Let \(\hat{\pi}_{1i}\) be the probability that \(Y=1\) predicted by the regression model at the \(i\text{th}\) observation \(X_i\) for \(i=1, \dots , N\) where \(N\) is the number of observations. Analogous to the approach above, each predicted probability may serve as a candidate cutpoint discriminating \(Y=1\ \text{from}\ Y=2\). Coordinates comprising the ROC curve may then be computed, except they are based on counts on the probability scale monotonically transformed by the regression model from the original continuous scale. As above, the best probability cutpoint \(\hat{\pi}^*\) may be selected with a suitable optimality criterion. The cutpoint on the scale of the continuous predictor \(X^*\) can be recovered by cross-referencing \(\hat{\pi}^*\) with its corresponding observed measurement. Whether using the scale of the continuous predictor or the predicted probability, the resulting ROC curves are identical because the curve is rank-based and invariant to monotonic transformations of the continuous predictor \cite{Agresti2014}. The first stage of the proposed approach exploits this invariance through a generalization of the logistic model embodied by the cumulative logit model.