcostis �p(v�c) (c�c)=(1�p)1�(1+) eq:(8)Thusfactoringinenvironmentalcostsisequivalenttoincreasingby100percent.Forexampleiftheenvironmentalcostof1kmoflostcyclingequalstheexpectedhealthbenetof1kmofcycling,then=1andfactoringinenvironmentalcostsisequivalenttoincreasingby100%.UsingthelowervaluesinTableIIasastartingpointand=1thanfactoringinenvironmentalcostsisequivalenttoapproximatelymovingfromthelowertothehigher.Henceevenwitha10%reductionincyclingandverypessimisticassumptionsabout,factoringinenvironmentalcostsof=1,suggestsnobenetforanycountryexceptforItaly.Substitutione ectscanbehandledsimilarly.Supposeistheproportionoflostkmsubstitutedwithotherformsofequallyhealthyexercise.Thenthenethealthimpactissimilarto(8)exceptthat�replaces.Hencesubstitutione ectsofareaccommodatedbyreducing.Environmentalandsubstitution,canbeincorporatedviaajointcalculation.Forexampleif70%oflostcyclingissubstitutedandtheenvironmentalcostsofeachkmoflostcyclingis2(v�c)then=2�0:7=1:3andhenceforpurposesofcomputing ,isincreasedby130%.Finallyconsiderthesituationwherebicyclistsaregroupedintodistinctgroupsiwithgroupicyclingmikm,havingaccidentratei,behavioralresponsepi,andbicyclingbenet{costratioi.Thentheoverallnethealthimpactis,assuminghelmetsconferacommonperaccidentbenetc�c, Pimiif(1�pi)(c�c)�pi(vi�ic)g Pimii(c�c)=Xiwi i;where iisthestandardizedhealthimpactforgroupiandwi=mii=Pimiiistheproportionofaccidentsarisingfromgroupi.Ananalysis,basedonpopulationaveragevaluesof,,eandq,maysuggest 0eventhoughsomeorevenall i&#x]TJ/;ø 9;&#x.962; Tf;&#x 10.;Ԗ ;� Td;&#x [00;0orviceversa.Thisagainarguesforad
etailedappraisalofthefourkeyparameters,thistimeatagrouplevel. 8PietdeJongTableII.Helmetlawnetimpactandannualpercapitahealthbenet deathcyclinghelmetp=0:10p=0:20 rateraterate Austria6.80.40.052.70.46.9-0.3-5.16.4-0.4-3.5-1.7-16.4Denmark2.31.70.039.9-1.1-29.7-3.1-87.220.7-3.2-45.0-7.5-103.8Finland5.00.70.204.00.12.0-0.8-16.49.0-0.9-9.2-2.8-28.6Germany3.60.80.025.9-0.3-6.0-1.6-32.512.9-1.7-17.3-4.4-44.9GreatBritain6.00.10.223.20.30.9-0.5-1.67.3-0.6-1.0-2.1-3.6Italy11.00.20.031.30.610.10.34.53.50.21.5-0.6-4.8Netherlands1.63.00.0114.6-2.0-70.2-5.1-175.230.2-5.2-89.3-11.3-196.0Norway3.00.40.087.3-0.6-4.6-2.1-17.215.7-2.2-9.0-5.5-22.0Sweden1.80.90.1712.9-1.7-16.5-4.4-42.826.8-4.5-21.9-9.9-48.6Switzerland3.70.50.105.8-0.3-3.1-1.5-18.312.5-1.6-9.7-4.2-25.6UnitedStates7.50.30.382.30.43.8-0.1-1.25.7-0.2-1.0-1.5-6.5 Notes:Deathrateisdeathsperhundredmillionkmofcycling.Cyclingrateiskmperpersonperday.(7,27)Thehelmetrateistheproportionofcyclistswearinghelmets.(28)Bicyclingbenet{costratioiderivedfromdeathrateasdiscussedintext. andassumeeq=0:5.7.CONCLUSIONSUsingelementarymathematicalmodelingandparameterestimatesfrompreviousstudies,leadstoreasonableboundsforthenethealthimpactofamandatorybicyclehelmetlaw.Themodelhighlightstheimportanceoffourparametersinanyevaluation:helmeteciency,thebehaviouralresponseofriderstothelaw,thebenet{costratioofcycling,andtheproportionofinjuriesincyclingduetoheadinjuries.Thesekeyparameterso ercriticaltestablepointsforassessingthenetimpact.A(positive)nethealthbenetemergesonlyindangerousbicyclingenvironmentsunderoptimisticassumptionsastotheecacyofhelmetsandaminorbehavioralresponse.Resolutionoftheissueforanyparticularjurisdictionrequiresdetailedinformationonthefourkeyparameters.Thecalculationsarebasedona\representative"bicyclistmodel.Itmaybethecasethatthosegivingupcyclingarenotrepresentative:theymaybemoreaccidentprone,lesssusceptibletothehealthstimulusormoreinclinedtosubstitutecyclingwithotherexerciseactivities.Adisaggregatedmodelcanbeusedtoaddresssuchissueswhichinturnrequiresadetailedappraisalofthefourkeyparametersatadisaggregatedgrouplevel.REFERENCES1.ThompsonRS,RivaraFP,ThompsonDC.Acase{controlstudyofthee ectivenessofbicyclesafetyhelmets.NewEnglandJournalofMedicine.1989;320(21):1361{1367.2.RobinsonDL.Headinjuriesandbicyclehelmetlaws.AccidentAnalysis&Prevention.1996;28(4):463{475.3.BMJ;2006.www.bmj.com/cgi/eletters/332/7543/722.4.RobinsonDL.Doenforcedbicyclehelmetlawsimprovepublichealth?BritishMedicalJournal.2006;332(7543):722{722.5.WardlawMJ.Threelessonsforabettercyclingfuture.BritishMedicalJournal.2000;321(7276):1582{1585.6.WardlawMJ.Assessingtheactualrisksfacedbycyclists.Tracengineering&control.2002;43(11):420{424.7.HurstR.TheArtofUrbanCycling:LessonsfromtheStreet.Guilford,CT.GlobePequotPress;2004.8.TownerE,DowswellT,BurkesM,DickinsonH,TownerJ,HayesM.BicycleHelmets:ReviewofE ectiveness.RoadSafetyResearchReports.2002;30.9.DeMarcoTJ.Buttingheadsoverbicyclehelmets.CanadianMedicalAssociationJournal.2002;167(4):337.10.Lu
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