False Discovery Rate Smoothing

We present false discovery rate (FDR) smoothing, an empirical-Bayes method for exploiting spatial structure in large multiple-testing problems. FDR smoothing automatically finds spatially localized regions of significant test statistics. It then relaxes the threshold of statistical significance within these regions, and tightens it elsewhere, in a manner that controls the overall false discovery rate at a given level. This results in increased power and cleaner spatial separation of signals from noise. The approach requires solving a nonstandard high-dimensional optimization problem, for which an efficient augmented-Lagrangian algorithm is presented. In simulation studies, FDR smoothing exhibits state-of-the-art performance at modest computational cost. In particular, it is shown to be far more robust than existing methods for spatially dependent multiple testing. We also apply the method to a dataset from an fMRI experiment on spatial working memory, where it detects patterns that are much more biologically plausible than those detected by standard FDR-controlling methods. All code for FDR smoothing is publicly available in Python and R (<i>https://github.com/tansey/smoothfdr</i>). Supplementary materials for this article are available online.

我们提出了错误发现率（False Discovery Rate，FDR）平滑方法，这是一种面向大规模多重检验问题、可挖掘空间结构信息的经验贝叶斯方法。该方法可自动定位具备显著检验统计量的空间局域区域，随后在这些区域内放宽统计显著性阈值，同时在其余区域收紧阈值，且整体仍可将错误发现率控制在预设水平。此举可提升检验效能，并实现信号与噪声间更清晰的空间区分。该方法需要求解一类非标准的高维优化问题，本文同时提出了一种高效的增广拉格朗日算法以解决该问题。在仿真实验中，FDR平滑方法仅需适中的计算开销，即可展现出顶尖的性能；尤为关键的是，相较于现有空间依赖型多重检验方法，该方法的鲁棒性显著更强。我们还将该方法应用于一项针对空间工作记忆的功能磁共振成像（functional magnetic resonance imaging, fMRI）实验数据集，其检测到的神经活动模式相较于传统FDR控制方法得到的结果，具备更强的生物学合理性。所有用于实现FDR平滑方法的代码均已在Python与R语言中公开可用（<i>https://github.com/tansey/smoothfdr</i>），本文的补充材料可在线获取。