War II to analyze the performance characteristics of people who operated RADAR receivers, but the
name has stuck, and now it is also referred to as an ROC curve.
An ROC graph has a curve that shows you the complete range of sensitivity and specificity that
can be achieved for any fitted logistic model based on the selected cut value. The software
generates an ROC curve by effectively trying all possible cut values of predicted probability
between 0 and 1, calculating the predicted outcomes, cross-tabbing them against the observed
outcomes, calculating sensitivity and specificity, and then graphing sensitivity versus specificity.
Figure 18-7 shows the ROC curve from the logistic model developed from the data in Figure 18-
1 (using R software; see Chapter 4).
© John Wiley & Sons, Inc.
FIGURE 18-7: ROC curve from dose mortality data.
As shown in Figure 18-7, the ROC curve always starts in the lower-left corner of the graph, where 0
percent sensitivity intersects with 100 percent specificity. It ends in the upper-right corner, where 100
percent sensitivity intersects with 0 percent specificity. Most software also draws a diagonal straight
line between the lower-left and upper-right corners because that represents the formula:
. If your model’s ROC curve were to match that line, it would indicate
the total absence of any predicting ability at all of your model.