We explore methods to reduce the impact of unobserved confounders on the causal mediation analysis of high-dimensional mediators with spatially smooth structures, such as brain imaging data. The key approach is to incorporate the latent individual effects, which influence the structured mediators, as unobserved confounders in the outcome model, thereby potentially debiasing the mediation effects. We develop BAyesian Structured Mediation analysis with Unobserved confounders (BASMU) framework, and establish its model identifiability conditions. Theoretical analysis is conducted on the asymptotic bias of the Natural Indirect Effect (NIE) and the Natural Direct Effect (NDE) when the unobserved confounders are omitted in mediation analysis. For BASMU, we propose a two-stage estimation algorithm to mitigate the impact of these unobserved confounders on estimating the mediation effect. Extensive simulations demonstrate that BASMU substantially reduces the bias in various scenarios. We apply BASMU to the analysis of fMRI data in the Adolescent Brain Cognitive Development (ABCD) study, focusing on four brain regions previously reported to exhibit meaningful mediation effects. Compared with the existing image mediation analysis method, BASMU identifies two to four times more voxels that have significant mediation effects, with the NIE increased by 41%, and the NDE decreased by 26%.

翻译：本文探讨了在具有空间平滑结构的高维中介变量（如脑成像数据）的因果中介分析中，降低未观测混杂因子影响的方法。核心方法是将影响结构化中介变量的潜在个体效应作为未观测混杂因子纳入结果模型，从而可能消除中介效应的偏差。我们开发了包含未观测混杂因子的贝叶斯结构化中介分析框架，并建立了其模型可识别性条件。理论分析了当中介分析忽略未观测混杂因子时，自然间接效应与自然直接效应的渐近偏差。针对该框架，我们提出了一种两阶段估计算法，以减轻这些未观测混杂因子对中介效应估计的影响。大量模拟实验表明，该框架能在多种场景下显著减少偏差。我们将该框架应用于青少年脑认知发展研究的fMRI数据分析，重点关注先前报道显示具有显著中介效应的四个脑区。与现有影像中介分析方法相比，该框架识别出的具有显著中介效应的体素数量增加2至4倍，其中自然间接效应增加41%，自然直接效应降低26%。