Analysis of Stepped-Wedge Cluster Randomized Trials: A Tutorial Using Marginal Models

Abstract

Stepped-wedge cluster randomized trials (SW-CRTs) are one-way crossover trials that randomize clusters (i.e., groups) of individuals to the time point (period) at which an intervention is introduced into the cluster. In these designs, the intervention under evaluation is introduced into all of the clusters by the end of the study in a series of "steps." Analysis of SW-CRTs using marginal models provides a population-averaged interpretation of the estimated intervention effect and flexible specification of the within-cluster, marginal pairwise association structure; the latter has practical application in reporting intraclass (i.e., pairwise) correlations and calculating power for CRTs. Despite these features, use of marginal modeling of SW-CRTs has been mostly limited to applications with working independence and simple exchangeable correlation structures that are suboptimal for multi-period CRTs when correlation among responses decays over time. However, there have been many methodological developments in marginal modeling of SW-CRTs over the past fifteen years, particularly on (i) multi-parameter, within-cluster correlation structures; (ii) paired generalized estimating equations (GEE) for simultaneous estimation of mean and correlation parameters with standard errors; and, when the number of clusters is small, (iii) corrections to reduce the bias of variance estimators, and that of correlation estimates using matrix-adjusted estimating equations (MAEE). The goal of the current tutorial is to survey these newer developments and to provide case studies to enable applied researchers to implement GEE/MAEE for marginal model analysis of SW-CRTs, with application to both cohorts and designs with repeated cross-sectional samples. The methods are also applicable to multi-period, parallel-arm and cluster-crossover CRTs.

Keywords: crossover CRT; exponential decay correlation structure; generalized estimating equations (GEE); intracluster correlation coefficient; matrix‐adjusted estimating equations (MAEE); multi‐period CRT; nested exchangeable correlation structure; small‐sample corrections.