Some Novel Statistical Methods for Neuroimaging Data Analysis Public

Abstract

In this dissertation, we propose three novel statistical methods for analyzing neuroimaging data. In the first topic, we propose a hierarchical covariate-adjusted ICA (hc-ICA) model that provides a formal statistical framework for estimating covariate effects and testing differences between brain functional networks. Our method provides a more reliable and powerful statistical tool for evaluating group differences in brain functional networks while appropriately controlling for potential confounding effects. We present two EM algorithms to obtain maximum likelihood estimates of our model. We introduce a voxel-wise approximate inference procedure which eliminates the need of computationally expensive covariance matrix estimation and inversion. We demonstrate the advantages of our methods over the existing method via simulation studies. We apply our method to an fMRI study to investigate differences in brain functional networks associated with post-traumatic stress disorder (PTSD). In the second topic, we propose a spatially varying coefficient model (SVCM) with structured sparsity and region-wise smoothness. A new class of nonparametric Bayesian priors is developed named thresholded Gaussian processes (TGP). We show that TGP has a large prior coverage on the space of region-wise smooth functions with restricted supports, leading to posterior consistency in both estimation and feature selection. Efficient posterior computation algorithms are developed by adopting a kernel convolution approach. Based on simulation studies, we demonstrate that our methods can achieve better performance in estimating functional coefficients and selecting imaging features. The application of our proposed method to a resting state functional magnetic resonance imaging (rs-fMRI) data provides biologically meaningful findings. In the third topic, we present a new independent component analysis (ICA) model with spatially dependent source signals. We model the conditional expectation of IC source signals using Bayesian nonparametrickernel models, which can generate flexible prior spatial dependence structures. We adopt a fully Bayesian approach to make posterior inference about our model through an efficient Markov chain Monte Carlo algorithm. Simulation studies show that, compared with existing ICA algorithms, our method estimates the mixing matrices more accurately and identifies the spatial activation patterns more precisely. When applied to a real fMRI dataset, our method elicits meaningful scientific findings.

Table of Contents

1 Introduction. 1

1.1 Overview. 1

1.2 Some current research topics. 2

1.2.1 Functional brain connectivity. 2

1.2.2 Activation study and feature selection. 6

1.2.3 Spatial dependence when performing ICA dempoition. 8

1.3 Literature Review. 12

1.4 Outlines. 16

2 Investigating dierences in brain functional networks using hierarchical covariate-adjusted independent component analysis. 17

2.1 Methods. 17

2.1.1 Preprocessing prior to ICA. 17

2.1.2 A hierarchical covariate-adjusted ICA model (hc-ICA). 18

2.1.3 Source signal distribution assumptions. 20

2.1.4 Maximum likelihood estimation. 21

2.1.5 Inference for covariate eects in hc-ICA model. 27

2.2 Application to fMRI data from Grady PTSD study. 30

2.2.1 Experimental design, image acquisition and pre-processing. 30

2.2.2 Analysis and findings. 31

2.3 Simulation Study. 36

2.3.1 Simulation study I: performance of the hc-ICAv.s. TCGICA. 36

2.3.2 Simulation study II: performance of the approximate EM. 38

2.3.3 Simulation study III: performance of the proposed inference procedures for covariate eects. 42

2.4 Discussion. 43

2.5 Appendices. 45

2.5.1 The Conditional Expectation Function in the E-step. 45

2.5.2 The derivation of conditional probabilities in the E-step. 46

2.5.3 Details of the M-step in the exact EM. 47

2.5.4 Proof of Theorem 1. 49

2.5.5 Remarks on the subspace-based approximate EM. 51

2.5.6 Thresholding the spatial maps based on the ML estimates for functional brain networks. 51

2.5.7 Specifying the initial values for hc-ICA. 51

2.5.8 Additional Simulation Studies. 52

2.5.9 Checking the stability of our EM algorithm for the PTSD data analysis. 56

3 Bayesian Spatial Feature Selection for Massive Neuroimaging Data via Thresholded Gaussian Processes. 59

3.1 Feature selection within the spatially varying coecient functions. 59

3.1.1 The spatially varying coecient model for neuroimaging data. 60

3.1.2 The thresholded Gaussian process priors. 62

3.2 Theoretical Results. 64

3.3 Posterior Inferences. 68

3.3.1 Model Representation. 68

3.3.2 Hyper Prior Specications. 70

3.3.3 Kernel Expansion for Massive Data Analysis. 72

3.3.4 A Markov chain Monte Carlo Algorithm. 73

3.3.5 Posterior Inference on SVCFs. 74

3.4 Numerical Examples. 75

3.4.1 Simulation Study: Synthetic Imaging Data. 75

3.4.2 RealData Application: TheAutism Brain ImagingData Exchange (ABIDE). 81

3.5 Discussion. 84

3.5.1 Proof of Theorem 1. 86

3.5.2 Proof of Theorem 2. 88

3.5.3 Proof of Theorem 3. 95

3.5.4 Details about the MCMC algorithm. 96

4 Bayesian Independent Component Analysis Involving Spatially Dependent SourcesWith Application to fMRI Data. 99

4.1 Method. 99

4.1.1 Preprocessing of fMRI data. 99

4.1.2 The spatially dependent ICA model for fMRI data. 100

4.1.3 Model representation, hyperprior specication and posterior inference. 104

4.2 Data Examples. 110

4.2.1 Simulated data. 110

4.2.2 Real resting-state fMRI data. 113

4.3 Discussion. 119

4.4 Appendices. 120

4.4.1 Proof of Theorem 5. 120

4.4.2 Details about the algorithm to draw from the posterior. 122

4.4.3 Functional eigen-decomposition for the generalized SE kernel. 125

5 Summary and Future Work. 127

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics Statistics Engineering, Biomedical
Mot-clé	Statistical Modeling Independent Component Analysis Bayesian Methods Neuroimgaing
Committee Chair / Thesis Advisor	Kang, Jian , Emory University Guo, Ying, Emory University
Committee Members	Kundu, Suprateek , Emory University Hu, Xiaoping P, Emory University

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