The hypothesis is that inviting people for a regular check up reduces mortality. If a lot of people don’t take up the offer because the procedure is too invasive, carries some risk, etc. then that is a very relevant variable to take into account. Vs, for example, fecal testing as mentioned in the article. It could have a lower precision, but if uptake is 100% instead of the ~40% for colonoscopy the outcomes could be much better.

Really?

You cannot simple compare the outcomes for the people who got an invitation AND got the procedure done with the outcomes for the people who didn’t get an invitation.

You need the compare them with the people who didn’t get an invitation BUT would have got the procedure done if they had been invited.

This is not an oversight on the part of the study designers. It's called "intention to treat", and studies are done this way to get past the problem that, when you invite a bunch of people to get colonoscopies (or tell them to comply with any medical procedure), the people who go through with it are statistically very different, in all kinds of ways, from the people who don't. This makes the direct comparison of "received treatment" vs "didn't receive treatment" mostly meaningless.

You're here advocating for everyone to ignore the study and do a direct comparison of "received treatment" vs "didn't receive treatment".

Don't do this.

Who?