A statistical analysis of brain morphology using wild bootstrapping

Statistical Learning Methods for Neuroimaging Data Analysis with Applications

The aim of this review is to provide a comprehensive survey of statistical challenges in neuroimaging data analysis, from neuroimaging techniques to large-scale neuroimaging studies and statistical learning methods. We briefly review eight popular neuroimaging techniques and their potential applications in neuroscience research and clinical translation. We delineate four themes of neuroimaging data and review major image processing analysis methods for processing neuroimaging data at the individual level. We briefly review four large-scale neuroimaging-related studies and a consortium on imaging genomics and discuss four themes of neuroimaging data analysis at the population level. We review nine major population-based statistical analysis methods and their associated statistical challenges and present recent progress in statistical methodology to address these challenges.

Functional hybrid factor regression model for handling heterogeneity in imaging studies

This paper develops a functional hybrid factor regression modelling framework to handle the heterogeneity of many large-scale imaging studies, such as the Alzheimer's disease neuroimaging initiative study. Despite the numerous successes of those imaging studies, such heterogeneity may be caused by the differences in study environment, population, design, protocols or other hidden factors, and it has posed major challenges in integrative analysis of imaging data collected from multicentres or multistudies. We propose both estimation and inference procedures for estimating unknown parameters and detecting unknown factors under our new model. The asymptotic properties of both estimation and inference procedures are systematically investigated. The finite-sample performance of our proposed procedures is assessed by using Monte Carlo simulations and a real data example on hippocampal surface data from the Alzheimer's disease study.

Brain amyloid burden, sleep, and 24-hour rest/activity rhythms: screening findings from the Anti-Amyloid Treatment in Asymptomatic Alzheimer's and Longitudinal Evaluation of Amyloid Risk and Neurodegeneration Studies

STUDY OBJECTIVES

To examine in a subsample at the screening phase of a clinical trial of a β-amyloid (Aβ) antibody whether disturbed sleep and altered 24-hour rest/activity rhythms (RARs) may serve as markers of preclinical Alzheimer's disease (AD).

METHODS

Overall, 26 Aβ-positive (Aβ+) and 33 Aβ-negative (Aβ-) cognitively unimpaired participants (mean age = 71.3 ± 4.6 years, 59% women) from the Anti-Amyloid Treatment in Asymptomatic Alzheimer's (A4) and the Longitudinal Evaluation of Amyloid Risk and Neurodegeneration (LEARN) studies, respectively, wore actigraphs for 5.66 ± 0.88 24-hour periods. We computed standard sleep parameters, standard RAR metrics (mean estimating statistic of rhythm, amplitude, acrophase, interdaily stability, intradaily variability, relative amplitude), and performed a novel RAR analysis (function-on-scalar regression [FOSR]).

RESULTS

We were unable to detect any differences between Aβ+ and Aβ- participants in standard sleep parameters or RAR metrics with our sample size. When we used novel FOSR methods, however, Aβ+ participants had lower activity levels than Aβ- participants in the late night through early morning (11:30 pm to 3:00 am), and higher levels in the early morning (4:30 am to 8:30 am) and from midday through late afternoon (12:30 pm to 5:30 pm; all p < .05). Aβ+ participants also had higher variability in activity across days from 9:30 pm to 1:00 am and 4:30 am to 8:30 am, and lower variability from 2:30 am to 3:30 am (all p < .05).

CONCLUSIONS

Although we found no association of preclinical AD with standard actigraphic sleep or RAR metrics, a novel data-driven analytic method identified temporally "local" RAR alterations in preclinical AD.

Brain Development in School-Age and Adolescent Girls: Effects of Turner Syndrome, Estrogen Therapy, and Genomic Imprinting

BACKGROUND

The study of Turner syndrome (TS) offers a unique window of opportunity for advancing scientific knowledge of how X chromosome gene imprinting, epigenetic factors, hormonal milieu, and chronologic age affect brain development in females.

METHODS

We described brain growth trajectories in 55 girls with TS and 53 typically developing girls (258 magnetic resonance imaging datasets) spanning 5 years. Using novel nonparametric and mixed effects analytic approaches, we evaluated influences of X chromosome genomic imprinting and hormone replacement therapy on brain development.

RESULTS

Parieto-occipital gray and white matter regions showed slower growth during typical pubertal timing in girls with TS relative to typically developing girls. In contrast, some basal ganglia, cerebellar, and limited cortical areas showed enhanced volume growth with peaks around 10 years of age.

CONCLUSIONS

The parieto-occipital finding suggests that girls with TS may be particularly vulnerable to altered brain development during adolescence. Basal ganglia regions may be relatively preserved in TS owing to their maturational growth before or early in typical pubertal years. Taken together, our findings indicate that particular brain regions are more vulnerable to TS genetic and hormonal effects during puberty. These specific alterations in neurodevelopment may be more likely to affect long-term cognitive behavioral outcomes in young girls with this common genetic condition.

Multivariate pattern analysis of the neural correlates of smoking cue attentional bias

The automatic capture of attention by drug cues, or attentional bias, is associated with craving and predicts future drug use. Despite its clinical significance, the neural bases of attentional bias to drug cues is not well understood. To address this gap, we undertook a neuroimaging investigation of the neural correlates of attentional bias towards smoking cues. Twenty-nine adults, including 14 active smokers and 15 non-smokers, completed a spatial cuing task during fMRI. A multivariate pattern analysis (MVPA) decoded the neural responses to the brief presentation of smoking versus neutral images. These data were correlated with behavioral measures of attentional bias, which included analyses targeting the neural correlates of response facilitation and cue-related task interference. We detected a set of brain-behavioral correlates that were similar across both smokers and non-smokers, indicating a role for stimuli salience in the absence of nicotine conditioning in smoking cue attentional bias. However, multiple smoking-related modifications to the neural correlates of attentional bias and its components were also identified. For example, regions demonstrating smoking-related differences in the neural correlates of attentional bias included the rostral anterior cingulate cortex and inferior frontal gyrus. Response facilitation effects of smoking were observed in the right orbitofrontal gyrus and bilateral middle temporal gyrus. Smoking-cue related task interference was related to smoking-related effects in the frontal eye fields. Our findings suggest that multiple cognitive, affective, and visual object recognition processes contribute to attentional bias towards smoking cues, and suggest multiple circuit modifications that may contribute to perpetuation of addiction.

A web-based system for neural network based classification in temporomandibular joint osteoarthritis

OBJECTIVE

The purpose of this study is to describe the methodological innovations of a web-based system for storage, integration and computation of biomedical data, using a training imaging dataset to remotely compute a deep neural network classifier of temporomandibular joint osteoarthritis (TMJOA).

METHODS

This study imaging dataset consisted of three-dimensional (3D) surface meshes of mandibular condyles constructed from cone beam computed tomography (CBCT) scans. The training dataset consisted of 259 condyles, 105 from control subjects and 154 from patients with diagnosis of TMJ OA. For the image analysis classification, 34 right and left condyles from 17 patients (39.9 ± 11.7 years), who experienced signs and symptoms of the disease for less than 5 years, were included as the testing dataset. For the integrative statistical model of clinical, biological and imaging markers, the sample consisted of the same 17 test OA subjects and 17 age and sex matched control subjects (39.4 ± 15.4 years), who did not show any sign or symptom of OA. For these 34 subjects, a standardized clinical questionnaire, blood and saliva samples were also collected. The technological methodologies in this study include a deep neural network classifier of 3D condylar morphology (ShapeVariationAnalyzer, SVA), and a flexible web-based system for data storage, computation and integration (DSCI) of high dimensional imaging, clinical, and biological data.

RESULTS

The DSCI system trained and tested the neural network, indicating 5 stages of structural degenerative changes in condylar morphology in the TMJ with 91% close agreement between the clinician consensus and the SVA classifier. The DSCI remotely ran with a novel application of a statistical analysis, the Multivariate Functional Shape Data Analysis, that computed high dimensional correlations between shape 3D coordinates, clinical pain levels and levels of biological markers, and then graphically displayed the computation results.

CONCLUSIONS

The findings of this study demonstrate a comprehensive phenotypic characterization of TMJ health and disease at clinical, imaging and biological levels, using novel flexible and versatile open-source tools for a web-based system that provides advanced shape statistical analysis and a neural network based classification of temporomandibular joint osteoarthritis.

Improving mass-univariate analysis of neuroimaging data by modelling important unknown covariates: Application to Epigenome-Wide Association Studies

Statistical inference on neuroimaging data is often conducted using a mass-univariate model, equivalent to fitting a linear model at every voxel with a known set of covariates. Due to the large number of linear models, it is challenging to check if the selection of covariates is appropriate and to modify this selection adequately. The use of standard diagnostics, such as residual plotting, is clearly not practical for neuroimaging data. However, the selection of covariates is crucial for linear regression to ensure valid statistical inference. In particular, the mean model of regression needs to be reasonably well specified. Unfortunately, this issue is often overlooked in the field of neuroimaging. This study aims to adopt the existing Confounder Adjusted Testing and Estimation (CATE) approach and to extend it for use with neuroimaging data. We propose a modification of CATE that can yield valid statistical inferences using Principal Component Analysis (PCA) estimators instead of Maximum Likelihood (ML) estimators. We then propose a non-parametric hypothesis testing procedure that can improve upon parametric testing. Monte Carlo simulations show that the modification of CATE allows for more accurate modelling of neuroimaging data and can in turn yield a better control of False Positive Rate (FPR) and Family-Wise Error Rate (FWER). We demonstrate its application to an Epigenome-Wide Association Study (EWAS) on neonatal brain imaging and umbilical cord DNA methylation data obtained as part of a longitudinal cohort study. Software for this CATE study is freely available at http://www.bioeng.nus.edu.sg/cfa/Imaging_Genetics2.html.

Which is the most appropriate strategy for conducting multivariate voxel-based group studies on diffusion tensors?

There is a real need in the neuroscience community for efficient tools to compare Diffusion Tensor Magnetic Resonance Imaging across cohorts of subjects. Most studies focus on the comparison of scalar images such as fractional anisotropy or mean diffusivity. Although different statistical frameworks have been proposed to compare the whole diffusion tensor information, they are still seldom used in neuroimaging studies. In this paper, we investigate on both simulated and real data whether there is a real added value of considering the whole tensor information for conducting voxel-based group studies. Then, we compare two statistical tests dedicated to tensor, namely the Cramér test and a tensor-based extension of the General Linear Model (GLM), the latter presenting the advantage to account for covariates. We also evaluate the impact of different metrics (Euclidean, Log-Euclidean and affine-invariant Riemannian metrics) for estimating the GLM parameters. Finally, we address the problem of interpreting the change detection maps obtained by tensor-based methods by proposing a way to characterize each of the detected clusters according to several scalar indices. Our study suggests that if there is no prior assumption about the nature of the expected changes, it is really preferable to use tensor-based rather than scalar-based statistical analysis. The Cramér test can advantageously be used when no confounding variable hampers the group comparison, otherwise the GLM should be considered. Finally, the different metrics show similar performance in the real scenario, with a significant computational overhead for the Riemannian framework.

FVGWAS: Fast voxelwise genome wide association analysis of large-scale imaging genetic data

More and more large-scale imaging genetic studies are being widely conducted to collect a rich set of imaging, genetic, and clinical data to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. Several major big-data challenges arise from testing genome-wide (NC>12 million known variants) associations with signals at millions of locations (NV~10(6)) in the brain from thousands of subjects (n~10(3)). The aim of this paper is to develop a Fast Voxelwise Genome Wide Association analysiS (FVGWAS) framework to efficiently carry out whole-genome analyses of whole-brain data. FVGWAS consists of three components including a heteroscedastic linear model, a global sure independence screening (GSIS) procedure, and a detection procedure based on wild bootstrap methods. Specifically, for standard linear association, the computational complexity is O (nNVNC) for voxelwise genome wide association analysis (VGWAS) method compared with O ((NC+NV)n(2)) for FVGWAS. Simulation studies show that FVGWAS is an efficient method of searching sparse signals in an extremely large search space, while controlling for the family-wise error rate. Finally, we have successfully applied FVGWAS to a large-scale imaging genetic data analysis of ADNI data with 708 subjects, 193,275voxels in RAVENS maps, and 501,584 SNPs, and the total processing time was 203,645s for a single CPU. Our FVGWAS may be a valuable statistical toolbox for large-scale imaging genetic analysis as the field is rapidly advancing with ultra-high-resolution imaging and whole-genome sequencing.

Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template.

Harnessing graphics processing units for improved neuroimaging statistics

Simple models and algorithms based on restrictive assumptions are often used in the field of neuroimaging for studies involving functional magnetic resonance imaging, voxel based morphometry, and diffusion tensor imaging. Nonparametric statistical methods or flexible Bayesian models can be applied rather easily to yield more trustworthy results. The spatial normalization step required for multisubject studies can also be improved by taking advantage of more robust algorithms for image registration. A common drawback of algorithms based on weaker assumptions, however, is the increase in computational complexity. In this short overview, we will therefore present some examples of how inexpensive PC graphics hardware, normally used for demanding computer games, can be used to enable practical use of more realistic models and accurate algorithms, such that the outcome of neuroimaging studies really can be trusted.

Morphological features of the neonatal brain support development of subsequent cognitive, language, and motor abilities

Knowledge of the role of brain maturation in the development of cognitive abilities derives primarily from studies of school-age children to adults. Little is known about the morphological features of the neonatal brain that support the subsequent development of abilities in early childhood, when maturation of the brain and these abilities are the most dynamic. The goal of our study was to determine whether brain morphology during the neonatal period supports early cognitive development through 2 years of age. We correlated morphological features of the cerebral surface assessed using deformation-based measures (surface distances) of high-resolution MRI scans for 33 healthy neonates, scanned between the first to sixth week of postmenstrual life, with subsequent measures of their motor, language, and cognitive abilities at ages 6, 12, 18, and 24 months. We found that morphological features of the cerebral surface of the frontal, mesial prefrontal, temporal, and occipital regions correlated with subsequent motor scores, posterior parietal regions correlated with subsequent language scores, and temporal and occipital regions correlated with subsequent cognitive scores. Measures of the anterior and middle portions of the cingulate gyrus correlated with scores across all three domains of ability. Most of the significant findings were inverse correlations located bilaterally in the brain. The inverse correlations may suggest either that a more protracted morphological maturation or smaller local volumes of neonatal brain tissue supports better performance on measures of subsequent motor, language, and cognitive abilities throughout the first 2 years of postnatal life. The correlations of morphological measures of the cingulate with measures of performance across all domains of ability suggest that the cingulate supports a broad range of skills in infancy and early childhood, similar to its functions in older children and adults.

In vivo GABA T2 determination with J-refocused echo time extension at 7 T

A method to measure the T2 relaxation time of GABA with spectral editing techniques is proposed. Spectral editing techniques can be used to unambiguously extract signals of low concentration J-coupled spins such as γ-aminobutyric acid (GABA) from overlapping resonances such as creatine and macromolecules. These sequences, however, generally have fixed and relatively long echo times. Therefore, for the absolute quantification of the edited spectrum, the T2 relaxation time must be taken into account. To measure the T2 relaxation time, the signal intensity has to be obtained at multiple echo times. However, on a coupled spin system such as GABA this is challenging, since the signal intensity of the target resonances is modulated not only by T2 decay but also by the J-coupling, which strongly influences the shapes and amplitudes of the edited signals, depending on the echo time. Here, we propose to refocus the J-modulation of the edited signal at different echo times by using chemical shift selective refocusing. In this way the echo time can be arbitrarily extended while preserving the shape of the edited signal. The method was applied in combination with the MEGA-sLASER editing technique to measure the in vivo T2 relaxation time of GABA (87 ± 11 ms, n = 10) and creatine (109 ± 8 ms, n = 10) at 7 T. The T1 relaxation time of these metabolites in a single subject was also determined (GABA, 1334 ± 158 ms; Cr, 1753 ± 12 ms). The T2 decay curve of coupled spin systems can be sampled in an arbitrary fashion without the need for signal shape correction. Furthermore, the method can be applied with any spectral editing technique. The shortest echo time of the method is limited by the echo time of the spectral editing technique.

VARYING COEFFICIENT MODEL FOR MODELING DIFFUSION TENSORS ALONG WHITE MATTER TRACTS

Diffusion tensor imaging provides important information on tissue structure and orientation of fiber tracts in brain white matter in vivo. It results in diffusion tensors, which are 3×3 symmetric positive definite (SPD) matrices, along fiber bundles. This paper develops a functional data analysis framework to model diffusion tensors along fiber tracts as functional data in a Riemannian manifold with a set of covariates of interest, such as age and gender. We propose a statistical model with varying coefficient functions to characterize the dynamic association between functional SPD matrix-valued responses and covariates. We calculate weighted least squares estimators of the varying coefficient functions for the Log-Euclidean metric in the space of SPD matrices. We also develop a global test statistic to test specific hypotheses about these coefficient functions and construct their simultaneous confidence bands. Simulated data are further used to examine the finite sample performance of the estimated varying co-efficient functions. We apply our model to study potential gender differences and find a statistically significant aspect of the development of diffusion tensors along the right internal capsule tract in a clinical study of neurodevelopment.

Functional Causal Mediation Analysis With an Application to Brain Connectivity

Mediation analysis is often used in the behavioral sciences to investigate the role of intermediate variables that lie on the causal path between a randomized treatment and an outcome variable. Typically, mediation is assessed using structural equation models (SEMs), with model coefficients interpreted as causal effects. In this article, we present an extension of SEMs to the functional data analysis (FDA) setting that allows the mediating variable to be a continuous function rather than a single scalar measure, thus providing the opportunity to study the functional effects of the mediator on the outcome. We provide sufficient conditions for identifying the average causal effects of the functional mediators using the extended SEM, as well as weaker conditions under which an instrumental variable estimand may be interpreted as an effect. The method is applied to data from a functional magnetic resonance imaging (fMRI) study of thermal pain that sought to determine whether activation in certain brain regions mediated the effect of applied temperature on self-reported pain. Our approach provides valuable information about the timing of the mediating effect that is not readily available when using the standard nonfunctional approach. To the best of our knowledge, this work provides the first application of causal inference to the FDA framework.

TwinMARM: two-stage multiscale adaptive regression methods for twin neuroimaging data

Twin imaging studies have been valuable for understanding the relative contribution of the environment and genes on brain structures and their functions. Conventional analyses of twin imaging data include three sequential steps: spatially smoothing imaging data, independently fitting a structural equation model at each voxel, and finally correcting for multiple comparisons. However, conventional analyses are limited due to the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and the decreased power in detecting environmental and genetic effects introduced by smoothing raw images. The goal of this paper is to develop a two-stage multiscale adaptive regression method (TwinMARM) for spatial and adaptive analysis of twin neuroimaging and behavioral data. The first stage is to establish the relationship between twin imaging data and a set of covariates of interest, such as age and gender. The second stage is to disentangle the environmental and genetic influences on brain structures and their functions. In each stage, TwinMARM employs hierarchically nested spheres with increasing radii at each location and then captures spatial dependence among imaging observations via consecutively connected spheres across all voxels. Simulation studies show that our TwinMARM significantly outperforms conventional analyses of twin imaging data. Finally, we use our method to detect statistically significant effects of genetic and environmental variations on white matter structures in a neonatal twin study.

FADTTS: functional analysis of diffusion tensor tract statistics

The aim of this paper is to present a functional analysis of a diffusion tensor tract statistics (FADTTS) pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies. The FADTTS integrates five statistical tools: (i) a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates, (ii) a weighted least squares estimation of the varying coefficient functions, (iii) a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties, (iv) a global test statistic to test hypotheses of interest, and (v) a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FADTTS. We apply FADTTS to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. FADTTS can be used to facilitate the understanding of normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles. The advantages of FADTTS compared with the other existing approaches are that they are capable of modeling the structured inter-subject variability, testing the joint effects, and constructing their simultaneous confidence bands. However, FADTTS is not crucial for estimation and reduces to the functional analysis method for the single measure.

FRATS: Functional Regression Analysis of DTI Tract Statistics

Diffusion tensor imaging (DTI) provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. This paper presents a functional regression framework, called FRATS, for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest, such as age, diagnostic status and gender, in real applications. The functional regression framework consists of four integrated components: the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles, a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates, a global test statistic for testing hypotheses of interest, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy, mean diffusivity, and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. Significant age and gestational age effects on the five diffusion properties were found in both tracts. The resulting analysis pipeline can be used for understanding normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles.

Comparing registration methods for mapping brain change using tensor-based morphometry

Measures of brain changes can be computed from sequential MRI scans, providing valuable information on disease progression for neuroscientific studies and clinical trials. Tensor-based morphometry (TBM) creates maps of these brain changes, visualizing the 3D profile and rates of tissue growth or atrophy. In this paper, we examine the power of different nonrigid registration models to detect changes in TBM, and their stability when no real changes are present. Specifically, we investigate an asymmetric version of a recently proposed Unbiased registration method, using mutual information as the matching criterion. We compare matching functionals (sum of squared differences and mutual information), as well as large-deformation registration schemes (viscous fluid and inverse-consistent linear elastic registration methods versus Symmetric and Asymmetric Unbiased registration) for detecting changes in serial MRI scans of 10 elderly normal subjects and 10 patients with Alzheimer's Disease scanned at 2-week and 1-year intervals. We also analyzed registration results when matching images corrupted with artificial noise. We demonstrated that the unbiased methods, both symmetric and asymmetric, have higher reproducibility. The unbiased methods were also less likely to detect changes in the absence of any real physiological change. Moreover, they measured biological deformations more accurately by penalizing bias in the corresponding statistical maps.

Automated 3D mapping of hippocampal atrophy and its clinical correlates in 400 subjects with Alzheimer's disease, mild cognitive impairment, and elderly controls

We used a new method we developed for automated hippocampal segmentation, called the auto context model, to analyze brain MRI scans of 400 subjects from the Alzheimer's disease neuroimaging initiative. After training the classifier on 21 hand-labeled expert segmentations, we created binary maps of the hippocampus for three age- and sex-matched groups: 100 subjects with Alzheimer's disease (AD), 200 with mild cognitive impairment (MCI) and 100 elderly controls (mean age: 75.84; SD: 6.64). Hippocampal traces were converted to parametric surface meshes and a radial atrophy mapping technique was used to compute average surface models and local statistics of atrophy. Surface-based statistical maps visualized links between regional atrophy and diagnosis (MCI versus controls: P = 0.008; MCI versus AD: P = 0.001), mini-mental state exam (MMSE) scores, and global and sum-of-boxes clinical dementia rating scores (CDR; all P < 0.0001, corrected). Right but not left hippocampal atrophy was associated with geriatric depression scores (P = 0.004, corrected); hippocampal atrophy was not associated with subsequent decline in MMSE and CDR scores, educational level, ApoE genotype, systolic or diastolic blood pressure measures, or homocysteine. We gradually reduced sample sizes and used false discovery rate curves to examine the method's power to detect associations with diagnosis and cognition in smaller samples. Forty subjects were sufficient to discriminate AD from normal and correlate atrophy with CDR scores; 104, 200, and 304 subjects, respectively, were required to correlate MMSE with atrophy, to distinguish MCI from normal, and MCI from AD.

VOXEL-WISE GROUP ANALYSIS OF DTI

Diffusion tensor MRI (DTI) is now a widely used modality to investigate the fiber tissues in vivo, especially the white matter in brain. An automatic pipeline is described in this paper to conduct a localized voxel-wise multiple-subject group comparison study of DTI. The pipeline consists of 3 steps: 1) Preprocessing, including image format converting, image quality check, eddy-current and motion artifact correction, skull stripping and tensor image estimation, 2) study-specific unbiased DTI atlas computation via affine followed by fluid nonlinear registration and warping of all individual DTI images into the common atlas space to achieve voxel-wise correspondence, 3) voxelwise statistical analysis via heterogeneous linear regression and wild bootstrap technique for correcting for multiple comparisons. This pipeline was applied to process data from a fitness and aging study and preliminary results are presented. The results show that this fully automatic pipeline is suitable for voxel-wise group DTI analysis.

White matter abnormalities revealed by diffusion tensor imaging in non-demented and demented HIV+ patients

HIV associated dementia (HAD) is the most advanced stage of central nervous system disease caused by HIV infection. Previous studies have demonstrated that patients with HAD exhibit greater cerebral and basal ganglia atrophy than non-demented HIV+ (HND) patients. However, the extent to which white matter is affected in HAD patients compared to HND patients remains elusive. This study is designed to address the potential white matter abnormalities through the utilization of diffusion tensor imaging (DTI) in both HND and HAD patients. DTI and T1-weighted images were acquired from 18 healthy controls, 21 HND and 8 HAD patients. T1 image-based registration was performed to 1) parcellate the whole brain white matter into major white matter regions, including frontal, parietal, temporal and occipital white matter, corpus callosum and internal capsule for statistical comparisons of the mean DTI values, and 2) warp all DTI parametric images towards the common template space for voxel-based analysis. The statistical comparisons were performed with four DTI parameters including fractional anisotropy (FA), mean (MD), axial (AD), and radial (RD) diffusivities. With Whitney U tests on the mean DTI values, both HND and HAD demonstrated significant differences from the healthy control in multiple white matter regions. In addition, HAD patients exhibited significantly elevated MD and RD in the parietal white matter when compared to HND patients. In the voxel-based analysis, widespread abnormal regions were identified for both HND and HAD patients, although a much larger abnormal volume was observed in HAD patients for all four DTI parameters. Furthermore, both region of interest (ROI) based and voxel-based analyses revealed that RD was affected to a much greater extent than AD by HIV infection, which may suggest that demyelination is the prominent disease progression in white matter.

Statistical Modelling of Brain Morphological Measures Within Family Pedigrees

Large, family-based imaging studies can provide a better understanding of the interactions of environmental and genetic influences on brain structure and function. The interpretation of imaging data from large family studies, however, has been hindered by the paucity of well-developed statistical tools for that permit the analysis of complex imaging data together with behavioral and clinical data. In this paper, we propose to use two methods for these analyses. First, a variance components model along with score statistics is used to test linear hypotheses of unknown parameters, such as the associations of brain measures (e.g., cortical and subcortical surfaces) with their potential genetic determinants. Second, we develop a test procedure based on a resampling method to assess simultaneously the statistical significance of linear hypotheses across the entire brain. The value of these methods lies in their computational simplicity and in their applicability to a wide range of imaging data. Simulation studies show that our test procedure can accurately control the family-wise error rate. We apply our methods to the detection of statistical significance of gender-by-age interactions and of the effects of genetic variation on the thickness of the cerebral cortex in a family study of major depressive disorder.

A note on the validity of statistical bootstrapping for estimating the uncertainty of tensor parameters in diffusion tensor images

Diffusion tensors are estimated from magnetic resonance images (MRIs) that are diffusion-weighted, and those images inherently contain noise. Therefore, noise in the diffusion-weighted images produces uncertainty in estimation of the tensors and their derived parameters, which include eigenvalues, eigenvectors, and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors. Although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters, we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise. The aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images. Whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters, such as fractional anisotropy (FA), depends critically on the morphology of the diffusion tensor that is being estimated. The wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction (PD) of isotropic (or oblate) tensor. We also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors, demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations. Simulation studies are also used to understand more thoroughly our theoretical results. Our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors, oblate tensors, or multiple tensors.

Adjusted exponentially tilted likelihood with applications to brain morphology

In this article, we develop a nonparametric method, called adjusted exponentially tilted (ET) likelihood, and apply it to the analysis of morphometric measures. The adjusted exponential tilting estimator is shown to have the same first-order asymptotic properties as that of the original ET likelihood. The adjusted ET likelihood ratio statistic is applied to test linear hypotheses of unknown parameters, such as the associations of brain measures (e.g., cortical and subcortical surfaces) with covariates of interest, such as age, gender, and gene. Simulation studies show that the adjusted exponential tilted likelihood ratio statistic performs as well as the t-test when the imaging data are symmetrically distributed, while it is superior when the imaging data have skewed distribution. We demonstrate the application of our new statistical methods to the detection of statistically significant differences in the morphology of the hippocampus between two schizophrenia groups and healthy subjects.

Generalized semiparametrically structured ordinal models

Semiparametrically structured models are defined as a class of models for which the predictors may contain parametric parts, additive parts of covariates with an unspecified functional form, and interactions which are described as varying coefficients. In the case of an ordinal response the complexity of the predictor is determined by different sorts of effects. Global effects and category-specific effects are distinguished; the latter allow the effect to vary across response categories. A general framework is developed in which global as well as category-specific effects may have unspecified functional form. The framework extends various existing methods of modeling ordinal responses. The Wilkinson-Rogers notation is extended to incorporate smooth model parts and varying coefficient terms, the latter being important for the smooth specification of category-specific effects.