A semiparametric hypothesis testing procedure for the ROC curve area under a density ratio model

We propose a semiparametric Wald statistic to test whether a diagnostic test is capable of discriminating between diseased and nondiseased subjects based on the receiver operating characteristic (ROC) curve area under a two-sample semiparametric density ratio model. The proposed Wald test is constructed on the basis of the maximum semiparametric likelihood estimator of the ROC curve area. The proposed test statistic has an asymptotic chi-squared distribution under the null hypothesis and an asymptotic noncentral chi-squared distribution under local alternatives to the null hypothesis. We present some results on a simulation study and on the analysis of two data sets.