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Stepped wedge cluster randomized trials (SW-CRTs) with binary outcomes areincreasingly used in prevention and implementation studies. Marginal modelsrepresent a flexible tool for analyzing SW-CRTs with population-averagedinterpretations, but the joint estimation of the mean and intraclasscorrelation coefficients (ICCs) can be computationally intensive due to largecluster-period sizes. Motivated by the need for marginal inference in SW-CRTs,we propose a simple and efficient estimating equations approach to analyzecluster-period means. We show that the quasi-score for the marginal meandefined from individual-level observations can be reformulated as thequasi-score for the same marginal mean defined from the cluster-period means.An additional mapping of the individual-level ICCs into correlations for thecluster-period means further provides a rigorous justification for thecluster-period approach. The proposed approach addresses a long-recognizedcomputational burden associated with estimating equations defined based onindividual-level observations, and enables fast point and interval estimationof the intervention effect and correlations. We further propose matrix-adjustedestimating equations to improve the finite-sample inference for ICCs. Byproviding a valid approach to estimate ICCs within the class of generalizedlinear models for correlated binary outcomes, this article operationalizes keyrecommendations from the CONSORT extension to SW-CRTs, including the reportingof ICCs.

Marginal modeling of cluster-period means and intraclass correlations in stepped wedge designs with binary outcomes