Comparing the areas under two correlated ROC curves: Parametric and non-parametric approaches

In order to compare the discriminatory effectiveness of two diagnostic markers the equality of the areas under the respective Receiver Operating Characteristic Curves is commonly tested. A non-parametric test based on the Mann-Whitney statistic is generally used. Weiand et al. (1989) present a parametric test based on normal distributional assumptions. We extend this test using the Box-Cox power family of transformations to non-normal situations. These three test procedures are compared in terms of significance level and power by means of a large simulation study. Overall we find that transforming to normality is to be preferred. An example of two pancreatic cancer serum biomarkers is used to illustrate the methodology.