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This article discusses optimal allocation of experimental units in a control versus intervention cluster randomized trial for binary responses. Optimal allocations are based on a well knownoptimality criterion. To address the issue of parameter dependency on design criterion, locally, Bayesian, and min–max optimal designs are proposed. An efficiency analysis is carried out to assess the performance of proposed optimal designs. All theoretically obtained optimal designs are complemented by numerical experiments including a real data example which demonstrate that designs proposed are associated with a substantial increment in efficiency compared to the commonly used balanced design.

Some design considerations for cluster randomized trials with binary responses