Statistical modelling and confounder selection for causal mediation analyses

拟议的研究计划涉及因果中介的统计方法的发展。中介分析是一种越来越流行的技术，用于估计暴露（治疗）效果，假设在暴露和结果之间的因果途径上存在中介变量。这种分析旨在将总暴露效应分解为通过中介的间接效应和避免中介路径的直接效应。该计划分为三个主题，解决因果中介中的相关建模问题：(1)为二元结果开发基于精确回归的中介方法；(2)采用两种现有的贝叶斯回归模型进行因果中介；(3)研究混杂因素选择对中介效应的有效估计。关于(1)，我们最近观察到，传统回归方法中对二元结果所做的“罕见结果假设”在实践中可能导致错误的推论。我们将提出一个自然直接和间接影响的精确估计，其理论有效性不依赖于结果的稀缺性（或普遍性）。这将在二元和连续介质中实现，在后一种情况下，对数正态表示将用于嵌套的反事实结果概率。对于主题(2)，我们计划通过建立两个具有吸引人的特征的回归模型来扩展贝叶斯中介方法。首先，我们提出了一个潜在的多元Student-t模型，作为二元结果和可能的多重二元中介的精确中介方法的基础。其次，我们的目标是阐述基于贝叶斯加性回归树（BART）模型的灵活中介策略。中介公式将用于表示两种模型规范的自然中介效应。目前缺乏关于如何选择协变量来调整因果中介模型的信息，因为只有实质性的知识不足以完成这项任务。在主题(3)中，我们将针对非中介环境引入的两种众所周知的混杂选择算法，并研究如何针对中介环境对它们进行修改，以产生直接和间接影响的无偏和有效估计。所有这三个主题都需要通过模拟研究进行理论发展和验证。将创建开放获取的软件，并提供全面的例子，以增加实质性研究人员的吸收。总而言之，本课程是关于因果中介分析的几个重要方面的原始和创新的统计发展。预期在许多应用研究领域（例如，社会科学、流行病学），这类分析获得的结果将更加可靠。

The proposed research program concerns the development of statistical methods for causal mediation. Mediation analyses are an increasingly popular class of techniques used for estimating exposure (treatment) effects under the assumption that there is a mediating variable on the causal pathway between exposure and outcome. Such an analysis aims to decompose the total exposure effect in an indirect effect through the mediator and in a direct effect which avoids the mediation path. The program is divided in three themes that address relevant modelling issues in causal mediation: (1) developing an exact regression-based mediation approach for a binary outcome; (2) adapting two existing Bayesian regression models for purposes of causal mediation; (3) investigating confounder selection for valid estimation of mediation effects. Regarding (1), we have recently observed that the "rare outcome assumption" made in the conventional regression approach for a binary outcome can lead to wrong inferences in practice. We will propose an exact estimator for the natural direct and indirect effects whose theoretical validity does not rely on the rareness (or commonness) of the outcome. This will be accomplished for both binary and continuous mediators, where a logit-normal representation will be used for the nested counterfactual outcome probabilities in the latter case. For theme (2), we are planning to expand on Bayesian mediation methodology by building on two regression models with attractive features. First, we propose a latent multivariate Student-t model as a basis for an exact mediation approach for a binary outcome and possibly multiple binary mediators. Secondly, we aim to elaborate a flexible mediation strategy based on Bayesian additive regression trees (BART) models. The Mediation Formula will be used to express the natural mediation effects from both model specifications. There is currently a lack of information regarding how to select covariates for adjustment in causal mediation models when substantive knowledge is alone not sufficient for this task. In theme (3), we will target two well known confounder selection algorithms introduced for non-mediated contexts and investigate how they can be modified for mediation contexts in order to yield unbiased and efficient estimators of direct and indirect effects. All three themes will require theoretical developments and validation through simulation studies. Open-access software will be created and comprehensive examples will be made available to increase uptake by substantive researchers. To conclude, this program is about original and innovative statistical developments on several important aspects of causal mediation analyses. It is expected to increase the reliability of results obtained from this type of analyses in many fields of applied research (e.g., social science, epidemiology).