Choosing the right term for this is a bit tricky because there are a number of closely related concepts (such as the placebo effect, and others which I'm not sure have names), and if a term actually comes into common use people will probably end up mixing this concept with a number of other concepts (like how psychosomatic, health anxiety, factitious disorder, malingering, self or mis-diagnosis, and exaggerating symptoms are all mixed up).
I personally like "treatment-inherent cognitive bias". Like Jonathan Edwards said, I think "treatment-induced cognitive bias" could probably be applied more broadly, such as in cases where people get side effects from the actual drug in a placebo controlled trial, and hence are more likely to think the drug is working. So it's a cognitive bias which is treatment induced, but it isn't treatment inherent in the same way that telling someone to lie about or ignore their symptoms is.
I think "treatment-inherent cognitive bias" also covers the problem with only using subjective outcomes as it's assumed a cognitive bias would apply to subjective but not objective outcomes. There are other issues like being told the treatment is or isn't evidence based, or feeling pressured to please the therapist or seem like a good patient, but I don't think they would be covered under that term, because they aren't really inherent to the treatment or necessarily a cognitive bias. Those could possibly be covered by a term like "practitioner-influenced response bias" (similar to "courtesy bias" or "social desirability bias" but more situation specific).
I personally like "treatment-inherent cognitive bias". Like Jonathan Edwards said, I think "treatment-induced cognitive bias" could probably be applied more broadly, such as in cases where people get side effects from the actual drug in a placebo controlled trial, and hence are more likely to think the drug is working. So it's a cognitive bias which is treatment induced, but it isn't treatment inherent in the same way that telling someone to lie about or ignore their symptoms is.
I think "treatment-inherent cognitive bias" also covers the problem with only using subjective outcomes as it's assumed a cognitive bias would apply to subjective but not objective outcomes. There are other issues like being told the treatment is or isn't evidence based, or feeling pressured to please the therapist or seem like a good patient, but I don't think they would be covered under that term, because they aren't really inherent to the treatment or necessarily a cognitive bias. Those could possibly be covered by a term like "practitioner-influenced response bias" (similar to "courtesy bias" or "social desirability bias" but more situation specific).