The problem is you can't run a study on colonoscopies that doesn't involve an invitation without forcing people to get a colonoscopy at gun point. Which would both be illegal and never pass an IRB.
You can control for the invitation vs no-invitation and colonoscopy vs no-colonoscopy and analyze the outcomes of all four cells (provided you have enough people in each cell) or the column or row independently.
It seems to me with electronic medical records that you could do population-wide studies using data that already exists (and I think that would pass IRB, or at least "ought to"). That would likely tell you "for the patients matching criteria X (are covered by BCBS and live in state X, or whatever), the 10 year outcome for patients who turned 50 in 2010 was Y vs Z conditioned on whether they had a colonoscopy".
