Logistic回歸-醫(yī)學統(tǒng)計學

1、Logistic regression首都醫(yī)科大學公共衛(wèi)生與家庭醫(yī)學學院首都醫(yī)科大學公共衛(wèi)生與家庭醫(yī)學學院流行病與衛(wèi)生統(tǒng)計學系流行病與衛(wèi)生統(tǒng)計學系講授教師：楊興華講授教師：楊興華201220122022-6-2022022-6-2032022-6-204ppxbxbxbby 221102022-6-205 logistic regression analysis 1 1、應用背景、應用背景 LogisticLogistic回歸模型是一種概率模型，適合于病例-對照研究、隨訪研究和橫斷面研究，且結(jié)果發(fā)生的變量取值必須是二項或多項分類。可用影響結(jié)果變量發(fā)生的因素為自變量，建立回歸方程。2022-6-

2、2072、LogisticLogistic回歸模型的數(shù)據(jù)結(jié)構(gòu)2022-6-2082022-6-209n2022-6-2010n2022-6-20112022-6-2012l 令：令： y=1 發(fā)病（陽性、死亡、治愈等）發(fā)?。栃?、死亡、治愈等）l y=0 未發(fā)?。幮浴⑸?、未治愈等）未發(fā)?。幮?、生存、未治愈等）l 將發(fā)病的概率記為將發(fā)病的概率記為P，它與自變量，它與自變量x x1 1, , x x2 2, ,x,xp p之間的之間的Logistic回歸模型為：回歸模型為：l可知，不發(fā)病的概率為：可知，不發(fā)病的概率為：l )exp(1)exp(110110ppppXXXXp )exp(111

3、110ppXXp 2022-6-2013經(jīng)數(shù)學變換得：定義：為Logistic變換，即： ppXXpp 110)1/(ln)1/(ln)(logpppitppXXpLogit 110)(2022-6-2014 4、回歸系數(shù)i的意義 流行病學的常用指標優(yōu)勢比（odds ratio,OR)或稱比值比，定義為：暴露人群發(fā)病優(yōu)勢與非暴露人群發(fā)病優(yōu)勢之比。 即Xi的優(yōu)勢比為：)1/()1/(0011PPPPORiiiPitPitORLn)0() 1()0(log)1 (log)(00ibi的標準差。為的標準差，為其中ySXSSSbbyiiyiii,/*影響越大。其因素對的估計值，此值越大，為Ybii)(

4、96. 1exp(iibSEb pii, 2 , 1 , 0, 0 0i20i0i計算統(tǒng)計量為：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) 開始方程中沒有變量，自變量由少到多一個一個引入回歸方程。按自變量對因變量的貢獻（P值的大?。┯尚〉酱笠来翁暨x，變量入選的條件是其P值小于規(guī)定進入方程的P界值Enter, 缺省值 P(0.05)。2022-6-20412022-6-20

10、422022-6-2043 調(diào)試法：P從大到小取值0.5，0.1，0.05， 一般實際用時， SLE，SLS應多次選取調(diào)整2022-6-20442022-6-20452022-6-20462022-6-20472022-6-20482022-6-20492022-6-20502022-6-2051成組資料的非條成組資料的非條件件LogisticLogistic回歸回歸配對資料的條件配對資料的條件LogisticLogistic回歸回歸兩分類反應變量的兩分類反應變量的LogisticLogistic回歸回歸多分類有序反應變量多分類有序反應變量LogisticLogistic回歸回歸多分類無序反應

11、變量多分類無序反應變量LogisticLogistic回歸回歸1:11:1配對資料的條件配對資料的條件LogisticLogistic回歸回歸1:m1:m配對資料的條件配對資料的條件LogisticLogistic回歸回歸n:mn:m配對資料的條件配對資料的條件LogisticLogistic回歸回歸LogisticLogistic回歸分析回歸分析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 單因素單因素Logis