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I am currently having confusion on a part in the paper:

Unal, Ilker. “Defining an Optimal Cut-Point Value in ROC Analysis: An Alternative Approach.” Computational and mathematical methods in medicine vol. 2017 (2017): 3762651. doi:10.1155/2017/3762651

Looking at Figure 2 and Table 2, why are the optimal cutoff values greater than 1? I always thought that it had to range between 0 to 1. Or are the concepts of cutoff values and thresholds two different things? Any help would be much appreciated!

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    $\begingroup$ If you have probability values, sure, but you can do ROC curves with log-odds from a logistic regression that are not limited to $[0,1]$. What’s being thresholded? $\endgroup$
    – Dave
    Feb 26, 2022 at 23:14
  • $\begingroup$ @Dave Ok, so not all classification models output the entries iny_prob in the range $[0,1]$. Then is it wrong to say that when we try to find the optimal cutoff value $c$ via Youden, Concordance Probability Method, and the Index of Union, the objective function we have to minimize/maximize will be over the interval $[0,1]$? So instead it should be over $\mathbb{R}^+$? Do you know of any examples or resources that clarify this for me? Thank you again! $\endgroup$
    – Ramiro Ramirez
    Feb 26, 2022 at 23:29
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    $\begingroup$ Log-odds in logistic regression can be any real number. For a resource, I would say to read the very paper you’re reading where something other than a probability is used. // You might not even want to look for a threshold using a ROC curve or even at all. Please refer to Vanderbilt’s Professor Frank Harrell’s blog. fharrell.com/post/mlconfusion fharrell.com/post/class-damage fharrell.com/post/classification $\endgroup$
    – Dave
    Feb 26, 2022 at 23:50

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