We consider the challenging problem of estimating causal effects from purely observational data in the bi-directional Mendelian randomization (MR), where some invalid instruments, as well as unmeasured confounding, usually exist. To address this problem, most existing methods attempt to find proper valid instrumental variables (IVs) for the target causal effect by expert knowledge or by assuming that the causal model is a one-directional MR model. As such, in this paper, we first theoretically investigate the identification of the bi-directional MR from observational data. In particular, we provide necessary and sufficient conditions under which valid IV sets are correctly identified such that the bi-directional MR model is identifiable, including the causal directions of a pair of phenotypes (i.e., the treatment and outcome). Moreover, based on the identification theory, we develop a cluster fusion-like method to discover valid IV sets and estimate the causal effects of interest. We theoretically demonstrate the correctness of the proposed algorithm. Experimental results show the effectiveness of our method for estimating causal effects in bi-directional MR.

翻译：我们考虑在双向孟德尔随机化（MR）中，从纯观测数据估计因果效应的挑战性问题，其中通常存在一些无效工具变量以及未测量的混杂因素。为解决此问题，现有大多数方法试图通过专家知识或假设因果模型为单向MR模型，来为目标因果效应寻找合适的有效工具变量（IVs）。因此，在本文中，我们首先从理论上研究了从观测数据中识别双向MR的问题。具体而言，我们给出了在何种必要且充分条件下，有效工具变量集能够被正确识别，从而使双向MR模型（包括一对表型（即处理与结果）的因果方向）可识别。此外，基于该识别理论，我们开发了一种类聚类融合方法来发现有效工具变量集并估计感兴趣的因果效应。我们从理论上证明了所提算法的正确性。实验结果表明，我们的方法在估计双向MR中的因果效应方面具有有效性。