Mendelian randomization (MR) is a pivotal tool in genetic epidemiology, leveraging genetic variants as instrumental variables to infer causal relationships between modifiable exposures and health outcomes. Traditional MR methods, while powerful, often rest on stringent assumptions such as the absence of feedback loops, which are frequently violated in complex biological systems. In addition, many popular MR approaches focus on only two variables (i.e., one exposure and one outcome) whereas our motivating applications have many variables. In this article, we introduce a novel Bayesian framework for \emph{multivariable} MR that concurrently addresses \emph{unmeasured confounding} and \emph{feedback loops}. Central to our approach is a sparse conditional cyclic graphical model with a sparse error variance-covariance matrix. Two structural priors are employed to enable the modeling and inference of causal relationships as well as latent confounding structures. Our method is designed to operate effectively with summary-level data, facilitating its application in contexts where individual-level data are inaccessible, e.g., due to privacy concerns. It can also account for horizontal pleiotropy. Through extensive simulations and applications to the GTEx and OneK1K data, we demonstrate the superior performance of our approach in recovering biologically plausible causal relationships in the presence of possible feedback loops and unmeasured confounding. The R package that implements the proposed method is available at \texttt{MR.RGM}.

翻译：孟德尔随机化（MR）是遗传流行病学中的关键工具，利用遗传变异作为工具变量来推断可改变暴露与健康结果之间的因果关系。传统MR方法虽然强大，但通常依赖于严格的假设（如不存在反馈循环），这些假设在复杂生物系统中经常被违反。此外，许多流行的MR方法仅关注两个变量（即一个暴露和一个结果），而我们的应用场景涉及多个变量。本文提出了一种新颖的贝叶斯框架用于*多变量*MR，可同时处理*未测量混杂*和*反馈循环*。我们方法的核心是采用稀疏误差方差-协方差矩阵的稀疏条件循环图模型。通过引入两种结构先验，实现了对因果关系及潜在混杂结构的建模与推断。该方法设计为在汇总水平数据上有效运行，适用于因隐私等问题无法获取个体水平数据的场景，并能处理水平多效性。通过对GTEx和OneK1K数据进行广泛模拟与应用，我们证明了该方法在存在潜在反馈循环和未测量混杂的情况下，能够以优越性能恢复生物学上合理的因果关系。实现该方法的R包发布于 \texttt{MR.RGM}。