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

$\text{logit}(\mathit{\text{AUC}})=\text{log}\left(\frac{\mathit{\text{AUC}}}{1-\mathit{\text{AUC}}}\right)$

Logit transformation of the AUC

$\text{expit}(·)=\frac{\mathit{\text{exp}}(·)}{\mathit{\text{exp}}(·)+1}$

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]

${\mathit{\text{AUC}}}^{\ast }=\mathrm{\Phi }\left(\frac{({\overline{X}}_1-{\overline{X}}_0)/s_1}{\sqrt{1+{(s_0/s_1)}^2}}\right)$

AUC for the binormal ROC curve (s _i ,i = 0,1,as empirical estimator of σ _i )

s ^∗

Empirical standard deviation of AUC ^∗

$t=\frac{z_{1-\alpha /2}^2}{n}$

Factor for the Wilson interval

$\widetilde{\mathit{\text{AUC}}}=\frac{\widehat{\mathit{\text{AUC}}}·n+2}{n+4}$

Modified AUC (for the A-C interval)

$k=\text{round}(\widehat{\mathit{\text{AUC}}}·n)$

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