标题： 高维设置中存在交互效应时中介功能的无偏估计量 显示英文标题

标题： A Debiased Estimator for the Mediation Functional in Ultra-High-Dimensional Setting in the Presence of Interaction Effects

摘要： 中介分析是一种关键工具，用于揭示处理如何影响结果的机制，提供更深入的因果见解并指导有效的干预措施。 尽管在分析固定/低维中介变量和协变量的中介效应方面取得了进展，但在存在(超)高维中介变量和协变量的情况下，对中介函数的估计和推断的理解仍然有限。 在本文中，我们提出了一种在高维设置下的中介函数估计器，该估计器能够容纳协变量和处理之间的相互作用在生成中介变量中的作用，以及协变量和处理与中介变量和处理之间的相互作用在生成响应中的作用。 我们证明了我们的估计器是$\sqrt{n}$一致的且渐近正态的，从而使得直接和间接处理效应的可靠推断成为可能，并具有渐近有效的置信区间。 我们工作的关键技术贡献是开发了一种多步骤去偏技术，该技术在其他具有类似结构复杂性的统计设置中也可能具有价值，其中准确的估计依赖于去偏。 我们通过广泛的模拟研究评估了我们提出的方法，并将其应用于TCGA肺癌数据集，以估计吸烟通过DNA甲基化介导对肺癌患者生存时间的影响。 显示英文摘要

摘要： Mediation analysis is a crucial tool for uncovering the mechanisms through which a treatment affects the outcome, providing deeper causal insights and guiding effective interventions. Despite advances in analyzing the mediation effect with fixed/low-dimensional mediators and covariates, our understanding of estimation and inference of mediation functional in the presence of (ultra)-high-dimensional mediators and covariates is still limited. In this paper, we present an estimator for mediation functional in a high-dimensional setting that accommodates the interaction between covariates and treatment in generating mediators, as well as interactions between both covariates and treatment and mediators and treatment in generating the response. We demonstrate that our estimator is $\sqrt{n}$-consistent and asymptotically normal, thus enabling reliable inference on direct and indirect treatment effects with asymptotically valid confidence intervals. A key technical contribution of our work is to develop a multi-step debiasing technique, which may also be valuable in other statistical settings with similar structural complexities where accurate estimation depends on debiasing. We evaluate our proposed methodology through extensive simulation studies and apply it to the TCGA lung cancer dataset to estimate the effect of smoking, mediated by DNA methylation, on the survival time of lung cancer patients.