This thesis presents research focused on developing statistical methods with emphasis on tools that can be used for the analysis of data in neuroimaging studies and cognitive science. The first contribution addresses the problem of determining the location and dynamics of brain activity when electromagnetic signals are collected using magnetoencephalography (MEG) and electroencephalography (EEG). We formulate a new spatiotemporal model that jointly models MEG and EEG data as a function of unobserved neuronal activation. To fit this model we derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The methodology is evaluated through extensive simulation studies and an application examining the visual response to scrambled faces. In the second contribution we develop a Bayesian spatial model for imaging genetics developed for analyses examining the influence of genetics on brain structure as measured by MRI. We extend the recently developed regression model of Greenlaw et al. (\textit{Bioinformatics}, 2017) to accommodate more realistic correlation structures typically seen in structural brain imaging data. We allow for spatial correlation in the imaging phenotypes obtained from neighbouring regions in the same hemisphere of the brain and we also allow for correlation in the same phenotypes obtained from different hemispheres (left/right) of the brain. This correlation structure is incorporated through the use of a bivariate conditional autoregressive spatial model. Both Markov chain Monte Carlo (MCMC) and variational Bayes approaches are developed to approximate the posterior distribution and Bayesian false discovery rate (FDR) procedures are developed to select SNPs using the posterior distribution while accounting for multiplicity. The methodology is evaluated through an analysis of MRI and genetic data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and we show that the new spatial model exhibits improved performance on real data when compared to the non-spatial model of Greenlaw et al. (2017). In the third and final contribution we develop and investigate tools for the analysis of binary data arising from repeated measures designs. We propose a Bayesian approach for the mixed-effects analysis of accuracy studies using mixed binomial regression models and we investigate techniques for model selection. / Graduate

1 / DONGDONG LIN

In the field of imaging genetics, brain function and structure are used as intermediate phenotypes between genes and cognition/diseases to validate and extend findings from behavioral genetics. In this thesis, three of the strongest candidate genes for episodic memory, KIBRA, BDNF, and APOE, were examined in relation to memory performance and hippocampal/parahippocampal fMRI blood-oxygen level-dependent (BOLD) signal. A common T allele in the KIBRA gene was previously associated with superior memory, and increased hippocampal activation was observed in noncarriers of the T allele which was interpreted as reflecting compensatory recruitment. The results from the first study revealed that both memory performance and hippocampal activation at retrieval was higher in T allele carriers (study I). The BDNF 66Met and APOE ε4 alleles have previously been associated with poorer memory performance, but their relation to brain activation has been inconsistent with reports of both increased and decreased regional brain activation relative to noncarriers. Here, decreased hippocampal/parahippocampal activation was observed in carriers of BDNF 66Met (study II) as well as APOE ε4 (study III) during memory encoding. In addition, there was an additive gene-gene effect of APOE and BDNF on hippocampal and parahippocampal activation (study III). Collectively, the results from these studies on KIBRA, BDNF, and APOE converge on higher medial temporal lobe activation for carriers of a high-memory associated allele, relative to carriers of a low-memory associated allele. In addition, the observed additive effect of APOE and BDNF demonstrate that a larger amount of variance in BOLD signal change can be explained by considering the combined effect of more than one genetic polymorphism. These imaging genetics findings support and extend previous knowledge from behavioral genetics on the role of these memory-related genes.

abstract: Imaging genetics is an emerging and promising technique that investigates how genetic variations affect brain development, structure, and function. By exploiting disorder-related neuroimaging phenotypes, this class of studies provides a novel direction to reveal and understand the complex genetic mechanisms. Oftentimes, imaging genetics studies are challenging due to the relatively small number of subjects but extremely high-dimensionality of both imaging data and genomic data. In this dissertation, I carry on my research on imaging genetics with particular focuses on two tasks---building predictive models between neuroimaging data and genomic data, and identifying disorder-related genetic risk factors through image-based biomarkers. To this end, I consider a suite of structured sparse methods---that can produce interpretable models and are robust to overfitting---for imaging genetics. With carefully-designed sparse-inducing regularizers, different biological priors are incorporated into learning models. More specifically, in the Allen brain image--gene expression study, I adopt an advanced sparse coding approach for image feature extraction and employ a multi-task learning approach for multi-class annotation. Moreover, I propose a label structured-based two-stage learning framework, which utilizes the hierarchical structure among labels, for multi-label annotation. In the Alzheimer's disease neuroimaging initiative (ADNI) imaging genetics study, I employ Lasso together with EDPP (enhanced dual polytope projections) screening rules to fast identify Alzheimer's disease risk SNPs. I also adopt the tree-structured group Lasso with MLFre (multi-layer feature reduction) screening rules to incorporate linkage disequilibrium information into modeling. Moreover, I propose a novel absolute fused Lasso model for ADNI imaging genetics. This method utilizes SNP spatial structure and is robust to the choice of reference alleles of genotype coding. In addition, I propose a two-level structured sparse model that incorporates gene-level networks through a graph penalty into SNP-level model construction. Lastly, I explore a convolutional neural network approach for accurate predicting Alzheimer's disease related imaging phenotypes. Experimental results on real-world imaging genetics applications demonstrate the efficiency and effectiveness of the proposed structured sparse methods. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2017

This thesis presents research focused on developing statistical methods with emphasis on techniques that can be used for the analysis of data in imaging studies and sparse estimations for applications in high-dimensional data. The first contribution addresses the pixel/voxel-labeling problem for spatial hidden Markov models in image analysis. We formulate a Gaussian spatial mixture model with Potts model used as a prior for mixture allocations for the latent states in the model. Jointly estimating the model parameters, the discrete state variables and the number of states (number of mixture components) is recognized as a difficult combinatorial optimization. To overcome drawbacks associated with local algorithms, we implement and make comparisons between iterated conditional modes (ICM), simulated annealing (SA) and hybrid ICM with ant colony system (ACS-ICM) optimization for pixel labelling, parameter estimation and mixture component estimation. In the second contribution, we develop ACS-ICM algorithm for spatiotemporal modeling of combined MEG/EEG data for computing estimates of the neural source activity. We consider a Bayesian finite spatial mixture model with a Potts model as a spatial prior and implement the ACS-ICM for simultaneous point estimation and model selection for the number of mixture components. Our approach is evaluated using simulation studies and an application examining the visual response to scrambled faces. In addition, we develop a nonparametric bootstrap for interval estimation to account for uncertainty in the point estimates. In the third contribution, we present sparse estimation strategies in linear mixed model (LMM) for longitudinal data. We address the problem of estimating the fixed effects parameters of the LMM when the model is sparse and predictors are correlated. We propose and derive the asymptotic properties of the pretest and shrinkage estimation strategies. Simulation studies is performed to compare the numerical performance of the Lasso and adaptive Lasso estimators with the pretest and shrinkage ridge estimators. The methodology is evaluated through an application of a high-dimensional data examining effective brain connectivity and genetics. In the fourth and final contribution, we conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set. We relate longitudinal effective brain connectivity estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR). / Graduate

Indiana University-Purdue University Indianapolis (IUPUI) / Imaging genetics is an emerging research field in neurodegenerative diseases. It studies the influence of genetic variants on brain structure and function. Genome-wide association studies (GWAS) of brain imaging has identified a few independent risk loci for individual imaging quantitative trait (iQT), which however display only modest effect size and explain limited heritability. This thesis focuses on mining high-level imaging genetic associations and their applications on neurodegenerative diseases. This thesis first presents a novel network-based GWAS framework for identifying functional modules, by employing a two-step strategy in a top-down manner. It first integrates tissue-specific network with GWAS of corresponding phenotype in regression models in addition to classification, to re-prioritize genome-wide associations. Then it detects densely connected and disease-relevant modules based on interactions among top reprioritizations. The discovered modules hold both phenotypical specificity and densely interaction. We applied it to an amygdala imaging genetics analysis in the study of Alzheimer's disease (AD). The proposed framework effectively detects densely interacted modules; and the reprioritizations achieve highest concordance with AD genes. We then present an extension of the above framework, named GWAS top-neighbor-based (tnGWAS); and compare it with previous approaches. This tnGWAS extracts densely connected modules from top GWAS findings, based on the hypothesis that relevant modules consist of top GWAS findings and their close neighbors. It is applied to a hippocampus imaging genetics analysis in AD research, and yields the densest interactions among top candidate genes. Experimental results demonstrate that precise context does help explore collective effects of genes with functional interactions specific to the studied phenotype. In the second part, a novel imaging genetic enrichment analysis (IGEA) paradigm is proposed for discovering complex associations among genetic modules and brain circuits. In addition to genetic modules, brain regions of interest also grouped to play role. We expand the scope of one-dimensional enrichment analysis into imaging genetics. This framework jointly considers meaningful gene sets (GS) and brain circuits (BC), and examines whether given GS-BC module is enriched in gene-iQT findings. We conduct the proof-of-concept study and demonstrate its performance by applying to a brain-wide imaging genetics study of AD.

Over the past ten years, more than 4,000 genome-wide association studies (GWAS) have helped to shed light on the genetic architecture of complex traits and diseases. In recent years, phenotyping of the samples has often gone beyond single traits and it has become common to record multi- to high-dimensional phenotypes for individu- als. Whilst these rich datasets offer the potential to analyse complex trait structures and pleiotropic effects at a genome-wide level, novel analytic challenges arise. This thesis summarises my research into genetic associations for high-dimensional phen- otype data. First, I developed a novel and computationally efficient approach for multivari- ate analysis of high-dimensional phenotypes based on linear mixed models, com- bined with bootstrapping (LiMMBo). Both in simulation studies and on real data, I demonstrate the statistical validity of LiMMBo and that it can scale to hundreds of phenotypes. I show the gain in power of multivariate analyses for high-dimensional phenotypes compared to univariate approaches, and illustrate that LiMMBo allows for detecting pleiotropy in a large number of phenotypic traits. Aside from their computational challenges in GWAS, the true dimensionality of very high-dimensional phenotypes is often unknown and lies hidden in high-dimen- sional space. Retaining maximum power for association studies of such phenotype data relies on using an appropriate phenotype representation. I systematically ana- lysed twelve unsupervised dimensionality reduction methods based on their per- formance in finding a robust phenotype representation in simulated data of different structure and size. I propose a stability criteria for choosing low-dimensional phen- otype representations and demonstrate that stable phenotypes can recover genetic associations. Finally, I analysed genetic variants for associations to high-dimensional cardiac phenotypes based on MRI data from 1,500 healthy individuals. I used an unsuper- vised approach to extract a low-dimensional representation of cardiac wall thickness and conducted a GWAS on this representation. In addition, I investigated genetic associations to a trabeculation phenotype generated from a supervised feature ex- traction approach on the cardiac MRI data. In summary, this thesis highlights and overcomes some of the challenges in per- forming genetic association studies on high-dimensional phenotypes. It describes new approaches for phenotype processing, and genotype to phenotype mapping for high-dimensional datasets, as well as providing new insights in the genetic structure of cardiac morphology in humans.

La structure asymétrique du lobe temporal a déjà été démontrée. Ces asymétries structurelles sont souvent supposées comme support à la latéralisation du langage chez l’homme. Une asymétrie remarquable est celle du sillon temporal supérieur (STS) observée dès la naissance chez l’homme, mais pas chez le chimpanzé. Dans cette thèse, nous nous intéressons aux origines génétiques sous-jacentes à cette asymétrie. Dans ce but, nous utilisons des méthodes d’extraction automatiques de structures asymétriques comme les racines sulcales ou les gyri transverses (plis de passage, PPs). Premièrement, nous reproduisons l’asymétrie de profondeur du STS dans deux grandes cohortes (HCP et UK Biobank) et nous démontrons que le STS gauche est plus souvent interrompu par un PP que son homologue à droite. Secondement, l’héritabilité de la profondeur des racines sulcales dans le STS et de la présence de PP est supérieure dans l’hémisphère gauche. Ceci suggère des signaux génétiques asymétriques qui contribuent à la formation des asymétries de structures du lobe temporal. Par ailleurs, nous avons montré que les activations fonctionnelles dans le gyrus angulaire ont une variance génétique partagée significative avec la performance cognitive. Enfin, nous avons identifié une zone cis-régulatrice du gène KCNK2, comme significativement associée avec la largeur et l’épaisseur corticale des sillons, qui sont des caractéristiques du vieillissement du cerveau. / The asymmetrical structure of the temporal lobe has already been demonstrated. These structural asymmetries are often assumed to contribute to the human language lateralization. One noticeable asymmetry is the one of the superior temporal sulcus (STS) depth observed from birth in humans, but not in chimpanzee. In this thesis, we were interested in the genetic roots underlying this asymmetry. To this aim, we used automated extraction method of asymmetrical structures such as the sulcal roots or transverse gyri (so called plis de passage, PPs). First, we reproduced the STS rightward depth asymmetry in two large cohorts (HCP and UK Biobank) and we demonstrated that the left STS is more often interrupted by a PP than its counterpart. Second, the heritability estimates of depth and convexity of sulcal roots in the STS and the presence of PP are higher in the left hemisphere. This suggests asymmetric genetic cues contributing to the formation of these asymmetrical structures in the temporal lobe. In addition, we have shown that the functional activations in the angular gyrus have a significant shared genetic variance with the human cognitive performance. Finally, we have identified a cis-regulating region of the KCNK2, as being significantly associated with the width and cortical thickness of the brain sulci, which are features of brain ageing.

MEG and fMRI offer complementary insights into connected human brain function. Evidence from the use of both techniques in the study of networked activity indicates that functional connectivity reflects almost every measurable aspect of human reality, being indicative of ability and deteriorating with disease. Functional network analyses may offer improved prediction of dysfunction and characterisation of cognition. Three factors holding back progress are the difficulty in synthesising information from multiple imaging modalities; a need for accurate modelling of connectivity in individual subjects, not just average effects; and a lack of scalable solutions to these problems that are applicable in a big-data setting. I propose two methodological advances that tackle these issues. A confound to network analysis in MEG, the artificial correlations induced across the brain by the process of source reconstruction, prevents the transfer of connectivity models from fMRI to MEG. The first advance is a fast correction for this confound, allowing comparable analyses to be performed in both modalities. A comparative study demonstrates that this new approach for MEG shows better repeatability for connectivity estimation, both within and between subjects, than a wide range of alternative models in popular use. A case-study analysis uses both fMRI and MEG recordings from a large dataset to determine the genetic basis for functional connectivity in the human brain. Genes account for 20% - 65% of the variation in connectivity, and outweigh the influence of the developmental environment. The second advance is a Bayesian hierarchical model for sparse functional networks that is applicable to both modalities. By sharing information over a group of subjects, more accurate estimates can be constructed for individuals' connectivity patterns. The approach scales to large datasets, outperforms state-of-the-art methods, and can provide a 50% noise reduction in MEG resting-state networks.

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