  Stepped wedge cluster randomized trials (SW-CRTs) with binary outcomes are
increasingly used in prevention and implementation studies. Marginal models
represent a flexible tool for analyzing SW-CRTs with population-averaged
interpretations, but the joint estimation of the mean and intraclass
correlation coefficients (ICCs) can be computationally intensive due to large
cluster-period sizes. Motivated by the need for marginal inference in SW-CRTs,
we propose a simple and efficient estimating equations approach to analyze
cluster-period means. We show that the quasi-score for the marginal mean
defined from individual-level observations can be reformulated as the
quasi-score for the same marginal mean defined from the cluster-period means.
An additional mapping of the individual-level ICCs into correlations for the
cluster-period means further provides a rigorous justification for the
cluster-period approach. The proposed approach addresses a long-recognized
computational burden associated with estimating equations defined based on
individual-level observations, and enables fast point and interval estimation
of the intervention effect and correlations. We further propose matrix-adjusted
estimating equations to improve the finite-sample inference for ICCs. By
providing a valid approach to estimate ICCs within the class of generalized
linear models for correlated binary outcomes, this article operationalizes key
recommendations from the CONSORT extension to SW-CRTs, including the reporting
of ICCs.
