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 single variance estimator which is consistent in either regime. 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. We additionally 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. Finally, we propose a covariate-adjusted estimator which adjusts for additional baseline covariates not used for treatment assignment, and establish conditions under which such an estimator leads to improvements in precision. A simulation study confirms the practical relevance of our theoretical results.

翻译：本文探讨了在治疗状态依据“匹配对”设计确定的群组随机试验中的推断问题。此处，群组随机实验指在群组层面上分配治疗；而“匹配对”设计则指根据基线群组层面协变量将群组样本配对，并在每对中随机选择一个群组接受治疗。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基于群组规模得出两组不同结论。随后提出一个单一方差估计量，该估计量在两种情形下均保持一致。结合这些结果，我们建立了基于这些估计量的检验的渐近精确性。接着，我们考察了基于线性回归构造的t检验两种常见检验程序的性质，并论证了两种方法在我们的框架下通常具有保守性。此外，我们研究了通过置换对内群组治疗状态实施的随机化检验，并证明了该检验在检验特定零假设时的有限样本与渐近有效性。最后，我们提出一种协变量调整估计量，该估计量针对未用于治疗分配的额外基线协变量进行调整，并确立了该估计量提升精度所需的条件。模拟研究验证了理论结果的实际相关性。