Genome-wide association analysis has generated much discussion about how to preserve power to detect signals despite the detrimental effect of multiple testing on power. We develop a weighted multiple testing procedure that facilitates the input of prior information in the form of groupings of tests. For each group a weight is estimated from the observed test statistics within the group. Differentially weighting groups improves the power to detect signals in likely groupings. The advantage of the grouped-weighting concept, over fixed weights based on prior information, is that it often leads to an increase in power even if many of the groupings are not correlated with the signal. Being data dependent, the procedure is remarkably robust to poor choices in groupings. Power is typically improved if one (or more) of the groups clusters multiple tests with signals, yet little power is lost when the groupings are totally random. If there is no apparent signal in a group, relative to a group that appears to have several tests with signals, the former group will be down-weighted relative to the latter. If no groups show apparent signals, then the weights will be approximately equal. The only restriction on the procedure is that the number of groups be small, relative to the total number of tests performed.
The R package (R Core Team (2016)) genMOSS is specifically designed for the Bayesian analysis of genome-wide association study data. The package implements the mode oriented stochastic search (MOSS) procedure as well as a simple moving window approach to identify combinations of single nucleotide polymorphisms associated with a response. The prior used in Bayesian computations is the generalized hyper Dirichlet.
Presented here is a simple method for cross-validated genome-wide association studies (cvGWAS). Focusing on phenotype prediction, the method is able to reveal a significant amount of missing heritability by properly selecting a small number of loci with implicit predictive ability. The results provide new insights into the missing heritability problem and the underlying genetic architecture of complex traits.
Motivated by genome-wide association screening studies (GWAS), we study high-dimensional marginal screenings of categorical variables where test statistics have approximate chi-square distributions. We characterize four new phase transitions in high-dimensional chi-square models, and derive the signal sizes necessary and sufficient for statistical procedures to simultaneously control false discovery (in terms of family-wise error rate or false discovery rate) and missed detection (in terms of family-wise non-discovery rate or false non-discovery rate) in large dimensions. Remarkably, degrees o…
We study variance estimation and associated confidence intervals for parameters characterizing genetic effects from genome-wide association studies (GWAS) misspecified mixed model analysis. Previous studies have shown that, in spite of the model misspecification, certain quantities of genetic interests are estimable, and consistent estimators of these quantities can be obtained using the restricted maximum likelihood (REML) method under a misspecified linear mixed model. However, the asymptotic variance of such a REML estimator is complicated and not ready to be implemented for practical use. …
A structural genetic model incorporating a modern understanding of the genome and common practice in genome-wide association studies is derived mathematically. The model shows the Haldane map distance as a direct consequence of the structure of the genome. An expression for genetic correlation is derived under the model and compared to data resulting from the BSB mouse cross. A correlation test plot is introduced for this comparison and shows the close agreement of the model and empirical results. Noteworthy departures in this plot indicate regions which warrant further investigation.
We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied by the limiting proportion of the nonzero random effects present in the LMM. The aymptotic results also …
A computationally simple genome-wide association study (GWAS) algorithm for estimating the main and epistatic effects of markers or single nucleotide polymorphisms (SNPs) is proposed. It is based on the intuitive assumption that changes of alleles corresponding to important SNPs in a pair of individuals lead to large difference of phenotype values of these individuals. The algorithm is based on considering pairs of individuals instead of SNPs or pairs of SNPs. The main advantage of the algorithm is that it weakly depends on the number of SNPs in a genotype matrix. It mainly depends on the numb…
We provide a view on high-dimensional statistical inference for genome-wide association studies (GWAS). It is in part a review but covers also new developments for meta analysis with multiple studies and novel software in terms of an R-package hierinf. Inference and assessment of significance is based on very high-dimensional multivariate (generalized) linear models: in contrast to often used marginal approaches, this provides a step towards more causal-oriented inference.
Genome-Wide Association Studies (GWAS) offer an exciting and promising new research avenue for finding genes for complex diseases. Traditional case-control and cohort studies offer many advantages for such designs. Family-based association designs have long been attractive for their robustness properties, but robustness can mean a loss of power. In this paper we discuss some of the special features of family designs and their relevance in the era of GWAS.
In genome-wide association studies, hundreds of thousands of genetic features (genes, proteins, etc.) in a given case-control population are tested to verify existence of an association between each genetic marker and a specific disease. A popular approach in this regard is to estimate local false discovery rate (LFDR), the posterior probability that the null hypothesis is true, given an observed test statistic. However, the existing LFDR estimation methods in the literature are usually complicated. Assuming a chi-square model with one degree of freedom, which covers many situations in genome-…
Despite significant progress in dissecting the genetic architecture of complex diseases by genome-wide association studies (GWAS), the signals identified by association analysis may not have specific pathological relevance to diseases so that a large fraction of disease causing genetic variants is still hidden. Association is used to measure dependence between two variables or two sets of variables. Genome-wide association studies test association between a disease and SNPs (or other genetic variants) across the genome. Association analysis may detect superficial patterns between disease and g…
Replication helps ensure that a genotype-phenotype association observed in a genome-wide association (GWA) study represents a credible association and is not a chance finding or an artifact due to uncontrolled biases. We discuss prerequisites for exact replication, issues of heterogeneity, advantages and disadvantages of different methods of data synthesis across multiple studies, frequentist vs. Bayesian inferences for replication, and challenges that arise from multi-team collaborations. While consistent replication can greatly improve the credibility of a genotype-phenotype association, it …
We introduce a method for computation of exact conditional efficiency robust enumeration p-values for detection of genotype--phenotype associations at a single bi-allelic genetic locus. Our method can be based on any arbitrary ranking test statistics, such as efficiency robust test statistics or asymptotic p-values. The resulting p-values are exact conditional enumeration p-values and satisfy the basic statistical validity property. Practically, the method allows performing statistically valid significance testing in genomic analyses with unknown modes of inheritance at individual bi-allelic g…
This paper presents and compares alternative transfer learning methods that can increase the power of conditional testing via knockoffs by leveraging prior information in external data sets collected from different populations or measuring related outcomes. The relevance of this methodology is explored in particular within the context of genome-wide association studies, where it can be helpful to address the pressing need for principled ways to suitably account for, and efficiently learn from the genetic variation associated to diverse ancestries. Finally, we apply these methods to analyze sev…
Traditional statistical methods for confidentiality protection of statistical databases do not scale well to deal with GWAS (genome-wide association studies) databases especially in terms of guarantees regarding protection from linkage to external information. The more recent concept of differential privacy, introduced by the cryptographic community, is an approach which provides a rigorous definition of privacy with meaningful privacy guarantees in the presence of arbitrary external information, although the guarantees come at a serious price in terms of data utility. Building on such notions…
Carnegie Mellon University（卡内基梅隆大学）；University of Chicago（芝加哥大学）
Motivated by empirical arguments that are well-known from the genome-wide association studies (GWAS) literature, we study the statistical properties of linear mixed models (LMMs) applied to GWAS. First, we study the sensitivity of LMMs to the inclusion of a candidate SNP in the kinship matrix, which is often done in practice to speed up computations. Our results shed light on the size of the error incurred by including a candidate SNP, providing a justification to this technique in order to trade-off velocity against veracity. Second, we investigate how mixed models can correct confounders in …
Conducting genome-wide association studies (GWAS) in copy number variation (CNV) level is a field where few people involves and little statistical progresses have been achieved, traditional methods suffer from many problems such as batch effects, heterogeneity across genome, leading to low power or high false discovery rate. We develop a new robust method to find disease-risking regions related to CNV's disproportionately distributed between case and control samples, even if there are batch effects between them, our test formula is robust to such effects. We propose a new empirical Bayes rule …
The X-chromosome is often excluded from genome-wide association studies because of analytical challenges. Some of the problems, such as the random, skewed or no X-inactivation model uncertainty, have been investigated. Other considerations have received little to no attention, such as the value in considering non-additive and gene-sex interaction effects, and the inferential consequence of choosing different baseline alleles (i.e.\ the reference vs.\ the alternative allele). Here we propose a unified and flexible regression-based association test for X-chromosomal variants. We provide theoreti…
Many common diseases are highly polygenic, modulated by a large number genetic factors with small effects on susceptibility to disease. These small effects are difficult to map reliably in genetic association studies. To address this problem, researchers have developed methods that aggregate information over sets of related genes, such as biological pathways, to identify gene sets that are enriched for genetic variants associated with disease. However, these methods fail to answer a key question: which genes and genetic variants are associated with disease risk? We develop a method based on sp…
We consider applying Bayesian Variable Selection Regression, or BVSR, to genome-wide association studies and similar large-scale regression problems. Currently, typical genome-wide association studies measure hundreds of thousands, or millions, of genetic variants (SNPs), in thousands or tens of thousands of individuals, and attempt to identify regions harboring SNPs that affect some phenotype or outcome of interest. This goal can naturally be cast as a variable selection regression problem, with the SNPs as the covariates in the regression. Characteristic features of genome-wide association s…
The family-wise error rate (FWER) has been widely used in genome-wide association studies. With the increasing availability of functional genomics data, it is possible to increase the detection power by leveraging these genomic functional annotations. Previous efforts to accommodate covariates in multiple testing focus on the false discovery rate control while covariate-adaptive FWER-controlling procedures remain under-developed. Here we propose a novel covariate-adaptive FWER-controlling procedure that incorporates external covariates which are potentially informative of either the statistica…
Motivation: The rapid growth in genome-wide association studies (GWAS) in plants and animals has brought about the need for a central resource that facilitates i) performing GWAS, ii) accessing data and results of other GWAS, and iii) enabling all users regardless of their background to exploit the latest statistical techniques without having to manage complex software and computing resources. Results: We present easyGWAS, a web platform that provides methods, tools and dynamic visualizations to perform and analyze GWAS. In addition, easyGWAS makes it simple to reproduce results of others, val…
Combining data from several case-control genome-wide association (GWA) studies can yield greater efficiency for detecting associations of disease with single nucleotide polymorphisms (SNPs) than separate analyses of the component studies. We compared several procedures to combine GWA study data both in terms of the power to detect a disease-associated SNP while controlling the genome-wide significance level, and in terms of the detection probability ($\mathit{DP}$). The $\mathit{DP}$ is the probability that a particular disease-associated SNP will be among the $T$ most promising SNPs selected …
Motivated by the important problem of detecting association between genetic markers and binary traits in genome-wide association studies, we present a novel Bayesian model that establishes a hierarchy between markers and genes by defining weights according to gene lengths and distances from genes to markers. The proposed hierarchical model uses these weights to define unique prior probabilities of association for markers based on their proximities to genes that are believed to be relevant to the trait of interest. We use an expectation-maximization algorithm in a filtering step to first reduce…
In genetic association studies, rare variants with extremely small allele frequency play a crucial role in complex traits, and the set-based testing methods that jointly assess the effects of groups of single nucleotide polymorphisms (SNPs) were developed to improve powers for the association tests. However, the powers of these tests are still severely limited due to the extremely small allele frequency, and precise estimations for the effect sizes of individual SNPs are substantially impossible. In this article, we provide an efficient set-based inference framework that addresses the two impo…
In this paper we have proposed a model for the distribution of allelic probabilities for generating populations as reliably as possible. Our objective was to develop such a model which would allow simulating allelic probabilities with different observed truncation and de- gree of noise. In addition, we have also introduced here a complete new approach to analyze a genome-wide association study (GWAS) dataset, starting from a new test of association with a statistical distribution and two effect sizes of each genotype. The new methodologi- cal approach was applied to a real data set together wi…
The standard paradigm for the analysis of genome-wide association studies involves carrying out association tests at both typed and imputed SNPs. These methods will not be optimal for detecting the signal of association at SNPs that are not currently known or in regions where allelic heterogeneity occurs. We propose a novel association test, complementary to the SNP-based approaches, that attempts to extract further signals of association by explicitly modeling and estimating both unknown SNPs and allelic heterogeneity at a locus. At each site we estimate the genealogy of the case-control samp…
The paramount importance of replicating associations is well recognized in the genome-wide associaton (GWA) research community, yet methods for assessing replicability of associations are scarce. Published GWA studies often combine separately the results of primary studies and of the follow-up studies. Informally, reporting the two separate meta-analyses, that of the primary studies and follow-up studies, gives a sense of the replicability of the results. We suggest a formal empirical Bayes approach for discovering whether results have been replicated across studies, in which we estimate the o…
Multivariate linear mixed models (mvLMMs) have been widely used in many areas of genetics, and have attracted considerable recent interest in genome-wide association studies (GWASs). However, fitting mvLMMs is computationally non-trivial, and no existing method is computationally practical for performing the likelihood ratio test (LRT) for mvLMMs in GWAS settings with moderate sample size n. The existing software MTMM perform an approximate LRT for two phenotypes, and as we find, its p values can substantially understate the significance of associations. Here, we present novel computationally-…
Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to use them to perform multiple testing under dependence. We propose a multiple testing procedure which is based on a Markov-random-field-coupled mixture model. The ground truth of hypotheses is represented by a latent binary Markov random field, and the observed test statistics appear as the coupled mixture variables. The parameters in our model can be automatic…
We investigate saddlepoint approximations applied to the score test statistic in genome-wide association studies with binary phenotypes. The inaccuracy in the normal approximation of the score test statistic increases with increasing sample imbalance and with decreasing minor allele count. Applying saddlepoint approximations to the score test statistic distribution greatly improve the accuracy, even far out in the tail of the distribution. By using exact results for an intercept model and binary covariate model, as well as simulations for models with nuisance parameters, we emphasize the need …
In genome-wide association studies (GWASs), there is an increasing need for detecting the associations between a genetic variant and multiple traits. In studies of complex diseases, it is common to measure several potentially correlated traits in a single GWAS. Despite the multivariate nature of the studies, single-trait-based methods remain the most widely-adopted analysis procedure, owing to their simplicity for studies with multiple traits as their outcome. However, the association between a genetic variant and a single trait sometimes can be weak, and ignoring the actual correlation among …
Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）
Genome-wide association studies (GWAS) have emerged as a rich source of genetic clues into disease biology, and they have revealed strong genetic correlations among many diseases and traits. Some of these genetic correlations may reflect causal relationships. We developed a method to quantify causal relationships between genetically correlated traits using GWAS summary association statistics. In particular, our method quantifies what part of the genetic component of trait 1 is also causal for trait 2 using mixed fourth moments $E(α_1^2α_1α_2)$ and $E(α_2^2α_1α_2)$ of the bivariate effect size …
Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with human traits or diseases in the past decade. Nevertheless, much of the heritability of many traits is still unaccounted for. Commonly used single-trait analysis methods are conservative, while multi-trait methods improve statistical power by integrating association evidence across multiple traits. In contrast to individual-level data, GWAS summary statistics are usually publicly available, and thus methods using only summary statistics have greater usage. Although many methods have been develop…
Controlling the joint local false discovery rate is more powerful than meta-analysis methods in joint analysis of summary statistics from multiple genome-wide association studies
As the sequencing costs are decreasing, there is great incentive to perform large scale association studies to increase power of detecting new variants. Federated association testing among different institutions is a viable solution for increasing sample sizes by sharing the intermediate testing statistics that are aggregated by a central server. There are, however, standing challenges to performing federated association testing. Association tests are known to be confounded by numerous factors such as population stratification, which can be especially important in multiancestral studies and in…
Linear mixed models (LMMs) are widely used for heritability estimation in genome-wide association studies (GWAS). In standard approaches to heritability estimation with LMMs, a genetic relationship matrix (GRM) must be specified. In GWAS, the GRM is frequently a correlation matrix estimated from the study population's genotypes, which corresponds to a normalized Euclidean distance kernel. In this paper, we show that reliance on the Euclidean distance kernel contributes to several unresolved modeling inconsistencies in heritability estimation for GWAS. These inconsistencies can cause biased her…
High-dimensional phenotypes hold promise for richer findings in association studies, but testing of several phenotype traits aggravates the grand challenge of association studies, that of multiple testing. Several methods have recently been proposed for testing jointly all traits in a high-dimensional vector of phenotypes, with prospect of increased power to detect small effects that would be missed if tested individually. However, the methods have rarely been compared to the extent of enabling assessment of their relative merits and setting up guidelines on which method to use, and how to use…
The problems of large-scale multiple testing are often encountered in modern scientific researches. Conventional multiple testing procedures usually suffer considerable loss of testing efficiency due to the lack of consideration of correlations among tests. In fact, the appropriate use of correlation information not only enhances the efficacy of multiple testing but also improves the interpretability of the results. Since the disease- or trait-related single nucleotide polymorphisms (SNPs) often tend to be clustered and exhibit serial correlations, the hidden Markov model (HMM) based multiple …
A genome-wide association study (GWAS) correlates marker variation with trait variation in a sample of individuals. Each study subject is genotyped at a multitude of SNPs (single nucleotide polymorphisms) spanning the genome. Here we assume that subjects are unrelated and collected at random and that trait values are normally distributed or transformed to normality. Over the past decade, researchers have been remarkably successful in applying GWAS analysis to hundreds of traits. The massive amount of data produced in these studies present unique computational challenges. Penalized regression w…
Genome-wide association studies (GWASs) aim to detect genetic risk factors for complex human diseases by identifying disease-associated single-nucleotide polymorphisms (SNPs). The traditional SNP-wise approach along with multiple testing adjustment is over-conservative and lack of power in many GWASs. In this article, we proposed a model-based clustering method that transforms the challenging high-dimension-small-sample-size problem to low-dimension-large-sample-size problem and borrows information across SNPs by grouping SNPs into three clusters. We pre-specify the patterns of clusters by min…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs) explaining most of total variance are tested for association with a predictor of interest, and the remaining PCs are ignored. This strategy has been widely applied in genetic epidemiology, however some of its aspects are not well appreciated in the context of single nucleotide polymorphisms (SNPs) association testing. In this study, we review the theoretical basis o…
Background: Identification of causal SNPs in most genome wide association studies relies on approaches that consider each SNP individually. However, there is a strong correlation structure among SNPs that need to be taken into account. Hence, increasingly modern computationally expensive regression methods are employed for SNP selection that consider all markers simultaneously and thus incorporate dependencies among SNPs. Results: We develop a novel multivariate algorithm for large scale SNP selection using CAR score regression, a promising new approach for prioritizing biomarkers. Specificall…
To date, genome-wide association studies (GWAS) have successfully identified tens of thousands of genetic variants among a variety of traits/diseases, shedding a light on the genetic architecture of complex diseases. Polygenicity of complex diseases, which refers to the phenomenon that a vast number of risk variants collectively contribute to the heritability of complex diseases with modest individual effects, have been widely accepted. This imposes a major challenge towards fully characterizing the genetic bases of complex diseases. An immediate implication of polygenicity is that a much larg…
Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequency evolution. We develop a general probabilistic model and an associated inference algorithm that unify the model-based and data-driven approaches to visualizing and inferring population structure. Ou…
Marginal association summary statistics have attracted great attention in statistical genetics, mainly because the primary results of most genome-wide association studies (GWAS) are produced by marginal screening. In this paper, we study the prediction accuracy of marginal estimator in dense (or sparsity free) high-dimensional settings with $(n,p,m) \to \infty$, $m/n \to γ\in (0,\infty)$, and $p/n \to ω\in (0,\infty)$. We consider a general correlation structure among the $p$ features and allow an unknown subset $m$ of them to be signals. As the marginal estimator can be viewed as a ridge esti…
In Genome-Wide Association Studies (GWAS) where multiple correlated traits have been measured on participants, a joint analysis strategy, whereby the traits are analyzed jointly, can improve statistical power over a single-trait analysis strategy. There are two questions of interest to be addressed when conducting a joint GWAS analysis with multiple traits. The first question examines whether a genetic loci is significantly associated with any of the traits being tested. The second question focuses on identifying the specific trait(s) that is associated with the genetic loci. Since existing me…
Genetic variants identified to date by genome-wide association studies only explain a small fraction of total heritability. Gene-by-gene interaction is one important potential source of unexplained heritability. In the first part of this dissertation, a novel approach to detect such interactions is proposed. This approach utilizes penalized regression and sparse estimation principles, and incorporates outside biological knowledge through a network-based penalty. The method is tested on simulated data under various scenarios. Simulations show that with reasonable outside biological knowledge, t…
We show that the signal-processing paradigm known as compressed sensing (CS) is applicable to genome-wide association studies (GWAS) and genomic selection (GS). The aim of GWAS is to isolate trait-associated loci, whereas GS attempts to predict the phenotypic values of new individuals on the basis of training data. CS addresses a problem common to both endeavors, namely that the number of genotyped markers often greatly exceeds the sample size. We show using CS methods and theory that all loci of nonzero effect can be identified (selected) using an efficient algorithm, provided that they are s…
In several modern applications, ranging from genetics to genomics and neuroimaging, there is a need to compare observations across different populations, such as groups of healthy and diseased individuals. The interest is in detecting a group effect. When the observations are vectorial, real-valued and follow a multivariate Normal distribution, multivariate analysis of variance (MANOVA) tests are routinely applied. However, such traditional procedures are not suitable when dealing with more complex data structures such as functional (e.g. curves) or graph-structured (e.g. trees and networks) o…
For the vast majority of genome wide association studies (GWAS) published so far, statistical analysis was performed by testing markers individually. In this article we present some elementary statistical considerations which clearly show that in case of complex traits the approach based on multiple regression or generalized linear models is preferable to multiple testing. We introduce a model selection approach to GWAS based on modifications of Bayesian Information Criterion (BIC) and develop some simple search strategies to deal with the huge number of potential models. Comprehensive simulat…
Although genome-wide association studies (GWAS) have proven powerful for comprehending the genetic architecture of complex traits, they are challenged by a high dimension of single-nucleotide polymorphisms (SNPs) as predictors, the presence of complex environmental factors, and longitudinal or functional natures of many complex traits or diseases. To address these challenges, we propose a high-dimensional varying-coefficient model for incorporating functional aspects of phenotypic traits into GWAS to formulate a so-called functional GWAS or fGWAS. The Bayesian group lasso and the associated MC…
