In cluster-randomized experiments, there is emerging interest in exploring the causal mechanism in which a cluster-level treatment affects the outcome through an intermediate outcome. Despite an extensive development of causal mediation methods in the past decade, only a few exceptions have been considered in assessing causal mediation in cluster-randomized studies, all of which depend on parametric model-based estimators. In this article, we develop the formal semiparametric efficiency theory to motivate several doubly-robust methods for addressing several mediation effect estimands corresponding to both the cluster-average and the individual-level treatment effects in cluster-randomized experiments -- the natural indirect effect, natural direct effect, and spillover mediation effect. We derive the efficient influence function for each mediation effect, and carefully parameterize each efficient influence function to motivate practical strategies for operationalizing each estimator. We consider both parametric working models and data-adaptive machine learners to estimate the nuisance functions, and obtain semiparametric efficient causal mediation estimators in the latter case. Our methods are illustrated via extensive simulations and two completed cluster-randomized experiments.

翻译：在整群随机实验中，探索群组层面处理通过中介变量影响结果的因果机制正受到日益关注。尽管过去十年因果中介分析方法取得了长足发展，但在整群随机研究中评估因果中介效应的研究仍属少数，且均依赖于基于参数模型的估计量。本文通过建立形式化的半参数效率理论，提出了多种双重稳健方法，用于估计整群随机实验中与群组平均处理效应和个体层面处理效应相对应的多种中介效应——自然间接效应、自然直接效应和溢出中介效应。我们推导了每种中介效应的有效影响函数，并通过精心参数化每个有效影响函数，提出了实现各估计量的实用策略。我们同时采用参数工作模型和数据自适应机器学习方法来估计冗余函数，并在后一种情况下获得了半参数高效的因果中介估计量。通过大量模拟实验和两项已完成的整群随机实验，我们展示了所提方法的有效性。