*Reviewed and revised 27 August 2015*

**OVERVIEW**

- Receiver Operating Characteristic (ROC) curves plot sensitivity versus false positive rate for several values of a diagnostic test
- By convention, sensitivity (the proportion of true positive results) is shown on the
*y*axis, going from 0 to 1 (0–100%) and 1-specificity (the proportion of false positive results) is shown on the*x*axis, going from 0 to 1 (0–100%) - illustrates the trade-off between sensitivity and specificity in tests that produce results on a numerical scale, rather than as an absolute positive or negative result

**USES**

- determination of the cut-off point at which optimal sensitivity and specificity are achieved (decision thresholds)
- visual and quantitative (AUC) assessment of the diagnostic accuracy of a test (can be used for comparisons)
- Can be used to generate confidence intervals for sensitivity and specificity and likelihood ratios

**ADVANTAGES**

- Simple and graphical
- Represents accuracy over the entire range of the test
- Independent of prevalence
- Tests may be compared on the same scale
- Allows comparison of accuracy between several tests

**CUTOFF VALUES**

- these are chosen according to whether one wants to maximise the sensitivity (e.g. D-dimer) or specificity (e.g. CTPA) of the test
- e.g. Troponin T levels in the diagnosis of MI

— several different TNT plasma concentrations would have been chosen and compared against a gold standard in diagnosing MI (ECHO: regional wall abnormalities)

— the sensitivity and specificity of each chosen TNT level would have been plotted - the ideal cut off is one which picks up a lot of disease (high sensitivity) but has very few false positives (high specificity)
- one method assumes that the best cut-off point for balancing the sensitivity and specificity of a test is the point on the curve closest to the (0, 1) point, i.e. high up on the left-hand side of the graph resulting in a large AUC method
- an alternative method is to use the Youden index (
*J*), where*J*is defined as the maximum vertical distance between the ROC curve and the diagonal or chance line

**ACCURACY AND AREA UNDER THE CURVE (AUC)**

- the higher the AUC, the more accurate test
- AUC = 0.5 means the test is no better than chance alone (plotted as a straight diagonal line)
- AUC = 1.0 means the test has perfect accuracy

**LIKELIHOOD RATIOS**

- the tangent at a point on the ROC curve corresponds to the likelihood ratio for a single test value represented by that point
- the slope between the origin and a point on the curve corresponds to the positive likelihood ratio using the point as a criterion for positivity;
- the slope between two points on the curve corresponds to the likelihood ratio for a test result in a defined level bounded by the two points

#### References and Links

*LITFL*

*Journal articles*

- Akobeng AK. Understanding diagnostic tests 3: Receiver operating characteristic curves. Acta Paediatr. 2007 May;96(5):644-7. Epub 2007 Mar 21. PMID: 17376185. [Free Full Text]
- Choi BC. Slopes of a receiver operating characteristic curve and likelihood ratios for a diagnostic test. Am J Epidemiol. 1998 Dec 1;148(11):1127-32. PMID: 9850136 [Free Full Text]
- Fan J, Upadhye S, Worster A. Understanding receiver operating characteristic (ROC) curves. CJEM. 2006 Jan;8(1):19-20. PMID: 17175625. [Free Full Text]

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