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Some interesting examples of binormal degeneracy and analysis using a contaminated binormal ROC model

Receiver operating characteristic (ROC) data with false positive fractions of zero are often difficult to fit with standard ROC methodology, and are sometimes discarded. Some extreme examples of such data were analyzed. A new ROC model is proposed that assumes that for a proportion of abnormalities, no signal information is captured and that those abnormalities have the same distribution as noise along the latent decision axis. Rating reports of fracture for single view ankle radiographs were also analyzed with the binormal ROC model and two proper ROC models. The conventional models gave ROC area close to one, implying a true positive fraction close to one. The data contained no such fractions. When all false positive fractions were zero, conventional ROC areas gave little or no hint of unmistakable differences in true positive fractions. In contrast, the new model can fit ROC data in which some or all of the ROC points have false positive fractions of zero and true positive fractions less than one without concluding perfect performance. These data challenge the validity and robustness of conventional ROC models, but the contaminated binormal model accounts for these data. This research has been published for a different audience.