Relationship between Roe and Metz simulation model for multireader diagnostic data and Obuchowski‐Rockette model parameters

For the typical diagnostic radiology study design, each case (ie, patient) undergoes several diagnostic tests (or modalities) and the resulting images are interpreted by several readers. Often, each reader is asked to assign a confidence‐of‐disease rating to each case for each test, and the diagnostic tests are compared with respect to reader‐performance outcomes that are functions of the reader receiver operating characteristic (ROC) curves, such as the area under the ROC curve. These reader‐performance outcomes are frequently analyzed using the Obuchowski and Rockette method, which allows conclusions to generalize to both the reader and case populations. The simulation model proposed by Roe and Metz (RM) in 1997 emulates confidence‐of‐disease data collected from such studies and has been an important tool for empirically evaluating various reader‐performance analysis methods. However, because the RM model parameters are expressed in terms of a continuous decision variable rather than in terms of reader‐performance outcomes, it has not been possible to evaluate the realism of the RM model. I derive the relationships between the RM and Obuchowski‐Rockette model parameters for the empirical area under the ROC curve reader‐performance outcome. These relationships make it possible to evaluate the realism of the RM parameter models and to assess the performance of Obuchowski‐Rockette parameter estimates. An example illustrates the application of the relationships for assessing the performance of a proposed upper one‐sided confidence bound for the Obuchowski‐Rockette test‐by‐reader variance component, which is useful for sample size estimation.