Essential Medical Statistics PDF
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This page intentionally left blank Essential Medical Statistics Dedication To our children: Daisyand SamKirkwood Max, Kittyand Emily Sterne SECOND EDITION Essential Medical Statistics Betty R. Kirkwood MAMScDIC,HonMFPHM,FMedSci ProfessorofEpidemiologyandInternationalHealth LondonSchoolofHygieneandTropicalMedicine UniversityofLondon AQ1 Jonathan A.C. Sterne MAMScPhD ProfessorofMedicalStatisticsandEpidemiology DepartmentofSocialMedicine UniversityofBristol #1988,2003byBlackwellScienceLtd aBlackwellPublishingcompany BlackwellScience,Inc.,350MainStreet, Malden,Massachusetts02148–5020,USA BlackwellPublishingLtd,9600GarsingtonRoad,Oxford OX42DQ,UK BlackwellScienceAsiaPtyLtd,550SwanstonStreet, Carlton,Victoria3053,Australia TherightoftheAuthortobeidentifiedastheAuthorofthis WorkhasbeenassertedinaccordancewiththeCopyright, DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybe reproduced,storedinaretrievalsystem,ortransmitted,in anyformorbyanymeans,electronic,mechanical, photocopying,recordingorotherwise,exceptaspermitted bytheUKCopyright,DesignsandPatentsAct1988, withoutthepriorpermissionofthepublisher. Firstpublished1988 Secondedition2003 2 2006 LibraryofCongressCataloging-in-PublicationData Kirkwood,BettyR. Essentialmedicalstatistics/BettyR.Kirkwood, JonathanA.C.Sterne.—2nded. p.;cm. Rev.ed.of:Essentialsofmedicalstatistics/BettyR.Kirkwood.1988. Includesbibliographicalreferencesandindex. ISBN0–86542–871–9 1. Medicine–Research–Statisticalmethods.2. Medicalstatistics. [DNLM:1.Statistics.2.Biometry.WA950K59e2003] I.Sterne,JonathanA.C.II.Kirkwood,BettyR.Essential medicalstatistics.III.Title. R853.S7K4972003 6100.7027—dc21 2002015537 ISBN:978–0–86542–871–3 AcataloguerecordforthistitleisavailablefromtheBritishLibrary BSL: Setin10/13ptTimesbyKolamInformationServicesPvt.Ltd,Pondicherry,India complete PrintedandboundinUnitedKingdombyMPGBooksLtd,Bodmin,Cornwall printer CommissioningEditor:FionaGoodgame details EditorialAssistant:VickyPinder ProductionEditor:KarenMoore ProductionController:KateCharman ForfurtherinformationonBlackwellPublishing,visitourwebsite: www.blackwellpublishing.com Contents Prefacetothesecondedition vii Part C: Analysisof binary outcomes Prefacetothefirstedition ix 14 Probability,riskandodds (ofdisease) 131 15 Proportionsandthebinomial Part A: Basics distribution 138 1 Usingthisbook 3 16 Comparingtwoproportions 148 2 Definingthedata 9 17 Chi-squaredtestsfor2(cid:2)2andlarger 3 Displayingthedata 15 contingencytables 165 18 Controllingforconfounding: stratification 177 Part B: Analysisof numerical outcomes 19 Logisticregression:comparingtwoor 4 Means,standarddeviations moreexposuregroups 189 andstandarderrors 33 20 Logisticregression:controllingfor 5 Thenormaldistribution 42 confoundingandotherextensions 205 6 Confidenceintervalforamean 50 21 Matchedstudies 214 7 Comparisonoftwomeans: confidenceintervals,hypothesis testsandP-values 58 PartD:Longitudinalstudies:Analysisof rates and survival times 8 UsingP-valuesandconfidenceintervals tointerprettheresultsofstatistical 22 Longitudinalstudies,ratesandthe analyses 71 Poissondistribution 227 9 Comparisonofmeansfromseveral 23 Comparingrates 240 groups:analysisofvariance 80 24 Poissonregression 249 10 Linearregressionandcorrelation 87 25 Standardization 263 11 Multipleregression 98 26 Survivalanalysis:displayingand 12 Goodnessoffitandregression comparingsurvivalpatterns 272 diagnostics 107 27 Regressionanalysisofsurvival 13 Transformations 118 data 287 vi Contents Part E: Statistical modelling Appendix: Statistical tables 28 Likelihood 297 A1 Areasintailofthestandardnormal distribution 470 29 Regressionmodelling 315 A2 Percentagepointsofthestandard 30 Relaxingmodelassumptions 343 normaldistribution 472 31 Analysisofclustereddata 355 A3 Percentage pointsofthet 32 Systematicreviewsand distribution 473 meta-analysis 371 A4 Two-sidedP-valuesforthet 33 Bayesianstatistics 388 distribution,accordingtothevalue oftheteststatistic 474 A5 Percentagepointsofthe(cid:2)2 Part F:Studydesign, analysis distribution 476 andinterpretation A6 Probits 477 34 Linkinganalysistostudydesign: A7 CriticalvaluesfortheWilcoxon summaryofmethods 395 matchedpairssignedranktest 479 35 Calculationofrequiredsample A8 CriticalrangesfortheWilcoxonrank size 413 sumtest 480 BSL: 36 Measurementerror:assessmentand A9 Randomnumbers 482 check implications 429 and 37 Measuresofassociationand complete Bibliography 487 impact 447 Pg.nos Index 493 38 Strategiesforanalysis 458 Preface to the second edition The practice of medical statistics has changed considerably since the first edition waswritten.Atthattimetheageofthepersonalcomputerwasjustbeginning,and serious statistical analyses were conducted by specialist statisticians using main- frame computers. Now, there is ready access to statistical computing—even the most sophisticated statistical analyses can be done using a personal computer. This has been accompanied by the growth of the evidence-based medicine move- ment and a commitment of medical journals to improve the statistical rigour of papers they publish. These changes mean that the boundary between what used to be considered ‘basic’ or ‘essential’ statistics and more advanced methods has been blurred. Astatisticalanalysispresentedinaleadinggeneralmedicaljournalismorelikely to use logistic regression (formerly considered a specialist technique) than to present results from (cid:2)2 tests. In this second edition we describe the most com- monly used regression models—multiple linear regression, logistic regression, Poisson regression and Cox regression—and explain how these include many basic methods as special cases. By including chapters on general issues in regres- sion modelling, interpretation of analyses and likelihood, we aim to present a unifiedviewofmedicalstatisticsandstatisticalinference,andtoreflecttheshiftin emphasisinmodernmedicalstatisticsfromhypothesistestingtoestimation.Other new chapters introduce methods, some relatively new, that allow common prob- lemsinstatisticalanalysistobeaddressed;theseincludemeta-analysis,bootstrap- ping, robuststandard errors,and analysis of clustered data. Our aim throughout has been to retain the strengths of the first edition, by keeping the emphasis on enabling the reader to know which method to apply when.Wehavethereforestructuredthebookintopartsrelatingtotheanalysisof differenttypesofoutcomevariable,andincludednewchaptersonlinkinganalysis to study design, measures of association and impact, and general strategies for analysis. Anumberofthelargerdatasetsusedinthechaptersonregressionmodellingare available for downloading from the book’s website (www.blackwellpublishing. com/essentialmedstats), to allow readers to reproduce the analyses presented or tryoutfurtheranalysesforthemselves.Readersarealsoinvitedtovisitthewebsite to check forcorrections and updates and togivefeedback, which we welcome. viii Prefacetothesecondedition Inwritingthissecondedition,wehavebenefitedfromadviceandsupportfrom many colleagues, students and friends. In particular, we would like to thank the manyreaderswhogavefeedbackonthefirsteditionandinspiredustoembarkon this,CesarVictora,KateTillingandSimonCousensforsowillinglycommenting onearlydraftsindetail,DavidClaytonandMichaelHillsforgenerousadviceand unstintinghelponmanyoccasions,GeorgeDaveySmithforhelpfulcommentson a number of draft chapters and the late Paul Arthur for his enduring encourage- mentandadvice.WewouldliketoexpressourappreciationtoChristopherBaum, James Carpenter, Matthias Egger, Stephen Frankel, David Gunnell, Richard Hayes, Sharon Huttly, Mike Kenward, Peter McCarron, Roger Newson, Steven Oliver,AndrewPolmear,BiancadeStavola,andLesleyWoodforhelpfuldiscus- sionsandforsharingtheirinsightsintostatisticalissues.WearegratefultoJames Carpenter,ErikChristensen,ShahEbrahim,AlisonElliot,RichardHayes,David Kessler, Carl-Johan Lamm, Debbie Lawlor, Steven Oliver, Mary Penny, Seif Shaheen and Bianca de Stavola, who generously provided datasets for use as examples. We would also like to thank Maggie Rae and Alan Haworth, whose generoushospitalityfacilitatedmuchwriting,andlastbutnotleastHarrietAston, Emily,KittyandMaxSterne,AlexKhot,andSamandDaisyKirkwood,fortheir supportand the difference theymakein our lives. Betty Kirkwood Jonathan Sterne
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