Cluster minimal sufficient balance (CMSB): an efficient covariate balancing randomization method for cluster randomized trials
Jiaxin Cai, Shanshan Suo, Valirie Ndip Agbor, Carole Khairallah, Binyan Zhang, Lingxia Zeng, Hong Yan, Fang Shao, Tao Chen, Chao Li · BMC Medical Research Methodology · 2026
BACKGROUND: Cluster randomized trials (CRTs) require balanced baseline covariates to yield unbiased estimates of treatment effects. Existing approaches such as constrained randomization can improve balance but may compromise allocation randomness. We introduce Cluster Minimal Sufficient Balance (CMSB), a cluster randomization method designed to enhance covariate balance while preserving allocation randomness and computational efficiency. METHODS: CMSB integrates dynamic imbalance monitoring with conditional biased randomization into a single procedure. The method accommodates both continuous and categorical covariates and was evaluated through simulation studies comparing its performance with constrained randomization, simple randomization, block randomization, stratified randomization, and minimization across varying numbers of clusters and covariate dimensions. An empirical application further assessed its practical utility. RESULTS: In high-dimensional settings with 10 covariates, CMSB achieved a 45% greater improvement in covariate balance compared to constrained randomization, while maintaining near-optimal allocation randomness (correct guess probability: 49.79% versus 61.03% for minimization). CMSB reduced mean allocation time from over 100 s under constrained randomization to 0.116 s per allocation, even when simulating up to 2,000 randomization schemes. In the empirical application, CMSB demonstrated a 76% improvement in covariate balance relative to simple randomization. CONCLUSIONS: CMSB effectively balances the competing demands of covariate balance, allocation randomness, and computational efficiency in cluster randomized trials. Its ability to handle high-dimensional covariates makes it particularly suitable for large-scale trials.