Randomized controlled trials (RCTs) are used to evaluate treatment effects. When individuals are grouped together, clustered RCTs are conducted. Stratification is recommended to reduce imbalance of baseline covariates between treatment and control. In practice, this can lead to comparisons between clusters of very different sizes. As a result, direct adjustment estimators that average differences of means within the strata may be inconsistent. We study differences of inverse probability weighted means of a treatment and a control group -- H\'ajek effect estimators -- under two common forms of stratification: small strata that increase in number; or larger strata with growing numbers of clusters in each. Under either scenario, mild conditions give consistency and asymptotic Normality. We propose a variance estimator applicable to designs with any number of strata and strata of any size. We describe a special use of the variance estimator that improves small sample performance of Wald-type confidence intervals. The H\'ajek effect estimator lends itself to covariance adjustment, and our variance estimator remains applicable. Simulations and real-world applications in children's nutrition and education confirm favorable operating characteristics, demonstrating advantages of the H\'ajek effect estimator beyond its simplicity and ease of use.

翻译：随机对照试验（RCTs）用于评估处理效应。当个体被分组时，会实施聚类随机对照试验。推荐采用分层设计以减少处理组与对照组间基线协变量的不平衡。在实践中，这可能导致规模差异极大的聚类之间的比较。因此，对层内均值差异进行平均的直接调整估计量可能不一致。我们研究了在两种常见分层形式下处理组与对照组的逆概率加权均值之差——即Hájek效应估计量：一种是数量增加的小规模分层；另一种是每层内聚类数量增长的大规模分层。在任一情形下，温和的条件即可保证估计量的一致性与渐近正态性。我们提出了一种适用于任意层数及任意层规模设计的方差估计量。我们描述了该方差估计量的一种特殊用途，可改进Wald型置信区间的小样本表现。Hájek效应估计量适用于协方差调整，且我们的方差估计量依然适用。儿童营养与教育领域的仿真与实际应用证实了其良好的操作特性，展现了Hájek效应估计量在简洁性与易用性之外的优越性。