医学诊断试验评价的ROC分析-重复测量诊断数据的ROC曲线

ROC3ROCROCROC,logistic,GEElogistic,ROCROCROClogisticTheROCAnalysisforEvaluationofDiagnosticAccuacyinRepeatedMeasurementsLiKang,WeiWei,WangBiny2ou,etal1,HarbinMedicalUniversity,Harbin150001AbstractObjectiveToexploretheROCanalysismethodsforrepeatedordinalcategoricaldataindiagnostictest.MethodsROCmodelsaregivenbasedonordinalregressionmodels,andcumulativelogisticmodelsareusedasthelinkfunction.Theparameterscanbeestimatedbyusinggeneralizedestimatingequations(GEE)method.ResultsROCcurveequation,areasundertheROCcurveandstandarderrorareestimatedbythecumulativelogisticmodels.ConclusionThemethodsinthispapercananalyzeandprocesseffectivelytherepeatedmeasuresdataintheimagediagnostictest.KeywordsDiagnostictestROCcurveRepeatedmeasurementLogisticmodels,,,,,,ROC,,,,,ROCROC,logisticX1ROC11ROCiD(Y)X1X2XpY1Y2Ym1d1x11x12x1py11y12y1m2d2x21x22x2py21y22y2m3d3x31x32x3py31y32y3mNdNxN1xN2xNpyN1yN2yNm,D,-11,D=-1,D=1;Yk(k=1,2,,m)g,P(Yc|D,X)=F(c+D+X+XD)(1)c=1,2,,g-1,c;,,;X=(X1,X2,,Xp)p,=(1,2,,p)pTP(true-negative)FP(false-positive),(TP)(1-FP),TPc=F(c++X+X)FPc=F(c-+X-X)(2)F(),(2)ROC,32001381X:1500013(30040039)(2)c,ROCTP=«(FP;+X)(3),ROCc2ROCGEEROC,GEE(generalizedestimatingequation),,Yc=1,2,,g,P(Yc|D,X)Y=cc=P(Yc|D,X)-P(Yc+1|D,X)m,Y01g-1,igri1,rii(rim)Yi=(Yi11,Yi21,,Yi(g-1)1,Yi12,Yi22,,Yi(g-1)2,,Yi1r,Yi2r,,Yi(g-1)ri)tYit=h,Yiht=1,Yict=0(ch)i=[i11,i21,,i(g-1)1,i12,i22,,i(g-1)2,,i1r,i2r,,i(g-1)ri]ict=ict(),Nc=1ict=1;,ROC=(,,),u()=Ni=1DiV-1i[Yi-i]=0(4)Di=Di()=d[i()]d(5)ViYi(workingcovariancema2trix),Vivar(Yi),Vivar(Yi),,Vi=Vi(),Ri=i11i12i1rii21i22i2rii31i32i3riwwiri1iri2iriri(6)ist(g-1)(g-1),itt=A-1/2itVitA-1/2it(7)Vit=Vit()=Diag(it)-itit,Diag(it)itA-1/2it=Diag[{i1t(1-i1t)}-1/2,{i2t(1-i2t)}-1/2,,{i(g-1)t(1-i(g-1)t)}-1/2]ist(st),,,10ri(g-1)ri(g-1),Vi=A1/2iRiA1/2i(8)A1/2i=Diag[{i11(1-i11)}1/2,{i21(1-i21)}1/2,,{i(g-1)1(1-i(g-1)1)}1/2,,{i1ri(1-i1ri)}1/2,{i2ri(1-i2ri)}1/2,,{i(g-1)ri(1-i(g-1)ri)}1/2]^Fisher(Fisher-scoringalgorthm),q+1^(q+1)=^(q)+Ni=1Di(^(q))[Vi(^(q))]-1Di(^(q))-1Ni=1Di(^(q))[Vi(^(q))]-1[Yi-i(^(q))](9),^-0,V=Ni=1DiV-1iDi-1Ni=1DiV-1ivar(Yi)V-1iDi-1Ni=1DiV-1iDi-1(10)var(Yi)=(Yi-^i)(Yi-^i),(0)ROC420013813ROClogisticROC,F()F(),logistic,,ROC(11)ROC,cROC,(12)TPc=11+exp[-(c++X+X)]FPc=11+exp[-(c-+X-X)]c=1,2,,g(11)TP=11+(FP-1-1)exp[-2(+X)](12)ROCA=10TPd(FP)=1-11-exp[2(+X)]-2exp[2(+X)]{1-exp[2(+X)]}2(+X)=1-11-OR-ORlnOR(1-OR)2(13)OR=exp[2(+X)](OR1),+X0,A=0.5;+X,A=1^^,(13)A^A^Avar(^A)=9A9^,^,X2var(^)+9A9^,^,X2var(^)+29A9^,^,X9A9^,^,Xcov(^,^)(14),(=0)var(^A)=9A9^2var(^)9A9OR=lnOR(1+OR)-2(OR-1)(OR-1)39A9=9A9OR9OR9=lnOR(1+OR)-2(OR-1)(OR-1)32ORSE(^A)=var(^A)=lnO^R(1+O^R)-2(O^R-1)(O^R-1)32O^RSE(^)(15)O^R=exp(2^),SE(^)^GEE42CT,32,CT,12CT(g=4,m=2),,TPc=11+exp[-(c+)]FPc=11+exp[-(c-)]32CT32(D)CT11442-1413-111414451346-1227-11181449124101441113412-11113-12114-14422-11123-1212413425-1112614427133291133013431-144321443CTROC(GEE)^SE(^)^ASE(^A)95%CICT1.58890.35460.8990.0470.8080.99152001381ROCTP=1(1-e-2^)+e-2^FP-1=1019583+010417FP-11CTROC5511ROC,ROC,,512ROCGEE,,,,:R,,,,GEE,R,,(),,,513logisticROC^ASE(^A),,YY3,,1..,1993,10(4):352,.ROC.,1996,13(3):93MetzCE1ROCmethodologyinradiologicalimaging,Invest.Radi2ol.,1986,21(9):7204LiangKYandZegerSL.Longitudinaldataanalysisusinggeneralizedlinearmodels.Biometrika.1986,73:135PrenticeRL.Correlatedbinaryregressionwithcovariatesspecifictoeachbinaryobservation.Biometrics.1988,44:10336LipisitzSR,etal.Generalizedestimatingequationsforcorrelatedbi2narydata:Usingtheoddsratioasmeasureofassociation.Biometri2ka.1991,78:1537LiprisitzSR,KimK,andZhaoL.Analysisofrepeatedcategoricaldatausinggeneralizedestimatingequations.Stat.Med.,1994,13:1149(:2001202214)X,,,,,,,1997199911997199948571,SPSS122.1(1)1(%)199713890291211019981652152131151999181606703169485711482310562001381X:272111