A nonparametric procedure for comparing the areas under correlated LROC curves

In contrast to the receiver operating characteristic (ROC) assessment paradigm, localization ROC (LROC) analysis provides a means to jointly assess the accuracy of localization and detection in an observer study. In a typical multireader, multicase (MRMC) evaluation, the data sets are paired so that correlations arise in observer performance both between readers and across the imaging conditions (e.g., reconstruction methods or scanning parameters) being compared. Therefore, MRMC evaluations motivate the need for a statistical methodology to compare correlated LROC curves. In this work, we suggest a nonparametric strategy for this purpose. Specifically, we find that seminal work of Sen on U-statistics can be applied to estimate the covariance matrix for a vector of LROC area estimates. The resulting covariance estimator is the LROC analog of the covariance estimator given by DeLong et al. for ROC analysis. Once the covariance matrix is estimated, it can be used to construct confidence intervals and/or confidence regions for purposes of comparing observer performance across imaging conditions. In addition, given the results of a small-scale pilot study, the covariance estimator may be used to estimate the number of images and observers needed to achieve a desired confidence interval size in a full-scale observer study. The utility of our methodology is illustrated with a human-observer LROC evaluation of three image reconstruction strategies for fan-beam x-ray computed tomography (CT).