In cluster-randomized trials (CRTs), there is emerging interest in exploring the causal mechanism in which a cluster-level treatment affects the outcome through an intermediate outcome. The majority of existing causal mediation methods are applicable to independent data and only a few exceptions have considered assessing causal mediation in CRTs, all of which heavily depend on parametric assumptions. In this article, we develop a formal semiparametric efficiency theory to motivate new doubly-robust methods for addressing different mediation effect estimands -- the natural indirect effect, individual mediation effect, and spillover mediation effect (the extent to which one's outcome is influenced by others' mediators). We derive the efficient influence function for each estimand, and carefully parameterize each efficient influence function to motivate practical estimators. We consider both parametric working models and data-adaptive machine learners to estimate the nuisance functions, and obtain the semiparametric efficient estimators in the latter case. We conduct simulation studies to demonstrate the finite-sample performance of our new estimators and illustrate our proposed methods by reanalyzing a real-world CRT.

翻译：在群组随机试验中，研究者日益关注探索群组层面处理通过中间变量影响结局的因果机制。现有因果中介分析方法大多适用于独立数据，仅少数研究尝试评估群组随机试验中的因果中介效应，且均严重依赖参数化假设。本文建立了形式化的半参数有效性理论，提出了针对不同中介效应估计目标——自然间接效应、个体中介效应及溢出中介效应（个体结局受他人中介变量影响的程度）的新型双重稳健估计方法。我们推导了各估计量的有效影响函数，并通过精心参数化处理构建了实用估计量。研究采用参数工作模型与数据自适应机器学习方法估计冗余函数，并在后一种情形下获得了半参数有效估计量。通过模拟研究验证了新估计量在有限样本下的性能，并通过对实际群组随机试验的再分析展示了所提方法的应用价值。