If doctors were to fine tune their prescriptions to take maximal advantage of the placebo effect, what would they do? It’s hard to answer this question even with existing data on the strength of the placebo effect because beliefs, presumably the key to the placebo effect, would adjust if placebo prescription were widespread.

Indeed, over the weekend I saw a paper presented by Emir Kamenica which strongly suggests that equilibrium beliefs matter for placebos. In an experiment on the effectiveness of anti-histamines, some subjects were shown drug ads at the same time they took the drug. The ads had an impact on the effectiveness of the drug but only for subjects with less prior experience with the same drug. The suggestion is that those with prior experience have already reached their equilibrium placebo effect. (It appears that the paper is not yet available for download.)

So we need a model of the placebo effect in equilibrium. Suppose that patients get a placebo a fraction of the time and a full dose the remaining fraction of the time. And let be the patient’s belief in the probability the prescription will work. Then the placebo effect means that the true probability that the prescription will work is determined by a function h which takes two arguments: the true dosage (=1 for full dose, 0 for placebo) and the belief . And in equilibrium beliefs are correct:

This equilibrium condition implicitly defines a function which gives the equilibrium efficacy as a function of the placebo rate .

The benefit of the model is that it allows us to notice something that may not have been obvious before. If instead of using placebos by varying , an alternative is to just lower the dose, deterministically. Then if we let be the dosage (somewhere between 0 and 1), we get

as the equilibrium condition which defines effectiveness now as a function of the fixed dose .

The something to notice is that, if the function is continuous and monotone, then the range of is the same whether we use placebos or deterministic doses . That is, any outcome that can be implemented with placebos can be implemented by just using lower doses and no placebos. This follows mathematically because the placebo model collapses to the determistic model at the boundary: and

Now this is just a statement about the feasible set. The benefit of placebo may come from the ability to implement the same outcome but with lower cost. In terms of the model this would occur if the that satisfies is larger than . That boils down to a cost-benefit calculation. But I doubt that this kind of calculation is going to be pivotal in a debate about using placebos as medicine.

## 2 comments

Comments feed for this article

May 19, 2010 at 2:28 am

ZacharyIt appears that there are some natural experiments available to test the efficacy of placebos distributed beside real drugs. Apparently counterfeit drugs are so prevalent in Africa (“for example in a recent study in Madagascar, Senegal and Uganda, between 26 and 44 percent of antimalarial drugs failed quality tests”) that a couple startups have developed a system for verifying if a package of drugs is from a legitimate source: Use a scratch card like instant win lottery tickets have to reveal a number and text that number to the service to find out if it’s real.

http://aidwatchers.com/2010/05/scratch-and-win-your-way-to-authentic-malaria-drugs/

July 20, 2010 at 1:20 pm

Managing Suspense « Cheap Talk[…] this under psychological mechanism design. Possibly related posts: (automatically generated)Placebo and […]