Learning causal relationships between pairs of complex traits from observational studies is of great interest across various scientific domains. However, most existing methods assume the absence of unmeasured confounding and restrict causal relationships between two traits to be uni-directional, which may be violated in real-world systems. In this paper, we address the challenge of causal discovery and effect inference for two traits while accounting for unmeasured confounding and potential feedback loops. By leveraging possibly invalid instrumental variables, we provide identification conditions for causal parameters in a model that allows for bi-directional relationships, and we also establish identifiability of the causal direction under the introduced conditions. Then we propose a data-driven procedure to detect the causal direction and provide inference results about causal effects along the identified direction. We show that our method consistently recovers the true direction and produces valid confidence intervals for the causal effect. We conduct extensive simulation studies to show that our proposal outperforms existing methods. We finally apply our method to analyze real data sets from UK Biobank.

翻译：从观测性研究中学习复杂性状对之间的因果关系，在多个科学领域具有重要价值。然而，现有方法大多假设不存在未测量的混杂因素，并将两个性状间的因果关系限制为单向，这在现实系统中可能不成立。本文针对两个性状的因果发现与效应推断问题，在考虑未测量混杂和潜在反馈循环的情况下展开研究。通过利用可能无效的工具变量，我们在允许双向关系的模型中给出了因果参数的识别条件，并在所引入的条件下建立了因果方向的可识别性。随后，我们提出一种数据驱动的方法来检测因果方向，并提供沿识别方向的因果效应推断结果。我们证明，该方法能一致地恢复真实方向，并为因果效应构建有效的置信区间。通过大量模拟研究，我们展示了所提方法优于现有方法。最后，我们将该方法应用于分析英国生物银行的实际数据集。