# Table 2 Formulas for the different confidence intervals from section Methods

Confidence interval (denotation) Range-preserving Result for AUC = 1 Limits
Logit-transformation-based (LT) Yes No $expit logit ( AUC ̂ ) ± z · s / AUC ̂ ( 1 - AUC ̂ ) n$
Mann-Whitney (MW) No No $AUC ̂ ±z·s/ n$
Bamber (Bamber) No Yes $AUC ̂ ±z·se$
Binormal (Binormal) No No $AU C ∗ ±z· s ∗ / n$
Wilson (Wilson) Yes Yes $AUC ̂ + 0.5 t / 1 + t ± AUC ̂ ( 1 - AUC ̂ ) t + 0.25 t 2 / 1 + t$
... with continuity correction (Wilson-cc) Yes Yes lower: $2 n AUC ̂ + z 2 - 1 - z z 2 - 2 - 1 / n + 4 AUC ̂ ( n ( 1 - AUC ̂ ) + 1 ) /$ (2(n + z 2))
upper: $2 n AUC ̂ + z 2 + 1 + z z 2 + 2 - 1 / n + 4 AUC ̂ ( n ( 1 - AUC ̂ ) + 1 ) /$ (2(n + z 2))
Agresti-Coull (A-C) No No $AUC ~ ±z AUC ~ ( 1 - AUC ~ ) n + 4$
Clopper-Pearson (C-P) Yes No lower: (k · f(α/2,2k,2(n - k + 1)))/ (n - k + 1 + k · f(α/2,2k,2(n - k + 1)))
upper: ((k + 1)f(1 - α/2,2(k + 1),2(n - k)))/ (n - k + (k + 1)f(1 - α/2,2(k + 1),2(n - k)))
Modified Wald (Wald) No No $AUC ̂ ±z AUC ̂ ( 1 - AUC ̂ ) 0.75 n - 1$
... with continuity correction(Wald-cc) No Yes $AUC ̂ ±z AUC ̂ ( 1 - AUC ̂ ) 0.75 n - 1 +1/(2n)$