Some efficiency comments on group sizes in study design.

In study designs to compare a binary response between two groups, standard formulae to determine sample sizes are available. Frequently, one of the groups can be increased in size with little additional effort. The efficiency gain as measured by a reduction in the asymptotic variance of the logarithm of the odds ratio depends on the response probabilities and a gain cannot always be expected. However, in some cases, efficiency can be doubled by selecting one group three times the size of the other. Graphs are provided to assess the possible efficiency gain. It is seldom advantageous to select one group larger than five or six times the size of the other.