Power analysis for stratified cluster randomisation trials with cluster size being the stratifying factor

Stratified cluster randomisation trial design is widely employed in biomedical research and cluster size has been frequently used as the stratifying factor. Conventional sample size calculation methods have assumed the cluster sizes to be constant within each stratum, which is rarely true in practice. Ignoring the random variability in cluster size leads to underestimated sample sizes and underpowered clinical trials. In this study, we proposed to directly incorporate the variability in cluster size (represented by coefficient of variability) into sample size calculation. This approach provides closed-form sample size formulas, and is flexible to accommodate arbitrary randomisation ratio and varying numbers of clusters across strata. Simulation study shows that the proposed approach achieves desired power and type I error over a wide spectrum of design configurations, including different distributions of cluster sizes. An application example is presented.