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Background  In cluster-randomized controlled trials (C-RCTs), covariate-constrained randomization (CCR) methods efficiently control imbalance in multiple baseline cluster-level variables, but the choice of imbalance metric to define the subset of “adequately balanced” possible allocation schemes for C-RCTs involving more than two arms and continuous variables is unclear. In an ongoing three-armed C-RCT, we chose the min(three Kruskal–Wallis [KW] test  P  values) > 0.30 as our metric. We use simulation studies to explore the performance of this and other metrics of baseline variable imbalance in CCR.    Methods  We simulated three continuous variables across three arms under varying allocation ratios and assumptions. We compared the performance of min(analysis of variance [ANOVA]  P  value) > 0.30, min(KW  P  value) > 0.30, multivariate analysis of variance (MANOVA)  P  value > 0.30, min(nine possible  t  test  P  values) > 0.30, and min(Wilcoxon rank-sum [WRS]  P  values) > 0.30.    Results  Pairwise comparison metrics ( t  test and WRS) tended to be the most conservative, providing the smallest subset of allocation schemes (10%–13%) meeting criteria for acceptable balance. Sensitivity of the min( t  test  P  values) > 0.30 for detecting non-trivial imbalance was 100% for both hypothetical and resampled simulation scenarios. The KW criterion maintained higher sensitivity than both the MANOVA and ANOVA criteria (89% to over 99%) but was not as sensitive as pairwise criteria.    Conclusions  Our criterion, the KW  P  value > 0.30, to signify “acceptable” balance was not the most conservative, but it appropriately identified imbalance in the majority of simulations. Since all are related, CCR algorithms involving any of these imbalance metrics for continuous baseline variables will ensure robust simultaneous control over multiple continuous baseline variables, but we recommend care in determining the threshold of “acceptable” levels of (im)balance.    Trial registration  This trial is registered on ClinicalTrials.gov (initial post: December 1, 2016; identifier:  NCT02979444 ).    Electronic supplementary material  The online version of this article (10.1186/s13063-019-3324-5) contains supplementary material, which is available to authorized users.

Choosing an imbalance metric for covariate-constrained randomization in multiple-arm cluster-randomized trials