Bayesian Mediation Analysis of Large-Scale Complex Imaging Data: Method, Theory and Computation - Xu, Yuliang (ProQuest Dissertations & Theses, 2024)
In neuroimaging studies, mediation analysis plays a crucial role in understanding the mechanisms through which certain exposures or interventions affect health outcomes. This dissertation develops a novel modeling framework for Bayesian mediation analysis tailored to large-scale and complex imaging data. The framework provides a robust theoretical basis for image mediation analysis and introduces innovative Bayesian inference methods and efficient computational tools. A rigorous theoretical analysis evaluates the method’s robustness, considering the impact of unmeasured confounders.In Chapter 2, we introduce a new spatially varying coefficient structural equation model for Bayesian image mediation analysis (BIMA). Using the potential outcome framework, we define the spatially varying mediation effects of the exposure on outcomes mediated through imaging mediators. We adopt the soft-thresholded Gaussian process (STGP) for prior specifications, which supports sparse and piece-wise smooth functions. We establish posterior consistency for the mediation effects and selection consistency for significant regions impacting the mediation. An efficient posterior computation algorithm for BIMA, scalable to largescale data, is developed and validated through extensive simulations, showing at least 20% increase in power over existing methods. We apply BIMA to analyze behavioral and fMRI data from the Adolescent Brain Cognitive Development (ABCD) study, focusing on mediation effects of parental education on children’s cognitive abilities through working memory brain activities. We identified important mediation regions such as the left Precuneus (involved in the recall of episodic memories), the left Inferior parietal gyrus (involved in sensory processing and sensorimotor integration), and the left Supplementary motor area(involved in motor sequencing).In Chapter 3, to enhance BIMA’s computational efficiency, we develop a general prior with variational inference algorithms for regression models with large-scale imaging data. We introduce a soft-thresholded conditional autoregressive (ST-CAR) prior, which is robust to pre-fixed correlation structures and facilitates active voxel selection. Applying ST-CAR to scalar-on-image and image-on-scalar regression models, we develop coordinate ascent variational inference (CAVI) and stochastic subsampling variational inference (SSVI) algorithms. Simulations demonstrate that the ST-CAR prior excels in selecting active areas with complex correlations, and CAVI and SSVI offer superior computational performance. We implement these methods in the ABCD study. The SSVI on Image-on-scalar regression brings down the computation time from 86 hours (BIMA) to 7.3 hours.In Chapter 4, we explore methods to reduce the impact of unobserved confounders on the causal mediation analysis of high-dimensional mediators with spatially smooth structures, such as brain imaging data. The key approach is to incorporate the latent individual effects, which influence the structured mediators, as unobserved confounders in the outcome model, thereby potentially debiasing the mediation effects. We develop BAyesian Structured Mediation analysis with Unobserved confounders (BASMU) framework, and establish its model identifiability conditions. Theoretical analysis is conducted on the asymptotic bias of the Natural Indirect Effect (NIE) and the Natural Direct Effect (NDE) when the unobserved confounders are omitted in mediation analysis. For BASMU, we propose a two-stage estimation algorithm to mitigate the impact of these unobserved confounders on estimating the mediation effect. Extensive simulations demonstrate that BASMU substantially reduces the bias in various scenarios. We apply BASMU to the analysis of fMRI data in the Adolescent Brain Cognitive Development (ABCD) study, focusing on four brain regions previously reported to exhibit meaningful mediation effects. Compared with the existing image mediation analysis method, BASMU identifies two to four times more voxels that have significant mediation effects, with the NIE increased by 41%, and the NDE decreased by 26%.