Question 7

Explain the following statistical terms:

a)    Sensitivity.    (20% marks)

b)    Specificity.    (20% marks)

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

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College answer

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


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


  • 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.


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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.

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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.