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

TL;DR

This paper introduces a computationally efficient method for marginal modeling of cluster-period means and intraclass correlations in stepped wedge designs with binary outcomes, facilitating faster and more accurate analysis.

Contribution

It proposes a simple estimating equations approach that reformulates individual-level quasi-scores using cluster-period means, improving computational efficiency and finite-sample inference for ICCs.

Findings

Efficient estimation of intervention effects and ICCs in SW-CRTs

Reformulation of quasi-scores from individual to cluster-period means

Enhanced finite-sample inference for ICCs using matrix adjustments

Abstract

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.