We propose efficient nonparametric statistics to compare medical imaging modalities in multi-reader multi-test data and to compare markers in longitudinal ROC data. The proposed methods are based on the weighted area under the ROC curve, which includes the area under the curve and the partial area under the curve as special cases. The methods maximize the local power for detecting the difference between imaging modalities. We develop the asymptotic results of the proposed methods under a complex correlation structure. Our simulation studies show that the proposed statistics result in much better powers than existing statistics. We apply the proposed statistics to an endometriosis diagnosis study. Copyright © 2012 John Wiley & Sons, Ltd.