Classifying binormal diagnostic tests using separation-asymmetry diagrams with constant-performance curves.
A method is proposed for classifying diagnostic tests that have underlying binormal distributions. The method involves using the parameters that characterize these distributions as axes of a two-dimensional graph called a separation-asymmetry (S-A) diagram. Each point on an S-A diagram corresponds to a possible diagnostic test. The diagram also has superimposed on it any of three possible families of curves of constant performance: curves of constant area under the ROC graph (iso-AUR), curves of constant overlap area (iso-OA), and curves of constant maximum information (iso-MaxInfo). Thus, the performance of any test can be determined immediately by identifying the iso-performance curve of the desired type that passes through the corresponding point of the S-A diagram. The concept of "eccentric" diagnostic tests is defined and incorporated into the S-A diagrams. The classification scheme is applied to 28 diagnostic tests. Excellent agreement is found in the ranking between the iso-OA and iso-MaxInfo measures of performance, but the iso-AUR produces markedly different results. Only three of the 28 tests were found to be eccentric. Several other interesting patterns emerged.
Psychiatry Service, Department of Veterans Affairs Medical Center, Cincinnati, Ohio 45220.
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D015982:Bias; D016010:Binomial Distribution; D003627:Data Interpretation, Statistical; D003955:Diagnostic Tests, Routine / Q000145:classification*; D006801:Humans; D012372:ROC Curve; D015203:Reproducibility of Results