Introduction
Since the study by Hussey and Hughes,Graphical representation of a stepped-wedge design with five sequences.The implementation of a stepped-wedge design has seen an increasing use in cluster randomized trials.Stepped-wedge designs are often implemented such that an equal number of clusters or individuals is assigned to each treatment sequence (i.e. a uniform allocation). However, for cluster randomized trials, it has already been shown that this is not necessarily the best choice.This contribution is organized as follows. In the ‘Methods’ section, the statistical model that relates outcome to time period and treatment condition is introduced and it is shown how the treatment effect and its variance are estimated in studies without and with attrition. The variance of the treatment effect estimate is used as optimality criterion and this section also shows how constrained optimization is used to numerically derive the optimal allocation to treatment sequences. The ‘Results’ section presents optimal allocations for three to six sequences along with the efficiency of the uniform allocation relative to the optimal allocation. The optimal allocations may not always be feasible from a practical point of view and the ‘Methods’ section deals with optimal allocations where the proportions of individuals allocated to each sequence are bounded by an upper and lower limit. Conclusion and discussion are given in the last section.