An overview of optimal designs under a given budget in cluster randomized trials with a binary outcome

Cluster randomized trial design may raise financial concerns because the cost to recruit an additional cluster is much higher than to enroll an additional subject in subject-level randomized trials. Therefore, it is desirable to develop an optimal design. For local optimal designs, optimization means the minimum variance of the estimated treatment effect under the total budget. The local optimal design derived from the variance needs the input of an association parameter ? in terms of a working correlation structure R ( ? ) in the generalized estimating equation models. When the range of ? instead of an exact value is available, the parameter space is defined as the range of ? and the design space is defined as enrollment feasibility, for example, the number of clusters or cluster size. For any value ? within the range, the optimal design and relative efficiency for each design in the design space is obtained. Then, for each design in the design space, the minimum relative efficiency within the parameter space is calculated. MaxiMin design is the optimal design that maximizes the minimum relative efficiency among all designs in the design space. Our contributions are threefold. First, for three common measures (risk difference, risk ratio, and odds ratio), we summarize all available local optimal designs and MaxiMin designs utilizing generalized estimating equation models when the group allocation proportion is predetermined for two-level and three-level parallel cluster randomized trials. We then propose the local optimal designs and MaxiMin designs using the same models when the group allocation proportion is undecided. Second, for partially nested designs, we develop the optimal designs for three common measures under the setting of equal number of subjects per cluster and exchangeable working correlation structure in the intervention group. Third, we create three new Statistical Analysis System (SAS) macros and update two existing SAS macros for all the optimal designs. We provide two examples to illustrate our methods.

Automated summary

Cluster randomized trial design is expensive and it is important to develop an optimal design to minimize costs. Local optimal designs aim to minimize the variance of the treatment effect under a fixed budget. This requires the input of an association parameter and involves the consideration of enrollment feasibility. Our contributions include summarizing available local optimal designs and proposing new designs for different scenarios, as well as developing Statistical Analysis System (SAS) macros for all optimal designs.