A3-无序多分类logistic回归分析-暨南大学高级医学统计学

高级《医学统计学》第十六章logistic回归分析第三节无序多分类logistic回归分析multinomiallogisticregression暨南大学医学院医学统计学教研室林汉生一、无序多分类logistic回归分析表1部分分化程度和细胞染色与恶性肿瘤组织类型关系的数据分化程度X1细胞染色X2组织类型Y鳞癌Y=1腺癌Y=2大细胞癌Y=3Ⅰ级：1阳性：1101726阴性：051250Ⅱ级：2阳性：1211726阴性：0161236Ⅲ级：3阳性：1151516阴性：0121220无序多分类logistic回归应变量为无序分类资料选择应变量Y中的一个类别作为参照，拟合其他类别与参照类别相比较的logistic回归模型。应变量Y有g个分类，多分类logistic回归就包括g-1个方程。g-1个回归方程中的自变量回归系数可以不同1.建立SPSS数据工作表，要Weight表1部分分化程度和细胞染色与恶性肿瘤组织类型关系的数据分化程度X1细胞染色X2组织类型Y鳞癌Y=1腺癌Y=2大细胞癌Y=3Ⅰ级：1阳性：1101726阴性：051250Ⅱ级：2阳性：1211726阴性：0161236Ⅲ级：3阳性：1151516阴性：01212202.AnalyzeRegressionMultinomialLogistic将分类变量X1和X2选入Factor栏Factor:分类变量；Covariates:数值变量Factors:Anindependent(predictor)categorical(ornumericwithafinitenumberofvalues)variable,usedtodefinegroupsofcases.Covariates:Covariatesarequantitativepredictorvariables,measuredinadditiontothedependentvariable.Thesecontinuousexplanatoryvariablesrepresentasourceofvariationinthedependentvariablethathasnotbeencontrolled.MultinominalLogistic对话框默认Last（Y=3，大细胞癌）为参照组分别单击Model、OptionsModel对话框可以逐步筛选变量进入模型？StepwiseMethodForwardentry.Thismethodbeginswithnostepwisetermsinthemodel.Ateachstep,themostsignificanttermisaddedtothemodeluntilnoneofthestepwisetermsleftoutofthemodelwouldhaveastatisticallysignificantcontributionifaddedtothemodel.Backwardelimination.Thismethodbeginsbyenteringalltermsspecifiedonthestepwiselistintothemodel.Ateachstep,theleastsignificantstepwisetermisremovedfromthemodeluntilalloftheremainingstepwisetermshaveastatisticallysignificantcontributiontothemodel.Forwardstepwise.Thismethodbeginswiththemodelthatwouldbeselectedbytheforwardentrymethod.Fromthere,thealgorithmalternatesbetweenbackwardeliminationonthestepwisetermsinthemodelandforwardentryonthetermsleftoutofthemodel.Thiscontinuesuntilnotermsmeettheentryorremovalcriteria.Backwardstepwise.Thismethodbeginswiththemodelthatwouldbeselectedbythebackwardeliminationmethod.Fromthere,thealgorithmalternatesbetweenforwardentryonthetermsleftoutofthemodelandbackwardeliminationonthestepwisetermsinthemodel.Thiscontinuesuntilnotermsmeettheentryorremovalcriteria.Options对话框（默认即可）单击OK3.数据的基本情况CaseProcessingSummary7923.4%8525.1%17451.5%12035.5%12837.9%9026.6%17551.8%16348.2%338100.0%033861鳞癌2腺癌3大细胞癌y肿瘤类型1I级2II级3III级x1分化程度0阴性1阳性x2细胞染色ValidMissingTotalSubpopulationNMarginalPercentage变量筛选过程StepSummaryEnteredIntercept78.915.Enteredx161.53917.3764.002Enteredx250.44511.0942.004Model012ActionEffect(s)-2LogLikelihoodModelFittingCriteriaChi-SquareadfSig.EffectSelectionTestsStepwiseMethod:ForwardEntryThechi-squareforentryisbasedonthelikelihoodratiotest.a.模型拟合情况：可认为回归系数不为0或不全为0（P=0.000），但伪决定系数（PseudoR-Square）很低。ModelFittingInformation78.91550.44528.4706.000ModelInterceptOnlyFinal-2LogLikelihoodModelFittingCriteriaChi-SquaredfSig.LikelihoodRatioTestsPseudoR-Square.081.093.041CoxandSnellNagelkerkeMcFadden经似然比检验，X1，X2的效应均有统计学意义LikelihoodRatioTests50.445a.0000.66.83016.3854.00361.53911.0942.004EffectInterceptx1x2-2LogLikelihoodofReducedModelModelFittingCriteriaChi-SquaredfSig.LikelihoodRatioTestsThechi-squarestatisticisthedifferencein-2log-likelihoodsbetweenthefinalmodelandareducedmodel.Thereducedmodelisformedbyomittinganeffectfromthefinalmodel.Thenullhypothesisisthatallparametersofthateffectare0.Thisreducedmodelisequivalenttothefinalmodelbecauseomittingtheeffectdoesnotincreasethedegreesoffreedom.a.则以X1=3，X2=1为参照ParameterEstimates9.14E-02.292.0981.755-1.315.38411.7271.001.269.127.570-.232.333.4861.486.793.4131.5220a..0....-.747.2827.0271.008.474.273.8230a..0....8.94E-02.290.0951.758-.656.3393.7301.053.519.2671.010-.475.3441.9151.166.622.3171.2190a..0....-.743.2717.5331.006.476.280.8090a..0....Intercept[X1=1][X1=2][X1=3][X2=0][X2=1]Intercept[X1=1][X1=2][X1=3][X2=0][X2=1]Y12BStd.ErrorWalddfSig.Exp(B)LowerBoundUpperBound95%ConfidenceIntervalforExp(B)Thisparameterissettozerobecauseitisredundant.a.结果解释用无序多分类logistic回归分析3种恶性肿瘤组织类型与分化程度和细胞染色的关系。分化程度为3个等级，以第3个等级为参照；细胞染色为阴性和阳性，以阳性为参照。以大细胞癌为参照组，分别建立鳞癌和腺癌两个logistic回归模型，结果如下：分化程度和细胞染色与恶性肿瘤组织类型均有关联，且OR值小于1。可认为分化程度低，细胞染色阴性，患鳞癌和腺癌的风险低于大细胞癌。