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、干预和行动的因果效应进行推断是决策的核心。在随机实验和观察性研究中，越来越普遍的是，治疗比较需要根据混杂的中间变量进行调整；也就是说，治疗后的变量可能会受到治疗的影响，也会影响到反应。在涉及中间变量的实际应用中，通常会收集多变量信息，但在因果推理中很少使用且无效。本研究项目将在鲁宾因果模型的主要分层框架下，为这种多变量分析开发通用的统计方法和软件。一个核心的方法论重点将是开发尖端的贝叶斯模型、方法和计算灵活的多变量分析、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绘制有效的因果推理。特别是，该项目将开发贝叶斯参数、半参数和非参数二元模型，利用不同类型的多个结果来改进二元或连续中间变量研究中弱识别因果估计的估计。一个贝叶斯因素模型也将发展与多个中间变量的因果研究。该项目将改进中间变量因果推理的统计分析，从而使跨多个学科的实验和观察性干预研究得出更准确的结论。这项研究将把理论和方法的发展与卫生政策、流行病学、社会科学和经济学等领域的激励应用相结合。该研究开发的开源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.