About the use of the overlap coefficient in the binary classification context

The overlap coefficient (OVL) measures the common area between two or more density functions. It has been used for measuring the similarity between distributions in different research fields including astronomy, economy or sociology, among others. Recently, different authors have studied the use of the OVL coefficient in the binary classification problem. They argue that, in particular settings, it could provide better accuracy measure than other stablished indices. We prove here that the OVL coefficient does not provide additional information to the Youden index and that, the potential advantages previously reported are based on the assumption that the classification rules underlying any classification process always assign more probability of being positive to the larger values of the marker. Particularly, we prove that, for a fixed continuous marker, the OVL coefficient is equivalent to the Youden index associated with the optimal classification rules based on this marker. We illustrate the problem studying the capacity of the white blood cells count to identify the type of disease in patients having either acute viral meningitis or acute bacterial meningitis.