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.