To maximize the efficiency (statistical power) of treatment comparisons, investigators typically employ equal allocation of patients to treatment groups (this assumes that the variability in the outcome measure is the same for each treatment).

Unequal allocation may be preferable in some situations. An unequal allocation that favors an experimental therapy over placebo could help recruitment and it would increase the experience with the experimental therapy. This also provides the opportunity to perform some subset analyses of interest, e.g., if more elderly patients are assigned to the experimental therapy, then the unequal allocation would yield more elderly patients on the experimental therapy.

Another example where unequal allocation may be desirable occurs when one therapy is extremely expensive in comparison to the other therapies in the trial. For budget reasons, you may not be able to assign as many to the expensive therapy.

If it is known that one treatment is more variable (less precise) in the outcome response than the other treatments, then the statistical power for treatment comparisons is maximized with unequal allocation. The allocation ratio should be

\(r = n_1/n_2 = \sigma^1 / \sigma^2\)

which is a ratio of the known standard deviations. Thus, the treatment that yields less precision (larger standard deviation) should receive more patients, an unequal allocation. Because there is more 'noise', more patients, larger sample size will help to cut through this noise.