Highly efficient stepped wedge designs for clusters of unequal size.

The stepped wedge design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approximation to the variance of the treatment effect, which is expressed in terms of the proportions of clusters and of individuals allocated to each sequence of the design. The roles of these sets of proportions in determining an efficient design are discussed and illustrated using two SWDs, one in the treatment of sexually transmitted diseases and one in renal replacement therapy. Cluster-balanced designs, which allocate equal numbers of clusters to each sequence, are shown to have excellent statistical and practical properties; suggestions are made about the practical application of the results for these designs. The paper concentrates on the cross-sectional case, where subjects are measured once, but it is briefly indicated how the methods can be extended to the closed-cohort design.