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Receiver operating characteristic curve

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ROC curves for the distinction between radicular and axial LBP based on StEP. The difference in area under the solid curve compared to the dashed curve is the value of adding the straight leg raise test to the StEP test.

In statistics and diagnostic tests, the receiver operating characteristic curve, also called ROC curve, is a "graphic means for assessing the ability of a screening test to discriminate between healthy and diseased persons; may also be used in other studies, e.g., distinguishing stimuli responses as to a faint stimuli or nonstimuli."[1]

Area under the ROC curve

The area under the ROC curve, called the AUC, AROC, c statistic, or c-index may measure discriminatory ability of a test of model. The c-index varies from 0 to 1 and a result of 0.5 indicates that the diagnostic test does not add to guessing.[2] If the diagnostic test gives ratings that are continuous, the AUC is the same as the Wilcoxon test of ranks (also called the Mann–Whitney U test).[2] Accordingly, the AROC is the probability that the diagnostic test will correctly order the likelihood of disease among two patients randomly selected from a test population.

Variations have been proposed.[3][4]


  1. Anonymous (2020), Receiver operating characteristic curve (English). Medical Subject Headings. U.S. National Library of Medicine.
  2. 2.0 2.1 Hanley JA, McNeil BJ (April 1982). "The meaning and use of the area under a receiver operating characteristic (ROC) curve". Radiology 143 (1): 29–36. PMID 7063747[e]
  3. Walter SD (July 2005). "The partial area under the summary ROC curve". Stat Med 24 (13): 2025–40. DOI:10.1002/sim.2103. PMID 15900606. Research Blogging.
  4. Bangdiwala SI, Haedo AS, Natal ML, Villaveces A (September 2008). "The agreement chart as an alternative to the receiver-operating characteristic curve for diagnostic tests". J Clin Epidemiol 61 (9): 866–74. DOI:10.1016/j.jclinepi.2008.04.002. PMID 18687288. Research Blogging.