研究生醫(yī)學(xué)統(tǒng)計(jì)中l(wèi)ogistic回歸.ppt

研究生醫(yī)學(xué)統(tǒng)計(jì)學(xué),Logistic regression,Logistic回歸,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,第一節(jié).非條件logistic回歸 第二節(jié).條件logistic回歸 第三節(jié). 應(yīng)用及其注意事項(xiàng),流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,醫(yī)學(xué)研究中常碰到應(yīng)變量的可能取值僅有兩個(gè)（即二分類變量），如發(fā)病與未發(fā)病、陽性與陰性、死亡與生存、治愈與未治愈、暴露與未暴露等，顯然這類資料不滿足多元（重）回歸的條件,什么情況下采用Logistic回歸,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,Brown(1980)在術(shù)前檢查了53例前列腺癌患者，擬用年齡(AGE)、酸性磷酸酯酶(ACID)兩個(gè)連續(xù)型的變量，X射線(X_RAY)、術(shù)前探針活檢病理分級(jí)(GRADE)、直腸指檢腫瘤的大小與位置(STAGE)三個(gè)分類變量與手術(shù)探查結(jié)果變量NODES（1、0分別表示癌癥淋巴結(jié)轉(zhuǎn)移與未轉(zhuǎn)移 ）建立淋巴結(jié)轉(zhuǎn)移的預(yù)報(bào)模型。,實(shí)例,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,（一）53例接受手術(shù)的前列腺癌患者情況,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,（二）26例冠心病病人和28例對(duì)照進(jìn)行病例對(duì)照研究,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,26例冠心病病人和28例對(duì)照者進(jìn)行病例對(duì)照研究,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,一、logistic回歸模型,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,概率預(yù)報(bào)模型,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,二、模型的參數(shù)估計(jì),Logistic回歸參數(shù)的估計(jì)通常采用最大似然法(maximum likelihood，ML)。最大似然法的基本思想是先建立似然函數(shù)與對(duì)數(shù)似然函數(shù)，再通過使對(duì)數(shù)似然函數(shù)最大求解相應(yīng)的參數(shù)值，所得到的估計(jì)值稱為參數(shù)的最大似然估計(jì)值。,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,參數(shù)估計(jì)的公式,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,三、回歸參數(shù)的假設(shè)檢驗(yàn),流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,優(yōu)勢比及其可信區(qū)間,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,標(biāo)準(zhǔn)化回歸參數(shù),用于評(píng)價(jià)各自變量對(duì)模型的貢獻(xiàn)大小,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,SAS程序,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,預(yù)報(bào)模型,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,預(yù)報(bào)模型,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,四、回歸參數(shù)的意義,當(dāng)只有一個(gè)自變量時(shí)，以相應(yīng)的預(yù)報(bào)概率 為縱軸，自變量 為橫軸，可繪制出一條S形曲線?；貧w參數(shù)的正負(fù)符號(hào)與絕對(duì)值大小，分別決定了S形曲線的方向與形狀,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,優(yōu)勢比改變exp(bj)個(gè)單位,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,五、整個(gè)回歸模型的假設(shè)檢驗(yàn),流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,似然比檢驗(yàn)（likelihood ratio test）,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,ROC曲線模型評(píng)價(jià),流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,ROC曲線模型評(píng)價(jià),圖16-2 Logistic回歸預(yù)報(bào)能力的ROC曲線,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,六、logistic逐步回歸（變量篩選）,MODEL語句加入選項(xiàng)“ SELECTION=STEPWISE SLE=0.10 SLS=0.10;” 常采用似然比檢驗(yàn)： 決定自變量是否引入或剔除。,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,模型中有X5、X6、X8， 看是否引入X1,模型含X5、X6、X8的模型的負(fù)二倍 對(duì)數(shù)似然為： 50.402 模型含X1、X5、X6、X8的模型的負(fù)二倍 對(duì)數(shù)似然為： 46.224,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,第二節(jié).條件logistic回歸,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,條件似然函數(shù),流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,1:3配對(duì)的例子,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,1:2配對(duì)的例子,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,表16-7條件logistic回歸的SAS程序,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,結(jié)果,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,第三節(jié) 應(yīng)用及其注意事項(xiàng),應(yīng)變量為（二項(xiàng)）分類的資料 （預(yù)測、判別、危險(xiǎn)因素分析等等）,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,注意事項(xiàng),分類自變量的啞變量編碼 為了便于解釋，對(duì)二項(xiàng)分類變量一般按0、1編碼，一般以0表示陰性或較輕情況，而1表示陽性或較嚴(yán)重情況。如果對(duì)二項(xiàng)分類變量按+1與-1編碼，那么所得的 ，容易造成錯(cuò)誤的解釋。,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,西、中西、中三種療法啞變量化,原資料,啞變量化,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,注意事項(xiàng),2.自變量的篩選 不同的篩選方法有時(shí)會(huì)產(chǎn)生不同的模型。實(shí)際工作中可同時(shí)采用這些方法，然后根據(jù)專業(yè)的可解釋性、模型的節(jié)約性和資料采集的方便性等，決定采用何種方法的計(jì)算結(jié)果。,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,注意事項(xiàng),3.交互作用 交互作用的分析十分復(fù)雜，應(yīng)根據(jù)臨床意義與實(shí)際情況酌情使用。,流行病與衛(wèi)生統(tǒng)計(jì)學(xué)系,注意事項(xiàng),4. 多分類logistic回歸 心理疾病分為精神分裂癥、抑郁癥、神經(jīng)官能癥等（名義變量nominal variables)；療效評(píng)價(jià)分為無效、好轉(zhuǎn)、顯效、痊愈(有序變量ordinal variables)。 參見第17章,應(yīng)變量,SPSS軟件計(jì)算,Analyze Regression Binary Logistic Dependent: y Covariates: x1 x8 Method: Forward Ward Save Predicted Values Probabilities Group membership Option CI for exp 95% Probability for Stepwise Entry: 0.1 Removal 0.15,DATA samp16_1; INPUT x_ray grade stage age acid nodes; CARDS; ; PROC LOGISTIC DESCENDING; MODEL nodes=x_ray grade stage age acid/RISKLIMITS; OUTPUT OUT=pred PROB=pred; PROC PRINT DATA=pred; RUN;,The SAS System 22:07 Monday, November 29, 2005 1 The LOGISTIC Procedure Model Information Data Set WORK.SAMP16_1 Response Variable nodes Number of Response Levels 2 Number of Observations 53 Model binary logit Optimization Technique Fishers scoring Response Profile Ordered Total Value nodes Frequency 1 1 20 2 0 33 Probability modeled is nodes=1.,Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 72.252 60.126 SC 74.222 71.948 -2 Log L 70.252 48.126 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr ChiSq Likelihood Ratio 22.1264 5 0.0005 Score 19.4514 5 0.0016 Wald 13.1406 5 0.0221,The SAS System 22:07 Monday, November 29, 2005 2 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr ChiSq Intercept 1 0.0618 3.4599 0.0003 0.9857 x_ray 1 2.0453 0.8072 6.4208 0.0113 grade 1 0.7614 0.7708 0.9759 0.3232 stage 1 1.5641 0.7740 4.0835 0.0433 age 1 -0.0693 0.0579 1.4320 0.2314 acid 1 0.0243 0.0132 3.4230 0.0643,The SAS System 22:07 Monday, November 29, 2005 2 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr ChiSq Intercept 1 0.0618 3.4599 0.0003 0.9857 x_ray 1 2.0453 0.8072 6.4208 0.0113 grade 1 0.7614 0.7708 0.9759 0.3232 stage 1 1.5641 0.7740 4.0835 0.0433 age 1 -0.0693 0.0579 1.4320 0.2314 acid 1 0.0243 0.0132 3.4230 0.0643 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits x_ray 7.732 1.589 37.614 grade 2.141 0.473 9.700 stage 4.778 1.048 21.783 age 0.933 0.833 1.045 acid 1.025 0.999 1.051,Association of Predicted Probabilities and Observed Responses Percent Concordant 84.5 Somers D 0.694 Percent Discordant 15.2 Gamma 0.696 Percent Tied 0.3 Tau-a 0.332 Pairs 660 c 0.847 Wald Confidence Interval for Adjusted Odds Ratios Effect Unit Estimate 95% Confidence Limits x_ray 1.0000 7.732 1.589 37.614 grade 1.0000 2.141 0.473 9.700 stage 1.0000 4.778 1.048 21.783 age 1.0000 0.933 0.833 1.045 acid 1.0000 1.025 0.999 1.051,Obs no x_ray grade stage age acid nodes _LEVEL_ pr