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Table 1 Needed notation for the formulas of the different confidence intervals in Table 2

From: A modified Wald interval for the area under the ROC curve (AUC) in diagnostic case-control studies

Notation Explanation
logit(AUC)=log AUC 1 - AUC Logit transformation of the AUC
expit(·)= exp ( · ) exp ( · ) + 1 Back transformation of the Logittransformation
z = z 1-α/2 1-α/2 quantile of the normal distribution
s Empirical standard deviation of AUC
se Standard error of AUC by Bamber [8]
AUC =Φ ( X ¯ 1 - X ¯ 0 ) / s 1 1 + ( s 0 / s 1 ) 2 AUC for the binormal ROC curve (s i ,i = 0,1,as empirical estimator of σ i )
s Empirical standard deviation of AUC
t= z 1 - α / 2 2 n Factor for the Wilson interval
AUC ~ = AUC ̂ · n + 2 n + 4 Modified AUC (for the A-C interval)
k=round( AUC ̂ ·n) Estimated number of successes (for the C-Pinterval)
f(1 - α/2,d f1,d f2) 1-α/2 quantile of the F distribution with d f1 and d f2 degrees of freedom
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