
 Network analysis of whole-brain connectome data is widely employed to examine systematic changes in connections among brain areas caused by clinical and experimental conditions. In these analyses, the connectome data, represented as a matrix, are treated as outcomes, while the subject conditions serve as predictors. The objective of network analysis is to identify connectome subnetworks whose edges are associated with the predictors. Data-driven network analysis is a powerful approach that automatically organizes individual predictor-related connections (edges) into subnetworks, rather than relying on pre-specified subnetworks, thereby enabling network-level inference. However, power calculation for data-driven network analysis presents a challenge due to the data-driven nature of subnetwork identification, where nodes, edges, and model parameters cannot be pre-specified before the analysis. Additionally, data-driven network analysis involves multivariate edge variables and may entail multiple subnetworks, necessitating the correction for multiple testing (e.g., family-wise error rate (FWER) control). To address this issue, we developed BNPower, a user-friendly power calculation tool for data-driven network analysis. BNPower utilizes simulation analysis, taking into account the complexity of the data-driven network analysis model. We have implemented efficient computational strategies to facilitate data-driven network analysis, including subnetwork extraction and permutation tests for controlling FWER, while maintaining low computational costs. The toolkit, which includes a graphical user interface and source codes, is publicly available at the following GitHub repository: https://github.com/bichuan0419/brain_connectome_power_tool

BNPower: a power calculation tool for data-driven network analysis for whole-brain connectome data

In this paper we study the two-sample problem for inhomogeneous Erd˝os-R´enyi (IER) random graph models in the L r norm, in the high-dimensional regime where the number of samples is smaller or comparable to the size of the graphs. Given two symmetric matrices P, Q ∈ [0 , 1] n × n (with zeros on the diagonals), the two-sample problem for IER graphs (with respect to the L r norm (cid:107) · (cid:107) r ) is to test the hypothesis H 0 : P = Q versus H 1 : (cid:107) P − Q (cid:107) r ≥ ε , given a sample of m graphs from the respective distributions. In this paper, we obtain the optimal sample complexity for testing in the L r norm, for all integers r ≥ 1 . We also derive the asymptotic distribution of the optimal tests under H 0 and develop a method for consistently estimating their variances. This allows us to efﬁciently implement the optimal tests with precise asymptotic level and establish their asymptotic consistency. We validate our theoretical results by numerical experiments for various natural IER models.

Two-Sample Tests for Inhomogeneous Random Graphs in Lr Norm: Optimality and Asymptotics

Brain connectome analysis commonly compresses high-resolution brain scans (typically composed of millions of voxels) down to only hundreds of regions of interest (ROIs) by averaging within-ROI signals. This huge dimension reduction improves computational speed and the morphological properties of anatomical structures; however, it also comes at the cost of substantial losses in spatial specificity and sensitivity, especially when the signals exhibit high within-ROI heterogeneity. Oftentimes, abnormally expressed functional connectivity (FC) between a pair of ROIs caused by a brain disease is primarily driven by only small subsets of voxel pairs within the ROI pair. This article proposes a new network method for detection of voxel-pair-level neural dysconnectivity with spatial constraints. Specifically, focusing on an ROI pair, our model aims to extract dense sub-areas that contain aberrant voxel-pair connections while ensuring that the involved voxels are spatially contiguous. In addition, we develop sub-community-detection algorithms to realize the model, and the consistency of these algorithms is justified. Comprehensive simulation studies demonstrate our method's effectiveness in reducing the false-positive rate while increasing statistical power, detection replicability, and spatial specificity. We apply our approach to reveal: (i) voxel-wise schizophrenia-altered FC patterns within the salience and temporal-thalamic network from 330 participants in a schizophrenia study; (ii) disrupted voxel-wise FC patterns related to nicotine addiction between the basal ganglia, hippocampus, and insular gyrus from 3269 participants using UK Biobank data. The detected results align with previous medical findings but include improved localized information.

pdf/network-method-for-voxel-pair-level-brain-connectivity-3nzs5ic5.pdf

Network method for voxel-pair-level brain connectivity analysis under spatial-contiguity constraints

Two-sample hypothesis testing for comparing two networks is an important yet difﬁcult problem. Major challenges include: potentially different sizes and sparsity levels; non-repeated observations of adjacency matrices; computational scalability; and theoretical investigations, especially on ﬁnite-sample accuracy and minimax optimality. In this article, we propose the ﬁrst provably higher-order accurate two-sample inference method by comparing network moments. Our method extends the classical two-sample t-test to the network setting. We make weak modeling assumptions and can effectively handle networks of different sizes and sparsity levels. We establish strong ﬁnite-sample theoretical guarantees, including rate-optimality properties. Our method is easy to implement and computes fast. We also devise a novel nonparametric framework of ofﬂine hashing and fast querying particularly effective for maintaining and querying very large network databases. We demonstrate the effectiveness of our method by comprehensive simulations. We apply our method to two real-world data sets and discover interesting novel structures.

Higher-order accurate two-sample network inference and network hashing

Resting state brain functional connectivity quantiﬁes the similarity between brain regions, each of which consists of voxels at which dynamic signals are acquired via neuroimaging techniques such as blood-oxygen-level-dependent signals in functional magnetic resonance imaging. Pearson correlation and similar metrics have been adopted by neuroscientists to estimate inter-regional connectivity, usually after averaging of signals within regions. However, dependencies between signals within each region and the presence of noise could contaminate such inter-regional correlation estimates. We propose a mixed-effects model with a novel covariance structure that explicitly isolates the different sources of variability in the observed BOLD signals, including correlated regional signals, local spatiotemporal variability, and measurement error. Methods for tackling the computational challenges associated with restricted maximum likelihood estimation will be discussed. Large sample properties are discussed and used for uncertainty quantiﬁcation. Simulation results demonstrate that the parameters of the proposed model parameters can be accurately estimated and is superior to the Pearson correlation of averages in the presence of spatiotemporal noise. The proposed model is also applied to a real data set of BOLD signals collected from rats to construct individual brain networks.

https://export.arxiv.org/pdf/2211.02192v2.pdf

A Mixed Model Approach for Estimating Regional Functional Connectivity from Voxel-level BOLD Signals

Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an $\ell_0$ norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks.

Identifying covariate-related subnetworks for whole-brain connectome analysis.

In the last two decades of Genome-wide association studies (GWAS), nicotine-dependence-related genetic loci (e.g., nicotinic acetylcholine receptor - nAChR subunit genes) are among the most replicable genetic findings. Although GWAS results have reported tens of thousands of SNPs within these loci, further analysis (e.g., fine-mapping) is required to identify the causal variants. However, it is computationally challenging for existing fine-mapping methods to reliably identify causal variants from thousands of candidate SNPs based on the posterior inclusion probability. To address this challenge, we propose a new method to select SNPs by jointly modeling the SNP-wise inference results and the underlying structured network patterns of the linkage disequilibrium (LD) matrix. We use adaptive dense subgraph extraction method to recognize the latent network patterns of the LD matrix and then apply group LASSO to select causal variant candidates. We applied this new method to the UK biobank data to identify the causal variant candidates for nicotine addiction. Eighty-one nicotine addiction-related SNPs (i.e.,-log(p) > 50) of nAChR were selected, which are highly correlated (average r 

An in-depth association analysis of genetic variants within nicotine-related loci: Meeting in middle of GWAS and genetic fine-mapping

U-statistics play central roles in many statistical learning tools but face the haunting issue of scalability. Significant efforts have been devoted into accelerating computation by U-statistic reduction. However, existing results almost exclusively focus on power analysis, while little work addresses risk control accuracy -- comparatively, the latter requires distinct and much more challenging techniques. In this paper, we establish the first statistical inference procedure with provably higher-order accurate risk control for incomplete U-statistics. The sharpness of our new result enables us to reveal how risk control accuracy also trades off with speed for the first time in literature, which complements the well-known variance-speed trade-off. Our proposed general framework converts the long-standing challenge of formulating accurate statistical inference procedures for many different designs into a surprisingly routine task. This paper covers non-degenerate and degenerate U-statistics, and network moments. We conducted comprehensive numerical studies and observed results that validate our theory's sharpness. Our method also demonstrates effectiveness on real-world data applications.

U-Statistic Reduction: Higher-Order Accurate Risk Control and Statistical-Computational Trade-Off, with Application to Network Method-of-Moments

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