Logistic回归-医学统计学

1、Logistic regression首都医科大学公共卫生与家庭医学学院首都医科大学公共卫生与家庭医学学院流行病与卫生统计学系流行病与卫生统计学系讲授教师：杨兴华讲授教师：杨兴华201220122022-6-2022022-6-2032022-6-204ppxbxbxbby 221102022-6-205 logistic regression analysis 1 1、应用背景、应用背景 LogisticLogistic回归模型是一种概率模型，适合于病例-对照研究、随访研究和横断面研究，且结果发生的变量取值必须是二项或多项分类。可用影响结果变量发生的因素为自变量，建立回归方程。2022-6-

2、2072、LogisticLogistic回归模型的数据结构2022-6-2082022-6-209n2022-6-2010n2022-6-20112022-6-2012l 令：令： y=1 发病（阳性、死亡、治愈等）发病（阳性、死亡、治愈等）l y=0 未发病（阴性、生存、未治愈等）未发病（阴性、生存、未治愈等）l 将发病的概率记为将发病的概率记为P，它与自变量，它与自变量x x1 1, , x x2 2, ,x,xp p之间的之间的Logistic回归模型为：回归模型为：l可知，不发病的概率为：可知，不发病的概率为：l )exp(1)exp(110110ppppXXXXp )exp(111

3、110ppXXp 2022-6-2013经数学变换得：定义：为Logistic变换，即： ppXXpp 110)1/(ln)1/(ln)(logpppitppXXpLogit 110)(2022-6-2014 4、回归系数i的意义 流行病学的常用指标优势比（odds ratio,OR)或称比值比，定义为：暴露人群发病优势与非暴露人群发病优势之比。 即Xi的优势比为：)1/()1/(0011PPPPORiiiPitPitORLn)0() 1()0(log)1 (log)(00ibi的标准差。为的标准差，为其中ySXSSSbbyiiyiii,/*影响越大。其因素对的估计值，此值越大，为Ybii)(

4、96. 1exp(iibSEb pii, 2 , 1 , 0, 0 0i20i0i计算统计量为：Wald2，自由度等于1。2022-6-20172022-6-20182022-6-20192022-6-20202022-6-20212022-6-20222022-6-20232022-6-20242022-6-20252022-6-2026Variables not in the Equation4.8211.0288.8891.00314.5261.000.1361.71319.6034.001X1X2X3X4VariablesOverall StatisticsStep0ScoredfSi

5、g.2022-6-2027Model Summary14.006.601.802Step1-2 LoglikelihoodCox & SnellR SquareNagelkerke RSquare2022-6-2028Classification Tablea14193.321386.790.0Observed01YOverall PercentageStep 101YPercentageCorrectPredictedThe cut value is .500a. 2022-6-2029Variables in the Equation2.5201.8211.9161.16612.4

6、313.9991.9754.1011.04354.568.189.0795.7081.0171.208-1.3061.583.6811.409.271-9.7814.0995.6941.017.000X1X2X3X4ConstantStep1aBS.E.WalddfSig.Exp(B)Variable(s) entered on step 1: X1, X2, X3, X4.a. 2022-6-20302022-6-20312022-6-20322022-6-20332022-6-20342022-6-20352022-6-2036Case Processing Summary1050.0%1

7、050.0%20100.0%0.0%0.0%0.0%0.0%20100.0%EventaCensoredTotalCases availablein analysisCases with missing valuesCases with non-positivetimeCensored cases beforethe earliest event in astratumTotalCases droppedTotalNPercentDependent Variable: OUTCOMEa. 2022-6-2037Omnibus Tests of Model Coefficientsa1.9207

8、.0932.02911.9432.003Step2-2 LogLikelihood Chi-squaredfSig.Overall (score)Chi-squaredfSig.Change From Previous BlockBeginning Block Number 1. Method: Forward Stepwise (Likelihood Ratio)a. 2022-6-2038Variables in the Equation1.7271.2491.9121.1675.6242.2841.6791.8521.1749.821X2X3Step2BSEWalddfSig.Exp(B

9、)2022-6-2039Variables not in the Equationa.0371.847X1Step 2ScoredfSig.Residual Chi Square = .037 with 1 df Sig. = .847a. 2022-6-2040（1 1）向前法）向前法(forward selection)(forward selection) 开始方程中没有变量，自变量由少到多一个一个引入回归方程。按自变量对因变量的贡献（P值的大小）由小到大依次挑选，变量入选的条件是其P值小于规定进入方程的P界值Enter, 缺省值 P(0.05)。2022-6-20412022-6-20

10、422022-6-2043 调试法：P从大到小取值0.5，0.1，0.05， 一般实际用时， SLE，SLS应多次选取调整2022-6-20442022-6-20452022-6-20462022-6-20472022-6-20482022-6-20492022-6-20502022-6-2051成组资料的非条成组资料的非条件件LogisticLogistic回归回归配对资料的条件配对资料的条件LogisticLogistic回归回归两分类反应变量的两分类反应变量的LogisticLogistic回归回归多分类有序反应变量多分类有序反应变量LogisticLogistic回归回归多分类无序反应

11、变量多分类无序反应变量LogisticLogistic回归回归1:11:1配对资料的条件配对资料的条件LogisticLogistic回归回归1:m1:m配对资料的条件配对资料的条件LogisticLogistic回归回归n:mn:m配对资料的条件配对资料的条件LogisticLogistic回归回归LogisticLogistic回归分析回归分析2022-6-20522022-6-20532022-6-20542022-6-20552022-6-20562022-6-20572022-6-20582022-6-20602022-6-20612022-6-20622022-6-20632022-6-2064 单因素单因素Logis