title: A simple decision analytic solution to the comparison of two binary diagnostic tests.
abstract: 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.
authors.affiliation: Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, New York, NY 10021, USA. vickersa@mskcc.org
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Vickers
authors.forename: Angel M
authors.initials: AM
authors.lastname: Cronin
authors.forename: Mithat
authors.initials: M
authors.lastname: Gönen
mesh_terms: D003657:Decision Making; D003955:Diagnostic Tests, Routine / Q000592:standards*; D006801:Humans; D008297:Male; D017430:Prostate-Specific Antigen / Q000097:blood; D011471:Prostatic Neoplasms / Q000175:diagnosis; D012680:Sensitivity and Specificity; D020840:Tissue Kallikreins / Q000097:blood
chemical_list: D020840:Tissue Kallikreins; D017430:Prostate-Specific Antigen