False Discovery Rate Smoothing

• Published in: Journal of the American Statistical Association Vol. 113; no. 523; pp. 1156 - 1171
• Main Authors: Tansey, Wesley, Koyejo, Oluwasanmi, Poldrack, Russell A., Scott, James G.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.07.2018; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Algorithms; data collection; Discovery; Empirical Bayes; equations; False discovery rate; FDR; Functional magnetic resonance imaging; Fused lasso; magnetic resonance imaging; Multiple hypothesis testing; Noise; Optimization; Regression analysis; Short term memory; Simulation; Smoothing; Spatial smoothing; Statistical methods; Statistical significance; Statistical tests; Statistics; system optimization; Theory and Methods
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2017.1319838

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 ( https://github.com/tansey/smoothfdr ). Supplementary materials for this article are available online.