Endgames Statistical Question

Receiver operating characteristic curves

BMJ 2013; 346 doi: http://dx.doi.org/10.1136/bmj.f2493 (Published 19 April 2013) Cite this as: BMJ 2013;346:f2493
  1. Philip Sedgwick, reader in medical statistics and medical education
  1. 1Centre for Medical and Healthcare Education, St George’s, University of London, Tooting, London, UK
  1. p.sedgwick{at}sgul.ac.uk

Researchers evaluated the performance of a cognitive test called “test your memory” as a screening test for Alzheimer’s disease. The screening test is designed to use minimal operator time and to be suitable for non-specialist use. It is self administered under medical supervision. The test has a minimum score of zero and a maximum score of 50; lower scores indicate greater cognitive impairment.1

The study was based in hospital outpatient departments. Participants included 94 patients diagnosed as having Alzheimer’s disease. For each patient, three age matched healthy controls without Alzheimer’s disease (n=282) were recruited from accompanying relatives. All patients and controls completed the screening test.

The optimal test score for discriminating between patients with Alzheimer’s disease and controls was investigated. Each score from 50 down to zero was taken successively as the cut-off point between a “negative” and “positive” screening test result; all scores less than or equal to the cut-off score were considered positive and others were considered negative. For each cut-off score the sensitivity and specificity of the screening test was calculated, and these values were used to derive a receiver operating characteristic curve (figure). The area under the receiver operating characteristic curve was 0.95.

Receiver operating characteristic curve for “test your memory” scores differentiating patients with Alzheimer’s disease (n=94) and age matched controls (n=282). Numbers on curve refer to a range of selected cut-off scores between “negative” and “positive” results

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

  • a) For successive cut-off scores, as the sensitivity of the screening test decreases in value the …

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