Proper receiver operating characteristic analysis: the bigamma model

The standard binormal model is the most commonly used model for fitting receiver operating characteristic rating data; however, it sometimes produces inappropriate fits that cross the chance line with degenerate data sets. The authors proposed and evaluated a proper constant-shape bigamma model to handle binormal degeneracy.

Monte Carlo samples were generated from both a standard binormal population model and a proper constant-shape bigamma model in a series of Monte Carlo studies.

The results confirm that the standard binormal model is robust in large samples with no degenerate data sets and that the standard binormal model is not robust in small samples because of degenerate data sets.

A proper constant-shape bigamma model seems to solve the problem of degeneracy without inappropriate chance line crossings. The bigamma fitting model outperformed the standard binormal fitting model in small samples and gave similar results in large samples.