Abstract

A central question in high-dimensional mediation analysis is to infer the significance of individual mediators. The main challenge is that the total number of potential paths that go through any mediator is super-exponential in the number of mediators. Most existing mediation inference solutions either explicitly impose that the mediators are conditionally independent given the exposure, or ignore any potential directed paths among the mediators. In this article, we propose a novel hypothesis testing procedure to evaluate individual mediation effects, while taking into account potential interactions among the mediators. Our proposal thus fills a crucial gap, and greatly extends the scope of existing mediation tests. Our key idea is to construct the test statistic using the logic of Boolean matrices, which enables us to establish the proper limiting distribution under the null hypothesis. We further employ screening, data splitting, and decorrelated estimation to reduce the bias and increase the power of the test. We show that our test can control both the size and false discovery rate asymptotically, and the power of the test approaches one, while allowing the number of mediators to diverge to infinity with the sample size. We demonstrate the efficacy of the method through simulations and a neuroimaging study of Alzheimer’s disease. A Python implementation of the proposed procedure is available at https://github.com/callmespring/LOGAN.

 抽象的

高维中介分析的一个核心问题是推断个体中介变量的重要性。主要的挑战是，经过任何中介的潜在路径总数是中介数量的超指数。大多数现有的中介推理解决方案要么明确地强制中介者在给定暴露的情况下是有条件独立的，要么忽略中介者之间任何潜在的有向路径。在本文中，我们提出了一种新的假设检验程序来评估个体中介效应，同时考虑中介者之间的潜在相互作用。因此，我们的建议填补了一个关键空白，并大大扩展了现有调解测试的范围。我们的关键思想是使用布尔矩阵的逻辑构建检验统计量，这使我们能够在原假设下建立适当的极限分布。我们进一步采用筛选、数据分割和去相关估计来减少偏差并提高测试的功效。我们表明，我们的测试可以渐进地控制大小和错误发现率，并且测试的功效接近 1，同时允许中介数量随着样本大小发散到无穷大。我们通过模拟和阿尔茨海默病的神经影像学研究证明了该方法的有效性。所提议过程的 Python 实现可在 https://github.com/callmespring/LOGAN 上找到。