To the extent that there’s a spread in those answers, a third possibility emerges: how can we, as health policy makers, find a way to make the invitations more effective at converting to administered colonoscopies?
Why would that be a goal? First you'd need to show that colonoscopies were helpful in general, or that invitations were going to a subpopulation in which colonoscopies were helpful.
If colonoscopies are helpful to avoid negative outcomes, but invitations to colonoscopies are not, looking into making invitations better seems like an obvious play to me.
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.
