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The following figures show examples of ROC curves:

t1

First of all ignoring the picture, from a logical point one can say: When the cutoff value decreases, more and more cases are allocated to class 1 and therefore the sensitivity will increase (true positives in relation to total actual positives). The specificity will decrease (these are true negatives in relation to total actual negatives and it will decrease, because less and less cases are allocated to class 0 so there will be less true negatives).

I got that and I think it is correct. But I got confused when I looked at the picture.

Lets take this point here:

t2

Now when I decrease the cutoff probability from this point, I move "down" so I get this point as a result:

t4

So I decrease the cutoff value, but one can see clearly that the value of the sensitivity on the y-axis also decreased ($x2<x1$).

Where is my logical error?

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  • $\begingroup$ What is your ultimate goal? Why does roc even remotely relate to it? $\endgroup$ – Frank Harrell Jun 24 '14 at 14:43
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I believe your logic is correct, and your drawing is wrong. In particular, the arrow labeled "cutoff" shows the direction you move as your make your cutoff more stringent.

You can see an example at:

http://ebp.uga.edu/courses/Chapter%204%20-%20Diagnosis%20I/8%20-%20ROC%20curves.html

They show an example of detecting cancer, using a cutoff value on uterine wall thickness, where in general a thicker uterine wall may be a sign of cancer. At the upper right portion of the ROC curve you see the cutoff value of 4mm. Note this is very low cutoff, and the sensitivity is very high.

Note that in some cases a lower cutoff can be more stringent, it just depends on the nature of the test. For example if you're testing for hypothyroidism, then a lower test reading is more likely to indicate a positive result, and a lower threshold is more restrictive. See: http://gim.unmc.edu/dxtests/roc2.htm

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