I think I should rephrase my question after reading a few replies. The original question is kept intact at the bottom. So maybe I should ask the question this way: if you use a ROC curve to find the predictive power of your predictor, will the slope on the ROC curve be a good metric to rely on?
Assume there is a undiscovered relationship f(x) = x(1-x), where 0 <= x <= 1. We also assume f(x) is a good predictor for our class label y. Now all you have is some (x, y) pairs. If you want to see how x predicts y, you generate a ROC curve and get your AUC, you would get a plot similar to what I have shown below, and my question about the predictive power of x on y remains the same.
Hope this is clearer.
------------------- original question ------------------------------ Is it true that the slope of a ROC implies prediction performance, i.e., the bigger the slope a segment on the ROC curve is, the better the prediction the segment corresponds to.
Take a look at the following ROC curve
Can I assume the beginning part (TP rate 0~0.2) and the ending part (FP rate 0.85 ~ 1) predict much better than the middle segment?
The reason I am asking is that I am wondering if I can throw away data points in the middle and use only data points correspond to the segments at the two ends. Does this make sense?
p.s. I understand I could have reversed the predictor so that AUC > 0.5, but the questions remain the same.