Bayesian Spatial Hierarchical Effects Model for Neuroimaging Data Analysis
Poster No:
1080
Submission Type:
Abstract Submission
Authors:
Yuan Zhong1, Gang Chen2, Paul Taylor2, Jian Kang1
Institutions:
1University of Michigan, Ann Arbor, MI, 2National Institutes of Mental Health, NIH, Bethesda, MD
First Author:
Co-Author(s):
Introduction:
Understanding brain functioning in neuroimaging often requires sophisticated statistical methods. Traditional voxelwise massive univariate statistical analysis with hypothesis testing encounters challenges such as large-scale multiple comparisons, limited statistical power, and the lack of explicit modeling for spatial dependencies. A region-based Bayesian multilevel (BML) model was recently proposed as an alternative approach with Hamiltonian Monte Carlo sampling, and it showed superior modeling efficiency while mitigating multiplicity in both numerical and real data studies (Chen et al., 2019; Taylor et al., 2023). However, this approach compromised spatial granularity within regions and omitted voxel-based estimations due to the prohibitive computational cost. We propose a Bayesian Spatial Hierarchical Effects (BSHE) model that simultaneously incorporates voxel-, region-, and individual-level variability and effects. By employing conjugate priors, we enable efficient Gibbs sampling to allow additional spatial effect estimates in the model while maintaining computational feasibility. Our proposed model is implemented in Python and validated on fMRI data, demonstrating its ability to perform robust statistical modeling while retaining low computational costs.
Methods:
Suppose that imaging data are collected for N individuals in P distinct brain regions, where each parcel contains Vp voxels for p=1,...,P. Our model specification is shown in Figure 1. We assume the mean effect includes the global mean, regions-level, voxel-level, individual-level, and individual-by-parcel level effects. The residual terms are assumed to follow normal distribution with region-specific variances. To ensure identifiability, model parameters except for the global mean are constrained to be centered to zero. For fully Bayesian inferences, we assign independent normal priors with mean zero and unknown standard deviations on effect parameters and half-Cauchy priors for the standard deviation parameters. With conjugate prior specifications, computational efficiency is achieved through full conditional distributions and vectorized Gibbs sampling.
·Model specification for the BSHE model.
Results:
We apply the BSHE model to publicly available fMRI data from the NARPS project (Botvinik-Nezer et al., 2020). Detailed processing steps are described in Taylor et al. (2023). The final data includes 47 participants with each having 116,961 voxels and 360 parcel regions from Glasser atlas (Glasser et al., 2016). We compare BSHE with standard two-sided t-tests and the BML model adapted for voxel-level data with Gibbs sampling. Compared to BSHE, the BML model here does not incorporate parcel-specific parameters. Voxel-level effect estimates and statistical evidence were compared across models, with t-statistics used for the t-tests and posterior means divided by posterior standard deviations used for the Bayesian methods. Model fitting is evaluated using posterior predictive checks (PPCs), which compare the posterior predictive density of data to the density of the observed data. As shown in Figure 2, the BSHE approach aligns well with the pattern of the other methods while providing a better model fit by modeling voxel- and region-level effects. Additionally, we show computational improvement by running four chains, each generating 1,000 posterior samples after 3,000 burn-in iterations, in three minutes using four processes on an Apple Silicon M3 chip with 18 GB RAM.
·Model performance comparison for fMRI data analysis.
Conclusions:
Our proposed BSHE model addresses key challenges in neuroimaging analysis by incorporating spatial hierarchical effects. To make fully Bayesian inferences on BSHE, we develop computationally efficient posterior computation algorithms significantly reducing computational costs. The BSHE model overcomes the reliance on arbitrary thresholds and the inefficiency of massive univariate analyses with traditional hypothesis testing approaches. Numerical experiments show that the BSHE mode achieves excellent model fitting with high computational efficiency.
Modeling and Analysis Methods:
Activation (eg. BOLD task-fMRI)
Bayesian Modeling 1
Methods Development 2
Keywords:
Computing
Data analysis
FUNCTIONAL MRI
Modeling
Statistical Methods
1|2Indicates the priority used for review
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Provide references using APA citation style.
Chen, G., Xiao, Y., Taylor, P. A., Rajendra, J. K., Riggins, T., Geng, F., Redcay, E., and Cox, R. W. (2019). Handling multiplicity in neuroimaging through Bayesian lenses with multilevel modeling. Neuroinformatics, 17:515–545.
Glasser, M. F., Coalson, T. S., Robinson, E. C., Hacker, C. D., Harwell, J., Yacoub, E., Ugurbil, K., Andersson, J., Beckmann, C. F., Jenkinson, M., et al. (2016). A multi-modal parcellation of human cerebral cortex. Nature, 536(7615):171–178.
Taylor, P. A., Reynolds, R. C., Calhoun, V., Gonzalez-Castillo, J., Handwerker, D. A., Bandet-tini, P. A., Mejia, A. F., and Chen, G. (2023). Highlight results, don’t hide them: enhance interpretation, reduce biases and improve reproducibility. Neuroimage, 274:120138.