Optimal Sample Allocation Under Unequal Costs in Cluster-Randomized Trials

Conventional optimal design frameworks consider a narrow range of sampling cost structures that thereby constrict their capacity to identify the most powerful and efficient designs. We relax several constraints of previous optimal design frameworks by allowing for variable sampling costs in cluster-randomized trials. The proposed framework introduces additional design considerations and has the potential to identify designs with more statistical power, even when some parameters are constrained due to immutable practical concerns. The results also suggest that the gains in efficiency introduced through the expanded framework are fairly robust to misspecifications of the expanded cost structure and concomitant design parameters (e.g., intraclass correlation coefficient). The proposed framework is implemented in the R package odr.