Statistical analysis of complex neuroimaging data

This dissertation is composed of two major topics: a) regression models for identifying noise sources in magnetic resonance images, and b) multiscale Adaptive method in neuroimaging studies. The first topic is covered by the first thesis paper. In this paper, we formally introduce three regression models including a Rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities, including diffusion weighted imaging (DWI) and functional MRI (fMRI). Estimation algorithms are introduced to maximize the likelihood function of the three regression models. We also develop a diagnostic procedure for systematically exploring MR images to identify noise components other than simple stochastic noise, and to detect discrepancies between the fitted regression models and MRI data. The diagnostic procedure includes goodness-of-fit statistics, measures of influence, and tools for graphical display. The goodness-of-fit statistics can assess the key assumptions of the three regression models, whereas measures of influence can isolate outliers caused by certain noise components, including motion artifact. The tools for graphical display permit graphical visualization of the values for the goodness-of-fit statistic and influence measures. Finally, we conduct simulation studies to evaluate performance of these methods, and we analyze a real dataset to illustrate how our diagnostic procedure localizes subtle image artifacts by detecting intravoxel variability that is not captured by the regression models. The second topic, multiscale adaptive methods for neuroimaging data, consists of two thesis papers.The goal of the first paper is to develop a multiscale adaptive regression model (MARM) for spatial and adaptive analysis of neuroimaging data. Compared with the existing voxel-wise approach in the analysis of imaging data,MARM has three unique features: being spatial, being hierarchical, and being adaptive. MARM creates a small sphere with a given radius at each location (called voxel), analyzes all observations in the sphere of each voxel, and then uses these consecutively connected spheres across all voxels to capture spatial dependence among imaging observations. MARM builds hierarchically nested spheres by increasing the radius of a spherical neighborhood around each voxel and utilizes information in each of the nested spheres at each voxel. Finally, MARM combine imaging observations with adaptive weights in the voxels within the sphere of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish the consistency and asymptotic normality of adaptive estimates and the asymptotic distributions of adaptive test statistics under some mild conditions. Three sets of simulation studies are used to demonstrate the methodology and examine the finite sample performance of the adaptive estimates and test statistics in MARM. We apply MARM to quantify spatiotemporal white matter maturation patterns in early postnatal population using diffusion tensor imaging. Our simulation studies and real data analysis confirm that the MARM significantly outperforms the voxel-wise methods. The goal of the second paper is to develop a multiscale adaptive generalized estimation equation (MAGEE) for spatial and adaptive analysis of longitudinal neuroimaging data. Longitudinal imaging studies have been valuable for better understanding disease progression and normal brain development/aging. Compared to cross-sectional imaging studies, longitudinal imaging studies can increase the statistical power in detecting subtle spatiotemporal changes of brain structure and function. MAGEE is a hierarchical, spatial, semiparametric, and adaptive procedure, compared with the existing voxel-wise approach. The key ideas of MAGEE are to build hierarchically nested spheres with increasing radii at each location, to analyze all observations in the sphere of each voxel using weighted generalized estimating equations, and to use the consecutively connected spheres across all voxels to adaptively capture spatial pattern. Simulation studies and real data analysis clearly show the advantage of MAGEE method over the existing voxel-wise methods. Our results also reveal i) the increase of fractional anisotropy in this early postnatal stage, and ii) five different growth patterns in the brain regions under examination