Sample Size and Power Calculation for Continuous Outcomes in Open-Cohort Stepped Wedge Designs With Multiple Interventions

Stepped wedge designs with multiple interventions (M-SWDs) are increasingly used to evaluate complex implementation strategies. In many such trials, participants enter and leave over time, giving rise to open-cohort sampling and complex correlation structures. Existing sample size and power calculation methods are largely restricted to single-intervention designs, closed cohorts, or simplified correlation assumptions. We develop a unified, parameter-based framework for sample size and power calculation in open-cohort M-SWDs. The proposed methodology accommodates several common multi-intervention designs, including concurrent, cross-over, supplementation, and factorial designs. Flexible open-cohort sampling schemes are incorporated to account for participant turnover, and both block-exchangeable and decay correlation structures are considered to capture within-cluster and within-individual dependence over time. Closed-form and generalized variance expressions for intervention effect estimators are derived, enabling efficient power calculation under a wide range of design settings. Extensive simulation studies demonstrate that the proposed formulas provide accurate power estimates, while further power analyses illustrate how the key correlation parameters and participant retention jointly influence power. This work provides practical and theoretically grounded guidance for planning multi-intervention stepped wedge trials under open-cohort sampling, facilitating more realistic and transparent design-stage decision-making.