Faculty of Arts and Sciences, Science Center, Harvard University, Cambridge, MA, USA.
Stat Methods Med Res. 2019 May;28(5):1378-1398. doi: 10.1177/0962280218756689. Epub 2018 Feb 16.
We present a randomization-based inferential framework for experiments characterized by a strongly ignorable assignment mechanism where units have independent probabilities of receiving treatment. Previous works on randomization tests often assume these probabilities are equal within blocks of units. We consider the general case where they differ across units and show how to perform randomization tests and obtain point estimates and confidence intervals. Furthermore, we develop rejection-sampling and importance-sampling approaches for conducting randomization-based inference conditional on any statistic of interest, such as the number of treated units or forms of covariate balance. We establish that our randomization tests are valid tests, and through simulation we demonstrate how the rejection-sampling and importance-sampling approaches can yield powerful randomization tests and thus precise inference. Our work also has implications for observational studies, which commonly assume a strongly ignorable assignment mechanism. Most methodologies for observational studies make additional modeling or asymptotic assumptions, while our framework only assumes the strongly ignorable assignment mechanism, and thus can be considered a minimal-assumption approach.
我们提出了一种基于随机化的推断框架，用于具有强可忽略分配机制的实验，其中单位具有独立的接受治疗的概率。以前关于随机化检验的工作通常假设这些概率在单位的块内是相等的。我们考虑了它们在单位之间不同的一般情况，并展示了如何进行随机化检验以及如何获得点估计和置信区间。此外，我们还开发了拒绝抽样和重要抽样方法，用于根据任何感兴趣的统计量（例如，接受治疗的单位数量或协变量平衡的形式）进行基于随机化的推断。我们证明了我们的随机化检验是有效的检验，并且通过模拟我们展示了拒绝抽样和重要抽样方法如何能够产生强大的随机化检验，从而实现精确的推断。我们的工作也对观察性研究有影响，观察性研究通常假设具有强可忽略的分配机制。大多数观察性研究的方法学都做了额外的建模或渐近假设，而我们的框架只假设了强可忽略的分配机制，因此可以被认为是一种最小假设的方法。
