DeepFDR: A Deep Learning-based False Discovery Rate Control Method for Neuroimaging Data

TL;DR

DeepFDR tackles voxelwise FDR control in neuroimaging by linking LIS-based testing with unsupervised deep image segmentation. It uses a modified W-net to produce segmentation probability maps that estimate $LIS_i(\boldsymbol{x}) = P(h_i=0|\boldsymbol{x})$, then applies an LIS-based procedure to control FDR while minimizing false nondiscoveries. The approach is validated via simulations and real ADNI FDG-PET data, showing robust FDR control, reduced FNR, and exceptional computational efficiency relative to existing spatial or supervised methods. This yields more reliable, scalable voxelwise inferences for brain imaging studies, including Alzheimer's disease research.

Abstract

Voxel-based multiple testing is widely used in neuroimaging data analysis. Traditional false discovery rate (FDR) control methods often ignore the spatial dependence among the voxel-based tests and thus suffer from substantial loss of testing power. While recent spatial FDR control methods have emerged, their validity and optimality remain questionable when handling the complex spatial dependencies of the brain. Concurrently, deep learning methods have revolutionized image segmentation, a task closely related to voxel-based multiple testing. In this paper, we propose DeepFDR, a novel spatial FDR control method that leverages unsupervised deep learning-based image segmentation to address the voxel-based multiple testing problem. Numerical studies, including comprehensive simulations and Alzheimer's disease FDG-PET image analysis, demonstrate DeepFDR's superiority over existing methods. DeepFDR not only excels in FDR control and effectively diminishes the false nondiscovery rate, but also boasts exceptional computational efficiency highly suited for tackling large-scale neuroimaging data.

Figures (13)

• Figure 1: The network architecture of DeepFDR.
• Figure 2: Simulation results for the cube with $P_1\approx 10\%$. All FDRs of NeuralFDR and almost all FDRs of OSEM are too large, and thus their FDRs are not shown in this figure; see Figure \ref{['fig:simulation_0.1']}, instead.
• Figure A.1: Simulation results for the cube with $P_1\approx 20\%$. FDRs for NeuralFDR and OSEM are too large and are thus not shown in this figure; see Figure \ref{['fig:simulation_0.2']}, instead.
• Figure A.2: Simulation results for the cube with $P_1\approx 30\%$. FDRs for NeuralFDR and OSEM are too large and are thus not shown in this figure; see Figure \ref{['fig:simulation_0.3']}, instead.
• Figure A.3: Simulation results with standard error bars for the cube with $P_1\approx 10\%$.