  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. The asymptotic results of
the proposed methods are developed under a complex correlation structure. Our
simulation studies show that the proposed statistics result in much better
powers than existing statistics. We applied the proposed statistics to an
endometriosis diagnosis study.
