ROC curve

#1
Hello, I would like to ask a question about the ROC curve that plots sensitivity against 1-specificity for all possible threshold settings of a diagnostic test. Each point on the ROC curve represents a different cutoff value. For a perfect diagnostic test the ROC curve would be vertical from (0,0) to (0,1) and then horizontal to (1,1). In this case of a perfect test I would like to know where are the other cutoff values represented in this line, as the perfect discrimination is assumed to be for only 1 cutoff value, which is the one generating the previous coordinates. Or in the case of a perfect test only the cutoff value giving the perfect discrimination is represented in the curve?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Is this theoretical or do you have data to work with? I would image you have complete data separation. So if you plotted the distribution of the screening tool for the two outcome groups the two histograms would not touch. However, if you wanted to make the threshold not in the neutral zone between the histograms you would continue to get a perfect values for either the Sen or 1-SPEC, and the other's value would start going down. Doing this could ensure if you went to generalize the threshold to a new sample you could minimize the risk for either false positives or false negatives. The ROC never really shows the values for the screening tool unless you label them. The best bet is to plot the histograms like I referenced. Get it?