[saurik]

The issue isn't that the patient is lying or doesn't know; the issue is that the patient is taking supplements or not for a reason that is itself correlated with the other side of our analysis: someone who is taking vitamins might be more desperate, or might have more money (and so be living in very different conditions or have less stress), or might be more likely to be doing other random "maybe this will help?" things that are also random effects you aren't asking about, or might be better at doing anything at all on a routine (including other medical steps), or might be more able to get up and walk/drive to take/buy vitamins, or might be experiencing a different level of digestive effects from their chemotherapy. The reason why we use controlled randomized trials is because they just fully solve this correlation analysis issue.