Intra-Class Correlation Coefficient Ignorable Clustered Randomized Trials for Detecting Treatment Effect Heterogeneity

Accurately estimating the intra-class correlation coefficient (ICC) is crucial for adequately powering clustered randomized trials (CRTs). Challenges arise due to limited prior data on the specific outcome within the target population, making accurate ICC estimation difficult. Furthermore, ICC can vary significantly across studies, even for the same outcome, influenced by factors like study design, participant characteristics, and the specific intervention. Power calculations are extremely sensitive to ICC assumptions. Minor variation in the assumed ICC can lead to large differences in the number of clusters needed, potentially impacting trial feasibility and cost. This paper identifies a special class of CRTs aiming to detect the treatment effect heterogeneity, wherein the ICC can be completely disregarded in calculation of power and sample size. This result offers a solution for research projects lacking preliminary estimates of the ICC or facing challenges in their estimate. Moreover, this design facilitates power improvement through increasing the cluster sizes rather than the number of clusters, making it particular advantageous in the situations where expanding the number of clusters is difficult or costly. This paper provides a rigorous theoretical foundation for this class of ICC-ignorable CRTs, including mathematical proofs and practical guidance for implementation. We also present illustrative examples to demonstrate the practical implications of this approach in various research contexts in healthcare delivery.