Stepped-wedge cluster randomised controlled trials: a generic framework including parallel and multiple-level designs

Stepped-wedge cluster randomised trials (SW-CRTs) are being used with increasing frequency in health service evaluation. Conventionally, these studies are cross-sectional in design with equally spaced steps, with an equal number of clusters randomised at each step and data collected at each and every step. Here we introduce several variations on this design and consider implications for power. One modification we consider is the incomplete cross-sectional SW-CRT, where the number of clusters varies at each step or where at some steps, for example, implementation or transition periods, data are not collected. We show that the parallel CRT with staggered but balanced randomisation can be considered a special case of the incomplete SW-CRT. As too can the parallel CRT with baseline measures. And we extend these designs to allow for multiple layers of clustering, for example, wards within a hospital. Building on results for complete designs, power and detectable difference are derived using a Wald test and obtaining the variance-covariance matrix of the treatment effect assuming a generalised linear mixed model. These variations are illustrated by several real examples. We recommend that whilst the impact of transition periods on power is likely to be small, where they are a feature of the design they should be incorporated. We also show examples in which the power of a SW-CRT increases as the intra-cluster correlation (ICC) increases and demonstrate that the impact of the ICC is likely to be smaller in a SW-CRT compared with a parallel CRT, especially where there are multiple levels of clustering. Finally, through this unified framework, the efficiency of the SW-CRT and the parallel CRT can be compared.