ROC AUC Calculator

This calculator computes the confidence interval and statistical significance for an Area Under the ROC Curve (AUC). The AUC measures a diagnostic test's ability to discriminate between positive and negative cases.

Enter AUC and sample sizes
AUC Value Area under the ROC curve (0 to 1)
Number of Positive Cases Subjects with the condition
Number of Negative Cases Subjects without the condition

Formula

Hanley-McNeil Standard Error

\( SE = \sqrt{\frac{AUC(1-AUC) + (n_1-1)(Q_1 - AUC^2) + (n_0-1)(Q_2 - AUC^2)}{n_1 \cdot n_0}} \)

where \( Q_1 = \frac{AUC}{2-AUC} \) and \( Q_2 = \frac{2 \cdot AUC^2}{1+AUC} \)

95% Confidence Interval

\( AUC \pm 1.96 \times SE \)

Interpreting AUC Values

The AUC represents the probability that a randomly chosen positive case will have a higher test value than a randomly chosen negative case:

  • AUC = 0.5 — No discrimination (equivalent to random guessing)
  • 0.6 ≤ AUC < 0.7 — Poor discrimination
  • 0.7 ≤ AUC < 0.8 — Fair discrimination
  • 0.8 ≤ AUC < 0.9 — Good discrimination
  • AUC ≥ 0.9 — Excellent discrimination

Understanding ROC Curves

A Receiver Operating Characteristic (ROC) curve plots sensitivity (true positive rate) against 1 - specificity (false positive rate) across all possible thresholds.

The AUC summarizes the overall diagnostic accuracy across all thresholds. A perfect test has AUC = 1.0, while a useless test has AUC = 0.5.

Assumptions & Limitations

  • Uses the Hanley-McNeil approximation for standard error
  • Assumes independent observations
  • May be inaccurate for very small sample sizes
  • AUC does not indicate the optimal threshold for clinical use
  • Does not account for the clinical consequences of false positives vs. false negatives

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