Optimal design for matched pair cluster randomized trials with heterogeneous correlations and costs

Conducting studies using cluster randomized trials (CRTs) is often a costly endeavor. When budget constraints are present, it becomes crucial to design CRTs optimally under the given cost limitations. A matched pair CRT, is a trial in which clusters are paired based on similar baseline characteristics, and one cluster from each pair is randomly assigned to the intervention while the other serves as control. Commonly, CRT designs assume equal intra-class correlation and sampling costs across clusters, but this assumption is rarely met in practice due to various factors. This article proposes optimal subject allocations within clusters for matched pair CRTs. The allocation is derived by minimizing the variance of treatment effect estimator under very general conditions, assuming heterogeneity in intra-class correlation, matching correlation, and sampling costs across clusters. The proposed design proves to be more efficient than the commonly used balanced design. To address the dependency on unknown parameters, min-max and pseudo-Bayesian optimal designs are also explored. Numerical examples based on real world data are provided to supplement the theoretical findings.