Matching is a common approach to covariate adjustment in estimating causal effects in observational studies. It is important to assess covariate balance of the matched samples. This is usually done informally, in ways that have a number of limitations. First, there are many diagnostics, even if covariates are assessed one at a time, which raises multiplicity issues. In addition, joint distributions of covariates, even bivariate distributions, are often ignored. Further, it is an open question whether diagnostics identify the major problems. To address these issues, a formal assessment of covariate balance is developed in the current paper. Unlike the common informal diagnostics, the proposed method compares both marginal distributions and joint distributions of the matched sample with those of the benchmark, complete randomizations. The method controls the probability of falsely identifying a covariate imbalance among many comparisons, yet it has a high probability of correctly detecting and identifying a major problem. An R package met implementing the proposed method is available on CRAN.

中文翻译：

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评估和改进抗抑郁药和骨密度的匹配比较

匹配是在观察性研究中估计因果效应时进行协变量调整的常用方法。评估匹配样本的协变量平衡很重要。这通常是非正式的，以有许多限制的方式进行。首先，即使一次评估一个协变量，也有许多诊断方法，这会引发多重性问题。此外，协变量的联合分布，甚至是双变量分布，常常被忽略。此外，诊断是否能确定主要问题是一个悬而未决的问题。为了解决这些问题，本文对协变量平衡进行了正式评估。与常见的非正式诊断不同，所提出的方法将匹配样本的边际分布和联合分布与基准的完全随机化进行比较。该方法控制了在许多比较中错误地识别协变量不平衡的概率，但它具有正确检测和识别主要问题的高概率。一个CRAN上提供了实现所提出方法的R包。