Inference on the difference of AUCs based on fitted values under the null

The difference of AUCs is a widely used measure of the improvement in class discrimination when comparing predictors. The predictors often take the form of indexes, the linear fitted values β̂Tw from some estimation procedure. Since the estimation procedure is often carried out using the same data as used to estimate the difference of AUCs, standard results on the distribution of the difference of AUCs, assuming independent observations, generally do not apply. Recent work has developed non parametric inference procedures under the assumption that the true difference is non zero, which is useful, e.g., for forming confidence intervals. The distribution under the assumption that the true difference is zero is of central importance for testing. However, the analysis is more complicated as the asymptotic distribution of the test statistic is generally non normal, and only special cases have appeared in the literature. The asymptotic distribution is presented here under general conditions and parametric and non parametric estimation are described. The previously published special cases are re-derived