In situations with non-manipulable exposures, interventions can be targeted to shift the distribution of intermediate variables between exposure groups to define interventional disparity indirect effects. In this work, we present a theoretical study of identification and nonparametric estimation of the interventional disparity indirect effect among the exposed. The targeted estimand is intended for applications examining the outcome risk among an exposed population for which the risk is expected to be reduced if the distribution of a mediating variable was changed by a (hypothetical) policy or health intervention that targets the exposed population specifically. We derive the nonparametric efficient influence function, study its double robustness properties and present a targeted minimum loss-based estimation (TMLE) procedure. All theoretical results and algorithms are provided for both uncensored and right-censored survival outcomes. With offset in the ongoing discussion of the interpretation of non-manipulable exposures, we discuss relevant interpretations of the estimand under different sets of assumptions of no unmeasured confounding and provide a comparison of our estimand to other related estimands within the framework of interventional (disparity) effects. Small-sample performance and double robustness properties of our estimation procedure are investigated and illustrated in a simulation study.

翻译：在非干预暴露的情形下，可通过干预手段改变暴露组与对照组之间中间变量的分布，从而定义干预差异间接效应。本文针对暴露人群中干预差异间接效应的识别与非参数估计开展理论研究。该目标估计量适用于评估暴露人群结局风险的应用场景——若通过专门针对该人群的（假设性）政策或健康干预改变中介变量分布，预计其风险将降低。我们推导了非参数有效影响函数，研究了其双重稳健性，并提出基于目标最小损失估计（TMLE）的算法。针对无删失和右删失生存结局两种情形，均给出了完整的理论结果与算法步骤。结合当前关于非干预暴露解释的讨论，我们在不同无混杂假设条件下探讨了该估计量的相关释义，并在干预（差异）效应框架下将其与其他相关估计量进行了比较。通过模拟研究考察并展示了所提估计方法的小样本表现与双重稳健性。