Information content of stepped wedge designs with unequal cluster-period sizes in linear mixed models: Informing incomplete designs

In practice, stepped wedge trials frequently include clusters of differing sizes. However, investigations into the theoretical aspects of stepped wedge designs have, until recently, typically assumed equal numbers of subjects in each cluster and in each period. The information content of the cluster-period cells, clusters, and periods of stepped wedge designs has previously been investigated assuming equal cluster-period sizes, and has shown that incomplete stepped wedge designs may be efficient alternatives to the full stepped wedge. How this changes when cluster-period sizes are not equal is unknown, and we investigate this here. Working within the linear mixed model framework, we show that the information contributed by design components (clusters, sequences, and periods) does depend on the sizes of each cluster-period. Using a particular trial that assessed the impact of an individual education intervention on log-length of stay in rehabilitation units, we demonstrate how strongly the efficiency of incomplete designs depends on which cells are excluded: smaller incomplete designs may be more powerful than alternative incomplete designs that include a greater total number of participants. This also serves to demonstrate how the pattern of information content can be used to inform a set of incomplete designs to be considered as alternatives to the complete stepped wedge design. Our theoretical results for the information content can be extended to a broad class of longitudinal (ie, multiple period) cluster randomized trial designs.