Power analyses for stepped wedge designs with multivariate continuous outcomes

Multivariate outcomes are not uncommon in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials (SW-CRTs) with multivariate outcomes that differentiate the within-period and between-period intracluster correlation coefficients (ICCs). To do so, we first extend the existing univariate linear mixed model for cross-sectional SW-CRTs to a multivariate linear mixed model that allows simultaneous estimation of the intervention effects on multiple outcomes. We then derive the joint distribution of the intervention test statistics which can be used for determining power under a wide class of hypotheses and provide an example using the commonly utilized intersection-union test for co-primary outcomes. Simplifications under a common treatment effect and common ICCs across endpoints and an extension to closed cohort designs are also provided. Finally, under the common ICC across endpoints assumption, we formally prove that the multivariate linear mixed model leads to a more efficient treatment effect estimator compared to the univariate linear mixed model, providing a rigorous justification on the use of the former with multivariate outcomes. We illustrate application of the proposed methods using data from an existing SW-CRT and present extensive simulations to validate the methods under a wide range of scenarios.