Staggered rollout cluster randomized experiments (SR-CREs) involve sequential treatment adoption across clusters, requiring analysis methods that address a general class of dynamic causal effects, anticipation, and non-ignorable cluster-period sizes. Without imposing any outcome modeling assumptions, we study regression estimators using individual data, cluster-period averages, and scaled cluster-period totals, with and without covariate adjustment from a design-based perspective. We establish consistency and asymptotic normality of each estimator under a randomization-based framework and prove that the associated variance estimators are asymptotically conservative in the Löwner ordering. Furthermore, we conduct a unified efficiency comparison of the estimators and provide recommendations. We highlight the efficiency advantage of using estimators based on scaled cluster-period totals with covariate adjustment over their counterparts using individual-level data and cluster-period averages. Our results rigorously justify linear regression estimators as model-assisted methods to address an entire class of dynamic causal effects in SR-CREs.

翻译：交错推出聚类随机实验涉及跨聚类的顺序处理采纳，需要分析方法来处理一类广泛的动态因果效应、预期效应以及不可忽略的聚类-时期规模。在不施加任何结果建模假设的前提下，我们从设计基的角度研究了使用个体数据、聚类-时期平均值以及缩放聚类-时期总和的回归估计量，包括协变量调整与未调整的情况。我们在随机化基的框架下建立了每个估计量的一致性和渐近正态性，并证明了在Löwner序意义下，相关的方差估计量是渐近保守的。此外，我们对这些估计量进行了统一的效率比较并提供了建议。我们强调了使用基于缩放聚类-时期总和并带有协变量调整的估计量，相较于使用个体层面数据和聚类-时期平均值的对应估计量，所具有的效率优势。我们的结果严格证明了线性回归估计量作为模型辅助方法，能够有效处理交错推出聚类随机实验中的一整类动态因果效应。