If the stat analysts find this psychological profile associated with a strong placebo response post hoc, then it’s experimental data mining.
If, on the other hand, the trial designers know about this psychological profile a priori, then the sensible thing to do is to exclude patients who have the profile.
Venturing into the philosophical, the only thing that makes "noise" noise is that it is unknown for the purposes of the whatever calculation you are making. For instance, communication devices, in this era of overlapping communications streams, often treat interference from neighbors as noise with characteristic X. Being treated as noise does NOT require that the thing be inherently unknowable - only that we choose to treat it as such.
It is according to this fairly well accepted definition of noise that I call the placebo effect noise in the PAD example.
Last comment on this subtopic - as we learn more and more about such 'noise' (e.g. placebo responders or, more real world examples such as Iressa responders predicted via genotype) I would contend it should absolutely not make trials more expensive to run. That is running the wrong direction. More knowledge should make things cheaper and faster, not more expensive and slower. Ok, if you know for sure that one group will not respond then, yes, they should be excluded. But if you aren't sure, should you exclude them? Or have an analysis plan that allows some compensation. Such as Cox Regression (I suspect that there are better methods since Cox Regression is a little too much like data mining. Maybe prespecifying the HR and then backing out the covariates before calculating HR?).
BTW - Finished the next step of my characterization of Cox Regression and it absolutely significantly decreases the p value even when the covariates are perfectly balanced.
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