Receiver Operating Characteristic - Further Interpretations

Further Interpretations

Sometimes, the ROC is used to generate a summary statistic. Common versions are:

• the intercept of the ROC curve with the line at 90 degrees to the no-discrimination line (also called Youden's J statistic)
• the area between the ROC curve and the no-discrimination line
• the area under the ROC curve, or "AUC" ("Area Under Curve"), or A' (pronounced "a-prime"), or "c-statistic".
• d' (pronounced "d-prime"), the distance between the mean of the distribution of activity in the system under noise-alone conditions and its distribution under signal-alone conditions, divided by their standard deviation, under the assumption that both these distributions are normal with the same standard deviation. Under these assumptions, it can be proved that the shape of the ROC depends only on d'.
• C (Concordance) Statistic: This is a rank order statistic related to Somers' D statistic. It is commonly used in the medical literature to quantify the capacity of the estimated risk score in discriminating among subjects with different event times. It varies between 0.5 and 1.0 with higher values indicating a better predictive model. For binary outcomes C is identical to the area under the receiver operating characteristic curve. Although bootstrapping to generate confidence intervals is possible, the power of testing the differences between two (or more) C statistics is low and alternative methods such as logistic regression should probably be used. The C statistic has been generalized for use in survival analysis and it is also possible to combine this with statistical weighting systems. Other extensions have been proposed.

However, any attempt to summarize the ROC curve into a single number loses information about the pattern of tradeoffs of the particular discriminator algorithm.