Causal Inference Methods for Mediation and Comparisons of Confidence Regions

在流行病学、临床研究和社会科学中，关于治疗和风险因素的因果效应的推论被用来设计更有效的干预措施。 这个项目的重点是因果推理的统计方法的发展。 本计画的第一部份将发展一种中介分析的因果推论方法。 如果一种治疗对结果有有益的影响，那么研究它影响结果的途径通常是有意义的。直接效应和间接效应将处理的效应分解为由协变量（中介变量）介导的部分和不受协变量介导的部分。 例如，在艾滋病毒/艾滋病研究中，重要的是要估计抗逆转录病毒疗法（ART）对艾滋病毒母婴传播的影响有多大程度上是由ART治疗对母亲血液中艾滋病毒载量的影响介导的。 在医学、心理学、政治学和经济学中，区分间接效应和直接效应变得越来越重要。 因此，至关重要的是，制定适当的统计方法，以估计在各种环境中的直接和间接影响，包括在其中有治疗后的调解人和结果的共同原因的设置。 本项目的第二部分将比较置信区域。 最近，统计界对远离p值进行了广泛的讨论。 P值可以使研究人员得出结论，即使这种效果非常小，并且与临床无关，治疗也具有显著的效果。 置信区域是p值的明显替代方案，因为它们提供了与数据最一致的感兴趣参数的值范围。 虽然对p值的比较进行了广泛的研究，并且定期报告置信区域，但置信区域的比较相对较少受到关注。 在这个项目中，置信区域将根据渐近等价的概念进行比较。 自然的直接和间接效应使用跨世界的反事实：在没有处理的情况下，中介“设置”其值的处理结果。 跨世界的反事实永远无法被观察到，因为它们涉及两种不同治疗方法下的数量，其中只有一种治疗方法被给予任何特定的患者或单位。 PI最近提出了有机的直接和间接影响，以避免使用跨世界的反事实。 当调解人无法“设定”时，有机的直接和间接效应也适用。 例如，母亲血液中的艾滋病毒载量无法设定;如果可以设定，医生会将其设定为零。 在这个项目的第一部分，有机的直接和间接影响将扩展到设置与治疗后的调解人和结果的共同原因。 它将被证明，与自然的直接和间接的影响，估计和置信区间，可以开发在该环境中的有机影响。 本项目的第二部分将比较置信区域。大多数关于置信区域比较的工作都研究了覆盖概率、置信区间长度和小样本性质。在本项目中，将根据不同置信区域之间Hausdorff距离的渐近行为，对大样本的置信区域进行比较。部分重叠的区间之间的豪斯多夫距离就是区间左极限和右极限之差的最大值。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

In epidemiology, clinical research, and the social sciences, inferences about the causal effects of treatments and risk factors are used to design more effective interventions. This project focuses on the development of statistical methods for causal inference. The first part of this project will develop a causal inference method for mediation analysis. If a treatment has a beneficial effect on an outcome, it is often of interest to investigate what are the pathways by which it affects the outcome. Direct and indirect effects decompose the effect of a treatment into the part that is mediated by a covariate (the mediator) and the part that is not. For example, in HIV/ AIDS research, it is important to estimate how much of the effect of Antiretroviral Therapy (ART) on mother-to-child-transmission of HIV is mediated by the effect of ART treatment on the HIV viral load in the mother's blood. In medicine, psychology, political science, and economics, differentiating between indirect and direct effects has become increasingly important. Therefore, it is paramount that appropriate statistical methods are developed to estimate direct and indirect effects in a variety of settings, including the setting in which there are post-treatment common causes of the mediator and the outcome. The second part of this project will compare confidence regions. Recently, there has been extensive discussion in the statistical community about a move away from p-values. P-values can lead researchers to conclude that a treatment has a significant effect even if that effect is very small, and clinically irrelevant. Confidence regions are the obvious alternative to p-values, as they provide a range of values of the parameters of interest that are most consistent with the data. While comparisons of p-values have been extensively researched and confidence regions are routinely reported, comparison of confidence regions has received relatively little attention. In this project, confidence regions will be compared based on the notion of asymptotic equivalence. Natural direct and indirect effects use cross-worlds counterfactuals: outcomes under treatment with the mediator "set" to its value without treatment. Cross-worlds counterfactuals can never be observed, as they involve quantities under two different treatments where only one treatment is given to any particular patient or unit. The PI has recently proposed organic direct and indirect effects to avoid the use of cross-worlds counterfactuals. Organic direct and indirect effects also apply when the mediator cannot be "set". For example, the HIV viral load in the mother's blood cannot be set; if it could be set, doctors would set it to zero. In the first part of this project, organic direct and indirect effects will be extended to settings with post-treatment common causes of the mediator and the outcome. It will be shown that, in contrast to natural direct and indirect effects, estimators and confidence intervals can be developed in that setting for organic effects. The second part of this project will compare confidence regions. Most work on the comparison of confidence regions has studied coverage probabilities, confidence interval length, and small sample properties. In this project, confidence regions will be compared for large samples, based on the asymptotic behavior of the Hausdorff distance between the different confidence regions. The Hausdorff distance between partly overlapping intervals is simply the maximum of the difference between the left limits and the right limits of the intervals. The Hausdorff distance has also been defined for non-convex sets and in higher dimensions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.