False discovery rate smoothing

TL;DR

FDR smoothing is an empirical-Bayes method that leverages spatial structure in large-scale multiple testing to improve detection power and control false discovery rate, demonstrated through simulations and fMRI data analysis.

Contribution

It introduces a novel FDR smoothing approach that exploits spatial information, with an efficient algorithm and superior robustness over existing methods.

Findings

Achieves state-of-the-art performance in simulations

More robust than existing spatial multiple testing methods

Detects biologically plausible patterns in fMRI data

Abstract

We present false discovery rate 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 non-standard 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 data set 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.