Mixed-effects models for the design and analysis of stepped wedge cluster randomized trials: An overview

Abstract

The stepped wedge cluster randomized design has received increasing attention in pragmatic clinical trials and implementation science research. The key feature of the design is the unidirectional crossover of clusters from the control to intervention conditions on a staggered schedule, which induces confounding of the intervention effect by time. The stepped wedge design first appeared in the Gambia hepatitis study in the 1980s. However, the statistical model used for the design and analysis was not formally introduced until 2007 in an article by Hussey and Hughes. Since then, a variety of mixed-effects model extensions have been proposed for the design and analysis of these trials. In this article, we explore these extensions under a unified perspective. We provide a general model representation and regard various model extensions as alternative ways to characterize the secular trend, intervention effect, as well as sources of heterogeneity. We review the key model ingredients and clarify their implications for the design and analysis. The article serves as an entry point to the evolving statistical literatures on stepped wedge designs.

Keywords: Cluster randomized trials; group-randomized trials; heterogeneity; intraclass correlation coefficient; mixed-effects regression; pragmatic clinical trials; sample size calculation.

Figure 1.

A schematic illustration of a stepped wedge CRT with I = 8 clusters and J = 5 periods. Each white cell indicates a cluster-period under the control condition and each gray cell indicates a cluster-period under the intervention condition. There are in total S = 4 distinct intervention sequences.

Figure 2.

Schematic illustrations of four intervention effect representations in a stepped wedge design with I = 4 clusters and J = 5 periods. Each cell with a zero entry indicates a control cluster-period and each cell with a non-zero entry indicates an intervention cluster-period.

Figure 3.

Three examples of within-cluster correlation patterns implied by the random coefficient model. A trial with J = 5 is assumed throughout; the diagonal cells present the within-period ICC values, while the off-diagonal cells present the between-period ICC values. White color indicates a smaller ICC value while red color indicates a larger ICC value. The variance components parameters are assumed as ${\sigma }_{\text{ϵ}}=6,{\tau }_{\alpha }=1,{\tau }_{\xi }=0.5$ and the covariance parameter (a) ${\sigma }_{\alpha \xi }=-0.5$, (b) ${\sigma }_{\alpha \xi }=0$, (c) ${\sigma }_{\alpha \xi }=0.5$. (a) Negative covariance σ_αξ = − 0.5; (b) Zero covariance σ_αξ = 0; (c) Positive covariance σ_αξ = 0.5.