Recently, there as been an increasing interest in the use of heavily restricted randomization designs which enforces balance on observed covariates in randomized controlled trials. However, when restrictions are too strict, there is a risk that the treatment effect estimator will have a very high mean squared error. In this paper, we formalize this risk and propose a novel combinatoric-based approach to describe and address this issue. First, some known properties of complete randomization and restricted randomization are re-proven using basic combinatorics. Second, a novel diagnostic measure that only use the information embedded in the combinatorics of the design is proposed. Finally, we identify situations in which restricted designs can lead to an increased risk of getting a high mean squared error and discuss how our diagnostic measure can be used to detect such designs. Our results have implications for any restricted randomization design and can be used to evaluate the trade-off between enforcing balance on observed covariates and avoiding too restrictive designs.
翻译：最近,人们越来越关注使用限制严格的随机化设计,这种设计在随机控制的试验中对观察到的共变体实行平衡。但是,如果限制过于严格,那么治疗效果估计器就有可能出现非常高的中度正方差。在本文件中,我们正式确定这一风险,并提出一种新的组合法来描述和解决这一问题。首先,使用基本的组合式组合法,重新发现一些已知的完全随机化和限制随机化的特性。第二,提出了新的诊断措施,仅使用设计组合法中所含的信息。最后,我们确定在何种情况下,限制设计可能会增加获得高度中度正方差的风险,并讨论如何使用我们的诊断措施来检测这种设计。我们的结果对任何限制性随机化设计都有影响,并可用于评估对观察到的共变体实施平衡和避免过于限制性的设计之间的利弊。
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