- We can determine theoptimalcut point, which is nearest to the upper left
cornerð 0 ; 1 Þ. This corner corresponds to 100% sensitivity and 100%
specificity. - We can estimate theseparation powerof the separatorX, which is esti-
mated by the area under the ROC curve estimated above. Given two
available separators, the better separator is the one with the higher sepa-
ration power.
Given two independent samples,fx 1 igim¼ 1 andfx 2 jgjn¼ 1 , frommcontrols and
ncases, respectively, theestimated ROC curve, often called thenonparametric
ROC curve, is defined as therandom walkfrom the left bottom cornerð 0 ; 0 Þto
the right top cornerð 1 ; 1 Þwhose next step is 1=mto the right or 1=nup,
according to whether the next observation in the ordered combined sample is a
controlðx 1 Þor a caseðx 2 Þ. For example, suppose that we have the samples
x 21 <x 22 <x 11 <x 23 <x 12 ðn¼ 3 ;m¼ 2 ÞThen the nonparametric ROC curve is as shown in Figure 9.3.
9.2.6 ROC Curve and Logistic Regression
In the usual (also referred to as Gaussian) regression analyses of Chapter 8,R^2
gives the proportional reduction in variation in comparing the conditional
variation of the response to the marginal variation. It describes the strength of
Figure 9.2 Receiving operating characteristic (ROC) curve.MULTIPLE REGRESSION ANALYSIS 337