A simple decision analytic solution to the comparison of two binary diagnostic tests Academic Article uri icon


MeSH Major

  • Decision Making
  • Diagnostic Tests, Routine


  • One of the most basic biostatistical problems is the comparison of two binary diagnostic tests. Commonly, one test will have greater sensitivity, and the other greater specificity. In this case, the choice of the optimal test generally requires a qualitative judgment as to whether gains in sensitivity are offset by losses in specificity. Here, we propose a simple decision analytic solution in which sensitivity and specificity are weighted by an intuitive parameter, the threshold probability of disease at which a patient will opt for treatment. This gives a net benefit that can be used to determine which of two diagnostic tests will give better clinical results at a given threshold probability and whether either is superior to the strategy of assuming that all or no patients have disease. We derive a simple formula for the relative diagnostic value, which is the difference in sensitivities of two tests divided by the difference in the specificities. We show that multiplying relative diagnostic value by the odds at the prevalence gives the odds of the threshold probability below which the more sensitive test is preferable and above which the more specific test should be chosen. The methodology is easily extended to incorporate combinations of tests and the risk or side effects of a test.

publication date

  • May 20, 2013



  • Academic Article



  • eng

PubMed Central ID

  • PMC3531575

Digital Object Identifier (DOI)

  • 10.1002/sim.5601

PubMed ID

  • 22975863

Additional Document Info

start page

  • 1865

end page

  • 76


  • 32


  • 11