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 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, we validate our new approach by re-proving some known properties of complete randomization and restricted randomization. Second, we propose a novel diagnostic measure for restricted designs that only use the information embedded in the combinatorics of the design. Third, we show that the variance of the mean squared error of the difference-in-means estimator in a randomized experiment is a linear function of this diagnostic measure. 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设计,这种设计在随机控制的试验中使观察到的共变体实现平衡。然而,如果限制严格,则处理效果估计器有可能发生非常高的中位方错误。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,我们通过重新证明某些已知的完全随机化和限制随机化的特性来验证我们的新办法。第二,我们建议对限制性设计采取新的诊断措施,即只使用设计组合器中所含的信息。第三,我们表明随机化试验中,处理效果估计器差异估计器的平均平方错误是这一诊断措施的线性功能。最后,我们确定受限制设计可能导致获取高端点误差的风险增加的情况,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,并且可以用来评估所观察到的组合体间平衡和避免过于限制性设计之间的交易。