Quantum noise influencing human behaviour could fake effectiveness of drugs in clinical trials

To test the effectiveness of a drug one can advice two randomly selected groups of patients to take or not to take it, respectively. It is well-known that the causal effect cannot be identified if not all patients comply. This holds even when the non-compliers can be identified afterwards since latent factors like patient's personality can influence both his decision and his physical response. However, one can still give bounds on the effectiveness of the drug depending on the rate of compliance. Remarkably, the proofs of these bounds given in the literature rely on models that represent all relevant latent factors (including noise) by hidden classical variables. In strong analogy to the violation of Bell's inequality, some of these bounds fail if patient's behavior is influenced by latent quantum processes (e.g. in his nervous system). Quantum effects could fake an increase of the recovery rate by about 13% although the drug would hurt as many patients as it would help if everyone took it. The other bounds are true even in the quantum case. We do not present any realistic model showing this effect, we only point out that the physics of decision making could be relevant for the causal interpretation of every-day life statistical data.