ROC Curves for Continuous Data

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“k10031final” — 2009/4/6 — 12:30 — page 85 — #93

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4.4. ERRORS IN MEASUREMENTS 85

that give numerical estimates of θ

2

values in different applications).

Under these assumptions, the actual observations S



Pi

and S



Ni

have

variance σ

2

(1 + θ

2

) rather than σ

2

, and hence

AUC



=Φ



μ

P

−μ

N



[2σ

2

(1 + θ

2

)]



.

A confidence interval can thus be constructed in the usual way starting

from AUC



(e.g., by using the method of Owen et al., 1964), and this

interval has limits Φ(δ

L

), Φ(δ

U

)whereδ

L

,δ

U

are the lower and upper

confidence limits for μ

P

− μ

N

. Thus, to take measurement errors into

account, δ

L

and δ

U

must both be multiplied by

√

1+θ

2

, and the limits

for AUC altered according ...