统计学文献17 8页

Biometrics59,1–8March2003PRESIDENTIALADDRESS:XXIInternationalBiometricConference,Freiburg,Germany,July2002AreStatisticalContributionstoMedicineUndervalued?NormanE.BreslowDepartmentofBiostatistics,Box357232,UniversityofWashington,Seattle,Washington98195-7232,U.S.A.email:norm@u.washington.eduSummary.EconometriciansDanielMcFaddenandJamesHeckmanwonthe2000NobelPrizeineco-nomicsfortheirworkondiscretechoicemodelsandselectionbias.Statisticiansandepidemiologistshavemadesimilarcontributionstomedicinewiththeirworkoncase-controlstudies,analysisofincompletedata,andcausalinference.InspiteofrepeatednominationsofsucheminentfiguresasBradfordHillandRichardDoll,however,theNobelPrizeinphysiologyandmedicinehasneverbeenawardedforworkinbiostatisticsorepidemiology.(The“exceptionwhoprovestherule”isRonaldRoss,who,in1902,wonthesecondmedicalNobelforhisdiscoverythatthemosquitowasthevectorformalaria.Rossthenwentontodevelopthemathematicsofepidemictheory—whichheconsideredhismostimportantscientificcontribution—andappliedhisinsightstomalariacontrolprograms.)Thelowesteemaccordedepidemiologyandbiostatisticsinsomemedicalcircles,andincreasinglyamongthepublic,correlateshighlywiththecontradictoryresultsfromobservationalstudiesthataredisplayedsoprominentlyinthelaypress.Inspiteofitsdemonstratedefficacyinsavinglives,the“blackbox”approachofriskfactorepidemiologyisnotwellrespected.Tocorrecttheseunfortunateperceptions,statisticianswoulddowelltofollowmorecloselytheirownteachings:conductlarger,fewerstudiesdesignedtotestspecifichypotheses,followstrictprotocolsforstudydesignandanalysis,betterintegratestatisticalfindingswiththosefromthelaboratory,andexercisegreatercautioninpromotingapparentlypositiveresults.Keywords:Blackbox;Epidemiology;NobelPrize;Observationalstudies;RonaldRoss.Theinternationalcommunityofstatisticianswaselatedtheselectioncommitteehasbroadlyinterpretedthedomainbynewsthatthe2000NobelPrizeineconomicshadbeenofeconomicscience,andhasgrantedawardsformethodologyawardedtoeconometriciansJamesHeckmanandDanielandinterdisciplinarywork.Previouseconomicsprizes,forex-McFadden.Heckmanwascitedforthe“developmentofthe-ample,hadgonetoFrischandTinbergenin1969fordevelop-oryandmethodsforanalyzingselectivesamples,”McFaddenmentof“dynamicmodelsforanalysisofeconomicprocesses,”“forhisdevelopmentoftheoryandmethodsforanalyz-toArrowandHicksin1972andDebreuin1983for“generalingdiscretechoice.”ThepresentationspeechbySwedisheconomicequilibriumtheory,”toSolowin1987formathe-economistProfessorKarlGustavJ¨oreskogmadeclearthatmaticalmodelsformacroeconomicgrowth,andtoHaavelmotheselectionofthe2000Nobelistswasbasedsquarelyin1988forthe“probabilitytheoryfoundationsofeconomet-ontheircontributionstothedevelopmentofstatisticalrics.”The2000prizewasadramaticconfirmationofthevaluemethodology(http://www.nobel.se/economics/laureates/andimportanceofstatisticalthinkinginthesocialsciences.2000/presentation-speech.html):McFadden’smethodfordiscretechoiceanalysis,devel-opedtoassistagraduatestudenttostudyfreewayroutingTheirmethodshavebecomestandardtoolsofmicroeconomicchoicesmadebytheCaliforniaDepartmentofTransporta-researchineconomicsaswellasinothersocialsciences,andtion,haditsbasisinformaltheoriesofeconomicbehavior.havebeenappliedtosolvingmanyimportantproblemsofUnderMarschak’srandomutilitymodel,observedeconomicsociety.choices—suchaswhethertoridethebusordrivethecarto...[Theyhave]madeitpossibletostudyindividualeconomicbehaviorinastatisticallycorrectway.work—resultfrommultinomialsampling(Becker,DeGroot,andMarschak,1963).PsychologistDuncanLuce(1959)addedTheBankofSwedenPrizeinEconomicSciencesinMem-theratherstrongconditionthattheratioofoddsforanytwooryofAlfredNobelwasestablishedin1968.Eversincethen,choiceswasindependentofthesetofotheravailablechoices.1\n2Biometrics,March2003TheseassumptionsledMcFadden(1973)tohis“conditional.se/economics/laureates/2000/press.html,italicsadded):logitmodel”“[Heckman]...hasalsoproposedtoolsforsolvingcloselyre-eν(s,x)latedproblemswithindividualdifferencesunobservedbythePr(x|s,B)=
,researcher.”Hisviewsoncounterfactualcausalitywereex-eν(s,y)y∈BplicitlyspelledoutinaveryreadablereviewintheJour-wherexisthechoiceselected,BisthesetofavailablenalofEducationalStatistics(Heckman,1989).Distillingthechoices,andsmeasuresattributesoftheindividualdecisionproblemtoitsessence,hedefinedY1tobetheoutcomemaker.Corollarydevelopmentsincludedmethodsforoutcomeifthesubjectwastreated,Y0theoutcomeifitwasnot,dependent,“choice-based”sampling.ManskiandLermanandRtobeabinaryindicatorofwhetherY1(R=1)(1977)proposedaweightedlikelihoodmethodwithoriginsorY0wasobserved.Thepopulationofinterestwastheinsamplingtheory.ManskiandMcFadden(1981)developedcausalpopulationspecifiedbythejointprobabilitydistribu-apseudolikelihoodproceduretowhichtheyreferredascondi-tionF(y1,y0).WhatcouldbeobservedwasthedistributiontionalmaximumlikelihoodorCML.Cosslett(1981)studiedG(y,r)oftheobservedoutcomeandthetreatmentindica-semiparametricefficient“maximumlikelihood”estimation.tor.CitingFisher(1951),Roy(1951),andCox(1958a)astheMcFaddenandReid(1975)realizedtheneedtocorrectforsourceoftheseideas,henotedthatthefundamentalproblemattenuationwhentryingtoforecastaggregatedemandfromofcausalinferencewasthefactthatdisaggregatedmodels,andproposedmethodsforthecombi-β=E(Y1−Y0)=E(Y|R=1)−E(Y|R=0).nationofdatafromindividualsandaggregates.AsIpointedoutinmy1995FisherLecturetotheJointOnepossiblewayofmakingprogresswastoidentifycovari-StatisticalMeetings(Breslow,1996),muchofthisworkinatesZsuchthattreatmentassignmentRwasindependentofeconometricswasparalleledbybiostatisticalcontributionstotreatmentoutcomes(Y1,Y0)conditionalonZ.Andhewastheanalysisofdatafromcase-controlstudiesinepidemiology.veryclearthatthiswasalwaysanassumption!Thesewerestimulatedbyresultsofthreecase-controlstud-Ifthisallsoundsveryfamiliar—itis!Preciselythesameiesoflungcancerandsmokingpublishedin1950,themostideasinvolvingcounterfactualcausalityhavebeenexploredinfluentialofwhichwasthatofDollandHill(1950).Theyatlengthinthestatisticalliterature.KeysourcesareRubinincludedCornfield’s(1951)demonstrationofthepreservation(1974)oncausalmodels,LittleandRubin(1987)ontheanal-oftheoddsratioundercase-controlsampling,Mantelandysisofincompletedata,RosenbaumandRubin(1984)ontheHaenszel’s(1959)summaryrelativeriskestimator,andCox’spropensityscore,Robins(1986)ontheG-computationalgo-(1958b,1966)semiparametricapproachtologisticregression.rithm,Robins,Hernan,andBrumback(2000)onthemarginalAnderson(1972)andPrenticeandPyke(1979)sanctionedap-structuralmodelforlongitudinalanalysis,andPearl(2000)plicationsof“prospective”logisticregressiontocase-controlongraphicalcausalmodels.Iwasmostdisappointedtolearnsamples,whileBreslowandDay(1980)developedextensionsthataninvitedpapersessionatthisconferencethatwasde-formatchedsamplesofcasesandcontrols.votedtothisimportanttopichashadtobecanceled.Heckman’sworkalsohasparallelsinthe(bio)statisticalThemainpointofallofthis,ofcourse,isthatstatis-literature.Hisselectionproblemwasbasedonthemodelticians,biostatisticians,andepidemiologistshavebeenjustasactiveandsuccessfulashavebeentheircounterpartsinπ(z)f(z)g(z)=,econometricsindevelopingstatisticalmethodsforcausalin-π(u)f(u)duference,discreteoutcomes,outcome-dependentsampling,andwheregistheprobabilitydistributionobservedforthese-manyotherstatisticalproblems.However,becausetheyhavelected(biased)sample,πistheselectionprobability,andfischosentoapplytheirworkinmedicineandpublichealth,thetarget(population)distribution.Solutionoftheproblemratherthaneconomicsandsocialscience,noneislikelyeverstemsfromtherealizationthatknowledgeorestimationofthetowinaNobelPrize.Ifirstbecameawareofthisissueinselectionprobabilityπallowsrecoveryofffromg.Theselec-1972,whenIwenttoworkfortheInternationalAgencyfortionmaybeduetobiasedsampling—suchasoccurswithcen-ResearchonCancer(IARC).Ilearnedoftheimpactofthesoredsurvivaldata,length-biasedsamplinginscreeningstud-pioneeringworkofDollandHill—notonlyonreductionofies,orchoice-based(case-control)sampling.Oritmaybeduedeathsfromlungcancerbyidentificationofitsmajorpre-toself-selectionbystudysubjects,whetherintothestudyinventablecause,butalsoonthedevelopmentofchronicdis-thefirstplace,intothetreatmentgroupinnonrandomizedeaseepidemiologyasadiscipline.RichardDollleftmathe-trials,orintothegroupofdropoutsinalongitudinalstudy.maticsformedicineattheuniversity,butneverabandonedHeckman’sinterestincorrectionforselectionbiaswasstim-hisinterestinstatistics.HejoinedBradfordHillin1948toulatedbyhisrealizationthatthiswascrucialforestimatingworkontheirlungcancerstudy(DollandHill,1950),whichtheeffectsofinterventionsinstructuraleconometricmodels.isstillregardedasamodelfortheapplicationofstatisticsHeckman(1979),forexample,noted:inmedicine.Stillactiveinhisnineties,Doll(2002)deliveredthe23rdFisherMemorialLectureinOxfordlastyearontheThewagesofmigrantsdonot,ingeneral,affordareliabletopic“ProofofCausality:DeductionfromEpidemiologicOb-estimateofwhatnonmigrantswouldhaveearnedhadtheyservation.”There,hereviewedthecarefulstepstakenin1948migrated.toaddressquestionsofbias:exclusionofselectionbiasbyThismakesclearthatthetargetsofinferenceareparam-showingthatsmokingratesincontrolswerethesameasinetersincounterfactualmodels,apointbroughtoutinthepatientswithothercancers;exclusionofinterviewandrecallpressreleaseannouncingtheNobelPrize(http://www.nobelbiasbystudyingsmokingratesinpatientswithafalsepositive\nAreStatisticalContributionstoMedicineUndervalued?3diagnosisoflungcancer.Itwouldbe20yearslaterbeforehecarcinogenesis,andboretheintriguingtitle“MutationandcouldpubliclydebateRonaldFisher—whoseStatisticalMeth-Cancer:StatisticalStudyofRetinoblastoma.”Itisaremark-odsforResearchWorkers(Fisher,1934)hadstimulatedhisableexampleofhowsimplestatisticalobservations—whenloveforstatistics—ontheissueofconfounding,andwhyitcleverlyandwiselyinterpreted—canfosterbasicsciencehy-couldnotplausiblyexplainthedataonsmokingandcancer.pothesesthathavenowbeenvalidatedatthemolecularlevel.AtIARC,Ialsobecameawareofthecontroversysurround-(ThispaperanditssequelaehavestimulatedmuchofmyingthefactthatthisworkhadnotyetbeenrecognizedbyownstatisticalworkwithWilmstumorofthekidney,an-theselectioncommitteefortheNobelPrizeinphysiologyandotherchildhoodneoplasminvolvingapairedorgan.)The2001medicine.Itisnow30yearslater,andtheyhaven’tgottenLaskerAwardforpublicservicewenttoWilliamFoege“forhisanywiser!BradfordHill,reveredbymanyasthemajorarchi-courageousleadershipinimprovingworldwidepublichealth,tectoftherandomizedclinicaltrial,isnolongerwithus.Al-andhisprominentroleintheeradicationofsmallpox.”thoughNobelnominationsareofficiallysecret,Iamtoldinfor-Finally,the1997EuropeanprixLouis-Jeantetdem´edecinemallybypersonsoutsidetheselectioncommitteethatRichardwasawardedtostatisticianandepidemiologistRichardPeto,Dollhasbeenputupatleast20times,includingineachofadiscipleandcolleagueofRichardDoll.(TheGenevafounda-thelastthreeyears.AneditorialintheLancet(1999),notingtionmakingtheawardstipulatesthatcandidatesbeselected,thatthepatterninNobelawardsis“oneofanoverwhelmingnotonlyfortheirpastrecord,butalsoforfuturepromise,preponderanceofbasicresearch,”arguedthat“researchmoreandtheprizemoneyistobeusedfortheirresearch.)Petodirectlyrelatedtohealthshouldnotbedisregarded”andthatalsohashadenormousimpactontobaccosalesandpublic“tohonor[Nobel’s]wishfully,clinicalandepidemiologicalre-policy,withhisquantificationofthehealthhazardsandmor-searchmustberewardedasmuchasbasicscience.”talityriskofcigarettesmoking.SomemeasureofthisimpactThefactthatneitherstatisticalnorepidemiologicalap-maybegleanedfromthefactthatherecentlyreceivedtheproachestomedicinehavebeenrecognizedbythemostpres-title“WHOMinisterofStatisticalPropaganda”fromaU.S.tigiousofawardsis,ofcourse,oflittlesignificanceinitsownlibertarianprosmokinglobby.Meta-analysesconductedattheright.ItisprimarilyofinterestasoneindicatorofthedegreeOxfordClinicalTrialsServiceUnitthathedirectshavehelpedtowhichstatisticalcontributionsinmedicinearevalued—setworldwidepolicyregardingtheuseofaspirin,tamoxifen,ornotvalued—bycertainsegmentsofthemedicalcommu-andothermedicaments.nity.Fortunately,thefoundersandselectioncommitteesforTheseexamplesdemonstratethatcontributionsofstatisti-otherprestigiousawardshavetakenabroaderview.Theciansandepidemiologistsareindeedrecognizedandappreci-GeneralMotorsCancerResearchFoundationawardsthreeatedbyaninfluentialsectorofthemedicalcommunity.Theprizesannually(http://www.gm.com/company/gmability/failureofanyofthesecontributionstoearnrecognitionwithphilanthropy/cancerresearch/index.htm):theKetteringaNobelPrizecanbeviewedprimarilyasareflectionofthePrize,“forthemostoutstandingrecentcontributiontotheviewpointsoftheindividualmembersofthevariousNobeldiagnosisortreatmentofcancer,”theMottPrize,whichsim-selectioncommittees.Iwasinformedthatnoexplicitpolicyilarlyrecognizeswork“relatedtothecauseorpreventionofrulesouttheselectionofanepidemiologist,andthatsomecancer,”andtheSloanPrize,for“basicsciencerelatedtooftheSwedishmedicalfacultywhoconstitutetheselectioncancerresearch.”RichardDollwasthefirstrecipientofthecommitteeareworkinghardtoovercometheperceivedbasicMottPrizein1979,beingcited“fordevelopmentofknowledgesciencebias.Indiscussionswithoneofthesefacultyregard-concerningtheenvironmentalcausesofcancerinman,”andingthelowesteemaccordedepidemiologyinsomescientificfor“definitiveinvestigationsoftherolesoftobaccosmokingcircles,mentionwasmadeofapossible“malignantsynergyandexposuretooccupationalandtherapeuticx-rays.”Davidbetweenthecharlatansandthemedia.”Indeed,agoodpartofCox,inawonderfulrecognitionofthevalueofstatisticsintheproblemthatwestatisticiansandepidemiologistsfaceinclinicalmedicine,receivedthe1990KetteringPrizefor“thehavingourworkvaluedashighlyasitshouldbestemsfromdevelopmentoftheProportionalHazardsRegressionModel.”ourownfailures.ManyofthesewerediscussedintheSci-Similarly,theAlbertandMaryLaskerAwards(http://encearticlebyGaryTaubes(1995),“EpidemiologyFacesitswww.laskerfoundation.org/awards/awards.html)havesep-Limits,”thatbeganwiththeobservation:“Thenewsaboutaratecategoriesforbasicmedicalresearch,clinicalmedicalhealthriskscomesthickandfastthesedays,anditseemsresearch,andpublicservice.Furthermore,theyspecificallyalmostconstitutionallycontradictory.”Thestatisticiansandfocuson“diseaseswhicharethemaincausesofdisabilityandepidemiologistsinterviewedforthearticleweregenerallyindeath.”Manyrecipientsinbasicresearchhavegoneontowinagreementthattherewereseriousproblems.Harvardepidemi-theNobelPrizeinmedicine.OfgreatersignificanceforusologistDimitriosTrichopoulos,forexample,opined:“Peopleisthefactthatepidemiologicalandstatisticalworkhasdon’ttakeusseriouslyanymore,andwhentheydotakeusformedthebasisforseveralrecentLaskerawards.Alfredseriously,wemayunintentionallydomoreharmthangood.”Sommerwascitedin1997,“fortheunderstandinganddemon-Manyofthoseinterviewedsuggestedthatresultsofindivid-strationthatlowdosevitaminAsupplementationinmillionsualobservationalstudies—eventhoseconductedaccordingtoofthirdworldchildrencanpreventdeathfrominfectiousdis-themoststringentstandards—shouldnotbeacceptedaspro-easeaswellasblindness.”AlfredKnudsonreceivedtheLaskervidingevidenceofacausalassocation,unlessthelowercon-in1998“forincisivestudiesinpatient-orientedresearchthatfidenceboundontherelativeriskexceeded3or4.Yet,withpavedthewayforidentifyinggeneticalterationsthatcausethepressureoninvestigatorstomakeacareerthroughpubli-cancerinhumans.”Thepaperthatlaunchedthisresearchcation,fewstudiespublishedintheliteratureandreported(Knudson,1971)laidoutthe2-stagemutationalmodelofinthemediameetthisstandard.Authorsthemselvesare\n4Biometrics,March2003oftenawareoftheweaknesses,butfailtocommunicatethesetradiction,inthedirectionoftheapparentinteractionbe-adequately—eitherinpublicationorinsubsequentcontacttweenbodymassandalcohol,resultedfromoneteambeingwithrepresentativesofthepress.soconcernedaboutconfoundingbetweenabstentionandun-Thesometimescapriciousnatureofepidemiologicfindingsmeasuredriskfactorsthatitdroppedtheabstainersfromthewasbroughthometomeandmystudentsinadramaticwayanalysisandsoughtadose-responserelationshipamongthethispastAutumnQuarter,whenItaughtasecond-yearclassdrinkersalone.Standardtexts,e.g.,ClaytonandHills(1993,formaster’slevelstatisticiansanddoctoral-levelepidemiolo-p.256),advocatethisstrategyundercertaincircumstances.giststhatfocusedlargelyonlogisticregressionanalysisofdataThisexerciseinvolvedteamsofbuddingepidemiologistsfromcase-controlstudies.Foruseinthetermproject,myes-andstatisticianswhoweregiventhesamesetofdata,andteemedcolleague,epidemiologistNoelWeiss,kindlyprovidedwhohadalljusthadthesameinstructioninlogisticregressiondatathathadalreadybeenanalyzedandpublishedforthemodelingtechniques.WhenIshowedtheresultstoWeiss,heprimaryquestion,butnotforasecondaryquestion,ofinter-hadtoadmitthathewasn’treallythatsurprised!Weagreedesttotheinvestigators.ThedocumentIhandedouttothethat,had12teamsbeenfundedtogooutandcollecttheirclassdescribedthestudyandtheprojectgoalsasfollows:owndataindifferentpartsoftheworld,thevariabilityinthereportedresultswouldhavebeenevengreater.Weissandcolleagueshaveconductedaseriesofcase-controlWhatcanbedonetoreducethisvariabilityand,insodo-studiesofendometrialcancerriskandhormonalreplace-menttherapyinWesternWashington...Thestudyquestion-ing,improvethestatusofepidemiologyasascientificdisci-nairecontainedsectionsondiet,smokinghistoryandlifelongpline?ThefewsuggestionsIwanttomentionhave,fortheconsumptionofalcoholicbeverages...Thepurposeofthismostpart,beenrepeatedlyemphasizedbyothers.BeforeIprojectistostudytheassociationbetweenalcoholconsump-gettothese,however,Iwouldliketotakeasidetripandtionandendometrialcancerusingbasicdescriptivestatisticsmentionsomethoughtsonthesubjectfromthewritingsofaandlogisticregressionmodelingtechniques...Somestudiesmostunlikelysource:thewinnerofthesecondNobelPrizeinhavesuggestedthatalcoholintheformofaparticularbev-physiologyandmedicine.Anexceptionwhoprovestherule,erageismostprotective...hewasabrilliantmanwhofirstwontheNobelandthenwentAmonthlater,afterreceiving12papersfromteamsofontobecomeanepidemiologistandbiostatistician.2–3studentseach,Ieditedandpresentedinclassthesum-IfirstheardofRonaldRoss(Figure1)in1967,whileapost-maryconclusionsfromeachteam.Hereisaselectionofex-docattheLondonSchoolofHygieneandTropicalMedicine,cerptsfromthoseconclusions(italicsadded):whichatthattimeboastedof“incorporatingtheRossInsti-tute.”IwasvaguelyawareofhisdiscoverylinkingmosquitoesTeam10Afteradjustmentforconfounding,alcoholcon-andmalaria,butitwasn’tuntilreadingthereviewbyDietzsumptiondoesnotappeartoaffecttheriskofdevelopingandSchenzle(1985)thatIlearnedofhisfundamentalcon-endometrialcancer.tributionstomathematicalepidemiology.RonaldRosswasTeam4Amildprotectiveeffectwasobservedforcombinedbornin1857intheHimalayanhilltownofAlmara,whenhisalcohol(OR=0.73,95%CI0.58,0.93).fatherwasacaptainwiththe66thregimentofGurkhas.HeTeam1AlcoholintakecanreducetheriskofendometrialwassenttoEnglandformedicalstudies,receivingalicentiatecancer,andthisprotectiveeffectonlyexistsfornon-obeseinmedicinein1879,fromSt.Bartholomew’sHospital.Rosswomen.returnedhomeasamilitarydoctorwiththeIndianMedicalTeam8Endometrialcancerriskisslightly,butnotmateri-Service,butapparentlyhadamplefreetimeforotherpur-allydecreasedbyalcoholconsumption.However,consump-suits.Betweenfishing,hunting,andtennismatchesatthetionofethanolof1.6–4.0gm/daymayreducetheriskofMadrasClub,hestudiedmathematicsonhisownandwroteendometrialcancerinobesewomen.poetryandprose.DuringvisitstoLondon,hedevelopedaTeam6Alcoholconsumptionisnotassociatedwithsignifi-closerelationshipwithparasitologistPatrickManson,ofthecantlyreducedriskforendometrialcancerafteradjustingLondonSchoolofHygieneandTropicalMedicine,whoforknownconfoundingcharacteristics.Theremaybesomeencouragedhimtospendhisfreetimeworkingonthelinkprotectiveeffectofwineconsumption,butthisneedsfur-betweenmosquitoesandmalaria.InAugust1897,Rosscom-therconfirmation.pletedhisworkonthelifecycleofthemalariaparasite,Team3Consumptionofbeerorwinewasassociatedwithshowingitstransmissionfrommantoanophelinemosquitoadecreasedriskofendometrialcancer,whileconsump-andbacktoman.(Infact,sincehumantransmissionwastionofliquorwasassociatedwithanincreasedrisk...lowintheregiontowhichhewasposted,RossworkedoutBeer,wineandliquorallshowedamonotonicdose-responsethefinalstepinthebirdpopulation.)Thediscoverywasre-relationship...Wewereunabletodemonstrateaninterac-portedthefollowingDecemberintheBritishMedicalJour-tionbetweenalcoholconsumptionandbodymassindex...nal.RossassessedthevalueofhisachievementbywritingaThecurrentstudygoesalongwaytowardsresolvingthepoem:inconsistentepidemiologicalliterature.Thefirstconclusionfromthesecontradictoryfindings,ofThisdayrelentingGodcourse,isthatImusthavefailedasateacher!WhenIlookedHathplacedwithinmyhandcloselyatthereasonsforthedramaticallydifferentconclu-Awondrousthing;andGodsions,however,itseemedclearthattheyweretheresultofBepraised.AtHiscommand.achainofeffectivelyarbitrarychoicesmadewithregardtoscalesofmeasurement,cutpointsfordiscretization,andvari-SeekingHissecretdeedablesselectedaspotentialconfounders.Themostblatantcon-Withtearsandtoilingbreath,\nAreStatisticalContributionstoMedicineUndervalued?5acaseofmalariainfection—firstappearedin1908,inare-portonmalariacontrolinMauritius(Fine,1975).ThecentralequationwasN=p·m·i·a·b·s·f,whereN=no.newinfectionspermonthp=averagepopulationm=proportionpopulationinfectedi=proportioninfectiousamonginfecteda=averageno.mosquitoes/personb=proportionofuninfectedmosquitoesthatfeedonmans=proportionofmosquitoesthatsurvivethroughincubationperiodf=proportionofinfectedmosquitoesthatfeedonmanRoss’sownexplanationforhisterminologyappearedinthesecondeditionofhisbookThePreventionofMalaria(Ross,1911):Weshalldealwithtime-to-timevariationsnotonlyofmalaria,butofalldisease,andnotonlyofdiseasesofman,butthoseofanylivingorganism.Stillfurther,asinfectionisonlyoneofmanykindsofeventswhichmayhappentosuchorganisms,weshalldealwithhappeningsingeneral.Themajorimportanceofthisequationwasthatitleddi-rectlytowhatRosscalled“thecriticalmosquitodensity,”thekeynumberforamalariacontrolprogram(Fine,1975).Let-tingrdenotetherecoveryrate,andassumingb=f,Rosssetthenumberofrecoveriespermonthr·m·pequaltotheFigure1.PhotoofRossinMauritius,1908,courtesyofnumberofnewinfectionsN,toarriveattheexpressionLondonSchoolofHygieneandTropicalMedicine.r110.2a=··≈=40.Ifindthycunningseeds,b2is(0.25)2(0.25)(0.33)Omillion-murderingDeath.Plugginginreasonablevaluesfortherecoveryrate,thepro-portionofmosquitoes(infectedoruninfected)thatfeedonIknowthislittlethingman,etc.,hearrivedattheconclusionthatmalariawouldAmyriadmenwillsave.dieoutifthemosquitodensitycouldbereducedtofewerODeath,whereisthysting,than40mosquitoesperpersoninthepopulation.Thismath-Thyvictory,OGrave!ematicalwayofthinkingcontradictedtheprevailingwis-Fiveyearslater,in1902,Rossreceivedtheinvitationtodominmedicineandpublichealth,however,whichheldStockholmforthesecondmedicalNobelPrize.Professorthatonlycompleteeliminationofthemosquitowouldcon-CountM¨orner,chairmanoftheNobelCommittee,summari-trolmalaria.Theonlywaytobesurewastotesttheconceptzedthesignificanceofhisaccomplishmentasfollows(http://inpractice.ThisRosshaddoneduringalate1902consul-www.nobel.se/medicine/laureates/1902/press.html):tancywiththeSuezCanalCompanyinIsmailia.Figure2,basedondatafromthepublishedversionofRoss’sNobelByyourdiscoveriesyouhaverevealedthemysteriesoflecture(http://www.nobel.se/medicine/laureates/1902/malaria.Youhaveenrichedsciencewithfactsofgreatbiologi-rosslecture.html),dramaticallyillustratesthesuccessofhiscalinterestandoftheverygreatestmedicalimportance.Youideas.havefoundedtheworkofpreventingmalaria,thisveritableRoss’stheoryevolvedfromtheproductformulashownscourgeofmanycountries.aboveforthenumberofnewinfectionspermonth,tofiniteRossturnedawayfrombiologyandmedicine,however,todifferenceequationsforthechangesfromonemonthtoan-continuehismathematicalwork,receivingin1904adoctorofother,andfinallytodifferentialequationsthatexpressthelawsciencedegreeinmathematicsfromtheUniversityofDublin.ofmassaction.Withx(t)denotingthenumberofsusceptiblesHetookapositioninitiallyattheLiverpoolSchoolofHygiene,attimet,andy(t)thenumberofinfectives:butlatermovedtoLondon,wherehehelpeddevelopthein-dxdystitutethatborehisname,dyingtherein1932.Throughout=−βxy,=βxy−γy,thisperiod,hedevotedhimselftomathematicalepidemiologydtdtanditsapplicationtothepreventionofmalaria.Histheoryofwhereβisthetransmissionrateandγtherecoveryrate.“dependenthappenings”—theparadigm“happening”beingTheseequations,whosesolutionwasapproximatedbyRoss’s\n6Biometrics,March2003400Table1TheSussers’sparadigmsinepidemiology350MosquitoPeriodEraParadigm300controloperations19thcenturySanitarystatisticsMiasma250commence1sthalf20thInfectiousdiseaseGermtheory200centuryepidemiology(apriori)1502ndHalf20thChronicdiseaseBlackbox100centuryepidemiology(aposteriori)Monthlycountofmalariacases500189718981899190019011902problemsofmodernepidemiologythusbethatwehavedriftedFigure2.Monthlycountsofmalariacasesrecordedbythebacktoaposteriorimethods—fittingblackboxequationstoSuezCanalCompanyoveraseven-yearperiod.data,ratherthanworkingoutpredictionsfrommathematicalmodelingofunderlyingprocesses?KlausDietzhasbeenonediscipleMcKendrickandahostoflaterworkers,formtheoftheforemostcontributorstotheaprioriapproach,yethisfoundationsformodernepidemictheory(DietzandSchenzle,1985reviewwithSchenzlestated1985).Theylead,forexample,totheconceptoftheba-Bynowaboutonethousandpapershavecontributedtosicreproductivenumber,today’sequivalentofRoss’scriticalmathematicalepidemiology,butsmallpoxeradicationwasmosquitodensity.Withtheadventoftheworldwideepidemicachievedwithouttheuseofanyofthem.ofHIVinfectionandrenewedinterestintropicalmedicine,DietzandSchenzlefollowedup,quotingthismoredetailedanewgenerationofresearchworkersislearningabouttheassessmentbyBartetal.(1983):fundamentalcontributionsofRonaldRoss.Severalsessionsatthisconferencearedevotedtothisworkanditsextensions.MathematicalformulationshavebeendevelopedtodescribeAlthoughhewontheNobelPrizeforhisbiology,inoutbreaksofinfectiousdisease,totestconcepts,andtopro-Ross’sownopinionhis“principalworkhasbeentoestablishvideinsightsintodiseasecontrolandpolicyformulation.Thethegenerallawsofepidemics.”Ross’sbiographersNyeandresultingequationssometimesmirrortheobservedevents,Gibson(1997,p.279)state:“IfRosshadbeenborn100yearsbuttodatehavehadlittleimpactupondiseasecontrolorpreventivepractice.Insteadtheyhavebeenusedmoreretro-laterhecouldhavebecomeaneminentbiostatistician.Hisspectivelytoreassureratherthanassistinthedevelopmentthinkinginthisareawaswellaheadofhistimeandperhapsofpolicy.didnotachievetherecognitionitdeserveduntilmuchlater.”Ross(1916)describedhowhisapproachtomedicalstatisticsIamverygladtoseethat,inspiteofthisapparentlypes-differedfromthatofothersasfollows:simisticassessment,Dietzhasnotabandonedhiswork.Hewillbepresentinganinvitedpaperatthisconference,andIThewholesubjectiscapableofstudybytwodistinctmeth-lookforwardtodiscussinghiscurrentthinkingwithhim.odswhichareusedinotherbranchesofscience,whichareRichardPeto(1985)hasmademuchthesamedistinc-complementaryofeachother,andwhichshouldconvergeto-tionsasdoRonaldRossandtheSussers.WritingaboutDollwardsthesameresults.andHill’slandmarkworkonsmokingandlungcancer,heTheapproachthatprevailedinRoss’sday,andinourown,said:wastermedbyhimtheaposteriorimethod:Theimportanceofthestoryofthisdiscoveryisthatitdidnot...wecommencewithobservedstatistics,endeavortofitdependonanyseriousunderstandingofthemechanismsofanalyticallawstothem,andsoworkbackwardstotheun-carcinogenesis[or]ofthe...causativecomponentsoftobaccoderlyingcause(asdoneinmuchstatisticalworkoftheday).smoke....Thisindicatesthattherearetwocomplementaryapproaches...Hisclearpreference,however,wasfortheapriorimethod:Onewasthemechanisticapproach,whichsuggeststhatone...weassumeaknowledgeofthecauses,constructourdif-mustfirstferentialequationsonthatsupposition,follow-upthelogicalconsequences,andfinallytestthecalculatedresultsbycom-...understandthemechanismsofcarcinogenesisandthepre-paringthemwiththeobservedstatistics.ventivemeasureswillfollow.MuchthesamedistinctionsbetweendifferentepidemiologicOpposingthiswastheblackboxapproach,whichapproacheshavebeenmadeinthereviewbySusserandSusser...seeks...correlates...oftherisk...ofcanceramong(1996)ofthedifferenterasinepidemiologyandtheirdistinc-people.[This]hasyieldedbyfarthe...mostimportanttiveparadigms—whichtheyuseasabasisfortheirvisionofresults...inthepreventionofchronicdisease.thefuture(Table1).TheSussersdefinethe“blackbox”ap-proachasonethatrelatesexposuretodisease“withoutneces-BothRossandPetonote,however,thatthetwoap-sityforinterveningfactorsorpathogenesis.”Couldoneoftheproaches(i)mechanistic,orapriori,versus(ii)blackbox,ora\nAreStatisticalContributionstoMedicineUndervalued?7posteriori,arecomplementarytoeachother—whichsuggestsE.R.,andGibson,M.E.(1997),iscopyrightcNye,E.thatasynthesisispossible.Resultsofobservationalepi-R.,andGibson,M.E.andisreprintedwithpermissionofdemiologicstudiesanalyzedusingblackboxtechniquesarePalgraveMacmillan.mostconvincingwhensupplementaryinformationonbiolog-icalprocessesthatsupporttheobservedassociationisavail-Resum´e´able.ThisprinciplewaswellcodifiedbyBradfordHillastheLes´econom`etresDanielMcFaddenetJamesHeckmanontcriterionofbiologicalplausibilityinhisguidelinesforcausalobtenulePrixNobeld’Economie2000pourleurstravaux´inference.surleschoixdemod`elesdiscretsetlesbiaisdes´election.LesInsummary,statisticiansandepidemiologistshavecon-statisticiensetles´epid´emiologuesontapport´edescontribu-tributedenormouslytothepreventionandtreatmentofdis-tions´equivalentesenm´edecinepardestravauxsurles´etudesease.Thelowesteemaccordedtheirworkbymanyinthecas-t´emoin,l’analysedesdonn´eesincompl`etes,etl’inf´erencemedicalprofessionisdueinparttothepublicationoftoocausale.End´epitdenominationsr´ep´et´eesaussi´eminentesquemanycontradictoryfindingsfromobservationalstudies.Lab-BradfordHilletRichardDoll,lePrixNobeldePhysiologieoratoryworkershavetheluxuryofbeingabletoquicklyre-etdeM´edecinen’ajamais´et´eattribu´epourdestravauxenbiostatistiqueouen´epid´emiologie(l’exceptionquiconfirmepeattheirexperiments;manyarecarefultodoso,andthuslar`egleestRonaldRossquiobtinten1902lesecondPrixreplicatetheirresultsbeforesubmittingthemforpublication.NobeldeM´edecinepourlad´ecouverteduvecteurlepalud-Epidemiologyalsosuffersfromaninherentaversionto“blackisme,lemoustique.Rossd´eveloppaalorslamath´ematiquebox”thinking,astheperjorativenatureofthistermimplies.d’uneth´eoriedel’´epid´emie,qu’ilconsid´eracommesaplusThishasbeenaclassicsourceofdisagreementbetweenpublicimportantecontributionscientifique,etappliquasesr´esultatshealthofficialswhowanttodeveloppolicybeforemechanisms`adesprogrammesdeluttecontrelepaludisme).Lefaiblearefullyunderstoodandcriticswhoinsistongreater“proof”int´erˆetaccord´eauxbiostatistiqueset`al’´epid´emiologiedansbeforeimplementingregulatoryactions.certainscerclesm´edicaux,etdeplusenplusdanslepublic,estSpecificrecommendationsforimprovementsinepidemio-´etroitementli´eauxr´esultatscontradictoiresd’´etudesobserva-logy—whichhopefullywillleadtoagreaterappreciationfortionnellespubli´eessicomplaisammentdanslapressedevul-garisation.End´epitdesonefficacit´ed´emontr´eepoursauverthediscipline—havebeenmadebymanyresearchers,includ-desvies,l’approche“boitenoire”´epid´emiologiquedesfac-ingthosementionedinthistalk.Thesameprinciplesareteursderisquen’estplusr´eellementrespect´ee.Pourrem´edierenunciatedincoursesandtextbooks,buttoooftenseemtobe`acesperceptionsmalheureuses,lesstatisticiensdevraientforgotten—evenbythosewhoprofessthem.Theseincludethesuivreplus´etroitementleurspropresprincipes:construiredescallforfewer,largerstudiesthataredesignedtotestspecific´etudesmoinsnombreusesmaispluslargespourtesterdesapriorihypotheses.Epidemiologistswoulddowelltoemulatehypoth`esessp´ecifiques,suivredesprotocolesstrictspourlatheclinicaltrialsspecialists,bydevelopingstrictprotocolsford´efinitiondeleurs´etudesetleuranalyse,mieuxint´egrerlesbothstudydesignandsubsequentanalysisofthecollectedr´esultatsstatistiquesaveclesfaitsdelaboratoire,etprendredata.DollandHillworkedfromsuchaprotocol,andhadplusdepr´ecautionsdansl’affichageder´esultatsapparemmenttheaddedadvantagethatthepunchcardtechnologyoftheirpositifs.eramadeanalysessotime-consumingthatitpreventeddataReferencesdredgingandtheinclusionofallbutthemostessentialvari-ablesintheanalysis.Weshouldpaymoreattentiontobiolog-Anderson,J.A.(1972).Separatesamplelogisticdiscrimina-icalmechanisms,andattemptwhereverpossibletointegratetion.Biometrika59,19–35.theepidemiologicfindingswiththoseemanatingfromthelab-Bart,K.J.,Orenstein,W.A.,Hinman,A.R.,andAmler,oratory.Theaprioriandaposterioriapproachesshouldin-R.W.(1983).Measlesandmodels.InternationalJournaldeedbeviewedascomplementary,ratherthancompeting.ofEpidemiology2,263–266.WeneedmoredefinitivereviewsandsynthesesofindividualBecker,G.M.,DeGroot,M.H.,andMarschak,J.(1963).datarecordsfromdifferentstudies.Finally,greatercautionStochasticmodelsofchoicebehavior.BehavorialScienceisclearlyneededinpromotingpositiveresults.Whileitmay8,41–55.notbefeasibletoreplicatealargestudybeforepublication,Breslow,N.E.(1996).Statisticsinepidemiology:thecase-itcouldbeprudenttowaituntilcompletionofanothersimi-controlstudy.JournaloftheAmericanStatisticalAssoci-larstudy,andthentopublishthetwotogether.Goodscienceation91,14–28.mustalwaysbethetoppriority.Breslow,N.E.andDay,N.E.(1980).StatisticalMethodsinCancerResearchI:TheAnalysisofCase-ControlStudies.Lyon:InternationalAgencyforResearchonCancer.AcknowledgementsClayton,D.andHills,M.(1993).StatisticalModelsinEpi-Iamgratefultothefollowingindividualsforconversationordemiology.Oxford:OxfordUniversityPress.correspondencerelatedtothethemeofthistalk:Hans-OlovCornfield,J.(1951).AmethodofestimatingcomparativeAdami,RichardDoll,EricFeigl,ElizabethHalloran,Michaelratesfromclinicaldata:ApplicationstocanceroftheHills,PaulFine,AlfredKnudson,DimitriosTrichopoulos,andlung,breast,andcervix.JournaloftheNationalCancerNoelWeiss.SpecialthanksgototheUniversityofWashingtonInstitute11,1269–1275.studentsinBiostatistics536,AutumnQuarter,2001.ThisCosslett,S.R.(1981).Maximumlikelihoodestimatorforworkwassupportedinpartbygrant5-R01-CA40644fromchoice-basedsamples.Econometrica49,1289–1316.theUnitedStatesPublicHealthService.Ross’sthree-stanzaCox,D.R.(1958a).PlanningofExperiments.NewYork:poem,fromRonaldRoss:MalariologistandPolymathbyNye,Wiley.\n8Biometrics,March2003Cox,D.R.(1958b).Theregressionanalysisofbinaryse-ease.JournaloftheNationalCancerInstitute22,719–quences.JournaloftheRoyalStatisticalSociety,Series748.B20,215–242.McFadden,D.(1973).Conditionallogitanalysisofqual-Cox,D.R.(1966).Someproceduresconnectedwiththelo-itativechoicebehavior.InFrontiersinEconometrics,gisticqualitativeresponsecurve.InResearchPapersinP.Zarembka(ed),Chapter4,105–142.NewYork:Aca-Statistics:FestschriftforJ.Neyman,F.N.David(ed),demicPress.55–71.NewYork:Wiley.McFadden,D.andReid,F.(1975).AggregatetraveldemandDietz,K.andSchenzle,K.(1985).Mathematicalmodelsforforecastingfromdisaggregatedbehavioralmodels.Trans-infectiousdiseasestatistics.InACelebrationofStatistics:portationResearchRecord534,24–37.TheISICentenaryVolume,A.C.AtkinsonandS.E.Nye,E.R.andGibson,M.E.(1997).RonaldRoss:Malariol-Fienberg(eds),Chapter8,167–204.NewYork:Springer.ogistandPolymath.NewYork:St.Martin’sPress.Doll,R.(2002).Proofofcausality:deductionfromepidemio-Pearl,J.(2000).Causality:Models,ReasoningandInference.logicalobservation.PerspectivesinBiologyandMedicineCambridge:CambridgeUniversityPress.45,499–515.Peto,R.(1985).Theneedforignoranceincancerresearch.Doll,R.andHill,A.B.(1950).SmokingandcarcinomaofInTheEncyclopaediaofMedicalIgnorance:Exploringthethelung:Preliminaryreport.BritishMedicalJournal2,FrontiersofMedicalKnowledge,R.DuncanandW.S.739–748.Miranda(eds),129–133.Oxford:PergamonPress.Fine,P.E.M.(1975).Ross’saprioripathometry—aper-Prentice,R.L.andPyke,R.(1979).Logisticdiseaseincidencespective.ProceedingsoftheRoyalSocietyofMedicine68,modelsandcase-controlstudies.Biometrika66,403–411.547–551.Robins,J.M.(1986).AnewapproachtocausalinferenceFisher,R.A.(1934).StatisticalMethodsforResearchWorkers,inmortalitystudieswithasustainedexposureperiod–5thedition.Edinburgh:OliverandBoyd.applicationtocontrolofthehealthyworkersurvivoref-Fisher,R.A.(1951).TheDesignofExperiments.Edinburgh:fect.MathematicalModelling7,1393–1512.OliverandBoyd.Robins,J.M.,Hernan,M.A.,andBrumback,B.(2000).Heckman,J.J.(1979).SampleselectionbiasasaspecificationMarginalstructuralmodelsandcausalinferenceinepi-error.Econometrica47,153–161.demiology.Epidemiology11,550–560.Heckman,J.J.(1989).Causalinferenceandnonrandomsam-Rosenbaum,P.R.andRubin,D.B.(1984).Reducingbiasples.JournalofEducationalStatistics14,159–168.inobservationalstudiesusingsubclassificationontheKnudson,A.G.(1971).Mutationandcancer:Statisticalpropensityscore.JournaloftheAmericanStatisticalAs-studyofretinoblastoma.ProceedingsoftheNationalsociation79,516–524.AcademyofSciencesoftheUnitedStatesofAmerica68,Ross,R.(1911).ThePreventionofMalaria.London:John820–823.Murray,2ndedition.Lancet(1999).NarrownessofNobelawardsforphysiologyorRoss,R.(1916).Anapplicationofthetheoryofprobabilitiesmedicine.Lancet354,1399.tothestudyofaprioripathometry,part1.ProceedingsLittle,R.J.A.andRubin,D.B.(1987).StatisticalAnalysisoftheRoyalSociety,SeriesA92,204–230.withMissingData.NewYork:Wiley.Roy,A.D.(1951).Somethoughtsonthedistributionofearn-Luce,R.(1959).IndividualChoiceBehavior.NewYork:Wiley.ings.OxfordEconomicPapers3,135–146.Manski,C.F.andLerman,S.R.(1977).TheestimationofRubin,D.B.(1974).Estimatingcausaleffectsoftreatmentschoiceprobabilitiesfromchoicebasedsamples.Econo-inrandomizedandnon-randomizedstudies.Journalofmetrica45,1977–1988.EducationalPsychology66,688–701.Manski,C.F.andMcFadden,D.(1981).Alternativeesti-Susser,M.andSusser,E.(1996).Choosingafutureforepi-matorsandsampledesignsfordiscretechoiceanaly-demiology:I.Erasandparadigms.AmericanJournalofsis.InStructuralAnalysisofDiscreteDatawithEcono-PublicHealth86,668–673.metricApplications,C.F.ManskiandD.McFaddenTaubes,G.(1995).Epidemiologyfacesitslimits.Science269,(eds),Chapter1,2–50.Cambridge,Massachusetts:MIT164–169.Press.Mantel,N.andHaenszel,W.(1959).StatisticalaspectsofReceivedOctober2002.RevisedOctober2002.theanalysisofdatafromretrospectivestudiesofdis-AcceptedOctober2002.