Beyond the hype

Sequencing studies are increasingly being conducted to identify rare variants associated with complex traits. The limited power of classical single-marker association analysis for rare variants poses a central challenge in such studies. We propose the sequence kernel association test (SKAT), a supervised, flexible, computationally efficient regression method to test for association between genetic variants (common and rare) in a region and a continuous or dichotomous trait while easily adjusting for covariates. As a score-based variance-component test, SKAT can quickly calculate p values analytically by fitting the null model containing only the covariates, and so can easily be applied to genome-wide data. Using SKAT to analyze a genome-wide sequencing study of 1000 individuals, by segmenting the whole genome into 30 kb regions, requires only 7 hr on a laptop. Through analysis of simulated data across a wide range of practical scenarios and triglyceride data from the Dallas Heart Study, we show that SKAT can substantially outperform several alternative rare-variant association tests. We also provide analytic power and sample-size calculations to help design candidate-gene, whole-exome, and whole-genome sequence association studies.

/pdf/rare-variant-association-testing-for-sequencing-data-with-54lmn4sfa4.pdf

Rare-Variant Association Testing for Sequencing Data with the Sequence Kernel Association Test

Autism spectrum disorders (ASDs) represent a formidable challenge for psychiatry and neuroscience because of their high prevalence, lifelong nature, complexity and substantial heterogeneity. Facing these obstacles requires large-scale multidisciplinary efforts. Although the field of genetics has pioneered data sharing for these reasons, neuroimaging had not kept pace. In response, we introduce the Autism Brain Imaging Data Exchange (ABIDE)-a grassroots consortium aggregating and openly sharing 1112 existing resting-state functional magnetic resonance imaging (R-fMRI) data sets with corresponding structural MRI and phenotypic information from 539 individuals with ASDs and 573 age-matched typical controls (TCs; 7-64 years) (http://fcon_1000.projects.nitrc.org/indi/abide/). Here, we present this resource and demonstrate its suitability for advancing knowledge of ASD neurobiology based on analyses of 360 male subjects with ASDs and 403 male age-matched TCs. We focused on whole-brain intrinsic functional connectivity and also survey a range of voxel-wise measures of intrinsic functional brain architecture. Whole-brain analyses reconciled seemingly disparate themes of both hypo- and hyperconnectivity in the ASD literature; both were detected, although hypoconnectivity dominated, particularly for corticocortical and interhemispheric functional connectivity. Exploratory analyses using an array of regional metrics of intrinsic brain function converged on common loci of dysfunction in ASDs (mid- and posterior insula and posterior cingulate cortex), and highlighted less commonly explored regions such as the thalamus. The survey of the ABIDE R-fMRI data sets provides unprecedented demonstrations of both replication and novel discovery. By pooling multiple international data sets, ABIDE is expected to accelerate the pace of discovery setting the stage for the next generation of ASD studies.

/pdf/the-autism-brain-imaging-data-exchange-towards-a-large-scale-32vwazsr5n.pdf

The autism brain imaging data exchange: towards a large-scale evaluation of the intrinsic brain architecture in autism

The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.

/pdf/estimating-psychological-networks-and-their-accuracy-a-ljt6ufq2za.pdf

Estimating Psychological Networks and their Accuracy : A tutorial paper

The cortical surface is organized into a large number of cortical areas; however, these areas have not been comprehensively mapped in the human. Abrupt transitions in resting-state functional connectivity (RSFC) patterns can noninvasively identify locations of putative borders between cortical areas (RSFC-boundary mapping; Cohen et al. 2008). Here we describe a technique for using RSFC-boundary maps to define parcels that represent putative cortical areas. These parcels had highly homogenous RSFC patterns, indicating that they contained one unique RSFC signal; furthermore, the parcels were much more homogenous than a null model matched for parcel size when tested in two separate datasets. Several alternative parcellation schemes were tested this way, and no other parcellation was as homogenous as or had as large a difference compared with its null model. The boundary map-derived parcellation contained parcels that overlapped with architectonic mapping of areas 17, 2, 3, and 4. These parcels had a network structure similar to the known network structure of the brain, and their connectivity patterns were reliable across individual subjects. These observations suggest that RSFC-boundary map-derived parcels provide information about the location and extent of human cortical areas. A parcellation generated using this method is available at http://www.nil.wustl.edu/labs/petersen/Resources.html.

/pdf/generation-and-evaluation-of-a-cortical-area-parcellation-3plntatxpn.pdf

Generation and Evaluation of a Cortical Area Parcellation from Resting-State Correlations

We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a multivariate rank statistic is exploited. At the model-level, we consider two settings: either that the leading eigenvectors of the covariance matrix are non-sparse or that they are sparse. Methodologically, we propose ECA procedures for both non-sparse and sparse settings. Theoretically, we provide both non-asymptotic and asymptotic analyses quantifying the theoretical performances of ECA. In the non-sparse setting, we show that ECA's performance is highly related to the effective rank of the covariance matrix. In the sparse setting, the results are twofold: (i) We show that the sparse ECA estimator based on a combinatoric program attains the optimal rate of convergence; (ii) Based on some recent developments in estimating sparse leading eigenvectors, we show that a computationally efficient sparse ECA estimator attains the optimal rate of convergence under a suboptimal scaling.

ECA: High Dimensional Elliptical Component Analysis in non-Gaussian Distributions

We consider the motivating problem of testing for association between a phenotype and multiple single nucleotide polymorphisms (SNPs) within a candidate gene or region. Various statistical approaches have been proposed, including those based on either (combining univariate) single-locus analyses or (multivariate) multilocus analyses. However, it is known in theory that there is no single uniformly most powerful test to detect association with multiple SNPs. On the other hand, several tests have been shown to be among frequent winners across a range of practical situations, but the identity of the most powerful one changes with the situation in an unknown way. Here we propose a novel test selection procedure to select from five such tests: a so-called UminP test that combines multiple univariate/single-locus score tests by taking the minimum of their p values as its test statistic, a multivariate score test and its two modifications, and a so-called sum test. We also illustrate its application to selecting genotype codings for the sum test since the performance of the sum test depends on its genotype coding in an unknown way. Our major contributions include the methodology of estimating the power of a given test with a given dataset and the idea of using the estimated power as the criterion for test selection. We also propose a fast simulation-based method to calculate p values for the test selection procedure and for any method of combining p values. Our numerical results indicated that the proposed test selection procedure always yielded power close to the most powerful test among the candidate tests at any given situation, and in particular, our proposed test selection performed either better than or as well as the popular combining method of taking the minimum p value of the candidate tests.

/pdf/test-selection-with-application-to-detecting-disease-1navii7fzd.pdf

Test selection with application to detecting disease association with multiple SNPs.

Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a "sign subgaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition.

/pdf/statistical-analysis-of-latent-generalized-correlation-24dzipygsu.pdf

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution.

In this paper, we analyze the performance of a semiparametric principal component analysis named Copula Component Analysis (COCA) (Han & Liu, 2012) when the data are dependent. The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. We study the scenario where the observations are drawn from non-i.i.d. processes (m-dependency or a more general ϕ-mixing case). We show that COCA can allow weak dependence. In particular, we provide the generalization bounds of convergence for both support recovery and parameter estimation of COCA for the dependent data. We provide explicit sufficient conditions on the degree of dependence, under which the parametric rate can be maintained. To our knowledge, this is the first work analyzing the theoretical performance of PCA for the dependent data in high dimensional settings. Our results strictly generalize the analysis in Han & Liu (2012) and the techniques we used have the separate interest for analyzing a variety of other multivariate statistical methods.

/pdf/principal-component-analysis-on-non-gaussian-dependent-data-4ql6lz9x6b.pdf

Principal Component Analysis on non-Gaussian Dependent Data

Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, it is not an effective estimator when facing heavy-tailed distributions. As a robust alternative, Han and Liu [J. Am. Stat. Assoc. 109 (2015) 275-287] advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in Han and Liu [J. Am. Stat. Assoc. 109 (2015) 275-287] for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a "sign sub-Gaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the fast rate of convergence. In both cases, we do not need any moment condition.

Fang Han

Papers

ECA: High Dimensional Elliptical Component Analysis in non-Gaussian Distributions

Test selection with application to detecting disease association with multiple SNPs.

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution.

Principal Component Analysis on non-Gaussian Dependent Data

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution