This paper considers the problem of inference in cluster randomized trials where treatment status is determined according to a "matched pairs'' design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the cluster; by a "matched pairs'' design we mean that a sample of clusters is paired according to baseline, cluster-level covariates and, within each pair, one cluster is selected at random for treatment. We study the large sample behavior of a weighted difference-in-means estimator and derive two distinct sets of results depending on if the matching procedure does or does not match on cluster size. We then propose a variance estimator which is consistent in either case. Combining these results establishes the asymptotic exactness of tests based on these estimators. Next, we consider the properties of two common testing procedures based on $t$-tests constructed from linear regressions, and argue that both are generally conservative in our framework. Finally, we study the behavior of a randomization test which permutes the treatment status for clusters within pairs, and establish its finite sample and asymptotic validity for testing specific null hypotheses. A simulation study confirms the practical relevance of our theoretical results.

翻译：本文探讨了在治疗状态根据"配对"设计确定的集群随机试验中的推断问题。所谓集群随机试验，是指治疗分配在集群层面进行；而"配对"设计则指根据基线层面的集群协变量对集群样本进行配对，并在每对中随机选择一个集群接受治疗。我们研究了加权均值差估计量的大样本性质，并根据匹配过程是否涉及集群规模，得出了两组不同的结论。随后，我们提出了一种在两种情形下均具有一致性的方差估计量。结合这些结果，我们证明了基于这些估计量的检验具有渐近精确性。接着，我们考察了两种基于线性回归构造的t检验常用程序的性质，并论证了在我们的框架中它们通常偏于保守。最后，我们研究了一种在配对内随机置换治疗状态的随机化检验的行为，并证明了其在有限样本和渐近条件下对特定原假设检验的有效性。模拟研究证实了我们理论结果的实际意义。