Medical Statistics A Guide to Data Analysis and Critical Appraisal Jennifer Peat Associate Professor, Department of Paediatrics and Child Health, University of Sydney and Senior Hospital Statistician, Clinical Epidemiology Unit, The Children’sHospitalatWestmead,Sydney,Australia Belinda Barton Head of Children’s Hospital Education Research Institute (CHERI) and Psychologist, Neurogenetics Research Unit, The Children’s Hospital at Westmead,Sydney,Australia ForewordbyMartinBland,ProfessorofHealthStatisticsattheUniversityof York Medical Statistics A Guide to Data Analysis and Critical Appraisal Medical Statistics A Guide to Data Analysis and Critical Appraisal Jennifer Peat Associate Professor, Department of Paediatrics and Child Health, University of Sydney and Senior Hospital Statistician, Clinical Epidemiology Unit, The Children’sHospitalatWestmead,Sydney,Australia Belinda Barton Head of Children’s Hospital Education Research Institute (CHERI) and Psychologist, Neurogenetics Research Unit, The Children’s Hospital at Westmead,Sydney,Australia ForewordbyMartinBland,ProfessorofHealthStatisticsattheUniversityof York (cid:2)C 2005byBlackwellPublishingLtd BMJBooksisanimprintoftheBMJPublishingGroupLimited,usedunderlicence BlackwellPublishingInc.,350MainStreet,Malden,Massachusetts02148-5020,USA BlackwellPublishingLtd,9600GarsingtonRoad,OxfordOX42DQ,UK BlackwellPublishingAsiaPtyLtd,550SwanstonStreet,Carlton,Victoria3053,Australia TherightoftheAuthortobeidentifiedastheAuthorofthisWorkhasbeenassertedin accordancewiththeCopyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrieval system,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photo- copying,recordingorotherwise,exceptaspermittedbytheUKCopyright,Designs andPatentsAct1988,withoutthepriorpermissionofthepublisher. Firstedition2005 LibraryofCongressCataloging-in-PublicationData Peat,JenniferK. Medicalstatistics:aguidetodataanalysisandcriticalappraisal/byJennifer PeatandBelindaBarton.–1sted. p.;cm. Includesbibliographicalreferencesandindex. ISBN-13:978-0-7279-1812-3 ISBN-10:0-7279-1812-5 1.Medicalstatistics. 2.Medicine–Research–Statisticalmethods. I.Barton,Belinda.II.Title. [DNLM:1.Statistics–methods. 2.ResearchDesign. 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Contents Foreword,vii Acknowledgements,ix Chapter1 Datamanagement:preparingtoanalysethedata,1 Chapter2 Continuousvariables:descriptivestatistics,24 Chapter3 Continuousvariables:comparingtwoindependentsamples,51 Chapter4 Continuousvariables:pairedandone-samplet-tests,86 Chapter5 Continuousvariables:analysisofvariance,108 Chapter6 Continuousdataanalyses:correlationandregression,156 Chapter7 Categoricalvariables:ratesandproportions,202 Chapter8 Categoricalvariables:riskstatistics,241 Chapter9 Categoricalandcontinuousvariables:testsofagreement,267 Chapter10 Categoricalandcontinuousvariables:diagnosticstatistics,278 Chapter11 Categoricalandcontinuousvariables:survivalanalyses,296 Glossary,307 Index,317 v Foreword Most research in health care is not done by professional researchers, but by health-care practitioners. This is very unusual; agricultural research is not done by farmers, and building research is not done by bricklayers. I am told that it is positively frowned upon for social workers to carry out research, whentheycouldbesolvingtheproblemsoftheirclients.Practitioner-ledre- searchcomesabout,inpart,becauseonlyclinicians,ofwhateverprofessional background, have access to the essential research material, patients. But it also derives from a long tradition, in medicine for example, that it is part of theroleofthedoctortoaddtomedicalknowledge.Itisimpossibletosucceed in many branches of medicine without a few publications in medical jour- nals.Thistraditionisnotconfinedtomedicine.LetusnotforgetthatFlorence Nightingalewasknownas‘thePassionateStatistician’andhergreatestinno- vationwasthatshecollecteddatatoevaluatehernursingpractice.(Shewas the first woman to become a fellow of the Royal Statistical Society and is a heroinetoallthinkingmedicalstatisticians.) Thereareadvantagestothissystem,especiallyforevidence-basedpractice. Clinicians often have direct experience of research as participants and are aware of some of its potential and limitations. They can claim ownership of theevidencetheyareexpectedtoapply.Thedisadvantageisthathealth-care researchisoftendonebypeoplewhohavelittletraininginhowtodoitand who have to do their research while, at the same time, carrying on a busy clinical practice. Even worse, research is often a rite of passage: the young researchercarriesoutoneortwoprojectsandthenmovesonanddoesnotdo researchagain.Thusthereisacontinualstreamofnewresearchers,needing tolearnquicklyhowtodoit,yetthereisashortageofseniorresearchersto actasmentors.Andresearchisnoteasy.Whenwedoapieceofresearch,we are doing something no one has done before. The potential for the explorer tomakeajourneywhichleadsnowhereisgreat. The result of practitioner-led research is that much of it is of poor quality, potentiallyleadingtofalseconclusionsandsub-optimaladviceandtreatment for patients. People can die. It is also extremely wasteful of the resources of institutions which employ the researchers and their patients. From the researchers’pointofview,readingthepublishedliteratureisdifficultbecause thefindingsofotherscannotbetakenatfacevalueandeachpapermustbe read critically and in detail. Their own papers are often rejected and even oncepublishedtheyareopentocriticismbecausethemostcarefulrefereeing procedureswillnotcorrectalltheerrors. Whenresearchersbegintoreadtheresearchliteratureintheirchosenfield, one of the first things they will discover is that knowledge of statistics is vii