# Question 7

Explain the following statistical terms:

a)    Sensitivity.    (20% marks)

b)    Specificity.    (20% marks)

c)    Receiver Operating Characteristic (ROC) Curve.    (60% marks)

Not available.

## Discussion

a)

• Sensitivity = true positives / (true positives + false negatives)
• This is the proportion of disease which was correctly identified

b)

• Specificity = true negatives / (true negatives + false positives)
• This is the proportion of healthy patients in who disease was correctly excluded

c)

• Receiver Operating Characteristic (ROC) curve is a plot of sensitivity vs. false positive rate, for a number of test results.
• Sensitivity is on the y-axis, from 0% to 100%
• The ROC curve graphically represents the compromise between sensitivity and specificity in tests which produce results on a numerical scale, rather than binary (positive vs. negative results)
• The ROC curve determines the cut off point at which the sensitivity and specificity are optimal.
• AUC is the Area Under the ROC curve.
• The higher the AUC, the more accurate the test
• An AUC of 1.0 means the test is 100% accurate
• An AUC of 0.5 (50%) means the ROC curve is a a straight diagonal line, which represents the "ideal bad test", one which is only ever accurate by pure chance.
• When comparing two tests, the more accurate test is the one with an ROC curve further to the top left corner of the graph, with a higher AUC.
• The best cutoff point for a test (which separates positive from negative values) is the point on the ROC curve which is closest to the top left corner of the graph.

## References

Hanley, James A., and Barbara J. McNeil. "The meaning and use of the area under a receiver operating characteristic (ROC) curve." Radiology 143.1 (1982): 29-36.

Zweig, Mark H., and Gregory Campbell. "Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine." Clinical chemistry 39.4 (1993): 561-577.

Cook, Nancy R. "Use and misuse of the receiver operating characteristic curve in risk prediction." Circulation 115.7 (2007): 928-935.

Jones, Catherine M., and Thanos Athanasiou. "Summary receiver operating characteristic curve analysis techniques in the evaluation of diagnostic tests."The Annals of thoracic surgery 79.1 (2005): 16-20.

Metz, Charles E. "ROC methodology in radiologic imaging." Investigative radiology 21.9 (1986): 720-733.

Søreide, Kjetil. "Receiver-operating characteristic curve analysis in diagnostic, prognostic and predictive biomarker research.Journal of clinical pathology 62.1 (2009): 1-5.

Lusted, Lee B. "ROC recollected." Medical Decision Making (1984): 131-135.