診斷試驗與ROC曲線分析

ROC、基本概念四格表基本統(tǒng)計基本指標(biāo)ROC二、實(shí)例各項（變量）別效果：模型：比較兩預(yù)測模型：ROC(Time-dependentROC)、基本概念1四格表基本統(tǒng)計基本指標(biāo)驗 金標(biāo)準(zhǔn)結(jié)果合計患病（D+）未患?。―-）陽性 a（真陽性）b（假陽性）a+b陰性 c（假陰性）d（真陰性）c+d合計 a+cb+dN=a+b+c+d(prevalence):是指被檢測的全部對象中，檢測出來的患者的比例。即：檢(a+b)/(a+b+c+d)(prevalence):是指被檢測的全部對象中，真正患者的比例。即：實(shí)際患病(a+c)/也稱為前概率，而預(yù)測值屬于后概率。敏感性:敏感性就是指由金標(biāo)準(zhǔn)確有病組內(nèi)所檢測出陽性病例數(shù)的比率。即本實(shí)的真陽性率。其敏感性越高，漏a/(a+c)為無病組內(nèi)所檢測出陰性人數(shù)的比率即本實(shí)驗的真陰性率。特異性越高，發(fā)生誤d/(b+d)檢測出的真陽性和真陰性例數(shù)之和，占總檢測人數(shù)的比例，即稱本臨床實(shí)(a+d)/(a+b+c+d)陽性似然比（positivelikelihood: 陽性似然比是指臨床診斷檢測出的真陽性率與假陽性率之間的比值，即陽性似然比=敏感性/（1-特異性）=(a/(a+c))/(b/(b+d))?？捎靡悦枋鲈\斷試驗陽性時，患病與不患病的機(jī)會比。提示正確判斷為陽性的可能性是錯誤判斷為陽性的可能性的倍數(shù)。陽性似然比數(shù)值越大，提示能夠確診患有該病的可能性越大。它不受患病率影響，比起敏感度和特異度更為穩(wěn)定。陰性似然比（negativeliklihoodratio）:陰性似然比是指臨床實(shí)驗診斷檢測出的假陰性率與真陰性率之比值，此值越小，說明該診斷方法越好?？捎靡悦枋鲈\斷試驗陰性時，患病與不患病的機(jī)會比。陰性似然比提示錯誤判斷為陰性的可能性是正確判斷為陰性的可能性的倍數(shù)。陰性似然比數(shù)值越小，提示能夠否定患有該病的可能性越大。陰性似然比=（1-敏感性）/特異性=(c/(a+c))/(d/(b+d))（OR）者與非患者的能力越大。診斷比值比=(a/(a+c)/(b/(b+d))/(c/(a+c)/(d/(b+d)))=(ab)/(cd)(NND)（）（1-）斷所需檢測數(shù),(NND)=1/(a/(a+c)-b/(b+d))Yuden指數(shù): Yuden指數(shù) =敏感性+特異性-1= a/(a+c)+d/(b+d)-1陽性預(yù)測值(postivepredictivevalue):又稱預(yù)測陽性結(jié)果的正確率，是指待評價的診斷試驗結(jié)果判為陽性例數(shù)中，真正患某病的例數(shù)所占的比例。即：陽性預(yù)測值 =真陽性/（真陽性+假陽性）=/陰性預(yù)測值(negativepredictivevalue)又稱預(yù)測陰性結(jié)果的正確率，是指臨床診斷實(shí)驗檢測出的全部陰性例數(shù)中，真正沒有患本病的例數(shù)所占的比例。即：陰性預(yù)測值真陰性/（真陰性+假陰性）ROC曲線：()（）ROC（1-）（1-）]的[（1-）]系中，用線，即為有分的ROC曲線。ROC（AUC）ROC在0.5-1=1-=意“”被ROC近0.5弱；近1準(zhǔn)強(qiáng)般認(rèn)0.50-0.70較；0.70-0.90>0.90ROCY01X11ROCROCROCAUC0.5“1”橫為1-所以橫就1因此就ROC圖上角也就+取大果認(rèn)為重性a此可選取a*+1*取大可以根據(jù)不同研究目閾果目篩查本宜選誤率充許的范圍內(nèi)截此保證了漏率低若目為本宜選漏率充許范圍內(nèi)截此誤率低。CutpointselectionOneofthebest-knownmethodsisbasedonselectingthecutpointthatprovidesthesamevalueforthesensitivityandspecificity.Thispointisknownastheequivalenceorsymmetrypoint(Greiner,1995;Defreitasetal.,2004;Adlhochetal.,2011).Graphically,itcorrespondswiththeoperatingpointontheROCcurvethatintersectstheperpendiculartothepositivediagonalline,thatis,y=1?x,wherexisthefalsepositiverate.Thesymmetrypointcanalsobeseenasthepointthatmaximizessimultaneouslybothtypesofcorrectclassifications(RiddleandStratford,1999;Gallopetal.,2003),thatis,itcorrespondstotheprobabilityofcorrectlyclassifyinganysubject,whetheritishealthyordiseased(Jiménez-Valverde,2012,2014).Additionally,theincorporationofcostsforthemisclassificationratesintheestimationofoptimalcutpointsiscrucialforevaluatingnotonlythetestaccuracybutalsoitsclinicalefficacy,althoughthisaspectisnottakenintoaccountmostofthetimes.So,aninterestinggeneralizationoftheequivalenceorsymmetrypoint,cS,thattakesintoaccountthecostsassociatedtothefalsepositiveandfalsenegativemisclassifications,CFPandCFN,respectively,isthegeneralizedequivalencepointorgeneralizedsymmetrypoint,cGS,thatsatisfiesthefollowingequation:ρ(1?Sp(cGS))=(1?Se(cGS)),(1)whereρ=CFP/CFNistherelativeloss(cost)ofafalse-positivedecisionascomparedwithafalse-negativedecision(seeLópez-Ratónetal.,2016,formoredetails).Similarlytothesymmetrypoint,thiscostbasedgeneralizationisobtainedbyintersectingtheROCcurveandtheliney=1?ρx,wherexisthefalsepositiverate.Obviously,whenρ=1inEquation1,thegeneralizedsymmetrypointyieldsthetraditionalsymmetrypoint.Thereadercanseesomemedicalexamples,thathavetakenintoaccountthemisclassificationcostsintheirROCanalysis,inthereviewconductedbyCantoretal.(1999)wheretheCost/Benefit(C/B)ratioisdiscussed(C/B=1/ρ).Additionally,SubtilandRabilloud(2015)includesomecommonvaluesfortheC/Bratio(C/B=2,5,10,100).HighvaluesofC/Bratiomeanthatitisconsideredmoreharmfulnottotreatadiseasedindividualthantotreatahealthyone.1diagpre“打開現(xiàn)有”，“用的”，選diagpre）使用的diagpred.xlsoutcome0/）變量，另有四診斷試驗結(jié)果變量XXXXXAgGender各診斷，及其不同診斷模型的診斷效果?！皵?shù)據(jù)”主菜單，選“診斷試驗與預(yù)測方程”，再選“診斷試驗與ROC”。各診斷變量）別診斷效果輸入界面：此處選擇1X檢測）Bootstrapsmooth將做平滑曲線ROC輸出結(jié)果：OUTCOME項10似然比項10似然比陽預(yù)陰預(yù)測值陽似然比陰似然診斷比值 診斷需要目(LR) 特異度 值 準(zhǔn)確度 比比數(shù)X10.24390.61110.2632 0.5867 0.6272 0.5069-6.8972110280.6272031441.2373X412370.0949212201.05373130.58544881.75615X51847.90241280Inf3130Inf4060.000050660.00001 0 ROC(AUC)95%1 0 ROC(AUC)95%95%X2X3417241720.74000.63550.837311.0800 0.51390.70730.2050 0.80560.6341檢檢目abcdX2X311.08000.51390.70730.58411.45510.20500.80560.63410.74343.26130.5695 2.5548 4.5207 0.4531 0.7551 29.000035.000012.000037.00000.4542 7.1810 2.2743 0.6500 0.7945 26.000014.000015.000058.0000AUC(Bootstrapresamplingtimes=500)+。各點(diǎn)對應(yīng)ROC（.xls）里果解釋：X1兩分類型的檢測項目，輸出結(jié)果包括：四格表a/(a+c/(b/(b+d)10/(10+31)/28*(28+44=0.6272=(c/(a+c))/(d/(b+d))=31/10+31/44/18+44=1.2373，=10/10+31）=44/(28+44)=10/10+28）=44/31+44)。X2、X3的定量指標(biāo)取不同的界會得到不同的與輸出：ROCROC帶有95ROCROCAUC95可信區(qū)間最佳界+最大點(diǎn)及其對應(yīng)的度與度，X4輸出：各結(jié)果的如oX4=1(2/(2+12+1+8+18))/(37/(37+20+3+8+4))=0.0949;oX4=2=12/(2+12+1+8+18)/20/(37+20+3+8+4)=1.0537X5不是診斷試驗結(jié)果:X5=1X5=3outcome=1X5=4X5=5outcome=0X。由里計算每預(yù)測值預(yù)測值進(jìn)行ROC。下面是一及兩比較。輸入界面：2X。輸出結(jié)果：OUTCOME:OUTCOME=-5.50467-0.11127*(X1=1)+0.07033*X2+2.48858*X3+3.52591*(X4=2)+3.03121*(X4=3)+3.67565*(X4=4)+5.04438*(X4=5)95上95上0.9256特異度-0.37960.8194Model141072ROC(AUC)0.873295%0.79720.78050.8053似然比4.3227陰似然比0.2679診斷比值比16.1368診斷需要檢測數(shù)1.6669預(yù)測值0.7111陰預(yù)測值0.8676a32.0000b13.0000c9.0000d59.0000AUC(Bootstrapresamplingtimes=500+ROC.xlsROC、95，預(yù)測+及其ROC“Delong”見參考文獻(xiàn)h.,d.gdl.Pearson(1988)``Comparingtheareasundertwoormorecorrelatedreceiveroperatingcharacteristiccurves:anonparametricapproach''.Biometrics44,837--845.3。出結(jié)果：OUTCOME:l17)+2+3+)+3.03121*(X4=3)+3.67565*(X4=4)+5.04438*(X4=5)Model2:OUTCOME=-7.08705-0.17213*(X1=1)+0.07560*X2+2.13148*X3+4.09902*(X4=2)+3.92358*(X4=3)+4.12173*(X4=4)+5.43902*(X4=5)+0.03827*AGE-1.34844*(GENDER=1)兩ROC檢項目Model1Model2P(compare)141410 7272ROC(AUC) 0.87320.89970.1890950.80760.8386950.92680.9539最佳閾值