More Specific Signal Detection in Functional Magnetic Resonance Imaging by False Discovery Rate Control for Hierarchically Structured Systems of Hypotheses.

Konstantin Schildknecht,Thorsten Dickhaus,Karsten Tabelow,Satoru Hayasaka

doi:10.1371/journal.pone.0149016

Abstract

Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis for which there is no strong evidence for containing true alternatives. We show control of the family-wise error rate at this first stage of testing. Then, at the second stage, we proceed to test the hypotheses within each non-excluded family and obtain asymptotic control of the FDR within each family at this second stage. Our main mathematical result is that this two-stage strategy implies asymptotic control of the FDR with respect to all hypotheses. In simulations we demonstrate the increased power of this new procedure in comparison with established procedures in situations with highly unbalanced families. Finally, we apply the proposed method to simulated and to real fMRI data.

Highlights

Modern research is increasingly concerned with large-scale experiments and complex experimental designs
This leads to high sensitivity regarding the voxels within such a group. This is combined with a Bonferronitype multiplicity adjustment in the first stage, implying a good specificity during the detection of active regions. We prove that this procedure controls the family-wise error rate (FWER) on the set of the family hypotheses, as well as, asymptotically as m ! 1, the false discovery rate (FDR) within each family and the global FDR, which is the FDR with respect to all individual hypotheses
This work focused on the use of structural information in a new procedure to control the FDR

Summary

Introduction

Modern research is increasingly concerned with large-scale experiments and complex experimental designs. From a statistical perspective the analysis of such experiments often involves the issue of multiple testing of a large number (say m) of individual hypotheses. The development of methods to deal with this issue is a very active field of research with many sophisticated procedures emerging, e. G., taking a specific structure in the set of hypotheses into account; see, for example, Sections 3.3 and 12.2 in [1]. False Discovery Rate Control in Functional Magnetic Resonance Imaging. Weierstrass Institute for Applied Analysis and Stochastics and the University of Bremen is gratefully acknowledged. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

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