Sample Size Calculations for Stepped Wedge Designs with Treatment Effects that May Change with the Duration of Time under Intervention.

The stepped wedge design is often used to evaluate interventions as they are rolled out across schools, health clinics, communities, or other clusters. Most models used in the design and analysis of stepped wedge trials assume that the intervention effect is immediate and constant over time following implementation of the intervention (the "exposure time"). This is known as the IT (immediate treatment effect) assumption. However, recent research has shown that using methods based on the IT assumption when the treatment effect varies over exposure time can give extremely misleading results. In this manuscript, we discuss the need to carefully specify an appropriate measure of the treatment effect when the IT assumption is violated and we show how a stepped wedge trial can be powered when it is anticipated that the treatment effect will vary as a function of the exposure time. Specifically, we describe how to power a trial when the exposure time indicator (ETI) model of Kenny et al. (Statistics in Medicine, 41, 4311-4339, 2022) is used and the estimand of interest is a weighted average of the time-varying treatment effects. We apply these methods to the ADDRESS-BP trial, a type 3 hybrid implementation study designed to address racial disparities in health care by evaluating a practice-based implementation strategy to reduce hypertension in African American communities.