A False Discovery Rate Control Method Using a Fully Connected Hidden Markov Random Field for Neuroimaging Data

TL;DR

This work tackles voxel-wise FDR control in neuroimaging by addressing complex spatial dependencies, instability across replications, and computational scalability. It introduces fcHMRF-LIS, which couples LIS-based testing with a fully connected HMRF and employs an EM algorithm fused with mean-field approximation, CRF-RNN, and permutohedral lattice filtering to achieve linear-time inference. Across extensive simulations and an ADNI FDG-PET study with 439,758 voxels, fcHMRF-LIS delivers accurate FDR control, higher power, and substantially reduced variability compared to nine competing methods, while maintaining CPU-based scalability. The approach yields neurobiologically plausible discoveries and demonstrates practical efficiency, suggesting broad applicability to high-dimensional spatial testing in neuroimaging and related domains where long-range dependencies are present.

Abstract

False discovery rate (FDR) control methods are essential for voxel-wise multiple testing in neuroimaging data analysis, where hundreds of thousands or even millions of tests are conducted to detect brain regions associated with disease-related changes. Classical FDR control methods (e.g., BH, q-value, and LocalFDR) assume independence among tests and often lead to high false non-discovery rates (FNR). Although various spatial FDR control methods have been developed to improve power, they still fall short of jointly addressing three major challenges in neuroimaging applications: capturing complex spatial dependencies, maintaining low variability in both false discovery proportion (FDP) and false non-discovery proportion (FNP) across replications, and achieving computational scalability for high-resolution data. To address these challenges, we propose fcHMRF-LIS, a powerful, stable, and scalable spatial FDR control method for voxel-wise multiple testing. It integrates the local index of significance (LIS)-based testing procedure with a novel fully connected hidden Markov random field (fcHMRF) designed to model complex spatial structures using a parsimonious parameterization. We develop an efficient expectation-maximization algorithm incorporating mean-field approximation, the Conditional Random Fields as Recurrent Neural Networks (CRF-RNN) technique, and permutohedral lattice filtering, reducing the time complexity from quadratic to linear in the number of tests. Extensive simulations demonstrate that fcHMRF-LIS achieves accurate FDR control, lower FNR, reduced variability in FDP and FNP, and a higher number of true positives compared to existing methods. Applied to an FDG-PET dataset from the Alzheimer's Disease Neuroimaging Initiative, fcHMRF-LIS identifies neurobiologically relevant brain regions and offers notable advantages in computational efficiency.

Figures (9)

• Figure 1: Comparison of nine FDR control methods under the simulation setting in Section \ref{['sim: setting']} with $(\mu_1,\sigma_1^2)=(-2, 1)$, approximately 30% signal proportion, and a nominal FDR level of 0.05.
• Figure 2: The CRF-RNN network. Gating functions $G_1$ and $G_2$ are given in \ref{['gate1']} and \ref{['gate2']}, respectively.
• Figure 3: Simulation results over 50 replications at a nominal FDR level of 0.05.
• Figure 4: Simulation results over 50 replications at a nominal FDR level of 0.1.
• Figure 5: The z-statistics of discoveries for EMCI2AD vs. CN.