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 traits may lose power. On the contrary, multiple-trait analysis, a method analyzes a group of traits simultaneously, has been proven to be more powerful by incorporating information from the correlated traits. Although existing methods have been developed for multiple traits, several drawbacks limit their wide application in GWASs. In this paper, we propose a multiple-trait adaptive Fisher's (MTAF) method to test associations between a genetic variant and multiple traits at once, by adaptively aggregating evidence from each trait. The proposed method can accommodate both continuous and binary traits and it has reliable performance under various scenarios. Using a simulation study, we compared our proposed method with several existing methods and demonstrated its competitiveness in terms of type I error control and statistical power. By applying the method to the Study of Addiction: Genetics and Environment (SAGE) dataset, we successfully identified several genes associated with substance dependence.
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…
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…
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…
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 …
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…
Genome-wide association studies (GWAS) have been widely used to examine the association between single nucleotide polymorphisms (SNPs) and complex traits, where both the sample size n and the number of SNPs p can be very large. Recently, cross-trait polygenic risk score (PRS) method has gained extremely popular for assessing genetic correlation of complex traits based on GWAS summary statistics (e.g., SNP effect size). However, empirical evidence has shown a common bias phenomenon that even highly significant cross-trait PRS can only account for a very small amount of genetic variance (R^2 oft…
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…
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…
Thousands of risk variants underlying complex phenotypes (quantitative traits and diseases) have been identified in genome-wide association studies (GWAS). However, there are still two major challenges towards deepening our understanding of the genetic architectures of complex phenotypes. First, the majority of GWAS hits are in the non-coding region and their biological interpretation is still unclear. Second, accumulating evidence from GWAS suggests the polygenicity of complex traits, i.e., a complex trait is often affected by many variants with small or moderate effects, whereas a large prop…
Advances of modern sensing and sequencing technologies generate a deluge of high dimensional space-temporal physiological and next-generation sequencing (NGS) data. Physiological traits are observed either as continuous random functions, or on a dense grid and referred to as function-valued traits. Both physiological and NGS data are highly correlated data with their inherent order, spacing, and functional nature which are ignored by traditional summary-based univariate and multivariate regression methods designed for quantitative genetic analysis of scalar trait and common variants. To captur…
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 …
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…
Since most analysis software for genome-wide association studies (GWAS) currently exploit only unrelated individuals, there is a need for efficient applications that can handle general pedigree data or mixtures of both population and pedigree data. Even data sets thought to consist of only unrelated individuals may include cryptic relationships that can lead to false positives if not discovered and controlled for. In addition, family designs possess compelling advantages. They are better equipped to detect rare variants, control for population stratification, and facilitate the study of parent…
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…
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…
The aim of this paper is to propose a novel estimation method of using genetic-predicted observations to estimate trans-ancestry genetic correlations, which describes how genetic architecture of complex traits varies among populations, in genome-wide association studies (GWAS). Our new estimator corrects for prediction errors caused by high-dimensional weak GWAS signals, while addressing the heterogeneity of GWAS data across ethnicities, such as linkage disequilibrium (LD) differences, which can lead to biased findings in homogeneity-agnostic analyses. Moreover, our estimator only requires one…
Multi-trait genome-wide association studies (GWAS) use multi-variate statistical methods to identify associations between genetic variants and multiple correlated traits simultaneously, and have higher statistical power than independent univariate analyses of traits. Reverse regression, where genotypes of genetic variants are regressed on multiple traits simultaneously, has emerged as a promising approach to perform multi-trait GWAS in high-dimensional settings where the number of traits exceeds the number of samples. We analyzed different machine learning methods (ridge regression, naive Baye…
The development of next generation sequencing (NGS) technology and genotype imputation methods enabled researchers to measure both common and rare variants in genome-wide association studies (GWAS). Statistical methods have been proposed to test a set of genomic variants together to detect if any of them is associated with the phenotype or disease. In practice, within the set of variants, there is an unknown proportion of variants truly causal or associated with the disease. Because most developed methods are sensitive to either the dense scenario, where a large proportion of the variants are …
Genome-wide association studies have proven to be essential for understanding the genetic basis of disease. However, many complex traits---personality traits, facial features, disease subtyping---are inherently high-dimensional, impeding simple approaches to association mapping. We developed a nonparametric Bayesian reduced rank regression model for multi-SNP, multi-trait association mapping that does not require the rank of the linear subspace to be specified. We show in simulations and real data that our model shares strength over SNPs and over correlated traits, improving statistical power …
With the recent advent of high-throughput genotyping techniques, genetic data for genome-wide association studies (GWAS) have become increasingly available, which entails the development of efficient and effective statistical approaches. Although many such approaches have been developed and used to identify single-nucleotide polymorphisms (SNPs) that are associated with complex traits or diseases, few are able to detect gene-gene interactions among different SNPs. Genetic interactions, also known as epistasis, have been recognized to play a pivotal role in contributing to the genetic variation…
Genome-wide Association Studies (GWASs) for complex diseases often collect data on multiple correlated endo-phenotypes. Multivariate analysis of these correlated phenotypes can improve the power to detect genetic variants. Multivariate analysis of variance (MANOVA) can perform such association analysis at a GWAS level, but the behavior of MANOVA under different trait models has not been carefully investigated. In this paper, we show that MANOVA is generally very powerful for detecting association but there are situations, such as when a genetic variant is associated with all the traits, where …
Genome-wide association studies (GWAS) have successfully identified over two hundred thousand genotype-trait associations. Yet some challenges remain. First, complex traits are often associated with many single nucleotide polymorphisms (SNPs), most with small or moderate effect sizes, making them difficult to detect. Second, many complex traits share a common genetic basis due to `pleiotropy' and and though few methods consider it, leveraging pleiotropy can improve statistical power to detect genotype-trait associations with weaker effect sizes. Third, currently available statistical methods a…
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
The Hong Kong University of Science and Technology（香港科技大学）
In genome wide association studies (GWAS), researchers are often dealing with non-normally distributed traits or a mixture of discrete-continuous traits. However, most of the current region-based methods rely on multivariate linear mixed models (mvLMMs) and assume a multivariate normal distribution for the phenotypes of interest. Hence, these methods are not applicable to disease or non-normally distributed traits. Therefore, there is a need to develop unified and flexible methods to study association between a set of (possibly rare) genetic variants and non-normal multivariate phenotypes. Cop…
Co-heritability is an important concept that characterizes the genetic associations within pairs of quantitative traits. There has been significant recent interest in estimating the co-heritability based on data from the genome-wide association studies (GWAS). This paper introduces two measures of co-heritability in the high-dimensional linear model framework, including the inner product of the two regression vectors and a normalized inner product by their lengths. Functional de-biased estimators (FDEs) are developed to estimate these two co-heritability measures. In addition, estimators of qu…
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…
Motivation: In spite of great success of genome-wide association studies (GWAS), multiple challenges still remain. First, complex traits are often associated with many single nucleotide polymorphisms (SNPs), each with small or moderate effect sizes. Second, our understanding of the functional mechanisms through which genetic variants are associated with complex traits is still limited. To address these challenges, we propose GPA-Tree and it simultaneously implements association mapping and identifies key combinations of functional annotations related to risk-associated SNPs by combining a deci…
Background: Many genome-wide association studies have detected genomic regions associated with traits, yet understanding the functional causes of association often remains elusive. Utilizing systems approaches and focusing on intermediate molecular phenotypes might facilitate biologic understanding. Results: The availability of exome sequencing of two populations of African-Americans and European-Americans from the Atherosclerosis Risk in Communities study allowed us to investigate the effects of annotated loss-of-function (LoF) mutations on 122 serum metabolites. To assess the findings, we bu…
Genome-wide association studies (GWAS) have identified many genetic factors underlying complex human traits. However, these factors have explained only a small fraction of these traits' genetic heritability. It is argued that many more genetic factors remain undiscovered. These genetic factors likely are weakly associated at the population level and sparsely distributed across the genome. In this paper, we adapt the recent innovations on Tukey's Higher Criticism (Tukey [The Higher Criticism (1976) Princeton Univ.]; Donoho and Jin [Ann. Statist. 32 (2004) 962-994]) to SNP-set analysis of GWAS, …
In this study, we consider the problem of variable selection and estimation in high-dimensional linear regression models when the complete data are not accessible, but only certain marginal information or summary statistics are available. This problem is motivated from the Genome-wide association studies (GWAS) that have been widely used to identify risk variants underlying complex human traits/diseases. With a large number of completed GWAS, statistical methods using summary statistics become more and more important because of restricted accessibility to individual-level data sets. Theoretica…
Heritability is a central parameter in quantitative genetics, both from an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within and between genotype variability. This approach estimates broad-sense heritability, and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human gen…
Meta-analysis of multiple genome-wide association studies (GWAS) is effective for detecting single or multi marker associations with complex traits. We develop a flexible procedure ("STAMP") based on mixture models to perform region based meta-analysis of different phenotypes using data from different GWAS and identify subsets of associated phenotypes. Our model framework helps distinguish true associations from between-study heterogeneity. As a measure of association we compute for each phenotype the posterior probability that the genetic region under investigation is truly associated. Extens…
Models for genome-wide prediction and association studies usually target a single phenotypic trait. However, in animal and plant genetics it is common to record information on multiple phenotypes for each individual that will be genotyped. Modeling traits individually disregards the fact that they are most likely associated due to pleiotropy and shared biological basis, thus providing only a partial, confounded view of genetic effects and phenotypic interactions. In this paper we use data from a Multiparent Advanced Generation Inter-Cross (MAGIC) winter wheat population to explore Bayesian net…
Motivation: Genome-wide association studies (GWASs), which assay more than a million single nucleotide polymorphisms (SNPs) in thousands of individuals, have been widely used to identify genetic risk variants for complex diseases. However, most of the variants that have been identified contribute relatively small increments of risk and only explain a small portion of the genetic variation in complex diseases. This is the so-called missing heritability problem. Evidence has indicated that many complex diseases are genetically related, meaning these diseases share common genetic risk variants. T…
We present a coherent Bayesian framework for selection of the most likely model from the five genetic models (genotypic, additive, dominant, co-dominant, and recessive) commonly used in genetic association studies. The approach uses a polynomial parameterization of genetic data to simultaneously fit the five models and save computations. We provide a closed-form expression of the marginal likelihood for normally distributed data, and evaluate the performance of the proposed method and existing method through simulated and real genome-wide data sets.
