Logistic回歸分析(重點(diǎn)、難點(diǎn))

1、Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦教學(xué)目標(biāo)教學(xué)目標(biāo)幾個(gè)重要的流行病學(xué)概念幾個(gè)重要的流行病學(xué)概念Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦幾個(gè)重要的流行病學(xué)概念幾個(gè)重要的流行病學(xué)概念v隊(duì)列研究（隊(duì)列研究（cohort studycohort study）

2、v病例對(duì)照研究（病例對(duì)照研究（case-control studycase-control study） v危險(xiǎn)度（危險(xiǎn)度（riskrisk）v相對(duì)危險(xiǎn)度（相對(duì)危險(xiǎn)度（relative riskrelative risk， RRRR） v比數(shù)比或優(yōu)勢(shì)比（比數(shù)比或優(yōu)勢(shì)比（odds ratioodds ratio， OROR） Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦隊(duì)列研究隊(duì)列研究Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦病例對(duì)照研究病例對(duì)照研究Department

3、ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦危險(xiǎn)度危險(xiǎn)度 Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦相對(duì)危險(xiǎn)度相對(duì)危險(xiǎn)度 Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦相對(duì)危險(xiǎn)度相對(duì)危險(xiǎn)度 )/()/(dccbaaRRDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦比數(shù)比比數(shù)比Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦

4、張彥琦比數(shù)比比數(shù)比bcaddcddccbabbaaOR/)/()/(/)/()/(ORbcaddcbadccbaaRR/)/()/(bcadOR/Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦一個(gè)病例對(duì)照研究資料一個(gè)病例對(duì)照研究資料Department ofHealth Statistics 什么情況下采用什么情況下采用LogisticLogistic回歸回歸Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦什么情況下采用什么情況下采用LogisticLogistic回歸回歸De

5、partment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦用途：用途：研究某種疾病或現(xiàn)象發(fā)生和多個(gè)危險(xiǎn)因素（或研究某種疾病或現(xiàn)象發(fā)生和多個(gè)危險(xiǎn)因素（或保護(hù)因子）的數(shù)量關(guān)系。保護(hù)因子）的數(shù)量關(guān)系。 用用 檢驗(yàn)（或檢驗(yàn)（或u u檢驗(yàn)）的檢驗(yàn)）的局限性局限性： 1.1.只能研究只能研究1 1個(gè)危險(xiǎn)因素；個(gè)危險(xiǎn)因素； 2.2.只能得出定性結(jié)論。只能得出定性結(jié)論。2什么情況下采用什么情況下采用LogisticLogistic回歸回歸Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦什么情況下采用什么情況下

6、采用LogisticLogistic回歸回歸Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦實(shí)例實(shí)例Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦實(shí)例實(shí)例Department ofHealth Statistics實(shí)例實(shí)例Department ofHealth Statistics實(shí)例實(shí)例Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦)1ln()(PPPLogit1 0 Y發(fā)生應(yīng)變量未發(fā)生12,mXXX自變量),| 1

7、(21mXXXYPP1P0)(PLogitDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Z)(exp11PLogitPDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦00.51-4-3-2-10123410.5PZ:, 0, : 0, 0.5, 1PZ Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦), 2 , 1(mjjjXmmXXXPPPLogit2211)1ln()(jXDepartment ofHealth S

8、tatistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦1100/(1)/(1)jPPORPPDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦111000010010/(1)lnlnlogitlogit/(1)()()()jmmjttjtttjtjjPPORPPPPcXcXcc對(duì)對(duì)比比某某一一危危險(xiǎn)險(xiǎn)因因素素兩兩個(gè)個(gè)不不同同暴暴露露水水平平1cXj與與0cXj的的發(fā)發(fā)病病情情況況（假假定定其其它它因因素素的的水水平平相相同同） ，其其優(yōu)優(yōu)勢(shì)勢(shì)比比的的自自然然對(duì)對(duì)數(shù)數(shù)為為: 10 exp()jjORcc即Department of

9、Health Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦0, 1 exp, 0, 1 0, 1 jjjjjjOROROROR無作用危險(xiǎn)因保子護(hù)因子則有101 , 1, 0 jccX暴非若暴露露10 exp()jjORcc即Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦1100/(1) 1, /(1)PPPORRRPP當(dāng)則有由 于jOR值 與 模 型 中的 常 數(shù)項(xiàng)0無 關(guān) ，0在 危 險(xiǎn) 因素 分 析中 通 常視 其 為無 效 參數(shù) 。 Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研

10、室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦 11(1)iinYYiiiLPP 1lnln(1)ln(1)niiiiiLYPYP mbbbb,210 Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦 )(exp01ccbROjj若自變量jX只有暴露和非暴露兩個(gè)水平， 則優(yōu)勢(shì)比jOR的1可信區(qū)間估計(jì)公式為 )exp(2/jbjSubDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦2, 1jjjjbbbbuSS2 或 Wald 檢驗(yàn) 將各參數(shù)的估計(jì)值jb與 0 比較，而用它的標(biāo)準(zhǔn)誤jbS作為參照

11、，檢驗(yàn)統(tǒng)計(jì)量為 2Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦vData Weight casesDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦vAnalyze

12、 Regression Binary LogisticDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Dependent Variable EncodingDependent Variable Encoding01Original Value.001.00Internal ValueVariables in the EquationVariables in the Equation.546.15811.9891.0011.727-.149.1091.8511.174.862吸煙史ConstantStep1aBS.E.WalddfSig.

13、Exp(B)Variable(s) entered on step 1: 吸煙史.a. Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics實(shí)例分析實(shí)例分析Department ofHealth StatisticsDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦實(shí)例分析實(shí)例分析Department ofHealth S

14、tatistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦條件條件LogisticLogistic回歸的原理回歸的原理Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦表表16-5 1: M 條件條件logistic回歸數(shù)據(jù)的格式回歸數(shù)據(jù)的格式 * t = 0 為病例，其他為對(duì)照 Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦條件條件LogisticLogistic回歸模型回歸模型 0112211 exp (.)iimmPXXX 1,2, in與非條件 logistic 回

15、歸模型不同之處在常數(shù)項(xiàng)上，不同匹配組的i 0可以各不相同，但內(nèi)在假定了每個(gè)危險(xiǎn)因素的致病能力在不同匹配組中相同。 Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦實(shí)例分析實(shí)例分析因素因素變量名變量名分級(jí)說明分級(jí)說明不良飲食習(xí)慣不良飲食習(xí)慣X X1 10 0、1 1、2 2、3 3、4 4表示程度（表示程度（0 0表示無，表示無，4 4表示最多）表示最多）喜吃鹵食和鹽喜吃鹵食和鹽漬食物漬食物X X2 20 0、1 1、2 2、3 3、4 4表示程度（表示程度（0 0表示不吃，表示不吃，4 4表示非常表示非常喜歡吃）喜歡吃）精神狀況精神狀況

16、X X3 30 0表示差，表示差，1 1表示好表示好Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦v數(shù)據(jù)準(zhǔn)備成4列：X1、X2、X3，配對(duì)號(hào)及疾病發(fā)生情況Y（1：病例，0：對(duì)照）。實(shí)例分析實(shí)例分析Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦v 模型擬合結(jié)果Variables in the EquationVariables in the Equation.991.30710.4081.0012.693.901.3317.4031.0072.462.505.534.8941.

17、3441.657X1X2X3BSEWalddfSig.Exp(B)v 顯然，存在不顯著的變量，可以進(jìn)行逐步回歸分析。實(shí)例分析實(shí)例分析Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦V Va ar ri ia ab bl le es s i in n t th he e E Eq qu ua at ti io on n.991.30710.4081.0012.693.901.3317.4031.0072.462.505.534.8941.3441.657.945.29410.3551.0012.572.882.3247.4041.0072

18、.416X1X2X3Step1X1X2Step2BSEWalddfSig.Exp(B)實(shí)例分析實(shí)例分析第三節(jié)第三節(jié) LogisticLogistic回歸的應(yīng)用回歸的應(yīng)用 及注意事項(xiàng)及注意事項(xiàng)Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦)ln(exp110XPDepartment ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦張彥琦Department ofHealth Statistics衛(wèi)生統(tǒng)計(jì)學(xué)教研室衛(wèi)生統(tǒng)計(jì)學(xué)教研室 張彥琦