Factors affecting power in stepped wedge trials when the treatment effect varies with time

Stepped wedge cluster randomized trials (SW-CRTs) have historically been analyzed using immediate treatment (IT) models, which assume the effect of the treatment is immediate after treatment initiation and subsequently remains constant over time. However, recent research has shown that this assumption can lead to severely misleading results if treatment effects vary with exposure time, i.e., time since the intervention started. Models that account for time-varying treatment effects, such as the exposure time indicator (ETI) model, allow researchers to target estimands such as the time-averaged treatment effect (TATE) over an interval of exposure time, or the point treatment effect (PTE) representing a treatment contrast at one time point. However, this increased flexibility results in reduced power.

In this paper, we use public power calculation software and simulation to characterize factors affecting SW-CRT power. Key elements include choice of estimand, study design considerations, and analysis model selection.

For common SW-CRT designs, the sample size (clusters per sequence or individuals per cluster-period) must be increased substantially, commonly by a factor of 1.5 to 3, but often by much more, to maintain 90% power when switching from an IT model to an ETI model (targeting the TATE over the study). However, the inflation factor is lower for TATE estimands over shorter periods that exclude longer exposure times. In general, SW-CRT designs (including the "staircase" variant) have much greater power for estimating "short-term effects" relative to "long-term effects." For an ETI model targeting a TATE estimand, substantial power can be gained by adding time points to the start of the study or increasing baseline sample size, but surprisingly, little power is gained from adding time points to the end of the study. More restrictive choices for modeling the exposure time or calendar time trends (e.g., splines or linear terms) have little effect on power for TATE estimands but increases power for PTE estimands. If the effect curve is constant after a washout period, a "delayed constant treatment" model that uses exposure time indicators during the washout period but assumes a constant effect thereafter can slightly increase power relative to an IT model that discards washout period data.