Someone on the IRBForum posed a theoretical question. Is running a three arm study troublesome from an ethical viewpoint because the probability that any subject in the trial receives the best possible treatment decreases from 50% to 33%?

The key thing to remember is that any randomized trial requires equipoise in order to be ethical. There are conflicting definitions of equipoise, but most definitions center around the concept that there is genuine uncertainty about which treatment is best. You can, for example, only use a placebo in a randomized trial if you are unsure whether the new treatment is better than the placebo.

If there was equipoise at the start of the trial, then the probability of receiving benefit does not change with the number of arms. Keep in mind that a two-arm study that excludes the only arm that ends up as effective would reduce the chances of receiving benefit to zero. Or if two arms are effective, then the chances of receiving benefit increase from 50% to 67% in a three arm trial. These scenarios end up balancing out the negative scenarios such as decreasing the probability from 50% to 33%.

If this is more than just a theoretical musing, perhaps you should investigate a concept known as adaptive randomization, where the chances of receiving a specific treatment increase or decrease during a trial to reflect the partial information that accumulates during the trial itself. Adaptive randomization does indeed reduce the chances that patients in a trial will end up receiving the inferior treatment.

**Further reading**

**Statistical properties of randomization in clinical trials.** Lachin
JM. Control Clin Trials 1988: 9(4); 289-311.
[Medline]

http://interstat.stat.vt.edu/InterStat/ARTICLES/2001/articles/Y01001.pdf

You can find an earlier version of this page on my original website.