I may have been unclear. What I meant was that it has nothing to do with the sort of antibody tests to gliadin being mentioned or total IgA levels. The standard screening test is the anti-tissue transglutaminase test as I indicated before and indicated in that website. But even that is not worth doing unless the person actually has relevant symptoms. Coeliac disease can be diagnosed without it (as the site indicates) and I suspect the diagnosis should remain even if the test is negative if the classic features are present.
I'm harping on the details of this because celiac is one of the things that is supposed to be ruled out before people are given an ME diagnosis, and It seems most doctors are not doing this - particularly if patients don't appear to fit the old ideas of what celiac looks like - ie if the patient is not underweight and doesn't have diarrhea.
The most common symptoms in adults (when the selection isn't skewed to patients presenting with GI symptoms) are things like joint pain, fatigue and iron-deficiency anemia - all of which can masquerade as ME. there are also a significant minority of Celiac patients who present with primarily or only neurological or neuro-psychiatric symptoms such as ataxia, peripheral neuropathy - which obviously could also be mistaken for ME.
See for example: