Sample Size and Cost-Efficient Planning for Stepped-Wedge Cluster Randomized Trials with Varying Cluster Size

Stepped-wedge (SW) designs are widely used in cluster randomized trials (CRTs), where clusters are assigned to sequences of measurement periods and transition from control to intervention at different time points. Compared with parallel-group CRTs, SW designs ensure that all clusters eventually receive the intervention and often provide logistical advantages in terms of cost and resource allocation. While SW designs with equal cluster sizes have been extensively studied, unequal cluster sizes are more common in practice. Such imbalance can substantially affect statistical efficiency and power, increase the variance of treatment effect estimates, and potentially introduce bias if not adequately addressed during the design and analysis stages.The Washington State community-level randomized trial of expedited partner therapy and the CASCADE trial exemplify SW designs conducted across clusters of varying sizes. Motivated by these studies, we derive a novel sample size formula for SW-CRTs and assess the relative efficiency of designs with equal and unequal cluster sizes under a block-exchangeable correlation structure. We also develop a cost-constrained optimization framework that accommodates cluster-size heterogeneity. Through numerical and graphical analyses, we show how cluster-size imbalance affects efficiency and trial performance, providing practical guidance for designing feasible, cost-effective, and statistically efficient SW CRTs.