Highly Efficient Stepped Wedge Designs for Clusters of Unequal Size
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The Stepped Wedge Designs(SWD) is a form of cluster randomized trial, usually comparing two treatments, which are divided into sequences and time periods. Clusters are allocated to sequences, with the treatment changing at different periods in the different sequences. Typically all sequences start with the standard treatment and end with the new treatment, which can make SWDs attractive to practitioners. The clusters allocated to the sequences will usually differ in size but the existing literature generally assumes that they have the same size. This paper considers the case when clusters have different sizes and determines optimal designs in some special cases and highly efficient designs in the general case, with bounds placed on the amount by which they fall short of optimal. The designs allocate the same proportion of subjects to each of the sequences of the SWD except for the extreme sequences, where treatments change after the first period or just before the final period, which receive a different proportion of subjects. The proportions depend on the cluster sizes, the duration of the study and the intra-class correlation. The paper concentrates on the cross-sectional design, where subjects are measured once but the results are extended to the closed-cohort design, in which each subject is measured in each period of the study.
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