Bayesian Detection of Causal Rare Variants under Posterior Consistency

Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variants can be consistently identified by them in the small--large- situation. We develop a new Bayesian method, the so-called Bayesian Rare Variant Detector (BRVD), to tackle this problem. The new method simultaneously addresses two issues: (i) (Global association test) Are there any of the variants associated with the disease, and (ii) (Causal variant detection) Which variants, if any, are driving the association. The BRVD ensures the causal rare variants to be consistently identified in the small--large- situation by imposing some appropriate prior distributions on the model and model specific parameters. The numerical results indicate that the BRVD is more powerful for testing the global association than the existing methods, such as the combined multivariate and collapsing test, weighted sum statistic test, RARECOVER, sequence kernel association test, and Bayesian risk index, and also more powerful for identification of causal rare variants than the Bayesian risk index method. The BRVD has also been successfully applied to the Early-Onset Myocardial Infarction (EOMI) Exome Sequence Data. It identified a few causal rare variants that have been verified in the literature.     

Detecting rare variant associations by identity-by-descent mapping in case-control studies

Identity-by-descent (IBD) mapping tests whether cases share more segments of IBD around a putative causal variant than do controls. These segments of IBD can be accurately detected from genome-wide SNP data. We investigate the power of IBD mapping relative to that of SNP association testing for genome-wide case-control SNP data. Our focus is particularly on rare variants, as these tend to be more recent and hence more likely to have recent shared ancestry. We simulate data from both large and small populations and find that the relative performance of IBD mapping and SNP association testing depends on population demographic history and the strength of selection against causal variants. We also present an IBD mapping analysis of a type 1 diabetes data set. In those data we find that we can detect association only with the HLA region using IBD mapping. Overall, our results suggest that IBD mapping may have higher power than association analysis of SNP data when multiple rare causal variants are clustered within a gene. However, for outbred populations, very large sample sizes may be required for genome-wide significance unless the causal variants have strong effects.     

Association Testing of Clustered Rare Causal Variants in Case-Control Studies

Biological evidence suggests that multiple causal variants in a gene may cluster physically. Variants within the same protein functional domain or gene regulatory element would locate in close proximity on the DNA sequence. However, spatial information of variants is usually not used in current rare variant association analyses. We here propose a clustering method (abbreviated as “CLUSTER”), which is extended from the adaptive combination of P-values. Our method combines the association signals of variants that are more likely to be causal. Furthermore, the statistic incorporates the spatial information of variants. With extensive simulations, we show that our method outperforms several commonly-used methods in many scenarios. To demonstrate its use in real data analyses, we also apply this CLUSTER test to the Dallas Heart Study data. CLUSTER is among the best methods when the effects of causal variants are all in the same direction. As variants located in close proximity are more likely to have similar impact on disease risk, CLUSTER is recommended for association testing of clustered rare causal variants in case-control studies.     

Prioritizing genetic variants for causality on the basis of preferential linkage disequilibrium

To date, the widely used genome-wide association studies (GWASs) of the human genome have reported thousands of variants that are significantly associated with various human traits. However, in the vast majority of these cases, the causal variants responsible for the observed associations remain unknown. In order to facilitate the identification of causal variants, we designed a simple computational method called the "preferential linkage disequilibrium (LD)" approach, which follows the variants discovered by GWASs to pinpoint the causal variants, even if they are rare compared with the discovery variants. The approach is based on the hypothesis that the GWAS-discovered variant is better at tagging the causal variants than are most other variants evaluated in the original GWAS. Applying the preferential LD approach to the GWAS signals of five human traits for which the causal variants are already known, we successfully placed the known causal variants among the top ten candidates in the majority of these cases. Application of this method to additional GWASs, including those of hepatitis C virus treatment response, plasma levels of clotting factors, and late-onset Alzheimer disease, has led to the identification of a number of promising candidate causal variants. This method represents a useful tool for delineating causal variants by bringing together GWAS signals and the rapidly accumulating variant data from next-generation sequencing.     

Predicting signatures of "synthetic associations" and "natural associations" from empirical patterns of human genetic variation

Genome-wide association studies (GWAS) have in recent years discovered thousands of associated markers for hundreds of phenotypes. However, associated loci often only explain a relatively small fraction of heritability and the link between association and causality has yet to be uncovered for most loci. Rare causal variants have been suggested as one scenario that may partially explain these shortcomings. Specifically, Dickson et al. recently reported simulations of rare causal variants that lead to association signals of common, tag single nucleotide polymorphisms, dubbed "synthetic associations". However, an open question is what practical implications synthetic associations have for GWAS. Here, we explore the signatures exhibited by such "synthetic associations" and their implications based on patterns of genetic variation observed in human populations, thus accounting for human evolutionary history -a force disregarded in previous simulation studies. This is made possible by human population genetic data from HapMap 3 consisting of both resequencing and array-based genotyping data for the same set of individuals from multiple populations. We report that synthetic associations tend to be further away from the underlying risk alleles compared to "natural associations" (i.e. associations due to underlying common causal variants), but to a much lesser extent than previously predicted, with both the age and the effect size of the risk allele playing a part in this phenomenon. We find that while a synthetic association has a lower probability of capturing causal variants within its linkage disequilibrium block, sequencing around the associated variant need not extend substantially to have a high probability of capturing at least one causal variant. We also show that the minor allele frequency of synthetic associations is lower than of natural associations for most, but not all, loci that we explored. Finally, we find the variance in associated allele frequency to be a potential indicator of synthetic associations.     

Increasing power of groupwise association test with likelihood ratio test

Sequencing studies have been discovering a numerous number of rare variants, allowing the identification of the effects of rare variants on disease susceptibility. As a method to increase the statistical power of studies on rare variants, several groupwise association tests that group rare variants in genes and detect associations between genes and diseases have been proposed. One major challenge in these methods is to determine which variants are causal in a group, and to overcome this challenge, previous methods used prior information that specifies how likely each variant is causal. Another source of information that can be used to determine causal variants is the observed data because case individuals are likely to have more causal variants than control individuals. In this article, we introduce a likelihood ratio test (LRT) that uses both data and prior information to infer which variants are causal and uses this finding to determine whether a group of variants is involved in a disease. We demonstrate through simulations that LRT achieves higher power than previous methods. We also evaluate our method on mutation screening data of the susceptibility gene for ataxia telangiectasia, and show that LRT can detect an association in real data. To increase the computational speed of our method, we show how we can decompose the computation of LRT, and propose an efficient permutation test. With this optimization, we can efficiently compute an LRT statistic and its significance at a genome-wide level. The software for our method is publicly available at http://genetics.cs.ucla.edu/rarevariants .     

Dissection of a Complex Disease Susceptibility Region Using a Bayesian Stochastic Search Approach to Fine Mapping

Identification of candidate causal variants in regions associated with risk of common diseases is complicated by linkage disequilibrium (LD) and multiple association signals. Nonetheless, accurate maps of these variants are needed, both to fully exploit detailed cell specific chromatin annotation data to highlight disease causal mechanisms and cells, and for design of the functional studies that will ultimately be required to confirm causal mechanisms. We adapted a Bayesian evolutionary stochastic search algorithm to the fine mapping problem, and demonstrated its improved performance over conventional stepwise and regularised regression through simulation studies. We then applied it to fine map the established multiple sclerosis (MS) and type 1 diabetes (T1D) associations in the IL-2RA (CD25) gene region. For T1D, both stepwise and stochastic search approaches identified four T1D association signals, with the major effect tagged by the single nucleotide polymorphism, rs12722496. In contrast, for MS, the stochastic search found two distinct competing models: a single candidate causal variant, tagged by rs2104286 and reported previously using stepwise analysis; and a more complex model with two association signals, one of which was tagged by the major T1D associated rs12722496 and the other by rs56382813. There is low to moderate LD between rs2104286 and both rs12722496 and rs56382813 (r² ≃ 0:3) and our two SNP model could not be recovered through a forward stepwise search after conditioning on rs2104286. Both signals in the two variant model for MS affect CD25 expression on distinct subpopulations of CD4⁺ T cells, which are key cells in the autoimmune process. The results support a shared causal variant for T1D and MS. Our study illustrates the benefit of using a purposely designed model search strategy for fine mapping and the advantage of combining disease and protein expression data.     

Imputation-based analysis of association studies: candidate regions and quantitative traits

We introduce a new framework for the analysis of association studies, designed to allow untyped variants to be more effectively and directly tested for association with a phenotype. The idea is to combine knowledge on patterns of correlation among SNPs (e.g., from the International HapMap project or resequencing data in a candidate region of interest) with genotype data at tag SNPs collected on a phenotyped study sample, to estimate ("impute") unmeasured genotypes, and then assess association between the phenotype and these estimated genotypes. Compared with standard single-SNP tests, this approach results in increased power to detect association, even in cases in which the causal variant is typed, with the greatest gain occurring when multiple causal variants are present. It also provides more interpretable explanations for observed associations, including assessing, for each SNP, the strength of the evidence that it (rather than another correlated SNP) is causal. Although we focus on association studies with quantitative phenotype and a relatively restricted region (e.g., a candidate gene), the framework is applicable and computationally practical for whole genome association studies. Methods described here are implemented in a software package, Bim-Bam, available from the Stephens Lab website http://stephenslab.uchicago.edu/software.html.     

A flexible Bayesian framework for modeling haplotype association with disease, allowing for dominance effects of the underlying causative variants

Multilocus analysis of single-nucleotide-polymorphism (SNP) haplotypes may provide evidence of association with disease, even when the individual loci themselves do not. Haplotype-based methods are expected to outperform single-SNP analyses because (i) common genetic variation can be structured into haplotypes within blocks of strong linkage disequilibrium and (ii) the functional properties of a protein are determined by the linear sequence of amino acids corresponding to DNA variation on a haplotype. Here, I propose a flexible Bayesian framework for modeling haplotype association with disease in population-based studies of candidate genes or small candidate regions. I employ a Bayesian partition model to describe the correlation between marker-SNP haplotypes and causal variants at the underlying functional polymorphism(s). Under this model, haplotypes are clustered according to their similarity, in terms of marker-SNP allele matches, which is used as a proxy for recent shared ancestry. Haplotypes within a cluster are then assigned the same probability of carrying a causal variant at the functional polymorphism(s). In this way, I can account for the dominance effect of causal variants, here corresponding to any deviation from a multiplicative contribution to disease risk. The results of a detailed simulation study demonstrate that there is minimal cost associated with modeling these dominance effects, with substantial gains in power over haplotype-based methods that do not incorporate clustering and that assume a multiplicative model of disease risks.     

Leveraging Prior Information to Detect Causal Variants via Multi-Variant Regression

Although many methods are available to test sequence variants for association with complex diseases and traits, methods that specifically seek to identify causal variants are less developed. Here we develop and evaluate a Bayesian hierarchical regression method that incorporates prior information on the likelihood of variant causality through weighting of variant effects. By simulation studies using both simulated and real sequence variants, we compared a standard single variant test for analyzing variant-disease association with the proposed method using different weighting schemes. We found that by leveraging linkage disequilibrium of variants with known GWAS signals and sequence conservation (phastCons), the proposed method provides a powerful approach for detecting causal variants while controlling false positives.     

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.     

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.     

Quantifying the underestimation of relative risks from genome-wide association studies

Genome-wide association studies (GWAS) have identified hundreds of associated loci across many common diseases. Most risk variants identified by GWAS will merely be tags for as-yet-unknown causal variants. It is therefore possible that identification of the causal variant, by fine mapping, will identify alleles with larger effects on genetic risk than those currently estimated from GWAS replication studies. We show that under plausible assumptions, whilst the majority of the per-allele relative risks (RR) estimated from GWAS data will be close to the true risk at the causal variant, some could be considerable underestimates. For example, for an estimated RR in the range 1.2-1.3, there is approximately a 38% chance that it exceeds 1.4 and a 10% chance that it is over 2. We show how these probabilities can vary depending on the true effects associated with low-frequency variants and on the minor allele frequency (MAF) of the most associated SNP. We investigate the consequences of the underestimation of effect sizes for predictions of an individual's disease risk and interpret our results for the design of fine mapping experiments. Although these effects mean that the amount of heritability explained by known GWAS loci is expected to be larger than current projections, this increase is likely to explain a relatively small amount of the so-called "missing" heritability.     

Accounting for a quantitative trait locus for plasma triglyceride levels: utilization of variants in multiple genes

Background

For decades, research efforts have tried to uncover the underlying genetic basis of human susceptibility to a variety of diseases. Linkage studies have resulted in highly replicated findings and helped identify quantitative trait loci (QTL) for many complex traits; however identification of specific alleles accounting for linkage remains elusive. The purpose of this study was to determine whether with a sufficient number of variants a linkage signal can be fully explained.

Method

We used comprehensive fine-mapping using a dense set of single nucleotide polymorphisms (SNPs) across the entire quantitative trait locus (QTL) on human chromosome 7q36 linked to plasma triglyceride levels. Analyses included measured genotype and combined linkage association analyses.

Results

Screening this linkage region, we found an over representation of nominally significant associations in five genes (MLL3, DPP6, PAXIP1, HTR5A, INSIG1). However, no single genetic variant was sufficient to account for the linkage. On the other hand, multiple variants capturing the variation in these five genes did account for the linkage at this locus. Permutation analyses suggested that this reduction in LOD score was unlikely to have occurred by chance (p = 0.008).

Discussion

With recent findings, it has become clear that most complex traits are influenced by a large number of genetic variants each contributing only a small percentage to the overall phenotype. We found that with a sufficient number of variants, the linkage can be fully explained. The results from this analysis suggest that perhaps the failure to identify causal variants for linkage peaks may be due to multiple variants under the linkage peak with small individual effect, rather than a single variant of large effect.     

Resequencing Three Candidate Genes for Major Depressive Disorder in a Dutch Cohort

Major depressive disorder (MDD) is a psychiatric disorder, characterized by periods of low mood of more than two weeks, loss of interest in normally enjoyable activities and behavioral changes. MDD is a complex disorder and does not have a single genetic cause. In 2009 a genome wide association study (GWAS) was performed on the Dutch GAIN-MDD cohort. Many of the top signals of this GWAS mapped to a region spanning the gene PCLO, and the non-synonymous coding single nucleotide polymorphism (SNP) rs2522833 in the PCLO gene became genome wide significant after post-hoc analysis. We performed resequencing of PCLO, GRM7, and SLC6A4 in 50 control samples from the GAIN-MDD cohort, to detect new genomic variants. Subsequently, we genotyped these variants in the entire GAIN-MDD cohort and performed association analysis to investigate if rs2522833 is the causal variant or simply in linkage disequilibrium with a more associated variant. GRM7 and SLC6A4 are both candidate genes for MDD from literature. We aimed to gather more evidence that rs2522833 is indeed the causal variant in the GAIN-MDD cohort or to find a previously undetected common variant in either PCLO, GRM7, or SLC6A4 with a higher association in this cohort. After next generation sequencing and association analysis we excluded the possibility of an undetected common variant to be more associated. For neither PCLO nor GRM7 we found a more associated variant. For SLC6A4, we found a new SNP that showed a lower P-value (P = 0.07) than in the GAIN-MDD GWAS (P = 0.09). However, no evidence for genome-wide significance was found. Although we did not take into account rare variants, we conclude that our results provide further support for the hypothesis that the non-synonymous coding SNP rs2522833 in the PCLO gene is indeed likely to be the causal variant in the GAIN-MDD cohort.     

Association Testing Strategy for Data from Dense Marker Panels

Genome wide association studies have been usually analyzed in a univariate manner. The commonly used univariate tests have one degree of freedom and assume an additive mode of inheritance. The experiment-wise significance of these univariate statistics is obtained by adjusting for multiple testing. Next generation sequencing studies, which assay 10-20 million variants, are beginning to come online. For these studies, the strategy of additive univariate testing and multiple testing adjustment is likely to result in a loss of power due to (1) the substantial multiple testing burden and (2) the possibility of a non-additive causal mode of inheritance. To reduce the power loss we propose: a new method (1) to summarize in a single statistic the strength of the association signals coming from all not-very-rare variants in a linkage disequilibrium block and (2) to incorporate, in any linkage disequilibrium block statistic, the strength of the association signals under multiple modes of inheritance. The proposed linkage disequilibrium block test consists of the sum of squares of nominally significant univariate statistics. We compare the performance of this method to the performance of existing linkage disequilibrium block/gene-based methods. Simulations show that (1) extending methods to combine testing for multiple modes of inheritance leads to substantial power gains, especially for a recessive mode of inheritance, and (2) the proposed method has a good overall performance. Based on simulation results, we provide practical advice on choosing suitable methods for applied analyses.     

General Framework for Meta-analysis of Rare Variants in Sequencing Association Studies

We propose a general statistical framework for meta-analysis of gene- or region-based multimarker rare variant association tests in sequencing association studies. In genome-wide association studies, single-marker meta-analysis has been widely used to increase statistical power by combining results via regression coefficients and standard errors from different studies. In analysis of rare variants in sequencing studies, region-based multimarker tests are often used to increase power. We propose meta-analysis methods for commonly used gene- or region-based rare variants tests, such as burden tests and variance component tests. Because estimation of regression coefficients of individual rare variants is often unstable or not feasible, the proposed method avoids this difficulty by calculating score statistics instead that only require fitting the null model for each study and then aggregating these score statistics across studies. Our proposed meta-analysis rare variant association tests are conducted based on study-specific summary statistics, specifically score statistics for each variant and between-variant covariance-type (linkage disequilibrium) relationship statistics for each gene or region. The proposed methods are able to incorporate different levels of heterogeneity of genetic effects across studies and are applicable to meta-analysis of multiple ancestry groups. We show that the proposed methods are essentially as powerful as joint analysis by directly pooling individual level genotype data. We conduct extensive simulations to evaluate the performance of our methods by varying levels of heterogeneity across studies, and we apply the proposed methods to meta-analysis of rare variant effects in a multicohort study of the genetics of blood lipid levels.