Smoothed jackknife empirical likelihood inference for the difference of ROC curves

For the comparison of two diagnostic markers at a flexible specificity, people apply the difference of two correlated receiver operating characteristic (ROC) curves to identify the diagnostic test with stronger discrimination ability. In this paper, we employ the jackknife empirical likelihood (JEL) method to construct confidence intervals for the difference of two correlated continuous-scale ROC curves. Using the jackknife pseudo-sample, we can avoid estimating several nuisance variables which have to be estimated in the existing methods. We prove that the smoothed jackknife empirical log likelihood ratio is asymptotically chi-squared distributed. Furthermore, the simulation studies in terms of the coverage probability and the average length of confidence intervals show good performance in small samples with a moderate computational cost. A real data set is used to illustrate our method.