A Hybrid Likelihood Model for Sequence-Based Disease Association Studies

In the past few years, case-control studies of common diseases have shifted their focus from single genes to whole exomes. New sequencing technologies now routinely detect hundreds of thousands of sequence variants in a single study, many of which are rare or even novel. The limitation of classical single-marker association analysis for rare variants has been a challenge in such studies. A new generation of statistical methods for case-control association studies has been developed to meet this challenge. A common approach to association analysis of rare variants is the burden-style collapsing methods to combine rare variant data within individuals across or within genes. Here, we propose a new hybrid likelihood model that combines a burden test with a test of the position distribution of variants. In extensive simulations and on empirical data from the Dallas Heart Study, the new model demonstrates consistently good power, in particular when applied to a gene set (e.g., multiple candidate genes with shared biological function or pathway), when rare variants cluster in key functional regions of a gene, and when protective variants are present. When applied to data from an ongoing sequencing study of bipolar disorder (191 cases, 107 controls), the model identifies seven gene sets with nominal p-values0.05, of which one MAPK signaling pathway (KEGG) reaches trend-level significance after correcting for multiple testing.     

To identify associations with rare variants, just WHaIT: Weighted haplotype and imputation-based tests

Empirical evidences suggest that both common and rare variants contribute to complex disease etiology. Although the effects of common variants have been thoroughly assessed in recent genome-wide association studies (GWAS), our knowledge of the impact of rare variants on complex diseases remains limited. A number of methods have been proposed to test for rare variant association in sequencing-based studies, a study design that is becoming popular but is still not economically feasible. On the contrary, few (if any) methods exist to detect rare variants in GWAS data, the data we have collected on thousands of individuals. Here we propose two methods, a weighted haplotype-based approach and an imputation-based approach, to test for the effect of rare variants with GWAS data. Both methods can incorporate external sequencing data when available. We evaluated our methods and compared them with methods proposed in the sequencing setting through extensive simulations. Our methods clearly show enhanced statistical power over existing methods for a wide range of population-attributable risk, percentage of disease-contributing rare variants, and proportion of rare alleles working in different directions. We also applied our methods to the IFIH1 region for the type 1 diabetes GWAS data collected by the Wellcome Trust Case-Control Consortium. Our methods yield p values in the order of 10⁻³, whereas the most significant p value from the existing methods is greater than 0.17. We thus demonstrate that the evaluation of rare variants with GWAS data is possible, particularly when public sequencing data are incorporated.     

A new testing strategy to identify rare variants with either risk or protective effect on disease

Rapid advances in sequencing technologies set the stage for the large-scale medical sequencing efforts to be performed in the near future, with the goal of assessing the importance of rare variants in complex diseases. The discovery of new disease susceptibility genes requires powerful statistical methods for rare variant analysis. The low frequency and the expected large number of such variants pose great difficulties for the analysis of these data. We propose here a robust and powerful testing strategy to study the role rare variants may play in affecting susceptibility to complex traits. The strategy is based on assessing whether rare variants in a genetic region collectively occur at significantly higher frequencies in cases compared with controls (or vice versa). A main feature of the proposed methodology is that, although it is an overall test assessing a possibly large number of rare variants simultaneously, the disease variants can be both protective and risk variants, with moderate decreases in statistical power when both types of variants are present. Using simulations, we show that this approach can be powerful under complex and general disease models, as well as in larger genetic regions where the proportion of disease susceptibility variants may be small. Comparisons with previously published tests on simulated data show that the proposed approach can have better power than the existing methods. An application to a recently published study on Type-1 Diabetes finds rare variants in gene IFIH1 to be protective against Type-1 Diabetes.     

Identification of Rare Causal Variants in Sequence-Based Studies: Methods and Applications to VPS13B,a Gene Involved in Cohen Syndrome and Autism

Pinpointing the small number of causal variants among the abundant naturally occurring genetic variation is a difficult challenge, but a crucial one for understanding precise molecular mechanisms of disease and follow-up functional studies. We propose and investigate two complementary statistical approaches for identification of rare causal variants in sequencing studies: a backward elimination procedure based on groupwise association tests, and a hierarchical approach that can integrate sequencing data with diverse functional and evolutionary conservation annotations for individual variants. Using simulations, we show that incorporation of multiple bioinformatic predictors of deleteriousness, such as PolyPhen-2, SIFT and GERP++ scores, can improve the power to discover truly causal variants. As proof of principle, we apply the proposed methods to VPS13B, a gene mutated in the rare neurodevelopmental disorder called Cohen syndrome, and recently reported with recessive variants in autism. We identify a small set of promising candidates for causal variants, including two loss-of-function variants and a rare, homozygous probably-damaging variant that could contribute to autism risk.     

A Novel Support Vector Machine-Based Approach for Rare Variant Detection

Advances in next-generation sequencing technologies have enabled the identification of multiple rare single nucleotide polymorphisms involved in diseases or traits. Several strategies for identifying rare variants that contribute to disease susceptibility have recently been proposed. An important feature of many of these statistical methods is the pooling or collapsing of multiple rare single nucleotide variants to achieve a reasonably high frequency and effect. However, if the pooled rare variants are associated with the trait in different directions, then the pooling may weaken the signal, thereby reducing its statistical power. In the present paper, we propose a backward support vector machine (BSVM)-based variant selection procedure to identify informative disease-associated rare variants. In the selection procedure, the rare variants are weighted and collapsed according to their positive or negative associations with the disease, which may be associated with common variants and rare variants with protective, deleterious, or neutral effects. This nonparametric variant selection procedure is able to account for confounding factors and can also be adopted in other regression frameworks. The results of a simulation study and a data example show that the proposed BSVM approach is more powerful than four other approaches under the considered scenarios, while maintaining valid type I errors.     

A Protein Domain and Family Based Approach to Rare Variant Association Analysis

BackgroundIt has become common practice to analyse large scale sequencing data with statistical approaches based around the aggregation of rare variants within the same gene. We applied a novel approach to rare variant analysis by collapsing variants together using protein domain and family coordinates, regarded to be a more discrete definition of a biologically functional unit.MethodsUsing Pfam definitions, we collapsed rare variants (Minor Allele Frequency ≤ 1%) together in three different ways 1) variants within single genomic regions which map to individual protein domains 2) variants within two individual protein domain regions which are predicted to be responsible for a protein-protein interaction 3) all variants within combined regions from multiple genes responsible for coding the same protein domain (i.e. protein families). A conventional collapsing analysis using gene coordinates was also undertaken for comparison. We used UK10K sequence data and investigated associations between regions of variants and lipid traits using the sequence kernel association test (SKAT).ResultsWe observed no strong evidence of association between regions of variants based on Pfam domain definitions and lipid traits. Quantile-Quantile plots illustrated that the overall distributions of p-values from the protein domain analyses were comparable to that of a conventional gene-based approach. Deviations from this distribution suggested that collapsing by either protein domain or gene definitions may be favourable depending on the trait analysed.ConclusionWe have collapsed rare variants together using protein domain and family coordinates to present an alternative approach over collapsing across conventionally used gene-based regions. Although no strong evidence of association was detected in these analyses, future studies may still find value in adopting these approaches to detect previously unidentified association signals.     

Demography and the Age of Rare Variants

Large whole-genome sequencing projects have provided access to much rare variation in human populations, which is highly informative about population structure and recent demography. Here, we show how the age of rare variants can be estimated from patterns of haplotype sharing and how these ages can be related to historical relationships between populations. We investigate the distribution of the age of variants occurring exactly twice ( variants) in a worldwide sample sequenced by the 1000 Genomes Project, revealing enormous variation across populations. The median age of haplotypes carrying variants is 50 to 160 generations across populations within Europe or Asia, and 170 to 320 generations within Africa. Haplotypes shared between continents are much older with median ages for haplotypes shared between Europe and Asia ranging from 320 to 670 generations. The distribution of the ages of haplotypes is informative about their demography, revealing recent bottlenecks, ancient splits, and more modern connections between populations. We see the effect of selection in the observation that functional variants are significantly younger than nonfunctional variants of the same frequency. This approach is relatively insensitive to mutation rate and complements other nonparametric methods for demographic inference.     

Rare Variant Association Testing by Adaptive Combination of P-values

With the development of next-generation sequencing technology, there is a great demand for powerful statistical methods to detect rare variants (minor allele frequencies (MAFs)<1%) associated with diseases. Testing for each variant site individually is known to be underpowered, and therefore many methods have been proposed to test for the association of a group of variants with phenotypes, by pooling signals of the variants in a chromosomal region. However, this pooling strategy inevitably leads to the inclusion of a large proportion of neutral variants, which may compromise the power of association tests. To address this issue, we extend the -MidP method (Cheung et al., 2012, Genet Epidemiol 36: 675–685) and propose an approach (named ‘adaptive combination of P-values for rare variant association testing’, abbreviated as ‘ADA’) that adaptively combines per-site P-values with the weights based on MAFs. Before combining P-values, we first imposed a truncation threshold upon the per-site P-values, to guard against the noise caused by the inclusion of neutral variants. This ADA method is shown to outperform popular burden tests and non-burden tests under many scenarios. ADA is recommended for next-generation sequencing data analysis where many neutral variants may be included in a functional region.     

Testing for an unusual distribution of rare variants

Technological advances make it possible to use high-throughput sequencing as a primary discovery tool of medical genetics, specifically for assaying rare variation. Still this approach faces the analytic challenge that the influence of very rare variants can only be evaluated effectively as a group. A further complication is that any given rare variant could have no effect, could increase risk, or could be protective. We propose here the C-alpha test statistic as a novel approach for testing for the presence of this mixture of effects across a set of rare variants. Unlike existing burden tests, C-alpha, by testing the variance rather than the mean, maintains consistent power when the target set contains both risk and protective variants. Through simulations and analysis of case/control data, we demonstrate good power relative to existing methods that assess the burden of rare variants in individuals.     

Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies

We propose in this paper a unified approach for testing the association between rare variants and phenotypes in sequencing association studies. This approach maximizes power by adaptively using the data to optimally combine the burden test and the nonburden sequence kernel association test (SKAT). Burden tests are more powerful when most variants in a region are causal and the effects are in the same direction, whereas SKAT is more powerful when a large fraction of the variants in a region are noncausal or the effects of causal variants are in different directions. The proposed unified test maintains the power in both scenarios. We show that the unified test corresponds to the optimal test in an extended family of SKAT tests, which we refer to as SKAT-O. The second goal of this paper is to develop a small-sample adjustment procedure for the proposed methods for the correction of conservative type I error rates of SKAT family tests when the trait of interest is dichotomous and the sample size is small. Both small-sample-adjusted SKAT and the optimal unified test (SKAT-O) are computationally efficient and can easily be applied to genome-wide sequencing association studies. We evaluate the finite sample performance of the proposed methods using extensive simulation studies and illustrate their application using the acute-lung-injury exome-sequencing data of the National Heart, Lung, and Blood Institute Exome Sequencing Project.     

Low-pass genome-wide sequencing and variant inference using identity-by-descent in an isolated human population

Whole-genome sequencing in an isolated population with few founders directly ascertains variants from the population bottleneck that may be rare elsewhere. In such populations, shared haplotypes allow imputation of variants in unsequenced samples without resorting to complex statistical methods as in studies of outbred cohorts. We focus on an isolated population cohort from the Pacific Island of Kosrae, Micronesia, where we previously collected SNP array and rich phenotype data for the majority of the population. We report identification of long regions with haplotypes co-inherited between pairs of individuals and methodology to leverage such shared genetic content for imputation. Our estimates show that sequencing as few as 40 personal genomes allows for inference in up to 60% of the 3000-person cohort at the average locus. We ascertained a pilot data set of whole-genome sequences from seven Kosraean individuals, with average 5× coverage. This assay identified 5,735,306 unique sites of which 1,212,831 were previously unknown. Additionally, these variants are unusually enriched for alleles that are rare in other populations when compared to geographic neighbors (published Korean genome SJK). We used the presence of shared haplotypes between the seven Kosraen individuals to estimate expected imputation accuracy of known and novel homozygous variants at 99.6% and 97.3%, respectively. This study presents whole-genome analysis of a homogenous isolate population with emphasis on optimal rare variant inference.     

Extending rare-variant testing strategies: analysis of noncoding sequence and imputed genotypes

Next Generation Sequencing Technology has revolutionized our ability to study the contribution of rare genetic variation to heritable traits. However, existing single-marker association tests are underpowered for detecting rare risk variants. A more powerful approach involves pooling methods that combine multiple rare variants from the same gene into a single test statistic. Proposed pooling methods can be limited because they generally assume high-quality genotypes derived from deep-coverage sequencing, which may not be available. In this paper, we consider an intuitive and computationally efficient pooling statistic, the cumulative minor-allele test (CMAT). We assess the performance of the CMAT and other pooling methods on datasets simulated with population genetic models to contain realistic levels of neutral variation. We consider study designs ranging from exon-only to whole-gene analyses that contain noncoding variants. For all study designs, the CMAT achieves power comparable to that of previously proposed methods. We then extend the CMAT to probabilistic genotypes and describe application to low-coverage sequencing and imputation data. We show that augmenting sequence data with imputed samples is a practical method for increasing the power of rare-variant studies. We also provide a method of controlling for confounding variables such as population stratification. Finally, we demonstrate that our method makes it possible to use external imputation templates to analyze rare variants imputed into existing GWAS datasets. As proof of principle, we performed a CMAT analysis of more than 8 million SNPs that we imputed into the GAIN psoriasis dataset by using haplotypes from the 1000 Genomes Project.     

Inferring the Joint Demographic History of Multiple Populations from Multidimensional SNP Frequency Data

Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic variants within and between populations. For candidate models we numerically compute the expected spectrum using a diffusion approximation to the one-locus, two-allele Wright-Fisher process, involving up to three simultaneous populations. Our approach is a composite likelihood scheme, since linkage between neutral loci alters the variance but not the expectation of the frequency spectrum. We thus use bootstraps incorporating linkage to estimate uncertainties for parameters and significance values for hypothesis tests. Our method can also incorporate selection on single sites, predicting the joint distribution of selected alleles among populations experiencing a bevy of evolutionary forces, including expansions, contractions, migrations, and admixture. We model human expansion out of Africa and the settlement of the New World, using 5 Mb of noncoding DNA resequenced in 68 individuals from 4 populations (YRI, CHB, CEU, and MXL) by the Environmental Genome Project. We infer divergence between West African and Eurasian populations 140 thousand years ago (95% confidence interval: 40–270 kya). This is earlier than other genetic studies, in part because we incorporate migration. We estimate the European (CEU) and East Asian (CHB) divergence time to be 23 kya (95% c.i.: 17–43 kya), long after archeological evidence places modern humans in Europe. Finally, we estimate divergence between East Asians (CHB) and Mexican-Americans (MXL) of 22 kya (95% c.i.: 16.3–26.9 kya), and our analysis yields no evidence for subsequent migration. Furthermore, combining our demographic model with a previously estimated distribution of selective effects among newly arising amino acid mutations accurately predicts the frequency spectrum of nonsynonymous variants across three continental populations (YRI, CHB, CEU).     

Associating Multivariate Quantitative Phenotypes with Genetic Variants in Family Samples with a Novel Kernel Machine Regression Method

The recent development of sequencing technology allows identification of association between the whole spectrum of genetic variants and complex diseases. Over the past few years, a number of association tests for rare variants have been developed. Jointly testing for association between genetic variants and multiple correlated phenotypes may increase the power to detect causal genes in family-based studies, but familial correlation needs to be appropriately handled to avoid an inflated type I error rate. Here we propose a novel approach for multivariate family data using kernel machine regression (denoted as MF-KM) that is based on a linear mixed-model framework and can be applied to a large range of studies with different types of traits. In our simulation studies, the usual kernel machine test has inflated type I error rates when applied directly to familial data, while our proposed MF-KM method preserves the expected type I error rates. Moreover, the MF-KM method has increased power compared to methods that either analyze each phenotype separately while considering family structure or use only unrelated founders from the families. Finally, we illustrate our proposed methodology by analyzing whole-genome genotyping data from a lung function study.     

Epistatic Module Detection for Case-Control Studies: A Bayesian Model with a Gibbs Sampling Strategy

The detection of epistatic interactive effects of multiple genetic variants on the susceptibility of human complex diseases is a great challenge in genome-wide association studies (GWAS). Although methods have been proposed to identify such interactions, the lack of an explicit definition of epistatic effects, together with computational difficulties, makes the development of new methods indispensable. In this paper, we introduce epistatic modules to describe epistatic interactive effects of multiple loci on diseases. On the basis of this notion, we put forward a Bayesian marker partition model to explain observed case-control data, and we develop a Gibbs sampling strategy to facilitate the detection of epistatic modules. Comparisons of the proposed approach with three existing methods on seven simulated disease models demonstrate the superior performance of our approach. When applied to a genome-wide case-control data set for Age-related Macular Degeneration (AMD), the proposed approach successfully identifies two known susceptible loci and suggests that a combination of two other loci—one in the gene SGCD and the other in SCAPER—is associated with the disease. Further functional analysis supports the speculation that the interaction of these two genetic variants may be responsible for the susceptibility of AMD. When applied to a genome-wide case-control data set for Parkinson's disease, the proposed method identifies seven suspicious loci that may contribute independently to the disease.     

Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data

Although whole-genome association studies using tagSNPs are a powerful approach for detecting common variants, they are underpowered for detecting associations with rare variants. Recent studies have demonstrated that common diseases can be due to functional variants with a wide spectrum of allele frequencies, ranging from rare to common. An effective way to identify rare variants is through direct sequencing. The development of cost-effective sequencing technologies enables association studies to use sequence data from candidate genes and, in the future, from the entire genome. Although methods used for analysis of common variants are applicable to sequence data, their performance might not be optimal. In this study, it is shown that the collapsing method, which involves collapsing genotypes across variants and applying a univariate test, is powerful for analyzing rare variants, whereas multivariate analysis is robust against inclusion of noncausal variants. Both methods are superior to analyzing each variant individually with univariate tests. In order to unify the advantages of both collapsing and multiple-marker tests, we developed the Combined Multivariate and Collapsing (CMC) method and demonstrated that the CMC method is both powerful and robust. The CMC method can be applied to either candidate-gene or whole-genome sequence data.     

Three ways of combining genotyping and resequencing in case-control association studies

We describe three statistical results that we have found to be useful in case-control genetic association testing. All three involve combining the discovery of novel genetic variants, usually by sequencing, with genotyping methods that recognize previously discovered variants. We first consider expanding the list of known variants by concentrating variant-discovery in cases. Although the naive inclusion of cases-only sequencing data would create a bias, we show that some sequencing data may be retained, even if controls are not sequenced. Furthermore, for alleles of intermediate frequency, cases-only sequencing with bias-correction entails little if any loss of power, compared to dividing the same sequencing effort among cases and controls. Secondly, we investigate more strongly focused variant discovery to obtain a greater enrichment for disease-related variants. We show how case status, family history, and marker sharing enrich the discovery set by increments that are multiplicative with penetrance, enabling the preferential discovery of high-penetrance variants. A third result applies when sequencing is the primary means of counting alleles in both cases and controls, but a supplementary pooled genotyping sample is used to identify the variants that are very rare. We show that this raises no validity issues, and we evaluate a less expensive and more adaptive approach to judging rarity, based on group-specific variants. We demonstrate the important and unusual caveat that this method requires equal sample sizes for validity. These three results can be used to more efficiently detect the association of rare genetic variants with disease.     

A revised indirect estimate of mutation rates in Amerindians

We have previously raised the possibility that the mutation rate resulting in rare electrophoretic variants is higher in tribal/tropical-dwelling/nonindustrialized societies than in civilized/temperate-dwelling/industrialized societies. Here, we report the results of examining 11 additional proteins for the occurrence of rare electrophoretic variants in 10 Amerindian tribes, for a total of 8,968 determinations and a total of 17,648 locus tests. When these data are combined with the results of all our previous similar studies of Amerindians, a total of 272,298 polypeptides, the products of 43 different loci, have been examined for the occurrence of rare electrophoretic variants. On the assumption that these variants are maintained by mutation pressure and are essentially neutral in their phenotypic effects, we have calculated by three different approaches that it requires an average mutation rate of 1.3 X 10(-5)/locus per generation to maintain the observed variant frequency. Concurrently, we are reporting elsewhere that a direct estimate of the mutation rate resulting in electromorphs in various studies of civilized industrialized populations is 0.3 X 10(-5)/locus per generation. Although this difference appears to have statistical significance, the nonquantifiable uncertainties to both approaches are such that our enthusiasm for a true difference in mutation rates between the two types of populations has diminished. However, even the lower of these estimates, when corrected for all the types of genetic variation that electrophoresis does not detect, implies total locus and gametic mutation rates well above those which in the past have dominated genetic thinking.     

Improved detection of rare genetic variants for diseases

Technology advances have promoted gene-based sequencing studies with the aim of identifying rare mutations responsible for complex diseases. A complication in these types of association studies is that the vast majority of non-synonymous mutations are believed to be neutral to phenotypes. It is thus critical to distinguish potential causative variants from neutral variation before performing association tests. In this study, we used existing predicting algorithms to predict functional amino acid substitutions, and incorporated that information into association tests. Using simulations, we comprehensively studied the effects of several influential factors, including the sensitivity and specificity of functional variant predictions, number of variants, and proportion of causative variants, on the performance of association tests. Our results showed that incorporating information regarding functional variants obtained from existing prediction algorithms improves statistical power under certain conditions, particularly when the proportion of causative variants is moderate. The application of the proposed tests to a real sequencing study confirms our conclusions. Our work may help investigators who are planning to pursue gene-based sequencing studies.     

Characteristics of Neutral and Deleterious Protein-Coding Variation among Individuals and Populations

Whole-genome and exome data sets continue to be produced at a frenetic pace, resulting in massively large catalogs of human genomic variation. However, a clear picture of the characteristics and patterns of neutral and deleterious variation within and between populations has yet to emerge, given that recent large-scale sequencing studies have often emphasized different aspects of the data and sometimes appear to have conflicting conclusions. Here, we comprehensively studied characteristics of protein-coding variation in high-coverage exome sequence data from 6,515 European American (EA) and African American (AA) individuals. We developed an unbiased approach to identify putatively deleterious variants and investigated patterns of neutral and deleterious single-nucleotide variants and alleles between individuals and populations. We show that there are substantial differences in the composition of genotypes between EA and AA populations and that small but statistically significant differences exist in the average number of deleterious alleles carried by EA and AA individuals. Furthermore, we performed extensive simulations to delineate the temporal dynamics of deleterious alleles for a broad range of demographic models and use these data to inform the interpretation of empirical patterns of deleterious variation. Finally, we illustrate that the effects of demographic perturbations, such as bottlenecks and expansions, often manifest in opposing patterns of neutral and deleterious variation depending on whether the focus is on populations or individuals. Our results clarify seemingly disparate empirical characteristics of protein-coding variation and provide substantial insights into how natural selection and demographic history have patterned neutral and deleterious variation within and between populations.