带有未测量混杂的Baron-Kenny中介方法的可解释敏感性分析
Interpretable sensitivity analysis for the Baron-Kenny approach to mediation with unmeasured confounding
AI总结：
本文针对未测量混杂下Baron-Kenny中介分析估计有偏的问题，推导了向量线性回归的遗漏变量偏差公式，提出了对应有向无环图自然分解的可解释敏感性参数，并定义了“中介稳健性值”以评估结果对未测量混杂的稳健性，同时证明了所有敏感性边界均紧致可达。
摘要：
中介分析评估暴露在多大程度上通过中介间接影响结局，以及在多大程度上通过其他路径直接产生影响。流行的Baron-Kenny方法基于线性回归估计暴露对结局的间接和直接效应。然而，当暴露和中介未被随机化时，由于未测量混杂，估计可能有偏。我们首先推导了具有向量响应和回归变量的线性回归中的一般遗漏变量偏差公式。然后我们利用这些公式开发了一种在存在未测量混杂时Baron-Kenny方法的敏感性分析方法。为确保可解释性，我们表达的敏感性参数对应于有向无环图联合分布的自然分解。它们分别测量未测量混杂因素与暴露、中介和结局之间的偏相关。我们进一步提出了一种称为“中介稳健性值”（或简称“稳健性值”）的新度量，以评估基于Baron-Kenny方法的结果对未测量混杂的稳健性。直观上，稳健性值测量了未测量混杂对暴露、中介和结局解释的变异比例的最大值的最小值，以推翻直接和间接效应估计的结果。重要的是，我们证明了所有敏感性边界都是可达的，因而是紧致的。
英文摘要：
Mediation analysis assesses the extent to which the exposure affects the outcome indirectly through a mediator and the extent to which it operates directly through other pathways. The popular Baron-Kenny approach estimates the indirect and direct effects of the exposure on the outcome based on linear regressions. However, when the exposure and the mediator are not randomized, the estimates may be biased due to unmeasured confounding. We first derive general omitted-variable bias formulas in linear regressions with vector responses and regressors. We then use the formulas to develop a sensitivity analysis method for the Baron-Kenny approach in the presence of unmeasured confounding. To ensure interpretability, we express the sensitivity parameters to correspond to the natural factorization of the joint distribution of the direct acyclic graph. They measure the partial correlation between the unmeasured confounder and the exposure, mediator, and outcome, respectively. We further propose a novel measure called the "robustness value for mediation" or simply the "robustness value", to assess the robustness of results based on the Baron-Kenny approach with respect to unmeasured confounding. Intuitively, the robustness value measures the minimum value of the maximum proportion of variability explained by the unmeasured confounding, for the exposure, mediator, and outcome, to overturn the results of the direct and indirect effect estimates. Importantly, we prove that all our sensitivity bounds are attainable and thus sharp.
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