[ex3xu]

They mention the 5 ASD out of 8 PA sample size, and they explicitly cite the .005 rate of ASD, but I think their PA incidence number is different than the one available on Wikipedia, and I couldn't find it in the paper so that may be where the discrepancy is from. I may be wrong but I don't think we need the combinatorics for this particular calculation since their calculation is trying to disprove that these events are independent rather than calculate the joint conditional probability. Obviously I can't comment on whether any cherry picking was done, or if these just happen to be the available sample of available children with this rare metabolic disorder. I'd agree and I think the authors of the study would agree that the sample size is too small for any definitive conclusions, but I think the body of evidence when considering the rest of the available PPA studies make a reasonable case for it to be a finding of interest.