How to establish equivalence between two treatments in ROC analysis

Abstract

We have applied the equivalence statistical test designs in the success rate to the equivalence test in the ROC analysis. Here, in the ROC analysis, it is difficult to determine the acceptable difference. We consider the ROC curve in the binormal model, and the maximum allowable value of the true difference in the area under the binormal ROC curve between two treatments is considered to be the one corresponding to the maximum acceptable value of the true difference in the sensitivity with the same specificity (or specificity with same sensitivity) between two treatments. Here, we have shown the tolerable true difference of the areas under the binormal ROC curve will be calculated in the case of the same slope in the binormal ROC plane, if an acceptable true difference of the sensitivity with same specificity (or specificity with same sensitivity) is given. So, one is able to test the equivalence in diagnostic performance of two medical image tests by using the ROC analysis, by testing a null hypothesis of an acceptable difference calculated from an acceptable sensitivity (or specificity) difference versus an alternative hypothesis of a true difference less than it.