Confidence intervals for the overlap coefficient under multimodal distributions: with an application to breast cancer diagnosis

Abstract

In medical diagnostic research, medical diagnostic tests with continuous values are widely employed to distinguish between diseased and non-diseased subjects. In light of the overlap coefficient’s (OVL) practical relevance and intuitive interpretability as a measure of distributional similarity, this measure has been proposed to assess the accuracy of these tests. Several inference methods for constructing confidence intervals for OVL have recently been developed. However, the most promising inference methods for constructing confidence intervals have not yet been systematically compared. In this paper, we first compare two of the most accurate approaches. The performances of these methods are evaluated empirically under a variety of distributional scenarios. At sight of these results, a novel delta method for mixtures of normal distributions is introduced and compared with the generalized pivotal quantity-based approach. Finally, all these approaches are applied to datasets on diabetes and breast cancer diagnosis to assess the glucose and the mean radius of the tumor cells, respectively.