Optimal Bayesian stepped-wedge cluster randomised trial designs for binary outcome data

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.