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Table 2 Formulas for the different confidence intervals from section Methods

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

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)
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