The ideal point of on a ROC curve is (0,1) where sensitivity = S = 1 and specificity = E = 1. The distance of a point on a ROC curve to this ideal point can be used to determine the optimum cutoff for the test.


distance =

= SQRT(((1 - S)^2) + ((1 - E)^2))


The optimum cutoff for a test is that point on the ROC curve with the minimum distance to the ideal point.


The authors do not give the source for this relationship, but it can be seen from a plot that the distance is the hypotenuse for a right triangle with sides (1 - S) and (1 - E).


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