统计学文献10 4页

alifeinstatisticsalifeinstatisticsPurposes,methods,philosophiesPeterArmitagehasenjoyedalonganddistinguishedcareerinbiostatistics,andhasalsogivenconsiderablethoughttothewayinwhichstatisticsistaughttonon-mathematicians,perhapsbecause,hesaysjokingly,healwaysfoundmathsabitdifficulthimself.Nowinretirement,heisstillcommunicatingstatisticalideasinhisrôleasEditoroftheEncyclopediaofBiostatistics1.ThewaryearsTherewasaresearchsectioninSR17,headedbyGeorgeBarnard,whohadpreviouslybeenanappliedAfterspecialisinginmathsatschoolinHuddersfield,statisticianwiththeengineeringfirmPlesseyandwhoYorkshire,ArmitageleftinJanuary1941,attheageofthereforealreadyhadastrongbackgroundinengineer-17,togotoCambridge.“Therewasatendencyattheingstatistics.“Hewasaverysuitablepersontostarttimetopushpeopleintostartingcollegeatawkwardtrainingpeopleondoingworkonsamplinginspectiontimesintheacademicyear,becausetheyweren’tsureandqualitycontrol,aboutwhichweallknewnothing.howlongyouweregoingtobeabletostaythere.SoIWereallydidn’tevenknowagreatdealaboutstatistics;didtwotermsofPartI,andthenanotheryeartakingwehadbeentothesecourses,butwedidn’thavemuchPrelims.”ofafeelingforthehands-onaspectofthesubject;toTherewasadriveinthesummerof1943torecruitsomeextentwewereteachingeachother,givinglittlepeopleintoindustrialstatisticsaspartofthewaref-seminarsandarguingwitheachother.”fort,andintheearlyautumnof1943ArmitagebeganSomeofArmitage’sfirstworkconcernedproblemsworkinaunitcalledSR17intheMinistryofSupplyofsamplinginspection,andearlyattemptstomakesomealongsidenumerousothernovicestatisticians,includ-progresswithsequentialanalysis.“Therewasageneraling,forexample,DennisLindley.Atthatpoint,hefeltfeelingthatsequentialinspectionwasthewayaheadinnoparticularaffinityforstatistics,havingoriginallyintendedtobeaschoolteacher.“IhadtakenacourseAlotofpeoplewhowouldbeonstatisticsduringPartIofnoparticularinterest,andabletounderstandthepurposesthenanotherwithJ.O.Irwin—hehadbeenworkinginofstatisticalmethods,andwouldLondonfortheMedicalResearchCouncilbeforethebeabletousethemsensibly,arewarandmovedtoCambridgeduringthewar.Thatwasmoderatelyinteresting,butreallyratherimpractical,wastingtheirtimeiftheyreallytryover-theoretical.”togodeeplyintothemaths170december2004008-lifeinstats.indd1708-lifeinstats.indd170223/11/200415:17:393/11/200415:17:39PProcessCyanrocessCyanPProcessMagentarocessMagentaPProcessYellowrocessYellowPProcessBlackrocessBlackPPANTONE1807CANTONE1807C\nalifeinstatisticsqualitycontrol,butnoover-ridingtheory,sowewereplayingaboutwithad-hockery.Inthemiddleofthis,AbrahamWalddevelopedhistheoryofsequentialanalysis2,andbeforeitwaspublishedinscientificjournalsitcameoverintechnicalreports;werealisedthattherewasanoverallpowerfulapproachwhichwestartedtotakeoverandworkon.”Workcontinuedforthenext2yearsandthenduringthefollowingyearsomeoftheunit,includingArmitage,weretransferredtotheNationalPhysicalLaboratory.“Thatintro-ducedmetosomeotherareasofappliedwork,notjustindustrial,andinparticulartosomebiologicalworkastheNationalPhysicalLabo-ratorywaspartofalargergovernmentgroup-ingofscientificwork.”MedicalstatisticsIn1946,havingfinishedhiswarservice,Ar-mitagewasabletoreturntoCambridgetocontinuehisstudiesandhecompletedPartIIoftheTripos.AlthoughhehadoriginallyintendedtoreturntotheNationalPhysicalLaboratory,whenhewasaskedtoapplyforajobinmedicalstatisticsintheLondonSchoolofHygieneandTropicalMedicine,hesaidyes.“ThiswasaveryfortuitoussortofthingasIhadnorealinterestinmedicalstatisticsandIonlyknewoneortwoofthepeopleworkinginthefield.IwasofferedajobandstartedinDecember1947,inaunitoftheMedicalRe-searchCouncil(MRC)housedintheSchoolofHygieneunderthehonorarydirectorshipofA.[laterSirAustin]BradfordHill.BradfordHillwasaProfessorofMedicalStatistics,andtateback,soyouhadthesetwoformsgrowing,Atthattime,BradfordHillwasinitiatinghehadasmallgroupofpeopleemployedbyandyouhadtoestimatethemutationratestwomajordevelopmentsinmedicalstatistics.theSchool,butaratherlargergroupemployedfromexperimentalobservations.”OnewastopromulgaterandomisedclinicalbytheMRC.”Healsorecallsworkestimatingthetrials,andtheotherwastodevelopaetiologicaloverlapofdustparticlesinsamplesofpol-surveys—surveystostudythepossiblecausa-BradfordHillhadagreatlutedair:“Ifyou’resamplingpollutedair,tiveeffectsofagentsondisease.“Thisledtotheabilitytodevelopexcellentyouwanttocounttheconcentrateddustfirststudyonsmokingandlungcancer,withresearchinnewareas,and,particles.Now,ifyouconcentratethesampleRichardDoll,whichtooksubjectswithcancertoomuchandputitoutonplates,thedustandcontrolsandaskedthemhowmuchtheyalthoughhewasnotahighlyparticlesoverlap,andyoucan’ttellwhetherasmoked.Theythenwentontodoalargeco-sophisticatedmathematicalparticularimageisonedustparticle,ortwohortstudy,lookingatapopulationofpeople,statistician,hewasaveryorthree.So,foragivendensityofparticles,discoveringhowmuchtheysmoked,andthengoodresearchstrategisthowmuchoverlappingistherelikelytobe,lookingforwardovertheyearstoseewhichandhowdoyouadjustforthat?Itwasre-diseasestheydiedfrom.HillhadagreatabilityArmitagewasappointedasanassist-allyamatterofmakingmodelsofparticlestodevelopexcellentresearchinnewareas,and,anttoJ.O.Irwinandworkedonproblemsofofvariousshapesfallingonanareaandask-althoughhewasnotahighlysophisticatedbiologicalassay,whichwasastronginterestofinghowmuchoverlaptherewouldbe.Andmathematicalstatistician,hewasaverygoodIrwin’s.Healsolookedatsomeproblemsfromitwasrelatedtoproblemsthatotherpeople,researchstrategist.microbiologyanditwasoneofthesethatheinoperationsresearch,hadworkedonwith“Therewasagreatdealofinterestinclini-developedintoaPhDthesis.Itconcernedthesaturationbombingduringthewar.Ifyoucaltrials,andIthoughttherewasaconnectiondynamicsofabacterialpopulationsubjecttohavetremendouslysaturatedbombing,somewhichlinkedbacktomyworkonsequentialmutation.“Youhadapopulationofbacteriaofitisgoingtobewastedbecauseit’sover-analysisinindustrialstatistics.Ifeltitwouldthatcouldmutatetoadifferentformandmu-lapping.”beusefultoseewhetheryoucouldcarryoutdecember2004171008-lifeinstats.indd1718-lifeinstats.indd171223/11/200415:17:413/11/200415:17:41PProcessCyanrocessCyanPProcessMagentarocessMagentaPProcessYellowrocessYellowPProcessBlackrocessBlackPPANTONE1807CANTONE1807C\nalifeinstatisticsclinicaltrialssequentially,therebeingaveryAsthe1960swentonversial.Themathematiciansdidn’tlikeitmuch,strongethicalreasonfordoingthis:nottogobecausetheythoughtthiswouldtakeawayIfeltmoreandmoreontoolongwithacomparisonwhenthean-someoftheirresponsibilityforteachingstatis-stronglythatweoughttoswerisobvious,andwhenperhapsyoushouldtics,andtheeconomistswereabitsuspiciousstartusingthebettertreatment.haveaspecialisedMScforbecausetheywantedtokeeptheirname.Also,“IfirstofallstartedtoseewhetherstatisticianssomeofthepeopleinourowndepartmentfeltWald’smethodswouldwork,andIthoughtwewerebetrayingourraisond’être,whichwastheywerenotreallywhollysuitable.One“Asthe1960swentonIfeltmoreandtolookafterbiologicalstatistics.”reasonwasthatthedesignswereinfiniteinmorestronglythatweoughttohaveaspe-Eventually,however,astatisticsdepart-length,andyoumightgoonforever.AndsocialisedMScforstatisticians.Therewerevar-mentwassetupandArmitagewasappointedIdevelopedclosedmethods,andafterhavingiousMSccoursesinstatistics,perhapshalfaheadofdepartment,remainingthereuntilhisseenhowthesemighthaveworkedonexistingdozen,butnone,Ibelieve,inmedicalstatis-retirementin1990.“IsupposeItoleratedit”,trials,reanalysingdata,Ihadtheopportunitytics.Oneofmymotivationsforthishadbeenhesaysoftheadministrativesideofhisduties.toworkwithsomepeopleonnewtrials.ItseeingwhathappenedintheStates,where“Ididn’tmindatallthegeneralsupervisionofseemedtoworkandtheyseemedtolikeit.Itheyhadbuiltupverystrongprogrammesthewholeactivity;whatwasmoreannoyingeventuallywroteabook3summarisingtheseinwhatwasgenerallycalledbiostatistics,andwasthecommitteeworkyouhadtogotoevenmethodsin1960.ThespecificmethodsIusedthesewereproducingpeoplewithasolidun-ifyoudidn’twantto,andtheformfilling.It’sarenowwhollyout-datedandtherearenowderstandingofmedicalresearch,aswellasaallmultipliedtremendouslyofcoursesinceImanybetterideas,butitwasinterestingwhilestrongbackgroundinstatisticaltheoryandretired.”itlasted.”methods.”Notsurprisingly,ArmitagehasremainedInthelate1950s,theNationalCancerIn-Itwasataboutthistimethatcomputersactiveinretirement,maintaininghislinkswithstituteinBethesda,Washington,invitedBrad-firststartedbeingusedinstatisticsandArmit-theRoyalStatisticalSocietyandtheBiometricfordHilltosendsomeoneovertoworkforaageadmitshedidnottakethemseriouslyatSociety,amongothers,anddoingcollaborativeyearandheaskedArmitageifhewouldlikethetime.“Intheearly1960sIrememberbeingworkinpharmaceuticalstatisticsandclinicaltogo.Armitageagreed,andsomovedouttoquitescepticalaboutthepossibilitythatcom-trials.Buthismainworkhasbeeninco-edit-theStateswithhisfamily.Hespentmuchofputerswouldeverbeusedinstatistics.FrankingtheEncyclopediaofBiostatistics,publishedtheyearworkingonscreeningsystemsforde-YatesatRothamsted,forexample,wasverybyWileyin1998.tectingpossibleanti-canceragents.“Theyhaddiscerningaboutthat.Ithoughtitwasmuch“IgotinvolvedwiththeEncyclopediainanenormousprogrammeinwhichtheyweretoocumbersomeatechnique,becauseyouhadthemid-1990s.TheBritishbranchofWileytryingtotestthousandsofcompounds;almosttoprogramthingsinarduousways,evenafterdecidedtogoinforageneralprogrammeofanythingthatanyonesuggestedmighthavetheadventofFortranandAlgol.BeforeFor-encyclopaediasofdifferentsorts,andonetheyanti-canceractivitywasputthroughthemill.tranandAlgolcamein,itseemednotworthparticularlywantedtoproducewasinbiosta-Thatwasasplendidyear.Ihadtheopportu-itreally,tospendallthattimeprogramming,tistics.Iwasaskedtobeajointeditor-in-chief,nitytotravelaroundtheStates,andespeciallybutofcourseIhadn’tforeseenthepowerofalongwithTedColton,astatisticianatBostonenjoyedasummerinBerkeley,meetingJerzypackages.”University.Thatwasveryinterestingindeed.Neymanandhiscolleagues.”In1976ArmitageappliedfortheChairinThepeoplewhowrotethearticlesdidtheBiomathematicsatOxford,whichhadprevi-mainbulkofthework(IwrotesomearticlesouslybeenheldbyMauriceBartlett.“Bartlettbutnotmany),thesectioneditorswhocom-FromstudenttoteacherwasoneofthemajorfiguresinBritish20th-missionedthosearticlescontributedgreatly,BythetimeArmitagereturnedtoEngland,centurystatistics,withverystrongtheoreticalandourjobwasjusttryingtokeepthewholeBradfordHillwasduetoretire,andtherewerecredentials,buthealwayshadaninterestinthingtogether,seeingwhatredundanciesandthreevacanciesthathadtobefilledasaresult.biologicalandmedicalwork,inparticular,forgapstherewere.ArmitagewasgiventheChairofMedicalSta-instance,stochastictheoriesofepidemics.He“AcoupleofyearsagoWileydecidedtotistics,RichardDolltheDirectorshipofthewasintriguedbythepossibilityofdoingmoreproduceasecondedition,whichmightseemMedicalResearchCouncilUnitandthePro-workinbiomathematics,andhadacceptedthatsurprisingsosoon,butthemainpointisthatitfessorofEpidemiology,DonaldReid,becamenameforhischairandforthedepartment.Hewillbeon-line,whichthefirstonewasn’t.Wetheheadofthedepartment.retired;Iappliedandgotthechair.”usedmostofthematerialfromthefirstedition,“Igavequitealotofthoughttotheteach-TheDepartmentofBiomathematicswasweinvitedeveryonetoupdatetheirarticlesandingprogramme,whichwasveryvaried.Youaverysmalldepartmentinthebiologyfaculty,wecommissionednewarticles.Thematerialishadtoteachthepeoplewhowereonone-withnoresponsibilityforteachingmathemat-nowentirelyinproduction.”yearcoursesinsuchareasaspublichealthorics,althoughitdidrunanMScinappliedsta-bacteriology,andtheyallhadtohaveashorttistics.“Oxfordhadan‘InstituteofEconomicsAchangingdisciplinecourseinstatistics.AndthenyouhadagroupandStatistics’,andtheeconomistshadsome-ofpart-timestudentswhocameinspeciallythingofaclaimontheuseofthewordstatis-Duringhiscareer,Armitagehasseenstatisticsforacourseinstatistics.Thatwasaninterest-tics.Atthattimeitwasthoughtimpropertodevelopfromanadd-ontocoursesineconom-ingtask,becauseyouhadtoteachthemratherhaveadepartmentofstatistics,buteventually,icsormathematicsintoasubjectinitsownmorethantheywouldgetinaveryperfunctoryinthemid-1980s,anumberofusthoughtweright,withitsowndepartmentsofferingtheirfirstcourseinstatistics.oughttopressforone.Thiswasverycontro-owndedicatedcourses.Havingtakenaleadrôle172december2004008-lifeinstats.indd1728-lifeinstats.indd172223/11/200415:17:413/11/200415:17:41PProcessCyanrocessCyanPProcessMagentarocessMagentaPProcessYellowrocessYellowPProcessBlackrocessBlackPPANTONE1807CANTONE1807C\nalifeinstatisticsinonesuchdevelopment,hehasstrongopin-ionsabouttheimplicationsforhowthesubjectshouldbetaught.“Ithinkit’sunreasonabletoexpectmostofthepeoplewhoneedtoknowaboutstatisticstobeabletodoverymuchmaths.I’vealwaysrathersympathisedwiththeproblemsofpeoplefromnon-mathemati-caldisciplinestryingtocope,perhapsbecauseIalwaysfoundmathsabitdifficultmyself.Icanseethatanawfullotofpeoplewhowouldbeabletounderstandthepurposesofstatisti-calmethods,andwouldbeabletousethemsensibly,arewastingtheirtimeiftheyreallytryPeterArmitage,JimDurbin,WulfRudoeandJohnNelder(fromlefttoright),London,October2004togodeeplyintothemaths.Inmyteaching,Itriedtogetacrosspurposes,methods,philoso-Armitage,however,isnotconvinced.“Iadmiregettingcancerearlyon,butgraduallyasyouphies,andreducethemathstoaminimum.”thepowerandtheaestheticattractionofthegetoldermoreandmorepeoplearestartingIn1971,Armitagewroteabook,Statisti-Bayesiansystem,andIcanseeitisatremen-toexperienceit.Ifpeoplelivedindefinitely,calMethodsinMedicalResearch4,whichisstilldouslyimportantbodyofwork,ifyouactuallyandhadnoothercausesofdeath,theneve-inprintandnowinitsfourthedition,inwhicharetryingtogetacalculusofbeliefs.Ifthatre-ryonewouldgetcancereventually,soweareheattemptedtodojustthisandtoreducetheallyiswhatyouwanttodo,tostudyhowbe-justseeingthefirstbitofthedistributionmathematicalelementofstudyingstatisticstoliefschange,thereisnodoubtaboutit,that’sfunction.aminimum.However,asArmitagehimselfthewaytodoit.Thequestioniswhetherthis“Onepossiblereasonfortherebeingade-pointsout,thisapproachisnotwithoutitsisausefulwayofproceedinginordinaryscien-layisthatthereissomesortofsequentialseriesowndangers,especiallynowwiththepreva-tificwork,andIhavemydoubts.ofstepsthathavetobegonethrough,aserieslenceofstatisticalsoftwarepackagesthatallow“Ithinkthenon-Bayesiancasehasratherofmutations.Variouspeoplehadtalkedaboutuserssimplytoinputthedataandtoletthefallenbydefault.Peoplewhoarenottremen-thisandtherewerepapersinthemedicallit-softwaredoeverythingelse.douslyenthusiasticBayesianstendtoshrugeraturefromthe1930sonwards—evensome“Ithinkthere’sagreatriskofpeopletheirshouldersandsay:‘Well,iftheywanttomathematicalones—butwithaspectsthatweusingcomputerpackageswrongly.WhatIspendtheirtimedoingthingslikethat,letthem,’didn’tmuchlike.Soweproducedapaperwithwouldlikeisforpeopletohaveinstructionandsotherehasn’t,onthewhole,beenaveryamodelastowhatmighthappenifyouhadtofromcoursesandbookstogivethemabetterpowerfulcasemade.Perhapspeoplewhofeelgothroughaseriesofsteps,essentiallyaPois-perspectiveoncomputerpackages,ratherthanabletomakepowerfulphilosophicalcasesfindsonprocesswaitingforthefirstevent,andthengostraighttothecomputerpackagemanualtheBayesianapproachmoreattractive.I’mjustanotheroneforthesecondeventandsoon.andexpecttolearnstatisticsfromthat,asof-morepragmaticthanthat.ItendtoberatherTheresultisthatyoudotendtogetapowertenhappens.scepticalofattemptstoexplainphenomenabycurveandweplayedaboutwiththisinvarious“Andwithcomputersthereisadangerall-embracingtheories.IthinkIwouldfeelthisways.Thisworkhasbeentakenupfrequentlythat,themorecomplicatedthemodelis,theinpolitics,inreligionandinscience.Iprefertosincethen;it’sstillbeingreferredto,halfacen-moredifficultitistoseewhatitisdoing,andlookatthingsfromallsortsofdifferentpointsturylater.”toknowwhethertheansweryougetistooofviewandgraduallyletacompositepicturemodeldependent.Ithinkthere’sagreatneedemerge.ThatmaybeamatteroftemperamentReferencesforsensitivitystudies,tryingdifferentsortsoforbackground,whoknows?”1.Armitage,P.andColton,T.(eds)(1998)modelsondataandseeingwhetherbroadlyEncyclopediaofBiostatistics.Chichester:Wiley.speakingyourconclusionsarethesame.”2.Wald,A.(1947)SequentialAnalysis.AlastingimpressionNewYork:Wiley.3.Armitage,P.(1960)SequentialMedicalIthinkthenon-BayesianOvertheyears,ArmitagehasproducedalargeTrials.Oxford:BlackwellScientific.casehasratherfallenbybodyofworkandmadealastingimpression4.Armitage,P.(1971)StatisticalMethodsonthestudyandteachingofstatistics.But,default.PerhapspeoplewhoinMedicalResearch.Oxford:BlackwellScience.feelabletomakepowerfulwhenaskedwhichofhiscontributionshe5.Armitage,P.andDoll,R.(1954)Theageismostproudof,hereplies:“Ineverreallydistributionofcancerandamultistagetheoryofphilosophicalcasesfindthethoughtaboutthat”.Aftersomethought,hecarcinogenesis.BritishJournalofCancer,8,1–12.BayesianapproachmorenominatesajointpaperwithRichardDollattractivefromthe1950s5.“Richardhadbeeninter-PeterArmitagewasPresidentoftheRoyalStatisticalestedinthequestionofwhydeathratesfromSocietyfrom1982to1984.HereceivedtheGuyMedalTheincreaseduseofcomputersforsta-cancerriseinproportiontoapowerofage.inBronzefromtheRoyalStatisticalSocietyin1962,theGuyMedalinSilverin1998andtheGuyMedalintisticalwork,andinparticulartheincreaseinYoucouldsaythisisjustduetoageing—asGoldin1990.Hisresearchhascentredonthedevel-computingpower,hashadanothermarkedyougetolderyougetmoresusceptible.Oropmentofmethodsformedicalstatistics,especiallyeffectonthediscipline,andthisistherapiditcouldbethatcancersjusttakealongtimeclinicaltrials.HewasappointedCBEin1984.growthoftheBayesianapproachtostatistics.todevelop,sothere’sverylittleprobabilityofdecember2004173008-lifeinstats.indd1738-lifeinstats.indd173223/11/200415:17:423/11/200415:17:42PProcessCyanrocessCyanPProcessMagentarocessMagentaPProcessYellowrocessYellowPProcessBlackrocessBlackPPANTONE1807CANTONE1807C