Stepped wedge designs: insights from a design of experiments perspective

Stepped wedge designs (SWDs) have received considerable attention recently, as they are potentially a useful way to assess new treatments in areas such as health services implementation. Because allocation is usually by cluster, SWDs are often viewed as a form of cluster-randomized trial. However, since the treatment within a cluster changes during the course of the study, they can also be viewed as a form of crossover design. This article explores SWDs from the perspective of crossover trials and designed experiments more generally. We show that the treatment effect estimator in a linear mixed effects model can be decomposed into a weighted mean of the estimators obtained from (1) regarding an SWD as a conventional row-column design and (2) a so-called vertical analysis, which is a row-column design with row effects omitted. This provides a precise representation of "horizontal" and "vertical" comparisons, respectively, which to date have appeared without formal description in the literature. This decomposition displays a sometimes surprising way the analysis corrects for the partial confounding between time and treatment effects. The approach also permits the quantification of the loss of efficiency caused by mis-specifying the correlation parameter in the mixed-effects model. Optimal extensions of the vertical analysis are obtained, and these are shown to be highly inefficient for values of the within-cluster dependence that are likely to be encountered in practice. Some recently described extensions to the classic SWD incorporating multiple treatments are also compared using the experimental design framework.