Multiscale adaptive generalized estimating equations for longitudinal neuroimaging data

Many large-scale longitudinal imaging studies have been or are being widely conducted to better understand the progress of neuropsychiatric and neurodegenerative disorders and normal brain development. The goal of this article is to develop a multiscale adaptive generalized estimation equation (MAGEE) method for spatial and adaptive analysis of neuroimaging data from longitudinal studies. MAGEE is applicable to making statistical inference on regression coefficients in both balanced and unbalanced longitudinal designs and even twin and familial studies, whereas standard software platforms have several major limitations in handling these complex studies. Specifically, conventional voxel-based analyses in these software platforms involve Gaussian smoothing imaging data and then independently fitting a statistical model at each voxel. However, the conventional smoothing methods suffer from the lack of spatial adaptivity to the shape and spatial extent of region of interest and the arbitrary choice of smoothing extent, while independently fitting statistical models across voxels does not account for the spatial properties of imaging observations and noise distribution. To address such drawbacks, we adapt a powerful propagation–separation (PS) procedure to sequentially incorporate the neighboring information of each voxel and develop a new novel strategy to solely update a set of parameters of interest, while fixing other nuisance parameters at their initial estimators. Simulation studies and real data analysis show that MAGEE significantly outperforms voxel-based analysis

Fast and accurate modelling of longitudinal and repeated measures neuroimaging data

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions (e.g., assumption of Compound Symmetry—the state of all equal variances and equal correlations—or spatially homogeneous longitudinal correlations). While some new methods have been proposed to more accurately account for such data, these methods are based on iterative algorithms that are slow and failure-prone. In this article, we propose the use of the Sandwich Estimator (SwE) method which first estimates the parameters of interest with a simple Ordinary Least Square model and second estimates variances/covariances with the “so-called” SwE which accounts for the within-subject correlation existing in longitudinal data. Here, we introduce the SwE method in its classic form, and we review and propose several adjustments to improve its behaviour, specifically in small samples. We use intensive Monte Carlo simulations to compare all considered adjustments and isolate the best combination for neuroimaging data. We also compare the SwE method to other popular methods and demonstrate its strengths and weaknesses. Finally, we analyse a highly unbalanced longitudinal dataset from the Alzheimer's Disease Neuroimaging Initiative and demonstrate the flexibility of the SwE method to fit within- and between-subject effects in a single model. Software implementing this SwE method has been made freely available at http://warwick.ac.uk/tenichols/SwE

Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time-Varying Covariates

Neuroimaging data collected at repeated occasions are gaining increasing attention in the neuroimaging community due to their potential in answering questions regarding brain development, aging, and neurodegeneration. These datasets are large and complicated, characterized by the intricate spatial dependence structure of each response image, multiple response images per subject, and covariates that may vary with time. We propose a multiscale adaptive generalized method of moments (MA-GMM) approach to estimate marginal regression models for imaging datasets that contain time-varying, spatially-related responses and some time-varying covariates. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. Further, instead of assuming independence of voxels (the components that make up each subject’s response image at each time point) as many current neuroimaging analysis techniques do, this method “adaptively smoothes” neuroimaging response data, computing parameter estimates by iteratively building spheres around each voxel and combining observations within the spheres with weights. MA-GMM’s development adds to the few available modeling approaches intended for longitudinal imaging data analysis. Simulation studies and an analysis of a real longitudinal imaging dataset from the Alzheimer’s Disease Neuroimaging Initiative are used to assess the performance of MA-GMM

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

Two-stage empirical likelihood for longitudinal neuroimaging data

Longitudinal imaging studies are essential to understanding the neural development of neuropsychiatric disorders, substance use disorders, and the normal brain. The main objective of this paper is to develop a two-stage adjusted exponentially tilted empirical likelihood (TETEL) for the spatial analysis of neuroimaging data from longitudinal studies. The TETEL method as a frequentist approach allows us to efficiently analyze longitudinal data without modeling temporal correlation and to classify different time-dependent covariate types. To account for spatial dependence, the TETEL method developed here specifically combines all the data in the closest neighborhood of each voxel (or pixel) on a 3-dimensional (3D) volume (or 2D surface) with appropriate weights to calculate adaptive parameter estimates and adaptive test statistics. Simulation studies are used to examine the finite sample performance of the adjusted exponential tilted likelihood ratio statistic and TETEL. We demonstrate the application of our statistical methods to the detection of the difference in the morphological changes of the hippocampus across time between schizophrenia patients and healthy subjects in a longitudinal schizophrenia study.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS480 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

STGP: Spatio-temporal Gaussian process models for longitudinal neuroimaging data

Longitudinal neuroimaging data plays an important role in mapping the neural developmental profile of major neuropsychiatric and neurodegenerative disorders and normal brain. The development of such developmental maps is critical for the prevention, diagnosis, and treatment of many brain-related diseases. The aim of this paper is to develop a spatio-temporal Gaussian process (STGP) framework to accurately delineate the developmental trajectories of brain structure and function, while achieving better prediction by explicitly incorporating the spatial and temporal features of longitudinal neuroimaging data. Our STGP integrates a functional principal component model (FPCA) and a partition parametric space-time covariance model to capture the medium-to-large and small-to-medium spatio-temporal dependence structures, respectively. We develop a three-stage efficient estimation procedure as well as a predictive method based on a kriging technique. Two key novelties of STGP are that it can efficiently use a small number of parameters to capture complex non-stationary and non-separable spatio-temporal dependence structures and that it can accurately predict spatio-temporal changes. We illustrate STGP using simulated data sets and two real data analyses including longitudinal positron emission tomography data from the Alzheimers Disease Neuroimaging Initiative (ADNI) and longitudinal lateral ventricle surface data from a longitudinal study of early brain development

Multiscale adaptive regression models for neuroimaging data: Multiscale Adaptive Regression Models

Neuroimaging studies aim to analyze imaging data with complex spatial patterns in a large number of locations (called voxels) on a two-dimensional (2D) surface or in a 3D volume. Conventional analyses of imaging data include two sequential steps: spatially smoothing imaging data and then independently fitting a statistical model at each voxel. However, conventional analyses suffer from the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and low statistical power in detecting spatial patterns. We propose a multiscale adaptive regression model (MARM) to integrate the propagation–separation (PS) approach (Polzehl and Spokoiny, 2000, 2006) with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects. MARM has three features: being spatial, being hierarchical, and being adaptive. We use a multiscale adaptive estimation and testing procedure (MAET) to utilize imaging observations from the neighboring voxels of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics. Our simulation studies and real data analysis confirm that MARM significantly outperforms conventional analyses of imaging data