Integrative Predictor-Dependent Learning of Network Data and Spatially Correlated Nodal Attributes for Multimodal Brain Imaging in Aging

Abstract

This article introduces a predictor-dependent joint modeling framework for network data obtained from multiple subjects over a shared set of nodes with spatial co-ordinates and spatially correlated nodal attributes. The framework is highly flexible, allowing concurrent inference on nodes significantly associated with a predictor, spatial associations of nodal attributes and the regression relationship between a predictor and edge connecting a pair of nodes or a specific nodal attribute. Empirical results indicate a superior performance of the proposed approach due to accounting for network structure and spatial correlation in the data simultaneously. The methodology analyzes multimodal brain imaging data collected first-hand in the coauthor's Lifespan Cognitive and Motor Neuroimaging Laboratory, with a focus on integrating structural and functional information. It examines brain connectivity, represented as a connectome network across regions of interest (ROIs) derived from functional magnetic resonance imaging (fMRI), while also incorporating ROI-specific attributes obtained from structural MRI data, for each subject. Subject-specific aging-related features and spatial locations of ROIs are incorporated in the analysis. This framework facilitates robust inference on the associations between predictors and brain connectivity patterns, the spatial relationships among ROI-specific attributes, and the regression relationships involving edges or ROI-specific attributes with aging-related predictors. By integrating these diverse data sources, the approach provides a deeper understanding of the complex interplay between brain structure, function, aging-related changes, and external predictors. As a model-based Bayesian approach, it provides uncertainty quantification for all inferences, offering robust and reliable results, particularly in scenarios with limited sample size.

Figures (8)

• Figure 1: Figure illustrates the whole-brain network, highlighting the subnetworks through red nodes.
• Figure 2: Diagram of the dependencies between observations (red), predictors (orange), latent variables (teal), and parameters (violet).
• Figure 3: Circos plots illustrating the true and estimated covariate-dependent associations between influential network nodes, as captured by the network coefficients under Scenario 1 ($1-\Delta^* = 0.8$, $\zeta^*= 0.05$), Scenario 4 ($1-\Delta^* = 0.5$, $\zeta^*= 0.1$), and Scenario 7 ($1-\Delta^* = 0.3$, $\zeta^*= 0.05$). The top row displays the true network coefficients between influential network nodes, while the bottom row shows the corresponding estimates obtained from the proposed model. Across all scenarios, the model demonstrates highly accurate recovery of the underlying associations.
• Figure 4: Scaled MSE for estimating the predictor coefficients corresponding to the network outcome and nodal attributes across the seven simulation combinations. We present results for the proposed spatial joint model along with those of its competitors: independent tensor model, independent network model, and non-spatial joint model. Since the independent tensor model and independent network model fit the same model for nodal attributes, they will offer identical results in estimating ${\boldsymbol \alpha} ^*$. Hence, only results for the independent network model are presented in Figure \ref{['mse-fig2']}. The results show the overall superior performance of the spatial joint model in coefficient estimation.
• Figure 5: Average length and coverage of 95% credible intervals for Bayesian competitors and 95% confidence intervals for frequentist competitors for ${\boldsymbol \beta}$ and ${\boldsymbol \alpha}$. The results show close to nominal coverage and overall shorter interval lengths for the spatial joint model, with most prominent advantages under scenarios 6 and 7, corresponding to low node sparsity and high spatial correlation.