Power calculation in stepped-wedge cluster randomized trial with reduced intervention sustainability effect

The stepped-wedge design for pragmatic clinical trials has received increased attention in health service-related research seeking to evaluate the effect of interventions. Compared with the parallel design, the stepped-wedge design is preferred when there is prior knowledge supporting the effectiveness and harmlessness of the intervention, and/or when practical or financial constraints exist such that the intervention can only be implemented sequentially on a fraction of clusters. In some health service studies, the study period may consist of two parts: an active implementation followed by a sustainability phase, where the intervention effect is possibly reduced. There is a gap in current literature of the stepped-wedge design for cluster randomization trials for dealing with this specific scenario. We aim to provide an analytical formula for power analysis under this situation to aid the stepped-wedge design of an ongoing PREVENT trial.