Does Intention-to-treat apply to the cases that should have been excluded but not able to do so during recruitment? I am working on a pharmacist-supported new medicine randomised trial. One of the criteria during the recruitment was that if a patient used medicine previously, he/she should not be recruited. 
However, there were some patients that simply forgot they took the medicine months ago (maybe just once), and pharmacist recruited them anyways. And we did not know that until we received the dispensing data from the government agency. 
In such a circumstance, does intention-to-treat apply or should I exclude them from the analysis?
 A: I guess yours is a randomized trial. If it is not, then the whole intention-to-treat (ITT) vs as-treated (AT) vs per-protocol (PP) Mexican standoff is meaningless (eg McCoy, 2017).
Accordingly, if they were not randomized, you could exclude them and still consider the corresponding analysis as an ITT one.
Otherwise, if they were unluckily randomized, then you should include them in the ITT analysis. You can always skip them in the PP analysis.
The bottomline is indeed that if you exclude them and call the corresponding analysis ITT, you will most likely find someone in a journal or an organization who will recommend you not to, and any discrepancy would undermine the whole trial.
A: This is a very interesting question and is unlikely to have a single right answer. I would argue that if they should never have been included in the trial in the first place then they should be excluded even post-randomisation and this would not affect the intention to teat analysis. The point of the trial is to be able to generalise to the population from which the trial participants were drawn and including people in the trial who do not, in fact, come from that population is going to disturb that generalisation. Consider some extreme cases. A patient is included who did not in fact have the condition being treated. An adult is included in a paediatric trial. A woman is included in a trial of ante-natal care who turns out not to have been pregnant at all.
In the case outlined in the question I would be happy to see them excluded.
