An Efficient Stepwise Statistical Test to Identify Multiple Linked Human Genetic Variants Associated with Specific Phenotypic Traits

Recent advances in genotyping methodologies have allowed genome-wide association studies (GWAS) to accurately identify genetic variants that associate with common or pathological complex traits. Although most GWAS have focused on associations with single genetic variants, joint identification of multiple genetic variants, and how they interact, is essential for understanding the genetic architecture of complex phenotypic traits. Here, we propose an efficient stepwise method based on the Cochran-Mantel-Haenszel test (for stratified categorical data) to identify causal joint multiple genetic variants in GWAS. This method combines the CMH statistic with a stepwise procedure to detect multiple genetic variants associated with specific categorical traits, using a series of associated I × J contingency tables and a null hypothesis of no phenotype association. Through a new stratification scheme based on the sum of minor allele count criteria, we make the method more feasible for GWAS data having sample sizes of several thousands. We also examine the properties of the proposed stepwise method via simulation studies, and show that the stepwise CMH test performs better than other existing methods (e.g., logistic regression and detection of associations by Markov blanket) for identifying multiple genetic variants. Finally, we apply the proposed approach to two genomic sequencing datasets to detect linked genetic variants associated with bipolar disorder and obesity, respectively.     

Genetic association studies of complex traits: design and analysis issues

Most common diseases and many important quantitative traits are complex genetic traits, with multiple genetic and environmental variables contributing to the observed phenotype. Because of the multi-factorial nature of complex traits, each individual genetic variant generally has only a modest effect, and the interaction of genetic variants with each other or with environmental factors can potentially be quite important in determining the observed phenotype. It remains largely unknown what sort of genetic variants explain inherited variation in complex traits, but recent evidence suggests that common genetic variants will explain at least some of the inherited variation in susceptibility to common disease. Genetic association studies, in which the allele or genotype frequencies at markers are determined in affected individuals and compared with those of controls (either population- or family-based), may be an effective approach to detecting the effects of common variants with modest effects. With the explosion in single nucleotide polymorphism (SNP) discovery and genotyping technologies, large-scale association studies have become feasible, and small-scale association studies have become plentiful. We review the different types of association studies and discuss issues that are important to consider when performing and interpreting association studies of complex genetic traits. Heritable and accurately measured phenotypes, carefully matched large samples, well-chosen genetic markers, and adequate standards in genotyping, analysis, and interpretation are all integral parts of a high-quality association study.     

Assessing Gene-Environment Interactions for Common and Rare Variants with Binary Traits Using Gene-Trait Similarity Regression

Accounting for gene–environment (G×E) interactions in complex trait association studies can facilitate our understanding of genetic heterogeneity under different environmental exposures, improve the ability to discover susceptible genes that exhibit little marginal effect, provide insight into the biological mechanisms of complex diseases, help to identify high-risk subgroups in the population, and uncover hidden heritability. However, significant G×E interactions can be difficult to find. The sample sizes required for sufficient power to detect association are much larger than those needed for genetic main effects, and interactions are sensitive to misspecification of the main-effects model. These issues are exacerbated when working with binary phenotypes and rare variants, which bear less information on association. In this work, we present a similarity-based regression method for evaluating G×E interactions for rare variants with binary traits. The proposed model aggregates the genetic and G×E information across markers, using genetic similarity, thus increasing the ability to detect G×E signals. The model has a random effects interpretation, which leads to robustness against main-effect misspecifications when evaluating G×E interactions. We construct score tests to examine G×E interactions and a computationally efficient EM algorithm to estimate the nuisance variance components. Using simulations and data applications, we show that the proposed method is a flexible and powerful tool to study the G×E effect in common or rare variant studies with binary traits.     

Comparison of Statistical Tests for Association between Rare Variants and Binary Traits

Genome-wide association studies have found thousands of common genetic variants associated with a wide variety of diseases and other complex traits. However, a large portion of the predicted genetic contribution to many traits remains unknown. One plausible explanation is that some of the missing variation is due to the effects of rare variants. Nonetheless, the statistical analysis of rare variants is challenging. A commonly used method is to contrast, within the same region (gene), the frequency of minor alleles at rare variants between cases and controls. However, this strategy is most useful under the assumption that the tested variants have similar effects. We previously proposed a method that can accommodate heterogeneous effects in the analysis of quantitative traits. Here we extend this method to include binary traits that can accommodate covariates. We use simulations for a variety of causal and covariate impact scenarios to compare the performance of the proposed method to standard logistic regression, C-alpha, SKAT, and EREC. We found that i) logistic regression methods perform well when the heterogeneity of the effects is not extreme and ii) SKAT and EREC have good performance under all tested scenarios but they can be computationally intensive. Consequently, it would be more computationally desirable to use a two-step strategy by (i) selecting promising genes by faster methods and ii) analyzing selected genes using SKAT/EREC. To select promising genes one can use (1) regression methods when effect heterogeneity is assumed to be low and the covariates explain a non-negligible part of trait variability, (2) C-alpha when heterogeneity is assumed to be large and covariates explain a small fraction of trait's variability and (3) the proposed trend and heterogeneity test when the heterogeneity is assumed to be non-trivial and the covariates explain a large fraction of trait variability.     

Genome survey on invasive veined rapa whelk (<Emphasis Type="Italic">Rapana venosa</Emphasis>) and development of microsatellite loci on large scale

Increasing evidence shows that one variant can affect multiple traits, which is a widespread phenomenon in complex diseases. Joint analysis of multiple traits can increase statistical power of association analysis and uncover the underlying genetic mechanism. Although there are many statistical methods to analyse multiple traits, most of these methods are usually suitable for detecting common variants associated with multiple traits. However, because of low minor allele frequency of rare variant, these methods are not optimal for rare variant association analysis. In this paper, we extend an adaptive combination of P values method (termed ADA) for single trait to test association between multiple traits and rare variants in the given region. For a given region, we use reverse regression model to test each rare variant associated with multiple traits and obtain the P value of single-variant test. Further, we take the weighted combination of these P values as the test statistic. Extensive simulation studies show that our approach is more powerful than several other comparison methods in most cases and is robust to the inclusion of a high proportion of neutral variants and the different directions of effects of causal variants.     

Progress and promise of genome-wide association studies for human complex trait genetics

Enormous progress in mapping complex traits in humans has been made in the last 5 yr. There has been early success for prevalent diseases with complex phenotypes. These studies have demonstrated clearly that, while complex traits differ in their underlying genetic architectures, for many common disorders the predominant pattern is that of many loci, individually with small effects on phenotype. For some traits, loci of large effect have been identified. For almost all complex traits studied in humans, the sum of the identified genetic effects comprises only a portion, generally less than half, of the estimated trait heritability. A variety of hypotheses have been proposed to explain why this might be the case, including untested rare variants, and gene-gene and gene-environment interaction. Effort is currently being directed toward implementation of novel analytic approaches and testing rare variants for association with complex traits using imputed variants from the publicly available 1000 Genomes Project resequencing data and from direct resequencing of clinical samples. Through integration with annotations and functional genomic data as well as by in vitro and in vivo experimentation, mapping studies continue to characterize functional variants associated with complex traits and address fundamental issues such as epistasis and pleiotropy. This review focuses primarily on the ways in which genome-wide association studies (GWASs) have revolutionized the field of human quantitative genetics.     

A Robust Model-free Approach for Rare Variants Association Studies Incorporating Gene-Gene and Gene-Environmental Interactions

Recently more and more evidence suggest that rare variants with much lower minor allele frequencies play significant roles in disease etiology. Advances in next-generation sequencing technologies will lead to many more rare variants association studies. Several statistical methods have been proposed to assess the effect of rare variants by aggregating information from multiple loci across a genetic region and testing the association between the phenotype and aggregated genotype. One limitation of existing methods is that they only look into the marginal effects of rare variants but do not systematically take into account effects due to interactions among rare variants and between rare variants and environmental factors. In this article, we propose the summation of partition approach (SPA), a robust model-free method that is designed specifically for detecting both marginal effects and effects due to gene-gene (G×G) and gene-environmental (G×E) interactions for rare variants association studies. SPA has three advantages. First, it accounts for the interaction information and gains considerable power in the presence of unknown and complicated G×G or G×E interactions. Secondly, it does not sacrifice the marginal detection power; in the situation when rare variants only have marginal effects it is comparable with the most competitive method in current literature. Thirdly, it is easy to extend and can incorporate more complex interactions; other practitioners and scientists can tailor the procedure to fit their own study friendly. Our simulation studies show that SPA is considerably more powerful than many existing methods in the presence of G×G and G×E interactions.     

Epistatic Gene-Based Interaction Analyses for Glaucoma in eMERGE and NEIGHBOR Consortium

Primary open angle glaucoma (POAG) is a complex disease and is one of the major leading causes of blindness worldwide. Genome-wide association studies have successfully identified several common variants associated with glaucoma; however, most of these variants only explain a small proportion of the genetic risk. Apart from the standard approach to identify main effects of variants across the genome, it is believed that gene-gene interactions can help elucidate part of the missing heritability by allowing for the test of interactions between genetic variants to mimic the complex nature of biology. To explain the etiology of glaucoma, we first performed a genome-wide association study (GWAS) on glaucoma case-control samples obtained from electronic medical records (EMR) to establish the utility of EMR data in detecting non-spurious and relevant associations; this analysis was aimed at confirming already known associations with glaucoma and validating the EMR derived glaucoma phenotype. Our findings from GWAS suggest consistent evidence of several known associations in POAG. We then performed an interaction analysis for variants found to be marginally associated with glaucoma (SNPs with main effect p-value <0.01) and observed interesting findings in the electronic MEdical Records and GEnomics Network (eMERGE) network dataset. Genes from the top epistatic interactions from eMERGE data (Likelihood Ratio Test i.e. LRT p-value <1e-05) were then tested for replication in the NEIGHBOR consortium dataset. To replicate our findings, we performed a gene-based SNP-SNP interaction analysis in NEIGHBOR and observed significant gene-gene interactions (p-value <0.001) among the top 17 gene-gene models identified in the discovery phase. Variants from gene-gene interaction analysis that we found to be associated with POAG explain 3.5% of additional genetic variance in eMERGE dataset above what is explained by the SNPs in genes that are replicated from previous GWAS studies (which was only 2.1% variance explained in eMERGE dataset); in the NEIGHBOR dataset, adding replicated SNPs from gene-gene interaction analysis explain 3.4% of total variance whereas GWAS SNPs alone explain only 2.8% of variance. Exploring gene-gene interactions may provide additional insights into many complex traits when explored in properly designed and powered association studies.     

U-statistics in genetic association studies

Many common human diseases are complex and are expected to be highly heterogeneous, with multiple causative loci and multiple rare and common variants at some of the causative loci contributing to the risk of these diseases. Data from the genome-wide association studies (GWAS) and metadata such as known gene functions and pathways provide the possibility of identifying genetic variants, genes and pathways that are associated with complex phenotypes. Single-marker-based tests have been very successful in identifying thousands of genetic variants for hundreds of complex phenotypes. However, these variants only explain very small percentages of the heritabilities. To account for the locus- and allelic-heterogeneity, gene-based and pathway-based tests can be very useful in the next stage of the analysis of GWAS data. U-statistics, which summarize the genomic similarity between pair of individuals and link the genomic similarity to phenotype similarity, have proved to be very useful for testing the associations between a set of single nucleotide polymorphisms and the phenotypes. Compared to single marker analysis, the advantages afforded by the U-statistics-based methods is large when the number of markers involved is large. We review several formulations of U-statistics in genetic association studies and point out the links of these statistics with other similarity-based tests of genetic association. Finally, potential application of U-statistics in analysis of the next-generation sequencing data and rare variants association studies are discussed.     

Sequence Kernel Association Tests for the Combined Effect of Rare and Common Variants

Recent developments in sequencing technologies have made it possible to uncover both rare and common genetic variants. Genome-wide association studies (GWASs) can test for the effect of common variants, whereas sequence-based association studies can evaluate the cumulative effect of both rare and common variants on disease risk. Many groupwise association tests, including burden tests and variance-component tests, have been proposed for this purpose. Although such tests do not exclude common variants from their evaluation, they focus mostly on testing the effect of rare variants by upweighting rare-variant effects and downweighting common-variant effects and can therefore lose substantial power when both rare and common genetic variants in a region influence trait susceptibility. There is increasing evidence that the allelic spectrum of risk variants at a given locus might include novel, rare, low-frequency, and common genetic variants. Here, we introduce several sequence kernel association tests to evaluate the cumulative effect of rare and common variants. The proposed tests are computationally efficient and are applicable to both binary and continuous traits. Furthermore, they can readily combine GWAS and whole-exome-sequencing data on the same individuals, when available, and are also applicable to deep-resequencing data of GWAS loci. We evaluate these tests on data simulated under comprehensive scenarios and show that compared with the most commonly used tests, including the burden and variance-component tests, they can achieve substantial increases in power. We next show applications to sequencing studies for Crohn disease and autism spectrum disorders. The proposed tests have been incorporated into the software package SKAT.     

Rare-variant association testing for sequencing data with the sequence kernel association test

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.     

Gene-Trait Similarity Regression for Multimarker-Based Association Analysis

Summary .  We propose a similarity-based regression method to detect associations between traits and multimarker genotypes. The model regresses similarity in traits for pairs of "unrelated" individuals on their haplotype similarities, and detects the significance by a score test for which the limiting distribution is derived. The proposed method allows for covariates, uses phase-independent similarity measures to bypass the needs to impute phase information, and is applicable to traits of general types (e.g., quantitative and qualitative traits). We also show that the gene-trait similarity regression is closely connected with random effects haplotype analysis, although commonly they are considered as separate modeling tools. This connection unites the classic haplotype sharing methods with the variance-component approaches, which enables direct derivation of analytical properties of the sharing statistics even when the similarity regression model becomes analytically challenging.     

Modifier effects between regulatory and protein-coding variation

Genome-wide associations have shown a lot of promise in dissecting the genetics of complex traits in humans with single variants, yet a large fraction of the genetic effects is still unaccounted for. Analyzing genetic interactions between variants (epistasis) is one of the potential ways forward. We investigated the abundance and functional impact of a specific type of epistasis, namely the interaction between regulatory and protein-coding variants. Using genotype and gene expression data from the 210 unrelated individuals of the original four HapMap populations, we have explored the combined effects of regulatory and protein-coding single nucleotide polymorphisms (SNPs). We predict that about 18% (1,502 out of 8,233 nsSNPs) of protein-coding variants are differentially expressed among individuals and demonstrate that regulatory variants can modify the functional effect of a coding variant in cis. Furthermore, we show that such interactions in cis can affect the expression of downstream targets of the gene containing the protein-coding SNP. In this way, a cis interaction between regulatory and protein-coding variants has a trans impact on gene expression. Given the abundance of both types of variants in human populations, we propose that joint consideration of regulatory and protein-coding variants may reveal additional genetic effects underlying complex traits and disease and may shed light on causes of differential penetrance of known disease variants.     

Powerful multilocus tests of genetic association in the presence of gene-gene and gene-environment interactions

In modern genetic epidemiology studies, the association between the disease and a genomic region, such as a candidate gene, is often investigated using multiple SNPs. We propose a multilocus test of genetic association that can account for genetic effects that might be modified by variants in other genes or by environmental factors. We consider use of the venerable and parsimonious Tukey's 1-degree-of-freedom model of interaction, which is natural when individual SNPs within a gene are associated with disease through a common biological mechanism; in contrast, many standard regression models are designed as if each SNP has unique functional significance. On the basis of Tukey's model, we propose a novel but computationally simple generalized test of association that can simultaneously capture both the main effects of the variants within a genomic region and their interactions with the variants in another region or with an environmental exposure. We compared performance of our method with that of two standard tests of association, one ignoring gene-gene/gene-environment interactions and the other based on a saturated model of interactions. We demonstrate major power advantages of our method both in analysis of data from a case-control study of the association between colorectal adenoma and DNA variants in the NAT2 genomic region, which are well known to be related to a common biological phenotype, and under different models of gene-gene interactions with use of simulated data.     

Rare variants regulate expression of nearby individual genes in multiple tissues

The rapid decrease in sequencing cost has enabled genetic studies to discover rare variants associated with complex diseases and traits. Once this association is identified, the next step is to understand the genetic mechanism of rare variants on how the variants influence diseases. Similar to the hypothesis of common variants, rare variants may affect diseases by regulating gene expression, and recently, several studies have identified the effects of rare variants on gene expression using heritability and expression outlier analyses. However, identifying individual genes whose expression is regulated by rare variants has been challenging due to the relatively small sample size of expression quantitative trait loci studies and statistical approaches not optimized to detect the effects of rare variants. In this study, we analyze whole-genome sequencing and RNA-seq data of 681 European individuals collected for the Genotype-Tissue Expression (GTEx) project (v8) to identify individual genes in 49 human tissues whose expression is regulated by rare variants. To improve statistical power, we develop an approach based on a likelihood ratio test that combines effects of multiple rare variants in a nonlinear manner and has higher power than previous approaches. Using GTEx data, we identify many genes regulated by rare variants, and some of them are only regulated by rare variants and not by common variants. We also find that genes regulated by rare variants are enriched for expression outliers and disease-causing genes. These results suggest the regulatory effects of rare variants, which would be important in interpreting associations of rare variants with complex traits.     

Rare Variants Create Synthetic Genome-Wide Associations

Genome-wide association studies (GWAS) have now identified at least 2,000 common variants that appear associated with common diseases or related traits (http://www.genome.gov/gwastudies), hundreds of which have been convincingly replicated. It is generally thought that the associated markers reflect the effect of a nearby common (minor allele frequency >0.05) causal site, which is associated with the marker, leading to extensive resequencing efforts to find causal sites. We propose as an alternative explanation that variants much less common than the associated one may create “synthetic associations” by occurring, stochastically, more often in association with one of the alleles at the common site versus the other allele. Although synthetic associations are an obvious theoretical possibility, they have never been systematically explored as a possible explanation for GWAS findings. Here, we use simple computer simulations to show the conditions under which such synthetic associations will arise and how they may be recognized. We show that they are not only possible, but inevitable, and that under simple but reasonable genetic models, they are likely to account for or contribute to many of the recently identified signals reported in genome-wide association studies. We also illustrate the behavior of synthetic associations in real datasets by showing that rare causal mutations responsible for both hearing loss and sickle cell anemia create genome-wide significant synthetic associations, in the latter case extending over a 2.5-Mb interval encompassing scores of “blocks” of associated variants. In conclusion, uncommon or rare genetic variants can easily create synthetic associations that are credited to common variants, and this possibility requires careful consideration in the interpretation and follow up of GWAS signals.     

Accounting for Population Structure in Gene-by-Environment Interactions in Genome-Wide Association Studies Using Mixed Models

Although genome-wide association studies (GWASs) have discovered numerous novel genetic variants associated with many complex traits and diseases, those genetic variants typically explain only a small fraction of phenotypic variance. Factors that account for phenotypic variance include environmental factors and gene-by-environment interactions (GEIs). Recently, several studies have conducted genome-wide gene-by-environment association analyses and demonstrated important roles of GEIs in complex traits. One of the main challenges in these association studies is to control effects of population structure that may cause spurious associations. Many studies have analyzed how population structure influences statistics of genetic variants and developed several statistical approaches to correct for population structure. However, the impact of population structure on GEI statistics in GWASs has not been extensively studied and nor have there been methods designed to correct for population structure on GEI statistics. In this paper, we show both analytically and empirically that population structure may cause spurious GEIs and use both simulation and two GWAS datasets to support our finding. We propose a statistical approach based on mixed models to account for population structure on GEI statistics. We find that our approach effectively controls population structure on statistics for GEIs as well as for genetic variants.     

Gene variation in resistant hypertension: multilocus analysis of the angiotensin 1-converting enzyme, angiotensinogen, and endothelial nitric oxide synthase genes

Resistant hypertension, a complex multifactorial hypertensive disease, is triggered by genetic and environmental factors and involves multiple physiological pathways. Single genetic variants may not reveal significant associations with resistant hypertension because their effects may be dependent on gene-gene or gene-environment interactions. We examined the interaction of angiotensin I-converting enzyme (ACE), angiotensinogen (AGT), and endothelial nitric oxide synthase (NOS3) polymorphisms with environmental factors (gender, age, body mass index, glycemia, total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglycerides, estimated glomerular filtration rate, and urinary sodium excretion) in 70 resistant, 80 well-controlled hypertensive patients, and 70 normotensive controls. All subjects were genotyped for ACE insertion/deletion (rs1799752); AGT M235T (rs699), and NOS3 Glu298Asp (rs 1799983). Multifactorial associations were tested using two statistical methods: the traditional parametric method (adjusted logistic regression analysis) and gene-gene and gene-environment interactions evaluated by multifactor dimensionality reduction analyses. While adjusted logistic regression found no significant association between the studied polymorphisms and controlled or resistant hypertension, the multifactor dimensionality reduction analyses showed that carriers of the AGT 235T allele were at increased risk for resistant hypertension, especially if they were older than 50 years. The AGT 235T allele constituted an independent risk factor for resistant hypertension.     

Associating somatic mutation with clinical outcomes through kernel regression and optimal transport

Somatic mutations in cancer patients are inherently sparse and potentially high dimensional. Cancer patients may share the same set of deregulated biological processes perturbed by different sets of somatically mutated genes. Therefore, when assessing the associations between somatic mutations and clinical outcomes, gene-by-gene analysis is often under-powered because it does not capture the complex disease mechanisms shared across cancer patients. Rather than testing genes one by one, an intuitive approach is to aggregate somatic mutation data of multiple genes to assess their joint association with clinical outcomes. The challenge is how to aggregate such information. Building on the optimal transport method, we propose a principled approach to estimate the similarity of somatic mutation profiles of multiple genes between tumor samples, while accounting for gene–gene similarities defined by gene annotations or empirical mutational patterns. Using such similarities, we can assess the associations between somatic mutations and clinical outcomes by kernel regression. We have applied our method to analyze somatic mutation data of 17 cancer types and identified at least five cancer types, where somatic mutations are associated with overall survival, progression-free interval, or cytolytic activity.     

The Impact of Population Demography and Selection on the Genetic Architecture of Complex Traits

Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequency, and effect sizes of mutations that contribute risk to complex traits. Because researchers are performing exome sequencing studies aimed at uncovering the role of low-frequency variants in the risk of complex traits, this topic is of critical importance. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynonymous variants segregating in the population, but does not affect the genetic load relative to a population that did not expand. Under a model where a mutation''s effect on a trait is correlated with its effect on fitness, rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand. Further, when using a single-marker test, for a given false-positive rate and sample size, recent population growth decreases the expected number of significant associations with the trait relative to the number detected in a population that did not expand. However, in a model where there is no correlation between a mutation''s effect on fitness and the effect on the trait, common variants account for much of the additive genetic variance, regardless of demography. Moreover, here demography does not affect the number of significant associations detected. These findings suggest recent population history may be an important factor influencing the power of association tests and in accounting for the missing heritability of certain complex traits.