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1 STAT IntroductiontoBiostatisticsLectureNotesI ntroduction StatisticsandBiostatistics The eldofstatistics Thestudyanduseoftheoryandmethodsforthean alysisofdataarisingfromrandomprocessesor phenomena Thestudyofhowwemakesenseofdata The eldofstatisticsprovidessomeofthemostfund amentaltoolsandtechniquesofthescienti cmethod forminghypotheses designingexperimentsandobservationalstud ies gatheringdata summarizingdata drawinginferencesfromdata e g testinghypotheses Astatistic ratherthanthe eldof statistics alsoreferstoanumericalquantitycomputedfr omsampledata e g themean themedian themaximum Roughlyspeaking the eldofstatisticscanbedividedinto MathematicalStatistics thestudyanddevelopmentofstatisticaltheor yandmethodsintheabstract and AppliedStatistics theapplicationofstatisticalmethodstosolv erealproblemsinvolvingrandomlygeneratedd ata andthedevelopmentofnewstatisticalmethodo logymotivatedbyrealproblems ReadCh ofourtext Biostatisticsisthebranchofappliedstatist icsdirectedtowardapplica tionsinthehealthsciencesandbiology

2 Biostatisticsissometimesdistinguishedfro mthe eldofbiometrybaseduponwhetherapplication sareinthehealthsciences bio statistics orinbroaderbiology biometry e g agriculture ecology wildlifebiology Otherbranchesof applied statistics psychometrics econometrics chemometrics astrostatistics environmetrics etc Whybiostatistics What sthedi erence Becausesomestatisticalmethodsaremoreheav ilyusedinhealthapplicationsthanelsewhere e g survivalanalysis longitudinaldataanalysis Becauseexamplesaredrawnfromhealthscience s Makessubjectmoreappealingtothoseinterest edinhealth Illustrateshowtoapplymethodologytosimila rproblemsen counteredinreallife Wewillemphasizethemethodsofdataanalysis butsomebasictheorywillalsobenecessarytoe nhanceunderstandingofthemethodsandtoallo wfurthercoursework Mathematicalnotationandtechniquesarenece ssary Noapologies Wewillstudywhattodoandhowtodoit butalsoveryimportantiswhythemethodsareap propriateandwhataretheconceptsjustifying thosemethods Thelatter thewhy willgetyoufurtherthantheformer thewhat Data DataTypes

3 Dataareobservationsofrandomvariablesmade ontheelementsofapopulationorsample Dataarethequantities numbers orqualities attributes measuredorobservedthataretobecollectedan d oranalyzed Theword data isplural datum issingular Acollectionofdataisoftencalledadataset singular Example LowBirthWeightInfantData AppendixBofourtextcontainsadatasetcalled lowbwtcontain ingmeasurementsandobservedattributeson lowbirthweightinfantsbornintwoteachingho spitalsinBoston MA Thevariablesmeasuredherearesbp systolicbloodpressuresex gender male female tox maternaldiagnosisoftoxemia yes no grmhem whetherinfanthadagerminalmatrixhemorrhag e yes no gestage gestationalage weeks apgar Apgarscore measuresoxygendeprivation at minutesafterbirth Dataarereproducedonthetopofthefollowingp age ReadCh ofourtext Thereare variableshere sbp sex etc measuredon units elements subjects theinfants ofarandomsampleofsize Anobservationcanrefertothevalueofasingle variableforapar ticularsubject butmorecommonlyitreferstotheobservedvalu esofallvariablesmeasuredonaparticularsub ject Thereare observationshere

4 TypesofVariables Variabletypescanbedistinguishedbasedonth eirscale Typically di er entstatisticalmethodsareappropriateforva riablesofdi erentscales ScaleCharacteristicQuestionExamplesNomin alIsAdi erentthanB MaritalstatusEyecolorGenderReligiousa liationRaceOrdinalIsAbiggerthanB StageofdiseaseSeverityofpainLevelofsatis factionIntervalByhowmanyunitsdoAandBdi er TemperatureSATscoreRatioHowmanytimesbigg erthanBisA DistanceLengthTimeuntildeathWeightOperat ionsthatmakesenseforvariablesofdi erentscales OperationsthatmakesenseAddition Multiplication ScaleCountingRankingSubtractionDivisionN ominalpOrdinalppIntervalpppRatiopppp Often thedistinctionbetweenintervalandratiosca lescanbeig noredinstatisticalanalyses Distinctionbetweenthesetwotypesandordina landnominalaremoreimportant Anotherwaytodistinguishbetweentypesofvar iablesisasquantitativeorqualitative Qualitativevariableshavevaluesthatareint rinsicallynonnumeric categorical E g Causeofdeath nationality race gender severityofpain mild moderate severe Qualitativevariablesgenerallyhaveeithern ominalorordinalscales

5 Qualitativevariablescanbereassignednumer icvalues e g male female buttheyarestillintrinsicallyqualitative Quantitativevariableshavevaluesthatarein trinsicallynumeric E g survivaltime systolicbloodpressure numberofchildreninafamily height age bodymassindex Quantitativevariablescanbefurthersubdivi dedintodiscreteandcon tinuousvariables Discretevariableshaveasetofpossiblevalue sthatiseither niteorcountablyin nite E g numberofpregnancies shoesize numberofmissingteeth Foradiscretevariabletherearegapsbetweeni tspossibleval ues Discretevaluesoftentakeinteger wholenumbers values e g counts butsomediscretevariablescantakenon integervalues Acontinuousvariablehasasetofpossiblevalu esincludingallvaluesinanintervaloftherea lline E g durationofaseizure bodymassindex height Nogapsbetweenpossiblevalues Thedistinctionbetweendiscreteandcontinuo usquantitativevariablesistypicallycleart heoretically butcanbefuzzyinpractice Inpracticethecontinuityofavariableislimi tedbytheprecisionofthemeasurement E g heightismeasuredtothenearestcentimeter orperhapsmillimeter

6 Soinpracticeheightsmeasuredinmillimeters onlytakeintegervalues Anotherexample survivaltimeismeasuredtothenearestday butcould theoretically bemeasuredtoanylevelofprecision Ontheotherhand thetotalannualattendanceatUGAfootballgam esisadiscrete inherentlyinteger valued variable but inprac tice canbetreatedascontinuous Inpractice allvariablesarediscrete butwetreatsomevariablesascontinuousbased uponwhethertheirdistributioncanbe wellapproximated byacontinuousdistribution DataSources Dataarisefromexperimentalorobservational studies anditisimportanttodistinguishthetwo Inanexperiment theresearcherdeliberatelyimposesatreatme ntononeormoresubjectsorexperimentalunits notnecessarilyhu man Theexperimenterthenmeasuresorobservesthe subjects responsetothetreatment Crucialelementisthatthereisaninterventio n Example Toassesswhetherornotsaccharineiscarcinog enic are searcherfeeds micedailydosesofsaccharine After months ofthe micehavedevelopedtumors Byde nition thisisanexperiment butnotaverygoodone Inthesaccharineexample wedon tknowwhether

7 Withtumorsishighbecausethereisnocontrolg rouptowhichcomparisoncanbemade Solution Select moremiceandtreatthemexactlythesamebutgiv ethemdailydosesofaninertsubstance aplacebo Supposethatinthecontrolgrouponly mousedevelopsatumor Isthisevidenceofacarcinogenice ect Maybe butthere sstillaproblem Whatifthemiceinthe groupsdi ersystematically E g group fromgeneticstrain group fromgeneticstrain Here wedon tknowwhethersaccharineiscarcinogenic orifgeneticstrain issimplymoresusceptibletotumors Wesaythatthee ectsofgeneticstrainandsaccharinearecon founded mixedup Solution Startingwith relativelyhomogeneous similar mice ran domlyassign tothesaccharinetreatment and tothecontroltreat ment Randomizationanextremelyimportantaspecto fexperimentalde sign Inthesaccharineexample weshouldstartoutwith homoge neousmice butofcoursetheywilldi ersome Randomizationensuresthatthetwoexperiment algroupswillbeprobabilisti callyalikewithrespecttoallnuisancevariab les potentialconfounders E g thedistributionofbodyweightsshouldbeabou tthesameinthetwogroups Anotherimportantconcept

8 Especiallyinhumanexperimentation isblind ing Anexperimentisblindifthesubjectsdon tknowwhichtreatmenttheyreceive E g supposewerandomize of migrainesu ererstoanactivedrugandtheremaining toaplacebocontroltreatment Experimentisblindifpillsinthetwotreatmen tgroupslookandtasteidenticalandsubjectsa renottoldwhichtreatmenttheyreceive Thisguardsagainsttheplaceboe ect Anexperimentisdouble blindiftheresearcherwhoadministersthetre atmentsandmeasurestheresponsedoesnotknow whichtreat mentisassigned Guardsagainstexperimentere ects Experimentermaybehavedi erentlytowardthesubjectsinthetwogroups ormeasuretheresponsedi erentlyinthetwogroups Experimentsaretobecontrastedwithobservat ionalstudies Nointervention Datacollectedonanexistingsystem Lessexpensive Easierlogistically Moreoftenethicallypractical Interventionsoftennotpossible Exper