How important is exact balance in treatment and control sample sizes to evaluations?

Abstract

Because it is well known that the power to measure differences between two groups is typically best with an even distribution of any given fixed sample size, great emphasis is often placed on exactly equal treatment and control allocations in evaluations of substance abuse interventions. Independent randomization of individuals (e.g., a “coin flip”) when study participants are enrolled in an ongoing fashion by multiple recruiters and assigned to treatment conditions does not guarantee exact balance, often prompting the use of schemes that are complex and burdensome to implement. Our results suggest that departures from simple randomization are only warranted for single-site trials involving fewer than 77 total subjects or for multisite trials with substantially fewer than 77 subjects per site. With such a rule, simple randomization will produce samples that are at least 95% as efficient as a fully balanced sample of equal size at least 95% of the time.