Causal inference

调解分析旨在通过某些调解人和围绕某些调解人来评估某些暴露对结果的影响。虽然在最近的文献中已经讨论了多调解人调解分析，但具有多个暴露的案件很少受到关注。在多重暴露的情况下，我们考虑允许变量选择和影响估计同时进行的正则化，从而稳定模型拟合并考虑模型不确定性。在线性结构方程模型的框架下，我们的分析表明，对回归系数进行正则化的两阶段方法不能保证单峰后验分布，而对直接和间接影响进行正则化的系数乘积方法往往会过度惩罚。相反，我们提出了一种正则化的系数差方法，该方法没有这些陷阱。利用频域正则化与具有拉普拉斯先验的贝叶斯分层模型之间的联系，我们提出了一种有效的马尔可夫链蒙特卡罗后验推断算法。仿真结果表明，该方法具有较好的估计性能。使用生殖流行病学的两个数据说明了这一方法。

Mediation analysis aims at assessing the effect of some exposures on an outcome both through and around some mediators. While multi-mediator mediation analysis has been addressed in recent literature, the case with multiple exposures received little attention. With the presence of multiple exposure, we consider regularizations that allow variable selection and effects estimations simultaneously, hence stabilize model fit and account for model uncertainty. In the framework of linear structural equation models, we analytically show that a two-stage approach that regularizes on regression coefficients does not guarantee unimodal posterior distribution, and a product-in-coefficient approach that regularizes on direct and indirect effects tend to penalize excessively. We instead propose a regularized difference-in-coefficient approach that is free of these pitfalls. Using connections between frequentist regularizations and Bayesian hierarchical models with Laplace priors, we develop an efficient Markov chain Monte Carlo algorithm for posterior inference. Through simulations, we show that the proposed approach has good empirical performance in estimation. The methodology is illustrated using two data from reproductive epidemiology.