In mediation analysis, the exposure often influences the mediating effect, i.e., there is an interaction between exposure and mediator on the dependent variable. When the mediator is high-dimensional, it is necessary to identify non-zero mediators (M) and exposure-by-mediator (X-by-M) interactions. Although several high-dimensional mediation methods can naturally handle X-by-M interactions, research is scarce in preserving the underlying hierarchical structure between the main effects and the interactions. To fill the knowledge gap, we develop the XMInt procedure to select M and X-by-M interactions in the high-dimensional mediators setting while preserving the hierarchical structure. Our proposed method employs a sequential regularization-based forward-selection approach to identify the mediators and their hierarchically preserved interaction with exposure. Our numerical experiments showed promising selection results. Further, we applied our method to ADNI morphological data and examined the role of cortical thickness and subcortical volumes on the effect of amyloid-beta accumulation on cognitive performance, which could be helpful in understanding the brain compensation mechanism.

翻译：在中介分析中，暴露变量常对中介效应产生影响，即暴露变量与中介变量在因变量上存在交互作用。当中介变量为高维数据时，有必要识别非零中介变量（M）以及暴露与中介变量的交互作用（X-by-M交互）。尽管现有若干高维中介分析方法可自然处理X-by-M交互，但在保留主效应与交互作用之间层级结构方面的研究尚显不足。为填补这一空白，我们提出XMInt程序，用于在高维中介变量情境下选择中介变量M及其与暴露变量的交互作用，同时保留层级结构。所提方法采用基于序贯正则化的前向选择策略，识别中介变量及其与暴露变量间具有层级保持的交互作用。数值实验表明该方法具有良好的选择效果。进一步，我们将该方法应用于ADNI形态学数据，检验皮质厚度与皮层下体积对β-淀粉样蛋白积累影响认知表现的调节作用，这有助于理解大脑补偿机制。