Examples of problems where ROC curves are more useful than PR curves I understand the formal differences between a ROC curve and a PR curve, but I am trying to build more intuition. For common applications such as Search and disease prediction, PR curves are more useful (I think)
What are some important / common problems where ROC curves are more useful than PR curves?

ROCs are sensitivity over 1 - specificity, which do not depend on the prevalence of the positive class*. This means that you can determine the ROC correctly even if your test cases are acquired with a sampling procedure that leads to relative fequencies of true positive and true negative cases that are different from the application prevalence.
In contrast, PR curves do depend on the prevalence (or incidence, whatever applies to your situation).
Two situations where this is important are:

*

*validation studies are often planned including x positive and y negative cases - with x : y not reflecting application prevalence at all.
(Of course, you can also (and should) correct your PPV calculation according to the application prevalence and then get the PR curve for your application scenario.)


*application prevalence may change substantially.
Consider rapid antigen tests for SARS-CoV2. Where I am, they have been used for mass tests of school children during summer with incidence about 1e-4/d and as a "gate-keeper" first test before PCR for people who suspect they have Covid with maybe 1 in 10 being truely positive. So 3 orders of magnitude difference in incidence/prevalence.
You can still directly use your ROC that was determined with 100 truly positive and 100 truly negative samples. You do need to account for application prevalence when interpreting your ROC, of course (e.g. saying, for these prevalences, we need sensitivity to be at least x and specificity to be at least y).

(Personally, I find it awkward with PR curves that the meaning of the denominator is different between sensitivity and PPV, so I prefer to look at ROC and PPV-NPV-curve - but maybe I'm missing something with the PR curve)

* there's some small print for specificity in case "negative" is not a homogenous group - but that would apply to PPV (and NPV) as well.
