Optimal unidirectional switch designs

Stepped wedge designs and delayed start designs can all be considered as special cases of the so-called unidirectional switch design. This paper provides optimal proportions of clusters that are allocated to switch patterns in a unidirectional switch design to minimize the asymptotic variance of the treatment effect estimator. This unique optimal design applies to certain cross-sectional and longitudinal variance component models. When the intraclass correlation coefficient is zero, the optimal unidirectional switch design coincides with the classic (cluster) parallel group design. The optimal unidirectional switch design is more efficient than the optimal stepped wedge design and delayed start designs. Compared with the uniform unidirectional switch design, the efficiency gain of the optimal unidirectional switch design can be substantial, but it depends on the intraclass correlation and the cluster size. We also showed that augmenting the optimal stepped wedge design with pure control pattern is more efficient than the optimal stepped wedge design. In addition, robust minimax design for unidirectional switch design, delayed start design, and stepped wedge design are provided.