Sample size calculations for stepped wedge and cluster randomised trials: a unified approach

OBJECTIVES: To clarify and illustrate sample size calculations for the cross-sectional stepped wedge cluster randomized trial (SW-CRT) and to present a simple approach for comparing the efficiencies of competing designs within a unified framework. STUDY DESIGN AND SETTING: We summarize design effects for the SW-CRT, the parallel cluster randomized trial (CRT), and the parallel cluster randomized trial with before and after observations (CRT-BA), assuming cross-sectional samples are selected over time. We present new formulas that enable trialists to determine the required cluster size for a given number of clusters. We illustrate by example how to implement the presented design effects and give practical guidance on the design of stepped wedge studies. RESULTS: For a fixed total cluster size, the choice of study design that provides the greatest power depends on the intracluster correlation coefficient (ICC) and the cluster size. When the ICC is small, the CRT tends to be more efficient; when the ICC is large, the SW-CRT tends to be more efficient and can serve as an alternative design when the CRT is an infeasible design. CONCLUSION: Our unified approach allows trialists to easily compare the efficiencies of three competing designs to inform the decision about the most efficient design in a given scenario.