Agreed with your push-back on the sample size thing being operative (this is a point I've made frequently on HN study threads), and agree that the primary desig

Agreed with your push-back on the sample size thing being operative (this is a point I've made frequently on HN study threads), and agree that the primary design consideration is the post-"treatment" measurement of the outcome making it more likely that having an autistic kid changes metabolites than that having different metabolites influences chance of having an autistic kid. Still, even with contemporaneous measurement, my guess is that there'd be a very real selection issue here; a non-random subset of people who could receive an autism diagnosis do, and to the extent the confounders into diagnosis (one presumes all the standard SES/race/access to healthcare factors are confounders here) constitutes a selection on the dependent variable, even a contemporaneous sample would not generalize to the population of interest.