Two sensitivity orders applied to the comparison of ROC curves

Abstract

The main aim of this article is to propose a conceptual support for ROC curves within the general field of inequalities by applying the theory of majorization of vectors. For our purpose, we will use the concept of sensitivity associated with a vector in $R_n^{+}$ which have been recently published in literature. Based on the sensitivity concept we first define an order between two vectors that we will call strong order sensitivity. Secondly, we will define a weak version of the previous order that enables us to expand the range of ROC curves that are comparable in absolute terms. Finally, we will apply the results to compare medical diagnostic procedures using ROC curves where we propose a new index of the reliability of diagnostic methods.

Keywords:

• Sensitivity order
• ROC curve
• sensitivity index
• medical diagnostic procedure

Acknowledgments

We are grateful to the anonymous referees for their useful comments on an earlier draft of this article.

Additional information

Funding

The research was partially supported by Ministerio de Economía y Competitividad (Spain) under grant MTM2017-89577-P.