An empirical comparison of discrete ratings and subjective probability ratings

The authors compared receiver operating characteristic (ROC) data from a five-category discrete scale with that from a 101-category subjective probability scale to determine how well the latter categories define the ROC curve.

The authors analyzed data from a pilot study performed for another purpose in which 10 radiologists provided both a five-point confidence rating and a subjective probability rating of abnormality for each interpretation. ROC operating points were plotted for a five-category scale and a 101-category scale to determine how well the observed points covered the range of false-positive probabilities. ROC curves were fitted to the subjective probability data according to the standard ROC model.

For these data, subjective probability ratings were somewhat more effective in populating the range of false-positive probability with ROC points. For three observers, the ROC curves inappropriately crossed the chance line. For another four, prevention of such crossing seemed to depend on one or two ROC points near the upper right corner of the ROC space, points based on discriminations within the discrete category "no abnormality to report."

Subjective probability rating should provide substantially better coverage of the ROC space with operating points, preventing inappropriate crossing of the chance line. Unfortunately, the protection offered by subjective probability ratings was unreliable and depended on ROC points derived from discriminations not directly related to apparent abnormality. The use of proper ROC models to fit data may offer a better solution.