Endgames Statistical Question

How to read a receiver operating characteristic curve

BMJ 2015; 350 doi: https://doi.org/10.1136/bmj.h2464 (Published 08 May 2015) Cite this as: BMJ 2015;350:h2464
  1. Philip Sedgwick, reader in medical statistics and medical education
  1. 1Institute for Medical and Biomedical Education, St George’s, University of London, London, UK
  1. p.sedgwick{at}sgul.ac.uk

Researchers investigated the use of vital signs as a screening test to identify brain lesions in patients with impaired consciousness. The setting was an emergency department in Japan. In total, 529 consecutive patients presenting with impaired consciousness, as assessed by a score of less than 15 on the Glasgow coma scale, were studied. Patients were followed until discharge. The vital signs of systolic and diastolic blood pressure plus pulse rate were recorded on arrival. The diagnosis of a brain lesion was determined on the basis of brain imaging and neurological examination. In total, 312 patients (59%) were diagnosed with a brain lesion.1

The performance of each vital sign as a screening test for diagnosed brain lesions was evaluated separately. The measurement scale for each vital sign was categorised using equal sized strata. Each stratum for a vital sign was taken successively as the threshold between a “negative” and “positive” screening test result; all measurements with values greater than the categorised strata were considered a “positive” result and all others were considered “negative.” If the result was positive, the patient was deemed at “high risk” of a brain lesion; otherwise the patient was deemed at “low risk” of a brain lesion. For each stratum of a vital sign the sensitivity and specificity were derived and used to plot a receiver operating characteristic curve for the vital sign (figure). The area beneath the curve was 0.90 for systolic blood pressure, 0.82 for diastolic pressure, and 0.63 for pulse rate.

Receiver operating characteristic curves for each of the three vital signs as screening tests for diagnosed brain lesions. For each vital sign, selected cut-off points between a positive and negative screening test result are shown

Which of the following statements, if any, are true?

  • a) The value of (1 minus specificity) …

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