Efficient treatment allocation in two-way nested designs

The usual treatment allocation in randomized trials and their factorial and nested extensions is balanced, that is, with equal sample size in each treatment arm. This is optimal only when the variances and study costs are the same in both treatment arms, or when the ratio of treatment-specific variances is equal to the ratio of treatment-specific costs. Focusing on 2x2 cluster randomized trials with a quantitative outcome, this entry shows the effects of heterogeneity of variance and costs on the optimal treatment allocation. Essentially, that allocation assigns a larger part of the sample to the treatment arm with the larger variance and the lower costs. Since outcome variances are unknown in the design stage of a trial, references are given to robust design.