Estimating natural effects is a core task in causal mediation analysis. Existing triply robust (TR) frameworks (Tchetgen Tchetgen & Shpitser 2012) and their extensions have been developed to estimate the natural effects. In this work, we introduce a new quadruply robust (QR) framework that enlarges the model class for unbiased identification. We study two modeling strategies. The first is a nonparametric modeling approach, under which we propose a general QR estimator that supports the use of machine learning methods for nuisance estimation. We also study high-dimensional settings, where the dimensions of covariates and mediators may both be large. In these settings, we adopt a parametric modeling strategy and develop a model quadruply robust (MQR) estimator to limit the impact of model misspecification. Simulation studies and a real data application demonstrate the finite-sample performance of the proposed methods.

翻译：估计自然效应是因果中介分析的核心任务。现有三重稳健（TR）框架（Tchetgen Tchetgen & Shpitser 2012）及其扩展已被开发用于估计自然效应。在本研究中，我们引入了一个新的四重稳健（QR）框架，该框架扩展了无偏识别的模型类别。我们研究了两种建模策略。第一种是非参数建模方法，在此框架下我们提出了一种通用的QR估计量，支持使用机器学习方法进行干扰参数估计。我们还研究了高维设置，其中协变量和中介变量的维度可能都很大。在这些设置中，我们采用参数化建模策略，并开发了一种模型四重稳健（MQR）估计量，以限制模型设定错误的影响。模拟研究和实际数据应用证明了所提方法在有限样本下的性能。