||In this paper, we consider testing the equivalence of two medical diagnostic methods in a case-control study where each subject receiving the two different diagnostics produces correlated paired measurements. Note that it occurs often in practice that the marginal distributions of the measurements are right-skewed. Therefore, we first apply the power transformation to the paired data so that they would behave like the bivariate normal data. One parametric equivalent test is then implemented based on the transformed data. On the other hand, we suggest and employ appropriate copula function which links two generalized gamma distributions to describe the joint distribution of the paired measurements. Under the joint distribution, an approximate test based on the difference between the areas under the two estimated Receiver Operating Characteristic (ROC) curves is then constructed. In this paper, we would like to test if the difference between the true areas is within an allowable region. The results of a simulation investigation of the level and power performances of the approximate test for different degrees of correlation in several possible copula functions with a variety of marginal distributions are reported. Finally, a real data set is illustrated by using the approximate test.|
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