I'm writing my medical thesis and I want to test our research group's hypothesis that the width of the foramen magnum can predict response or non-response to a certain surgical intervention in a neurological disease. The sample is however quite small (only 23 patients) so any biological signal whould have to be quite strong to cut through the noise. I asked stats support who wanted me to "find some exact version of the ROC analysis, some analogue to Fisher's exact test", but I can't really find anything like that in the literature. Generative AI tends to point me towards Mann-Whitney U-tests, exact logistic regression and/or Firth regression, but cannot point me towards any supporting literature. Intuitively that's not a bad idea. I might test if the FM width is normally distributed with Shapiro-Wilk, then test for differences with t-test/U-test depending on distribution and only then proceed towards ROC-analyses/logistic regression if an interesting pattern emerges. But I will have to motivate the chosen approach formally. Is there an actual recommended approach? Is there any literature discussing the pros and cons of different strategies given this particular dilemma?

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