ROC Curves for Continuous Data

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“k10031final” — 2009/4/6 — 12:30 — page 122 — #130

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122 CHAPTER 6. COMPARING ROC CURVES

6.3.1, so that the confidence interval excludes zero whenever

W = z

2

y



ˆ

b

2

12

− 2F

2,n−4,α

V



ˆ

b

12



+2z

y



2F

2,n−4,α

C



ˆa

12

,

ˆ

b

12



− ˆa

12

ˆ

b

12



+



ˆa

2

12

− 2F

2,n−4,α

V (ˆa

12

)



= Az

2

y

+ Bz

y

+ C

is greater than zero. Since this is a quadratic expression in z

y

,wecan

easily solve W = 0 to find the values of z

y

for which W is zero, and

hence deduce those values for which W>0.

6.6 Further reading

The test of equality of two ROC curves under the binormal assumption

was developed by Metz and Kronman (1980) and Metz et al. (1984).

The nonparametric test for paired curves was described by Venkatra-

man and Begg (1996). McClish (1990) developed the test for ranges of

false positive values f