ROC area discrimination (ROCAD) curve: a new method of evaluating the discriminating ability of ordinal scales

The area under the receiver operating characteristic (ROC) curve has been frequently used to assess the ability of diagnostic tests to discriminate between individuals with and without a disease. In this paper, we propose to use the ROC area to evaluate the discriminating power of ordinal measures, such as many subjective ratings or multioption questionnaire items.

Applications of the method are illustrated with examples from a study designed to select multioption items for a quality-of-life questionnaire in persons with arthritis.

DISCRIMINATION was defined as the ability to discriminate between subjects above and below a given threshold value for the attribute being measured. The ROC curve for an ordinal scale was obtained for each observed value of the attribute and the areas under the ROC curves were estimated and plotted on a graph. The resultant curve is referred to as the ROC Area Discrimination (ROCAD) curve. In contrast to standard measures of validity for ordinal scales, such as a correlation coefficient, the ROCAD curve describes the performance of the scale for each point along the spectrum of the measured attribute.

ROCAD curves can be useful in evaluating the discriminating power of ordinal scales.