Relative efficiency of unequal cluster sizes in stepped wedge and other trial designs under longitudinal or cross‐sectional sampling

Background: A cluster trial with unequal cluster sizes often has lower precision than one with equal clusters, with a corresponding inflation of the design effect. For parallel group trials, adjustments to the design effect are available under sampling models with a single intracluster correlation. Design effects for equal clusters under more complex scenarios have appeared recently (including stepped wedge trials under cross‐sectional or longitudinal sampling). We investigate the impact of unequal cluster size in these more general settings. Results: Assuming a linear mixed model with an exchangeable correlation structure that incorporates cluster and subject autocorrelation, we compute the relative efficiency (RE) of a trial with clusters of unequal size under a size‐stratified randomization scheme, as compared to an equal cluster trial with the same total number of observations. If there are no within‐cluster time effects, the RE exceeds that for a parallel trial. In general, the RE is a weighted average of the RE for a parallel trial and the RE for a crossover trial in the same clusters. Existing approximations for parallel designs are extended to the general setting. Increasing the cluster size by the factor (1 + CV(2)), where CV is the coefficient of variation of cluster size, leads to conservative sample sizes, as in a popular method for parallel trials. Conclusion: Methods to assess experimental precision for single‐period parallel trials with unequal cluster sizes can be extended to stepped wedge and other complete layouts under longitudinal or cross‐sectional sampling. In practice, the loss of precision due to unequal cluster sizes is unlikely to exceed 12%.