Under a generalised estimating equation analysis approach, approximate design theory is used to determine Bayesian D-optimal designs. For two examples, considering simple exchangeable and exponential decay correlation structures, we compare the efficiency of identified optimal designs to balanced stepped-wedge designs and corresponding stepped-wedge designs determined by optimising using a normal approximation approach. The dependence of the Bayesian D-optimal designs on the assumed correlation structure is explored; for the considered settings, smaller decay in the correlation between outcomes across time periods, along with larger values of the intra-cluster correlation, leads to designs closer to a balanced design being optimal. Unlike for normal data, it is shown that the optimal design need not be centro-symmetric in the binary outcome case. The efficiency of the Bayesian D-optimal design relative to a balanced design can be large, but situations are demonstrated in which the advantages are small. Similarly, the optimal design from a normal approximation approach is often not much less efficient than the Bayesian D-optimal design. Bayesian D-optimal designs can be readily identified for stepped-wedge cluster randomised trials with binary outcome data. In certain circumstances, principally ones with strong time period effects, they will indicate that a design unlikely to have been identified by previous methods may be substantially more efficient. However, they require a larger number of assumptions than existing optimal designs, and in many situations existing theory under a normal approximation will provide an easier means of identifying an efficient design for binary outcome data.

翻译：在广义估计方程分析框架下，利用近似设计理论确定贝叶斯D最优设计。通过两个算例，考虑简单可交换和指数衰减相关结构，将所识别的最优设计效率与平衡阶梯楔形设计及基于正态近似优化得到的相应阶梯楔形设计进行比较。探讨了贝叶斯D最优设计对假定相关结构的依赖性：在设定场景中，时间区间结局间相关性衰减越小，结合组内相关系数越大，则设计越趋近于最优的平衡设计。与正态数据不同，对于二元结局情况，最优设计未必具有中心对称性。贝叶斯D最优设计相对于平衡设计的效率可能显著，但某些情形下其优势较小。类似地，基于正态近似的最优设计效率通常不亚于贝叶斯D最优设计。对于二元结局数据的阶梯楔形整群随机试验，可便捷识别贝叶斯D最优设计。在某些条件下（尤其是存在强时间效应时），此类设计可能指示出显著优于现有方法识别结果的方案。然而，与现有最优设计相比，贝叶斯D最优设计需要更多假定，而在多数情况下，基于正态近似的现有理论可为二元结局数据提供更简便的高效设计识别途径。