标题： 孟德尔随机化中存在许多无效工具变量时：分层经验贝叶斯估计 显示英文标题

标题： Mendelian Randomization when Many Instruments are Invalid: Hierarchical Empirical Bayes Estimation

摘要： 估计暴露对结果的因果效应是许多经济和生物研究中的重要任务。特别是，孟德尔随机化利用遗传变异作为工具变量来估计流行病学研究中的因果效应。然而，传统的工具变量方法依赖于一些不可检验的假设，在实际问题中这些假设可能会被违反。本文采用贝叶斯框架，并构建分层模型以纳入工具变量的无效效应。我们通过使用高斯混合先验引入了一个经验贝叶斯估计器，其中一些工具变量是无效的。提供了理论性能和算法实现，并进行了说明。所提出的方法在多种模拟设置以及关于HDL胆固醇和LDL胆固醇对2型糖尿病的因果效应的真实数据集上展示了可靠的表现。 显示英文摘要

摘要： Estimating the causal effect of an exposure on an outcome is an important task in many economical and biological studies. Mendelian randomization, in particular, uses genetic variants as instruments to estimate causal effects in epidemiological studies. However, conventional instrumental variable methods rely on some untestable assumptions, which may be violated in real problems. In this paper, we adopt a Bayesian framework and build hierarchical models to incorporate invalid effects of instruments. We introduce an empirical Bayes estimator for which some of the instruments are invalid by utilizing a Gaussian mixture prior. Theoretical performance and algorithm implementations are provided and illustrated. The reliable performance of the proposed method is demonstrated in various simulation settings and on real datasets concerning the causal effects of HDL cholesterol and LDL cholesterol on type 2 diabetes.