Spatial Bayesian Modeling and Computation with Application To Neuroimaging Data

Abstract

As both clinical and cognitive neuroscience matures, the need for sophisticated neuroimaging analyses becomes more important. The use of imaging markers to predict clinical outcomes, or even imaging outcomes, can have great impact on public health. However, such analyses are still under development since it is challenging for several reasons: 1) the images are of high dimension, and 2) the images may exhibit complex spatial correlation structure. Bayesian methods play an important role in solving these problems by dealing with spatial data flexibly and applying efficient sampling algorithms. This dissertation aims to develop spatial Bayesian models to predict either scalar or imaging outcomes by using imaging predictors and seeks computationally efficient approaches. In Chapter I, we propose a Bayesian scalar-on-image regression model with application to Multiple Sclerosis (MS) Magnetic Resonance Imaging (MRI) data. Specifically, we build up a multinomial logistic regression model to predict the clinical subtypes of MS patients by using their 3D MRI lesion data. Parameters corresponding to MRI predictors are spatially varying in the image space and are assumed to have a Gaussian Process (GP) prior distribution. Since the covariates are highly correlated, we use the Hamiltonian Monte Carlo algorithm, which is more statistically efficient than other Markov Chain Monte Carlo methods when the parameters are highly correlated. Finally, to reduce computational burden, we code the problem to run in parallel on a graphical processing unit. Results from simulation studies and a real MS data set show that our method has high prediction accuracy as evaluated by leave-one-out cross validation using an importance-sampling scheme. In Chapter II, we propose a novel image-on-image regression model, by extending a spatial Bayesian latent factor model to neuroimaging data, where low dimensional latent factors are adopted to make connections between high-dimensional image outcomes and image predictors. We assign GP priors to the spatially varying regression coefficients in the model, which capture the complex spatial dependence among image outcomes as well as that among the image predictors. We perform simulation studies to evaluate the out-of-sample prediction performance of our method compared with linear regression and voxel-wise regression methods for different scenarios. We apply the proposed method to analysis of multimodal image data in the Human Connectome Project (HCP) where we predict task-related contrast maps using sub-cortical volumetric seed maps. The proposed method achieves a better prediction accuracy than simpler models by effectively accounting for the spatial dependence and efficient reduction of image dimension with latent factors. In Chapter III, we extend the image-on-image regression model proposed in Chapter II to the case where outcome is a cortical surface image and predictors images are volumetric seed maps. We expand the surface image on a set of spherical harmonics basis functions, where coefficients are linked to image predictors through a latent factor model. We assign GP priors to the spatially varying regression coefficients of the volumetric predictor images. Compared to ridge regression, the proposed method performs better in prediction according to simulation studies, and it can identify active brain regions in spherical z-score images from the HCP.