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1、CriticalCareFebruary2005Vol9No1Bewicketal.ReviewStatisticsreview14:LogisticregressionVivBewick1,LizCheek1andJonathanBall21SeniorLecturer,SchoolofComputing,MathematicalandInformationSciences,UniversityofBrighton,Brighton,UK2SeniorRegistrarinICU,LiverpoolHospital,Sydney,AustraliaCorrespondinga
2、uthor:VivBewick,v.bewick@brighton.ac.ukPublishedonline:13January2005CriticalCare2005,9:112-118(DOI10.1186/cc3045)Thisarticleisonlineathttp://ccforum.com/content/9/1/112©2005BioMedCentralLtdAbstractThisreviewintroduceslogisticregression,whichisamethodformodellingthedependenceofabinaryresponse
3、variableononeormoreexplanatoryvariables.Continuousandcategoricalexplanatoryvariablesareconsidered.Keywordsbinomialdistribution,Hosmer–Lemeshowtest,likelihood,likelihoodratiotest,logitfunction,maximumlikelihoodestimation,medianeffectivelevel,odds,oddsratio,predictedprobability,WaldtestIntrodu
4、ctionThelogitfunctionisdefinedasthenaturallogarithm(ln)ofLogisticregressionprovidesamethodformodellingabinarytheodds[1]ofdeath.Thatis,responsevariable,whichtakesvalues1and0.Forexample,wemaywishtoinvestigatehowdeath(1)orsurvival(0)ofplogit(p)=ln()patientscanbepredictedbythelevelofoneormore1–p
5、metabolicmarkers.Asanillustrativeexample,considerasampleof2000patientswhoselevelsofametabolicmarkerWherepistheprobabilityofdeath.havebeenmeasured.Table1showsthedatagroupedintocategoriesaccordingtometabolicmarkerlevel,andtheFigure2showsthelogit-transformedproportionsfromFig.1.proportionofdeat
6、hsineachcategoryisgiven.TheThepointsnowfollowanapproximatelystraightline.Theproportionsofdeathsareestimatesoftheprobabilitiesofrelationshipbetweenprobabilityofdeathandmarkerlevelxdeathineachcategory.Figure1showsaplotofthesecouldthereforebemodelledasfollows:proportions.Itsuggeststhattheprobab
7、ilityofdeathincreaseswiththemetabolicmarkerlevel.However,itcanlogit(p)=a+bxbeseenthattherelationshipisnonlinearandthattheprobabilityofdeathchangesverylittleatthehighorlowAlthoughthismodellookssimilartoasimplelinearregressionextremesofmarkerlevel.Th
