In many practical studies, learning directionality between a pair of variables is of great interest while notoriously hard, especially for mechanistic relationships. This paper presents a method that examines directionality in exposure-outcome pairs when a priori assumptions about their relative ordering are unavailable. We propose a coefficient of asymmetry to quantify directional asymmetry using Shannon's entropy and propose a statistical estimation and inference framework for said estimand. Large-sample theoretical guarantees are established through data-splitting and cross-fitting techniques. The proposed methodology is extended to allow both measured confounders and contamination in outcome measurements. The methodology is extensively evaluated through extensive simulation studies, a benchmark dataset, and a real data application.

翻译：在许多实际研究中，探究一对变量间的方向性具有重要价值，但这一任务尤为困难，特别是在机制性关系方面。本文提出了一种方法，用于在缺乏关于变量相对顺序的先验假设时，检验暴露-结果对中的方向性。我们提出了一种非对称系数，利用香农熵来量化方向性非对称，并为该估计量构建了统计估计与推断框架。通过数据分割与交叉拟合技术，建立了大样本理论保证。所提出的方法进一步扩展至允许存在已测量的混杂因素及结果测量中的污染。通过大量模拟研究、基准数据集和实际数据应用，对该方法进行了全面评估。