# Area under the curve (AUC)

The area under (a ROC) curve is a measure of the accuracy of a quantitative diagnostic test.

A point estimate of the AUC of the empirical ROC curve is the Mann-Whitney U estimator (DeLong et. al., 1988). The confidence interval for AUC indicates the uncertainty of the estimate and uses the Wald Z large sample normal approximation *(DeLong et al., 1998)*. A test with no better accuracy than chance has an AUC of 0.5, a test with perfect accuracy has an AUC of 1.

The interpretation of the AUC is:

- The average value of sensitivity for all possible values of specificity (Zhou, Obuchowski, McClish, 2001).
- The average value of specificity for all possible values of sensitivity (Zhou, Obuchowski, McClish, 2001).
- The probability that a randomly selected subject with the condition has a test result indicating greater suspicion than that of a randomly chosen subject without the condition (Hanley & McNeil, 1982).

AUC can be misleading as it gives equal weight to the full range of sensitivity and specificity values even though a limited range, or specific threshold, may be of practical interest.

**Related tasks**

**Related information**

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Measures of diagnostic accuracy
- Estimating sensitivity and specificity of a diagnostic test
- Comparing the sensitivity and specificity two diagnostic tests
- ROC plot
- Plotting a single ROC curve
- Comparing two or more ROC curves
- Area under the curve (AUC)
- Testing the area under the curve
- Difference between the areas under two curves
- Testing the difference between the areas under two curves
- Decision thresholds
- Decision plot
- Finding the optimal decision threshold
- Predicting the decision threshold
- Study design
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023