标题： 超高维设置下存在交互效应时的中介函数的无偏估计量 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： 中介分析是一种重要的工具，用于揭示治疗如何影响结果的机制，提供更深层次的原因洞见并指导有效的干预措施。尽管在分析具有固定/低维度中介变量和协变量的中介效应方面取得了进展，但我们对在（超）高维度中介变量和协变量存在的情况下中介函数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估计中介函数的方法，该方法可以适应协变量和治疗在生成中介变量时的相互作用，以及协变量和治疗以及中介变量和治疗在生成响应时的相互作用。我们证明了我们的估计量是$\sqrt{n}$一致且渐近正态的，从而能够通过渐近有效的置信区间可靠地推断直接和间接的治疗效果。我们工作的关键技术贡献在于开发了一种多步去偏技术，这在其他具有类似结构复杂性的统计环境中也可能有价值，在这些环境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，并将其应用于癌症基因组图谱肺癌数据集，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.