Causal mediation analysis methods for polytomous, functional and high-dimensional data

拟议研究计划的长期目标是开发数据自适应方法，以产生因果途径和机制的证据，并将其扩展到复杂类型的数据。在特定目标参数的估计中综合统计推断和机器学习已成为统计学的关键研究领域之一，旨在减少对模型中不直接感兴趣的部分的参数假设。目标参数通常是干预/暴露的因果效应，并且对此的估计通常涉及暴露和/或结果变量的建模，这是控制与非实验数据混淆所需的。灵活的数据自适应方法可用于此任务;例如，最近在应用问题中使用深度神经网络的复苏促使人们尝试将这些方法纳入构建统计估计器。然而，在过度拟合引起的方差膨胀和正则化引入的偏差之间找到合适的折衷方案来控制变化并不容易。最近的进展，在建立所产生的程序的理论特性的背景下，双稳健估计，同时采用两种模型减少了偏见的估计。 因果中介分析的目的是通过将总的因果效应分解为通过特定中介变量的间接效应和通过其他途径操作的直接效应来产生因果途径的证据。虽然存在用于二分和连续暴露、中介变量和结果变量的方法，但需要对更复杂类型的数据进行扩展。此外，半参数因果推理的进展需要扩展到因果中介分析，结合数据自适应方法来控制高维混杂因素。 拟议的研究计划将有助于通过开发新的效果分解和估计多类别多分割暴露和功能暴露的因果中介分析的理论和方法学知识基础，开发半参数估计因果中介分析结合深度神经网络，并开发基于成像数据的高维中介分析方法。这些方法将在多个研究领域中得到应用;对多分支暴露的兴趣是由教育和医疗保健等机构的比较引起的。功能性暴露的一个例子是以剂量-体积直方图表示的辐射暴露。许多其他调解问题的动机是由高通量技术产生的数据，其中高维生物标志物不是因果变量，而是因果途径上潜在因素的表现，调解分析必然需要降维技术。

The long-term goal of the proposed research program is to develop data-adaptive methods for the purpose of producing evidence of causal pathways and mechanisms, and extend these to complex types of data. Synthesizing statistical inference and machine learning in the estimation of specific target parameters has become one of the key research areas in statistics, aimed at reducing parametric assumptions about parts of the model that are not of direct interest. The target parameter is often a causal effect of an intervention/exposure, and estimation of this usually involves modeling of the exposure and/or outcome variables, needed for controlling for confounding with non-experimental data. Flexible data-adaptive methods can be used for this task; for example, the recent resurgence in the use of deep neural networks for applied problems has motivated attempts to incorporate these in constructing statistical estimators. However, finding the right compromise between variance inflation due to overfitting and bias introduced by regularization in attempts to control the variation has not been easy. Recent progress in establishing the theoretical properties of the resulting procedures has been made in the context of doubly robust estimators, where employing two models simultaneously reduces bias in the estimation. Causal mediation analysis aims at producing evidence of causal pathways by decomposing total causal effects into indirect effects through specific mediator variables, and direct effects operating through other pathways. While methods exist for dichotomous and continuous exposure, mediator and outcome variables, extensions are needed for more complex types of data. Furthermore, advances in semi-parametric causal inference need to be extended to causal mediation analysis, incorporating data-adaptive methods to control for high-dimensional confounders. The proposed research program will contribute towards the theoretical and methodological knowledge base of causal mediation analysis through developing novel effect decompositions and estimators for multi-category polytomous exposures and functional exposures, developing semi-parametric estimators for causal mediation analysis incorporating deep neural networks, and developing methods for high-dimensional mediation analysis based on imaging data. The methods will have applications in multiple fields of research; the interest in polytomous exposures is motivated by institutional comparisons for example in education and healthcare. An example of a functional exposure is radiation exposure represented in terms of a dose-volume histogram. Many of the other mediation questions are motivated by data produced by high throughput technology where the high-dimensional biomarkers are not causal variables as such, but manifestations of latent factors on the causal pathway, and mediation analysis will necessarily require dimension reduction techniques.