Bayesian Multivariate Analysis for Causal Inference with Intermediate Variables

在广泛的学术学科，政府机构和商业部门中，对治疗，干预和行动的因果影响进行推断是决策的核心。 在随机化实验和观察性研究中，治疗比较需要对混杂的中间变量进行调整的情况越来越普遍;即，治疗后变量可能受到治疗的影响，也会影响疗效。 在涉及中间变量的实际应用中，经常会收集多元信息，但在因果推理中很少使用。 本研究计划将在鲁宾因果模型的主要分层框架下开发通用的统计方法和软件。 方法论的核心重点是开发尖端的贝叶斯模型、方法和计算，用于灵活的多元分析、潜在结构、非参数分析、模型选择和因子分析，以便在存在中间变量的情况下得出有效的因果推断。 特别是，该项目将开发贝叶斯参数，半参数和非参数双变量模型，这些模型利用不同类型的多个结果来改善二元或连续中间变量研究中弱识别因果被估量的估计。 还将为具有多个中间变量的因果关系研究开发贝叶斯因素模型。该项目将改进中间变量因果推断的统计分析，从而使许多学科的实验和观察干预研究得出更准确的结论。 该研究将理论和方法的发展与激励应用领域，包括卫生政策，流行病学，社会科学和经济学相结合。从研究中开发的开源R/Matlab软件将为科学界提供有价值的数据分析和教育工具。

Across a wide range of academic disciplines, government agencies, and business sectors, drawing inferences about causal effects of treatments, intervention, and actions is central to decision making. In both randomized experiments and observational studies, it is increasingly common that treatment comparisons need to be adjusted for confounded intermediate variables; i.e., post-treatment variables potentially affected by the treatment and also affecting the response. Multivariate information is routinely collected in real-world applications involving intermediate variables, but it is infrequently and ineffectively used in causal inference. This research project will develop general purpose statistical methods and software for such multivariate analysis under the principal stratification framework within the Rubin Causal Model. A core methodological focus will be to develop cutting-edge Bayesian models, methods, and computation for flexible multivariate analysis, latent structure, nonparametric analysis, model selection, and factor analysis for drawing valid causal inferences in the presence of intermediate variables. In particular, this project will develop Bayesian parametric, semi-parametric, and non-parametric bivariate models that exploit multiple outcomes of different types to improve the estimation of weakly identified causal estimands in studies with binary or continuous intermediate variables. A Bayesian factor model also will be developed for causal studies with multiple intermediate variables. This project will improve statistical analyses for causal inference with intermediate variables, hence enabling more accurate conclusions from experimental and observational intervention studies across many disciplines. The research will blend theory and methodological developments with motivating applications in areas including health policy, epidemiology, social sciences, and economics. The open source R/Matlab software developed from the research will provide valuable data analysis and educational tools for the scientific community.