The use of the 'binormal' model for parametric ROC analysis of quantitative diagnostic tests

The binormal model is widely used for parametric receiver operating characteristic (ROC) analyses of data concerning the accuracy of medical diagnostic tests. Empirical evaluation of the performance of this model in the face of departures from binormality has been limited to interpretations of radiology-type examinations recorded on a rating scale. This paper extends the investigation to the performance of the model with biochemical and other tests recorded on an interval scale. In order to describe non-binormal pairs of distributions, a useful standardized graphical display is developed; this display also illustrates several features of ROC curves. We consider non-binormal pairs of distributions with or without a monotone likelihood ratio and show that by transformation of the underlying scale, one can make many such pairs resemble closely the binormal model. These findings justify Metz's use of the binormal model in the 'LABROC' software for ROC analyses of laboratory type data even when the raw data may 'look' decidedly non-Gaussian.