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It is common for researchers to correct for imperfect adherence in a RCT with "as-treated," "per-protocol" and "on-treatment" analyses. These are all wrong, always and everywhere, because these methods reintroduce the confounding that necessitated an RCT in the first place
Why researchers believe that reintroducing confounding reduces confounding is a special pathology, and speaks to the terrible state of statistical knowledge in medicine. @JAMA_current offers us a smart, primer on the wrong-headedness behind these ways: https://jamanetwork.com/journals/jama/fullarticle/2719368?guestAccessKey=3cc215fc-5dcf-452a-a065-31d3e03b65fc&utm_source=silverchair&utm_medium=email&utm_campaign=article_alert-jama&utm_content=olf&utm_term=121718 …
One method that is underused for ITT (Intent to Treat) estimates is the use of bounds-- a la Chuck Manski. This kind of sensitivity analysis is incredibly useful, transparent, and easy to implement. It's not been deployed in medicine and public-health as much as it ought to be.
Another approach to deal with imperfect compliance is the use of Instrumental Variables (IV) where one instruments for treatment using (random) treatment assignment-- ie using 2SLS to estimate treatment on treated; another method from economics that is underutilized in medicine.
We looked at possibly helpful approaches to deal with nonadherence here and compared them with ITT.https://www.jclinepi.com/article/S0895-4356(18)30493-1/ …
Are these all code words for "assume non-compliance was random"?
At first I thought he was saying my ITT estimates were wrong and I had a brief personal crisis about it
It's becoming less common, but AT & PP analysis are still done. No disagreement at all w/ ur assessment, tho. 
https://www.bmj.com/content/340/bmj.c2073 …
Yeah that is really problematic.
After reading your comments, I’m impressed with your grasp of the statistical nuances of RCTs. I suspect you’ve never actually placed a patient on a clinical RCT. Many well thought out trials are ‘outdated’ during their development. Subjects on cancer RCTs /1
Are never as uniform as trial designers would like. Making entry criteria too strict disables clinical trials but allowing accrual to a snails pace ... when the trial completes, the results may be far less relevant. Using your principles in designing trials/2
.... would be a step forward, unless they slow accrual enough to threaten the relevance of the results. We owe our greatest debt to the patients who offer their lives as subjects in these RCTs. We repay that debt by being certain that results of their sacrifice is meaningful./3
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