Using the half normal distribution to quantify covariate balance in cluster-randomized pragmatic trials

Area of Science:

• Clinical Trials Methodology
• Biostatistics
• Health Services Research

Background:

• Pragmatic trials frequently employ cluster-randomized controlled trials (C-RCTs), where randomization occurs at the site level.
• Covariate-constrained randomization (CCR) is used to mitigate imbalances in site characteristics, which can arise by chance in small-scale randomizations.
• Current methods lack consensus on assessing balance and selecting appropriate allocations in CCR.

Purpose of the Study:

• To introduce and evaluate an overall imbalance index (I) for assessing site balance in CCR.
• To provide guidance on acceptable levels of site balance in C-RCTs using CCR.

Main Methods:

• Derivation of the theoretical distribution for the overall imbalance index (I).
• Simulation studies to assess the empirical properties of I under diverse covariate distributions and inter-correlations.
• Evaluation of the index's robustness with varying numbers of site characteristics (k) and covariate inter-correlations.

Main Results:

• The overall imbalance index (I) has a theoretical expected value of 0.798 and a variance of 0.363/k for independent site characteristics.
• Simulation results demonstrate that I is robust when the number of covariates (k) exceeds 3 and covariates are not highly inter-correlated.
• The index's properties remain reliable across various covariate distributions and inter-correlation levels.

Conclusions:

• Recommend using the 10th percentile of the overall imbalance index (I) as a threshold for sufficient site balance in CCR.
• Suggest incorporating individual covariate criteria alongside overall balance criteria for defining acceptable randomizations in CCR.