Chapter 1 Longitudinal Data Analysis

1 Themostcommonmedicalresearch designsis a \pre-post"studyinwhich a singlebaselinehealthstatusmeasurement is obtained,aninterven-tionis administered,anda singlefollow-upmeasurement is theoutcomemeasurement canbe as-sociatedwiththechangein example,if somesubjectsaregivenplacebo whileothersaregivenanactive drug,thetwogroupscanbe comparedto seeif thechangein theoutcomeis di erent forthosesubjectswhoareactivelytreatedas comparedto viewed as thesimplestformof a prospective nition: Alongitudinalstudyrefersto aninvestigationwherepartici-pant outcomesandpossiblytreatments or exposuresarecollectedat longitudinalstudygenerallyyieldsmultiple or \repeated"measurementsoneach example,HIVpatients may be followedover timeandmonthlymeasuressuch as CD4counts,or viralloadarecollectedto charac-terizeimmunestatusanddiseaseburde nrespectively. Such repeatedmea-suresdataarecorrelatedwithin subjectsandthus secondimportant outcomethatis commonlymeasuredin a longitudinalstudyis thetimeuntil a key clinicalevent such as diseaserecurrenceor LONGITUDINALDATA ANALYSISA nalysisof event timeendpoints is thefocusofsurvivalanalysiswhich iscoveredin Chapter ?

2 ?.Longitudinalstudiesplay a key rolein epidemiology, clinicalresearch, characterizenormalgrowthandaging,to assessthee ectof riskfactorsonhumanhealth,andto evaluatethee ectivenessof a greatdealof e ortbuto erseveralbene- tsinclude:Bene tsof recorded. A prospective longitudinalstudymea-suresthenewoccuranc eof diseaseonsetcanbecorrelatedwithrecent changesin patient exposure. In a prospective studypartic-ipants canhave theirexposurestatusrecordedat recalltheirexposure(a formofmeasurement error).In additionthetemporalorderof exposuresandoutcomesis individualchangein outcomes. A keystrengthof alongitudinalstudyis theability to measurechangein outcomesand/orexposureat to observe individualpatternsof timee ects:Cohort,Period, Age. Whenstudyingchangeover timetherearemany timescalesto birthsuch as 1945or 1963,periodis thecurrent timesuchas2003,andageis (period - cohort),forexample58= 2003-1945,and40 = longitudinalstudywithmeasurements at timest1; t2; : : : tncansimultaneouslycharacterizemultiplet imescalessuch asageandcohorte ectsusingcovariatesderivedfromthecalenda rtimeof visitandtheparticipant'sbirthyear:theage of subjectiat timetjis ageij= (tj birthi); andtheircohortis simplycohortij= [1996]discussesage,period, andcohorte ectsin theanalysisof forcohorte ects.

3 Ina cross-sectionalstudythecomparisonof subgroupsof di erent agescombinesthee ectsof agingandthee ectsof di erent , comparisonof outcomesmeasuredin 2003among58yearoldsubjectsandamong40year oldsubjectsre ectsboththefactthatthegroupsdi erby 18years(aging)andthefactthatthesubjectsw erebornin di erent example,thepublichealthinterventionssuch as vaccinationsavailablefora childunder10yearsof agemay diferduring1945-1955as comparedto thepreventive interventionsexperiencedin longitudinalstudythecohortunderstudyis xedandthus changesin timearenotconfoundedby cohortdi longitudinaldataanalysisopportunitiesin respiratoryepi-demiologyis presentedin WeissandWare[1996].Thebene tsof a :Challengesof Thereis theriskof biasdueto incompletefollow-up,or \drop-out"of subjectsthatarefollowed totheplannedendof studydi erfromsubjectswhodiscontinue follow-upthena naive analysismay providesummariesthatarenotrepresenta-tiv e of correlated data . Statisticalanalysisof longitudinaldatarequiresmethods thatcanproperlyaccount fortheintra-subjectcor-relationof such correlationis ignoredtheninferencessuch as statisticaltestsor con denceintervalscanbe Althoughlongitudinaldesignso ertheop-portunity to associatechangesin exposurewithchangesin theoutcomeof interest,thedirectionof causality canbe complicatedby \feedback" example,in anobserva-tionalstudyof thee ectsof a drugonspeci cindicatorsof health,a patient'scurrent healthstatusmay in uencethedrugexposureordosagereceivedin cinterestliesin thee ectof medicationonhealth,thisexamplehasrecipro calin uence4 CHAPTER1.

4 LONGITUDINALDATA Analysis betweenexposureandoutcomeandposesanalyti caldi culty whentryingto separatethee ectof medicationonhealthfromthee thissubsectionwe give someexamplesof longitudinalstudiesandfocusontheprimarys cienti cmotivationin additionto keyoutcomeandcovariatemeasurements.( )ChildAsthmaManagement Program(CAMP){ In thisstudychildrenarerandomizedto di erent asthmamanagement multicenterclinicaltrialwhoseprimaryaimi s theevaluationof thelong-terme ectsof dailyinhaledanti-in ammatorymedicationuseonasthmastatusandlu nggrowthin childrenwithmildto moderateashtma(Sze eret ).Outcomesincludecontinuousmeasuresof pulmonaryfunctionandcatergoricalindicato rsof ambient pollutionandtheprevalenceof anenvironmentalexposurerequiresspeci cationof a lagbetweentheday of exposureandtheresultinge theairpollutionliteratureshortlagsof 0 to 2 days arecommonlyused(Sametet ;Yu et ).For boththeevaluationof treatmentandexposureto environmentalpollutionthescienti cquestionsfocusontheassociationbetweenan exposure(treatment, pollution) outcomesis of secondaryinterest,butmustbe acknowledgedto obtainvalidstatisticalinference.}

5 ( )CysticFibrosisandPulmonaryFunction{ TheCysticFibro-sisFoundationmaintainsa registryof longitudinaldataforsubjectswithcystic asthe1-secondforcedexpiratoryvolume(FEV1 )andpatient healthindicatorssuch as infectionwithPseudomonasaeruginosahave cobjective is to characterizethenaturalcourseof thediseaseandto estimatetheaveragerateof declinein determinewhethermeasuredpatient characteristicssuch asgenderandgenotype correlatewithdiseaseprogression,or withanincreasedrateof declinein a typicalobservationaldesignwherethelongit udinalnatureof thedataareimportant changein healthoutcomessuch as lungfunction.( )TheMulti-CenterAIDSC ohortStudy(MACS){ TheMACS studyenrolledmorethan3,000menwhowereat riskforacquisitionof HIV1(Kaslow et ).Thisprospective cohortstudyobservedN= 479inci-dent HIV1infectionsandhasbeenusedto particular,thisstudyhasdemonstratedthee ectof HIV1infectiononindicatorsof immunologicfunctionsuch as cquestionis whetherbaselinecharacteristicssuchas viralloadmeasuredimmediatelyafterserocon versionareassociatedwitha poor patient prognosisas indicatedby a greaterrateof declinein usethesedatato illustrateanalysisapproachesforcontinuou slongitudinalresponsedata.}}

6 ( )HIVNETI nformedConsent Substudy{ Numerousreportssug-gestthattheprocessof obtaininginformedconsent in orderto participateinresearch studiesis ,forpreventive HIVvaccinetrialsa prototype informedconsent processwas evaluatedamongN= 4;892subjectsparticipatingin theVaccinePreparednessStudy(VPS).Approxi -mately20%of subjectswereselectedat randomandasked to participatein amock informedconsent process(Colettiet ).Participant knowledgeof key vaccinetrialconceptswas evalulatedat baselinepriorto theinformedconsent visitwhich occuredduringa special3 month thenassessedforallpar-ticipants at thescheduled6, 12, basiclongitudinalextensionof a ,anda totalscorethatcalculatesthenumber of correctresponsesminusthenumber of subsetof focusonsubjectswhowereconsideredat highriskof HIVacquisitiondueto thischapterwe useYijto denotetheoutcomemeasuredon subjectiat timetij. Theindexi= 1;2; : : : ; Nis forsubject,andtheindexj= 1;2; : : : ; nis forobservationswithina designedlongitudinalstudythemeasurement timeswillfollow a protocolwitha commonsetof follow-up6 CHAPTER1.}

7 LONGITUDINALDATA Analysis times,tij=tj. For example,in theHIVNETI nformedConsent Studysub-jectsweremeasuredat baseline,t1= 0, at 6 monthsafterenrollment,t2= 6months,andat 12and18months,t3= 12months,t4= letXijdenotecovariatesassociatedwithobse rvationYij. Commoncovariatesin a longitudinalstudyincludethetime,tij, andperson-level characteristicssuch as treatment assignment, or cinterestoftenfocusesonthemeanresponseas a func-tionof covariatessuch astreatment andtime,proper statisticalinferencemustaccount forthewithin-personcorrelationof ne jk=corr(Yij; Yik), thewithin-subjectcorrelationbetweenobser vationsat timestjandtk. In thefollowingsectionwe discussmethods forexploratingthestruc-tureof within-subjectcorrelation,andin discussestimationmethods longitudinaldataseeksto discover patternsof sys-tematicvariationacrossgroupsof patients,aswellasaspectsof timeWhenscienti cinterestis in theaverageresponseover time,summarystatis-ticssuch asmeansandstandarddeviationscanrevealwhe therdi erentgroupsarechangingin a similaror di erent subgroupsin theHIVNETI nformedConsent Substudy.

8 At baselinetheinterventionandcontrolgroupsh ave is determinedby randomizationwhichoccursafterenrollment. At aninterim3 monthvisittheinterventionsub-jectsaregiv ena mock informedconsent forparticipationin a hypotheticalphaseIII vaccinee theinterventioncanbe seenby themeanscoresat the6 6 monthsis ( ),upslightlyfromthebaselinemeanof ( ).In contrast,theinterventiongrouphasa 6 month data ( ),a largeincreasefromthebaselinemeanof ( ).Theinterventionandcontrolgroupsaresign i cantlydi erent at 6 montsbasedona laterfollow-uptimesfurtherchangeis meanthatincreasesto the12 monthvisitandto uctuatesslightlywithmeansof ( )at month 12, ( ) signi cante ectonknowledge,andthatsmallimprovement is seenover timein :Meanknowledgescoresover timeby treatment group,HIVNETI nformedConsent LONGITUDINALDATA ANALYSISE xample2 IntheMACS studywe comparedi erent groupsof subjectsformedonthebasisof theirinitialviralloadmeasurement. Low viralloadisde nedby a baselinevaluelessthan15 103, mediumas 15 103- 46 103,andhighviralloadis classi edforsubjectswitha baselinemeasurementgreaterthan46 103.

9 TheaverageCD4count foreach timeforeach of :MeanCD4count andstandarderrorover nedby ( )mean( )mean( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )Thesubjectswiththelowestbaselinevirallo adhave a meanof rstyearafterseroconversionandthendecline to a meancount of smallerthanthedeclineobservedforthemediu mviralloadgroup, ,andthehighviralloadgroup, ,thesesum-mariessuggestthathigherbaselin eviralloadmeasurements areassociatedwithgreatersubsequent reductionin theHIVNETI nformedConsent Substudywe saw a substan-tialimprovement in is alsorelevent to considerkeyindividualitemsthatcompriseth etotalscoresuch as the\safety item"orthe\nurseitem."Regardingsafety, participants wereaskedwhetherit wastrueor falsethat\Oncea large-scaleHIVvaccinestudybegins,we canbesurethevaccineis completelysafe." of respond-ingsubjectsat each visitandthepercent of subjectswhocorrectlyansweredthatthesafet y statement is thatthecontrolandinterventiongroupshave a comparableunderstandingof thesafety data :Number of subjectsandpercent answeringcorrectlyforthesafetyitemfromth eHIVNETI nformedConsent correctN% , mock informedconsentwas administeredat a 3 month visitfortheinterventionsubjectsonly.

10 Theimpactof interventionsubjectscorrectlyrespondinga t 6 a theproportionansweringcorrectly, buta 2-samplecomparisonof inter-ventionandcontrolproportionsat 6 months( )is notstatisticallysigni cant. Finally, themodestinterventionimpactdoes notap-pearto be retainedas 12 18 ,thesedatasuggesta smallbut eetingimprovement in participant understandingthata vaccinestudiedin a phaseIII trialcannotbe guaranteedto be di erent was trueor falsethat\Thestudynursewilldecidewhogets therealvaccineandwhogetstheplacebo." ,butforthenurseitemwe seea largeincreasein thefractionansweringcorrectlyamonginterv entionsubjectsat6 is statisticallysigni cant di erencein theproportionansweringcorrectlyat 6 monthswitha con denceinterval forthedi erencein proportionsof (0:199;0:349).Althoughthemagnitudeof 6 monthsto 18months,thecon denceinterval forthedi erencein proportionsat 18 monthsis (0:096;0:260)andexcludesthenullcompariso n,p1 p0= ,thesedatasuggestthattheinterventionhasa substantialandlastingimpactonunderstandi ngthatresearch nursesdonotdetermineallocationto real10 CHAPTER1.