I'd like to hear more about the study design / quality of the science. How are they correcting for correlation between the ability to afford the more money-exp

I'd like to hear more about the study design / quality of the science. How are they correcting for correlation between the ability to afford the more money-expensive or more time-expensive ends of rich people with experts that cook for them, and health nuts (or suffers of seriously annoying allergies) that cook for themselves even though it's more time expensive?