HST 190: Introduction to Biostatistics - Harvard University · 2019-09-23 · 6 HST 190: Intro to Biostatistics •Ask questions during the lecture as well as on Piazza §take notes!

HST190:IntroductiontoBiostatistics

Lecture1:Basicprinciplesofstatisticaldata

analysis

1 HST190:IntrotoBiostatistics

Welcome!

• Statisticalreasoningistheprocessofdrawingscientificconclusionsfromdatainarational,consistentway

• Goalsforthecourse:§ developanintuitionforthekeyconceptsthatunderpinthestatisticalanalysisofdata

§ readthe“Methods”sectionofanarticle,andunderstand/critiquetheapproachtaken

§ learntoanalyzeanddrawscientificconclusionsfromyourowndata

HST190:IntrotoBiostatistics2

Outline

Lecture Topic(s)1 Basicprinciplesofstatistical dataanalysis

2 Principlesofprobability&Estimationofparameters

3 Two-sample comparisons,hypothesistestingandpower/samplesizecalculations

4 Clinicaltrials&Simplelinearregression

5 Multiplelinear regression

6 Methodsforbinaryoutcomes

7 Logisticregression

8 Analysis oftime-to-eventdata

9 Projectpresentations

10 Reviewbeforetheexam


CourseLogistics


• Eightlectures§ each2-2.5hourslong

• Readingwillbeassignedpriortoeachlecture§ giventhepaceofthecourse,thisisstronglyencouraged

• Problemsetsfollowingeachlecture§ includeMatlab exercises§ dueat9amonthedayofthefollowinglecture(unlessspecifiedotherwise)


• Duringbreaksinthemiddlewewill:§ completegroupexercises§ learnMatlab§ discusscourseprojects

• Youwillalsoworkonagroupproject andpresentresultsduringoneoftheclassmeetings

• In-classexamwilltakeplaceduringlastmeeting§ 28th August§ open-book

Suggestions


• AskquestionsduringthelectureaswellasonPiazza§ takenotes!

• MaterialpresentedindifferentsequencefromRosner§ consultRosnerforadifferentapproach

• Lotsofmaterialinashorttime§ feelfreetoaskforhelp!

• Therewillbemanyformulae§ goalisnottomemorizethem

§ eventhoughwehaveaccesstosoftware,handcalculationscanhelpcultivateintuition

HowtoPrioritize


• Thecourseispass/fail.

• Examisopen-book,sodon’tspendtimememorizingformulas.Learnwhenandwhytouseeachprocedure;youcanalwaysrefertoyournotestoseehow.

• Togetthemostoutofthiscourse,youshould:§ attendlectures

§ submitsolutionstoalltheproblemsets

§ participateinclassdiscussions,groupexercises,andPiazza

§ completeaproject

§ takethefinalexam

Resources


• LectureNotes(Canvas->Files)§ Getbonuspointsforfindingtypos!

• IntroductiontoMatlab (Canvas->Files)

• Rosnertextbook,7thed.(required;alifelongreference)

• Piazza

• Pagano&Gavreau textbook

• SeeSyllabusforadditionalreferences.

Basicstepsofdataanalysis

• Tosetthestage,let’sconsidertwomotivatingquestions:1) isthereanassociationbetweentimespentintheoperatingroom

andpost-surgicaloutcomesforlungcancerresection?

2) canwedevelopanenhancedbreastcancerriskmodel?

• Thequestionshavebeenleftdeliberatelyvague!it’softenthecasethatscientificquestionsareinitiallyimpreciselyposed

• Integraltotheprocessofresearchistranslatingscienceintostatistics,andbackagain§ asyoureadpapers,itisimportanttoconsiderhowtheauthorsthoughtthroughthisprocess


• Therearemany(possiblyinfinite!)waysinwhichonecouldcharacterize‘basicsteps’butareasonableoutlinemightbe:I. Understandthecontextoftheanalysis

II. Establishthescientificgoals

III. Translatethescientificgoalsintostatisticallanguage

IV. Choosestatisticalmethodstoemploy

V. Implementationandrunningtheanalysis

VI. Interpretation



• Sometimes,thewayforwardisclearand,inthatsense,theprocessisprescriptive§ features/issuesthatarecommontoallanalyses

• Inmanyinstances,however,thewayforwardisn’tclear§ aspectsoftheanalysisdon’tfitinwithwhatyoucurrentlyknow

§ thesemayrelatetothescience,dataand/orstatisticsaspects

• Solutionsinclude:§ appealingtothepublishedliterature(scientificandstatistical)

§ adoptingoradaptingexistingmethods

§ developingnewmethods

• Regardless,dealingwiththeseissueswillrequiresomecreativity,andthereisseldom,ifever,one‘correct’dataanalysis§ differentdataanalysescorrespondtodifferentscientificquestions

§ whichscientificquestionis‘right’?

I.UnderstandingtheContext

• Fromtheperspectiveofabiostatistician,thepurposeofdataanalysisistolearnaboutsomepopulationusinginformationinasample

• Learnaboutcovariatesintermsofassociationwithorpredictionofanoutcome§ notationally weoftenthinkintermsof𝑋 and𝑌

§ possiblywithinoracrosscertainsub-populationsdenoted,say,by𝑍

• Contextusuallyinvolvesthreethings:1) thebackgroundscience

2) thenatureoftheavailabledata

3) thepopulationofinterest,oftencalledthe‘targetpopulation’


Lungcancersurgery


Q:Isthereanassociationbetweentimespentintheoperatingroomandpost-surgicaloutcomes?

• Backgroundscience:§ longeroperatingtime–>greaterexposuretoanesthesia

§ shorteningoperatingtimemightreduceadversepost-surgicaloutcomes

o complicationsduringthehospitalstay

o recurrenceoflungcancer

o mortality

§ mayalsoleadtodecreasedcosts/increasedefficiencyo increasedcapacityfortheoperatingroom

o shorterpost-surgicalhospitalstay


• Availabledata:§ ≈400surgeriesatBrighamandWomen’sHospital

§ performedbetween1997-2008

§ demographic,clinical,tumorandfollow-upinformation

• Targetpopulation:§ patientswhoundergoelectivesurgeryforearlystagenon-smallcelllungcancer

§ needtobeawareofdifferentsurgerysub-types

o lobectomy,segmentectomy,wedgeresection

o thorachotomy,videoassistedthoracicsurgery

§ whatdowethinkaboutthe(relatively)longtimeframe?

§ generalizabilitybeyondBWH?

Breastcancerrisk


Q:Canwedevelopanenhancedbreastcancerriskmodel?

• Backgroundscience:§ the‘Gailmodel’forbreastcancerriskwasdevelopedinthelate1980s

o age,race,

o ageatmenarche,ageatbirthoffirstchild

o familyhistory,numberofpriorbiopsyexaminationsandatypicalhyperplasia

§ themodelwasvalidatedinanumberofsubsequentstudies

§ subsequentresearchidentifiedanumberofadditionalriskfactorsforbreastcancer

o breastdensity,useofhormonereplacementtherapyandbodymassindex


• Availabledata:§ 2,392,998screeningmammogramsfromtheBreastCancerSurveillanceConsortium

o NCI-fundednationwidenetworkofmammographyregistries

§ mammogramsperformedbetween1996-2002

§ outcomesareascertainedvialinkageswithcancerregistries

• Targetpopulation:§ screeningmammogramsperformedonwomenaged35-84years

o unitofanalysisisthemammogram,notthewoman

§ whoundergoesscreening?whodoesn’t?

o howmightthisimpacttheinterpretationofthestudy?

Natureoftheavailabledata


• Whatwerethedatacollectionprocedures?§ conveniencesampleorpartofadesignedstudy?

§ whatwasthesetting/timeframe?

§ observationalstudyorrandomizeddesign?

§ cross-sectional,prospective,orretrospective?

§ stratificationand/ormatching?

• Howweretheproceduresfollowed?§ anysystematicdeviationsfromthe‘ideal’datacollectionprocess?

§ maybeduetopatients?o refusaltoparticipate/respond

o inaccurateresponses


§ maybeduetoresearchers?

o wereuniformproceduresappliedtoall(potential)participants?

o areweactuallymeasuringwhatwethinkwearemeasuring?

• Havetherebeenanyinterimdatacleaning/manipulationefforts?§ cleaningof‘strange’values

o settosomethresholdvalueortomissing

o exclusionfromthedataset

§ constructionofderivedvariables

Populations


• Inpractice,the‘population’canbe§ anactual,potentiallyobservablepopulation

§ ahypothetical(sometimesinfinite)population

• Mightrefertothe‘targetpopulation’toemphasizethatthereisaspecificpopulationinmind

• Definingthetargetpopulationiscrucialinthatitprovidesthecontextthescientificquestionofinterest§ whowouldwelikeourresultstogeneralizetoo?

• Narrowvs.broaddefinitionsofthetargetpopulation§ heterogeneityvs.homogeneity

§ whatarethetrade-offs?


• Whatcomesfirst...thedataorthepopulation?§ dependsonwhenyougetinvolved

• Ifthedatahasalreadybeencollected:§ forwhichpopulationcouldweconsiderthesampleasbeing‘representative’?

§ mayneedtofocusthedatasetbyexcludingcertainfolkso implicitlychangesthepopulationtowhichonecangeneralize

o samplesizevs.mixingofeffects

§ istherescopeforadditionaldatacollectionefforts?

• Ifthedatahasnotbeencollected:§ muchgreaterflexibilityforchoosing/definingthepopulationofinterest

Learningfromdata


• Recall,thegoalistolearnabouttherelationshipsbetweenasubsetofcovariates

• Achievedbycollectingandanalyzingasamplefromthepopulation§ animportantaspectof‘context’isthatthisisindeedwhatwearedoing

o or,atleast,hopingtodo!

• Supposewecouldenumeratetheentirepopulation§ thatis,thesampleisthepopulation

• Inthiscaseobserveddatacharacterizesrelationshipscompletely


• Notewhenwehaveacompleteenumeration,thereisnosamplingvariability§ wedon’thavetoworryaboutmakingstatementsaboutthepopulationonthebasisofinformationinthesample

§ thesampleisthepopulation

• Wedon’thavetoconsiderorquantifyuncertaintyassociatedwithonlyobservingasub-sample§ noneedforstandarderrors,confidenceintervalsorp-values

§ maybenoneedforstatisticalmethods!

• Mostofthetimewecan’tenumeratetheentirepopulation§ typically,thisisn’tlogisticallyand/orfinanciallyfeasible

• So…

II.Establishthescientificgoals

• Broadlyspeakingonecanclassifyscientificgoalsas:§ descriptionorexplorationofapopulation

§ evaluationofsomehypothesis

§ predictionoffutureoutcomes

• Asingleanalysismayhaveseveralgoals§ dependsonscientificsettingandbackground


Lungcancersurgery



• Description/exploration:§ whatisthenatureoftheassociation?

§ doestheassociationdifferacrosssurgerytypes?

• Hypothesistesting:§ apriorihypothesisamongthecollaboratorsthatshortertimesareassociatedwithbetterpost-surgicaloutcomes

Breastcancerrisk



• Prediction:§ usealltheavailableinformationinthebestpossiblewaytopredicttheriskofbreastcancer

§ buildpredictionmodelsthatcatertospecificsettingswithvaryingamounts/typeofinformation?

o athome/online

o inthephysiciansoffice

• Whymightdescription/explorationandhypothesistestingbeoflessinterest?

Description/exploration


• Goalistocharacterizetherelationshipsamongasetofcovariatesinthepopulationofinterest

• Animportantissueiswhetherornotthegoalistoestablishcausation§ typicallyrequiresagreaterunderstandingofthescience

• Typically,althoughnotalways,viewedashypothesisgenerating§ wehaveacooldataset,let’sseewhatwecanfind...

§ thereisafine,oftenblurrylinebetweenexplorationandhypothesistesting

o whatcamefirst...thedataorthequestion?

Hypothesistesting


• Goalistomakesomeconfirmatorystatement

• Typicallyframedinthecontextofmakinga‘decision’betweentwocompetinghypotheses𝐻%:nullhypothesis

𝐻&:alternativehypothesis

• Assumethenullhypothesisholdsandlookforevidencetothecontrary

• Standardhypothesistestingreducesthepotentialdecisionsto:1. failtoreject𝐻%2. reject𝐻% (implicitlyinfavorof𝐻&)

§ decisionshouldbeaccompaniedbysomemeasureofuncertainty

Prediction


• Goalistoestimatefutureoutcomesorrisk§ Typicallyframedintermsofbuildingthebestpossiblemodel

• Whatdowemeanby‘best’?§ needsomemeansofjudgingaccuracyandpenalizingpoorpredictions

§ ideallybasedonrealworldconsequenceso e.g.false-positivevs.false-negativeforbreastcancer

• Sometimesasinglebestmodelisinappropriate§ amodelmayworkwellinonepopulationandnotothers

§ inputsmaynotalwaysbeavailable(e.g.geneticinformation)

• Towhatextentdoweneedtocareaboutcausation?§ doweneedtounderstandthe‘true’underlyingmechanisms?

Therealworld


• Unfortunately,thescientificgoalsarenotalwaysclearattheoutset

• Typically,itisthecasethat:§ therearemanyscientificgoalsthatareofinterest,and/or

§ thegoalcanbeinterpretedinanumberofways

• Primarilyaproblembecauseinvestigatorsneedprecisestatementstobeabletoproceed§ totranslatethescientificgoalsintostatisticalones

• Towardsrefiningstudygoals,acoupleofusefulquestionsare:1) whoistheintended(primary)audience?

2) whatwillbeactionablefromtheresults?


• Considerthequestion:WhatisMrs.Jones’riskofbreastcancer?

• Howoneproceedsdepends,atleastinpart,onhowthisinformationwillbeused:Researchers

o determineeligibilityforarandomizedstudyofsomenovelpreventativeagent

Patientso decisionastowhetherornotsheshouldgetintouchwithherphysician

Physicianso planningforfuturescreeningschedule

Policy-makerso monitorthepublichealthburdenofbreastcancer


• Relatedquestionsinclude:§ isinterestinallbreastcancersorsomespecifictumortype?

§ riskoverwhichtimeframe?o 1year?

o 5years?

o lifetime?

§ howmuchinformationwilltheinterested‘user’haveaccessto?

o willdetailedfamilyhistoryinformationbeavailable?

o willgeneticinformationbeavailable?

• Differentanswerstoallthesequestionsdefinedifferentscientificgoals

III.Translatingscientificgoalsintostatisticalterms/tasks

• Oncethescientificgoalsare‘established’weneedtotranslatethemintothelanguageofstatistics

• Movingforwardrequires:§ preciseandcleardefinitionsofallrelevantcovariates

§ specificationofkeyrelationshipsofinterest


Scientificgoal StatisticaltaskDescription/exploration Estimation

Hypothesistesting InferencePrediction Estimation

Preciselydefiningcovariates


• Eachofthepotentialgoalsistryingtosaysomethingabouttherelationshipsamongasetofcovariates

• Priortoanyanalysisweneedcleardefinitionsforallrelevantcovariates:§ responsevariables

§ exposure(s)ofinterest

§ interactiontermsand/oreffectmodifiers

§ predictorsoftheresponse

§ predictorsoftheexposure(s)ofinterest

• Therewillbeoverlapacrossthesevarioustypesofvariables§ e.g.,acovariatemaybeapredictorofboththeresponseandoftheexposureofinterest


• Oftennotasstraightforwardasonemightthink,mainlybecausethereisoftenchoiceinvolved

• Supposetheresponseofinterestis‘diagnosisofbreastcancer’§ overwhichtimeframe?

§ forwhichsub-types?

• Supposetheexposureofinterestis‘operatingtime’§ whendoestimestart?

§ whendoestimestop?

• Define(andperhapsre-define)untileverythingisclear!

Lungcancersurgery



• Responses:§ hospitalstayof>7days(binary)

§ numberofmajorcomplicationsduringhospitalstay(count)

o needalistof‘major’complications

§ timetodeath(continuous,right-censored)

• Exposureofinterest:§ operatingtimedefinedasthetimefromthefirstincisiontothetimeofthefirststitchtocloseup(continuous)

Breastcancerrisk



• Response:§ diagnosisofbreastcancerwithin1yearofthescreeningmammogram(binary)

• Exposureofinterest:§ age,race,education,breastdensity,HRTuse...

§ atotalof13potentialpredictors

§ allcategorical

o atleastintheavailabledataset

IV.Choosingstatisticalmethods

• Onewayofviewingallthestatisticalmethodsavailableisasacollectionoftools§ differentstatisticaltoolsfordifferentstatisticaltasks

§ developunderstandingofacollectionoftoolsoverthecourseofyourcareer

• Atoolboxofstatisticaltools/methods§ basicmethods,thateveryoneshouldbeabletouse

§ specializedmethods

o sophisticatedtoolsthatrequire‘training’

o constantlybeingdevelopedandpublishedintheliterature

§ sometimesnewquestionsrequirenewmethods



• Forthemostpart,thetoolsthatresearchersemployaredeterminedbytheissueswe’veconsideredsofar§ scientificgoals

§ natureoftheavailabledata

§ populationofinterest

• Evengivenallthisinformation,thereareoftenseveralchoicesofstatisticaltools/methods

• Howtochoosebetweenalltheavailableapproaches?§ interpretation(tobediscussedlater)

§ operatingcharacteristicso e.g.biasandstatisticalefficiency

V.Implementationandrunningtheanalysis

• Seeminglythemost‘prescriptive’ofthesteps§ inaperfectworld,turnthehandle...andyou’redone!

• Unfortunately,actuallyperformingtheanalysisisnotalwaysstraightforward

• Manychoicesforstatisticalsoftware§ R,Matlab,SAS,Stata,WinBUGS,...

§ eachhasnumerousresources,includingalready-writtencodeavailableonline

§ notallmethodshavebeenimplementedinallsoftwarepackages



• Performingtheanalysescanalsohighlightallsortsofproblems§ EDAmighthighlightdataissues

o missingdata

o unusualvalues

o unusualobservedrelationships

• Issueslikethismayrequireare-thinkofthescientificgoals§ ifyoucan’tanswerthisquestion,whichquestioncanyouanswer?

VI.Interpretation

• It’simportanttodistinguishinterpretationofthemodel frominterpretationoftheresults

• Specificationofthemodelissomethingthatwehavecontrolover§ itshouldbestraightforwardtoprovideapreciseinterpretationofits’components

o youcannotbepedanticenoughonthispoint

§ shouldbeabletodothisbeforeyouevenseethatdata

• Considerthelinearregressionmodel:𝐸 𝑌 𝑋 = 𝛽% + 𝛽&𝑋

§ Howdoweinterpret𝛽&?


Interpretationoftheresults


• Herearesomeresults...whatdoesitallmean?!?§ translationofstatisticsbacktoscience

• Interpretingtheresultsrequiresadetailedunderstandingboththescientificandstatisticalcontext§ usuallyrequiresdiscussionwithcollaborators

• Sometimestheresultsdon’tsupporttheinitialhypotheses!§ e.g.,Breitner etal(2008)Neurology

§ RiskofdementiaandADwithpriorexposuretoNSAIDsinanelderlycommunity-basedcohort

§ seethenextslide



• Thesecanbeparticularlychallengingsituations

• Aretheseresults‘right’?§ arewemisinterpretingourassumptions/models?

§ aretheredataissuesthatwearen’tawareof?

§ isthecodewrong?

§ aretheresultssensitivetoparticularanalysischoices?

• Itmaybethattheresultsare‘right’§ perhapsanewunderstandingofthemechanismofinterest

§ perhapstheresultspertaintoapopulationthathasn’tbeenstudiedbefore

Learningaboutpopulations

• Itisseldompossibletospecifyone,singletargetpopulation§ oftenthecasetherearemanyinterestingtargetpopulations

• Flexibilitytoconsiderdifferentpopulationsdependsonwhetherornotthesamplehasbeencollected

• Ifthesamplehasnotbeencollected,onemightconsider§ arangeofscientificquestions

§ thefeasibilityofcollectingdataacrossdifferentpopulations

• Ifthesamplehasbeencollected,flexibilitydependsonthenatureandscopeoftheavailabledata


Breastcancerscreening


• Broadgoalofscreeningistodetectcancerasearlyaspossible§ balancebetweenpublichealthgoalsandcosts

§ cannotscreeneveryoneallofthetime

§ therearealso‘harms’associatedwithscreening

§ mammographyisnotperfect

§ realconsequencesassociatedwithfalse-positives

• Currentrecommendationsare(broadly):§ allwomenaged50oroldergetscreenedeverytwoyears

§ also,womenintheir40’swhoareat‘highrisk’

Q:Howgoodismammographyasascreeningmodality?§ answerdepends,inpart,onthepopulationofinterest


• Rosenbergetal(2006)Radiology.§ allwomenwhoundergoscreeningmammography


• Yankaskas et al (2010) JNCI.


• Miglioretti etal(2004)JAMA.


• Goldmanetal(2008)MedicalCare.

Remarks

• Exceptinthemosttrivialofsettings,thedataanalysisprocessiscollaborativeanditerative

• Howyouproceedwilldependonmanythings:§ thenatureofthedata

§ yourphilosophy

§ thephilosophyofyourcollaborators

• Gettingthescience‘right’isoftenthehardestpart§ goalsareseldompreciseattheoutset

§ goingback-and-forthbetweenthescienceandstatisticsistypicallyaveryinstructiveprocess

§ todoagoodjobusuallyrequiresknowledgeofthescience



• Moreoftenthannot,thereisscopeforprescriptionaswellasforcreativity§ sometimesthereisanobviouswayforward

§ othertimesthereisn’t

• Whatcamefirst...thequestionorthedata?

• Thereisseldomone‘right’scientificquestionordataanalysis§ BoxandDraper(1987):

Essentially,allmodelsarewrongbutsomeareuseful.

HST 190: Introduction to Biostatistics - Harvard University · 2019-09-23 · 6 HST 190: Intro to Biostatistics •Ask questions during the lecture as well as on Piazza §take notes!

Documents