Center on Aging and Health, Division of Geriatric Medicine and Gerontology, Johns Hopkins University, 2024 East Monument Street, Baltimore, MD, 21205, USA.
Trials. 2021 Mar 6;22(1):190. doi: 10.1186/s13063-021-05122-x.
Pragmatic trials often consist of cluster-randomized controlled trials (C-RCTs), where staff of existing clinics or sites deliver interventions and randomization occurs at the site level. Covariate-constrained randomization (CCR) methods are often recommended to minimize imbalance on important site characteristics across intervention and control arms because sizable imbalances can occur by chance in simple randomizations when the number of units to be randomized is relatively small. CCR methods involve multiple random assignments initially, an assessment of balance achieved on site-level covariates from each randomization, and the final selection of an allocation that produces acceptable balance. However, no clear consensus exists on how to assess imbalance or identify allocations with sufficient balance. In this article, we describe an overall imbalance index (I) that is based on the mean of the absolute value of the standardized differences in means on the site characteristics.
We derive the theoretical distribution of I, then conduct simulation studies to examine its empirical properties under the varying covariate distributions and inter-correlations.
I has an expected value of 0.798 and, assuming independent site characteristics, a variance of 0.363/k, where k is the number of site characteristics being balanced. Simulations indicated that the properties of I are robust under varying covariate circumstances as long as k is greater than 3 and the covariates are not too highly inter-correlated.
We recommend that values of I below the 10th percentile indicate sufficient overall site balance in CCRs. Definitions of acceptable randomizations might also include individual covariate criteria specified in advance, in addition to overall balance criteria.
实用临床试验通常由整群随机对照试验（C-RCT）组成，其中现有诊所或站点的工作人员提供干预措施，并且随机化发生在站点级别。通常建议使用协变量约束随机化（CCR）方法来最小化干预组和对照组之间重要站点特征的不平衡，因为在随机化单位数量相对较小时，简单随机化可能会因机会而导致相当大的不平衡。CCR 方法最初涉及多次随机分配，评估每次随机分配在站点水平协变量上实现的平衡，以及最终选择产生可接受平衡的分配。然而，对于如何评估不平衡或确定具有足够平衡的分配，目前尚无明确共识。在本文中，我们描述了一种基于站点特征的均值标准化差异绝对值的总体不平衡指数（I）。
我们推导出 I 的理论分布，然后进行模拟研究，以在不同协变量分布和相互关联下检验其经验特性。
I 的期望值为 0.798，并且假设站点特征独立，方差为 0.363/k，其中 k 是要平衡的站点特征数量。模拟表明，只要 k 大于 3 且协变量之间的相关性不太高，I 的特性在不同的协变量情况下是稳健的。
我们建议，在 CCR 中，I 值低于第 10 个百分位数表示总体站点平衡足够。可接受的随机化的定义也可能包括预先指定的个别协变量标准，以及总体平衡标准。
