Multiple SNP Set Analysis for Genome‐Wide Association Studies Through Bayesian Latent Variable Selection

The power of genome‐wide association studies (GWAS) for mapping complex traits with single‐SNP analysis (where SNP is single‐nucleotide polymorphism) may be undermined by modest SNP effect sizes, unobserved causal SNPs, correlation among adjacent SNPs, and SNP‐SNP interactions. Alternative approaches for testing the association between a single SNP set and individual phenotypes have been shown to be promising for improving the power of GWAS. We propose a Bayesian latent variable selection (BLVS) method to simultaneously model the joint association mapping between a large number of SNP sets and complex traits. Compared with single SNP set analysis, such joint association mapping not only accounts for the correlation among SNP sets but also is capable of detecting causal SNP sets that are marginally uncorrelated with traits. The spike‐and‐slab prior assigned to the effects of SNP sets can greatly reduce the dimension of effective SNP sets, while speeding up computation. An efficient Markov chain Monte Carlo algorithm is developed. Simulations demonstrate that BLVS outperforms several competing variable selection methods in some important scenarios.     

Semiparametric Bayesian variable selection for gene-environment interactions

Many complex diseases are known to be affected by the interactions between genetic variants and environmental exposures beyond the main genetic and environmental effects. Study of gene-environment (G×E) interactions is important for elucidating the disease etiology. Existing Bayesian methods for G×E interaction studies are challenged by the high-dimensional nature of the study and the complexity of environmental influences. Many studies have shown the advantages of penalization methods in detecting G×E interactions in “large p, small n” settings. However, Bayesian variable selection, which can provide fresh insight into G×E study, has not been widely examined. We propose a novel and powerful semiparametric Bayesian variable selection model that can investigate linear and nonlinear G×E interactions simultaneously. Furthermore, the proposed method can conduct structural identification by distinguishing nonlinear interactions from main-effects-only case within the Bayesian framework. Spike-and-slab priors are incorporated on both individual and group levels to identify the sparse main and interaction effects. The proposed method conducts Bayesian variable selection more efficiently than existing methods. Simulation shows that the proposed model outperforms competing alternatives in terms of both identification and prediction. The proposed Bayesian method leads to the identification of main and interaction effects with important implications in a high-throughput profiling study with high-dimensional SNP data.     

Bayesian variable selection using partially observed categorical prior information in fine-mapping association studies

Several methods have been proposed to allow functional genomic information to inform prior distributions in Bayesian fine-mapping case–control association studies. None of these methods allow the inclusion of partially observed functional genomic information. We use functional significance (FS) scores that combine information across multiple bioinformatics sources to inform our effect size prior distributions. These scores are not available for all single-nucleotide polymorphisms (SNPs) but by partitioning SNPs into naturally occurring FS score groups, we show how missing FS scores can easily be accommodated via finite mixtures of elicited priors. Most current approaches adopt a formal Bayesian variable selection approach and either limit the number of causal SNPs allowed or use approximations to avoid the need to explore the vast parameter space. We focus instead on achieving differential shrinkage of the effect sizes through prior scale mixtures of normals and use marginal posterior probability intervals to select candidate causal SNPs. We show via a simulation study how this approach can improve localisation of the causal SNPs compared to existing mutli-SNP fine-mapping methods. We also apply our approach to fine-mapping a region around the CASP8 gene using the iCOGS consortium breast cancer SNP data.     

Comparison of association mapping methods in a complex pedigreed population

Association mapping methods were compared using a simulation with a complex pedigree structure. The pedigree was simulated while keeping the present Danish Holstein population pedigree in view. A total of 15 quantitative trait loci (QTL) with varying effect sizes (10%, 5% and 2% of total genetic variance) were simulated. We compared the single‐marker test, haplotype‐based analysis, mixed model approach, and Bayesian analysis. The methods were compared for power, precision of location estimates, and type I error rates. Results found the best performance in a Bayesian method that included genetic background effects and simultaneously fitted all single‐nucleotide polymorphisms (SNPs) with a variable selection method. A mixed model analysis that fitted genetic background effects and tested one SNP at a time performed nearly as well as the Bayesian method. For the Bayesian method, it proved necessary to collect SNP signals in intervals, to avoid the scattering of a QTL signal over multiple neighboring SNPs. Methods not accounting for genetic background (full pedigree information) performed worse, and methods using haplotypes were considerably worse with a high false‐positive rate, probably due to the presence of low‐frequency haplotypes. It was necessary to account for full relationships among individuals to avoid excess false discovery. Although the methods were tested on a cattle pedigree, the results are applicable to any population with a complex pedigree structure. Genet. Epidemiol. 34: 455–462, 2010. © 2010 Wiley‐Liss, Inc.     

Finding factors influencing risk: comparing Bayesian stochastic search and standard variable selection methods applied to logistic regression models of cases and controls

When modeling the risk of a disease, the very act of selecting the factors to be included can heavily impact the results. This study compares the performance of several variable selection techniques applied to logistic regression. We performed realistic simulation studies to compare five methods of variable selection: (1) a confidence interval (CI) approach for significant coefficients, (2) backward selection, (3) forward selection, (4) stepwise selection, and (5) Bayesian stochastic search variable selection (SSVS) using both informed and uniformed priors. We defined our simulated diseases mimicking odds ratios for cancer risk found in the literature for environmental factors, such as smoking; dietary risk factors, such as fiber; genetic risk factors, such as XPD; and interactions. We modeled the distribution of our covariates, including correlation, after the reported empirical distributions of these risk factors. We also used a null data set to calibrate the priors of the Bayesian method and evaluate its sensitivity. Of the standard methods (95 per cent CI, backward, forward, and stepwise selection) the CI approach resulted in the highest average per cent of correct associations and the lowest average per cent of incorrect associations. SSVS with an informed prior had a higher average per cent of correct associations and a lower average per cent of incorrect associations than the CI approach. This study shows that the Bayesian methods offer a way to use prior information to both increase power and decrease false-positive results when selecting factors to model complex disease risk.     

A Bayesian hierarchical variable selection prior for pathway-based GWAS using summary statistics

While genome-wide association studies (GWASs) have been widely used to uncover associations between diseases and genetic variants, standard SNP-level GWASs often lack the power to identify SNPs that individually have a moderate effect size but jointly contribute to the disease. To overcome this problem, pathway-based GWASs methods have been developed as an alternative strategy that complements SNP-level approaches. We propose a Bayesian method that uses the generalized fused hierarchical structured variable selection prior to identify pathways associated with the disease using SNP-level summary statistics. Our prior has the flexibility to take in pathway structural information so that it can model the gene-level correlation based on prior biological knowledge, an important feature that makes it appealing compared to existing pathway-based methods. Using simulations, we show that our method outperforms competing methods in various scenarios, particularly when we have pathway structural information that involves complex gene-gene interactions. We apply our method to the Wellcome Trust Case Control Consortium Crohn's disease GWAS data, demonstrating its practical application to real data.     

Hierarchical Bayesian Model for Rare Variant Association Analysis Integrating Genotype Uncertainty in Human Sequence Data

Next‐generation sequencing (NGS) has led to the study of rare genetic variants, which possibly explain the missing heritability for complex diseases. Most existing methods for rare variant (RV) association detection do not account for the common presence of sequencing errors in NGS data. The errors can largely affect the power and perturb the accuracy of association tests due to rare observations of minor alleles. We developed a hierarchical Bayesian approach to estimate the association between RVs and complex diseases. Our integrated framework combines the misclassification probability with shrinkage‐based Bayesian variable selection. It allows for flexibility in handling neutral and protective RVs with measurement error, and is robust enough for detecting causal RVs with a wide spectrum of minor allele frequency (MAF). Imputation uncertainty and MAF are incorporated into the integrated framework to achieve the optimal statistical power. We demonstrate that sequencing error does significantly affect the findings, and our proposed model can take advantage of it to improve statistical power in both simulated and real data. We further show that our model outperforms existing methods, such as sequence kernel association test (SKAT). Finally, we illustrate the behavior of the proposed method using a Finnish low‐density lipoprotein cholesterol study, and show that it identifies an RV known as FH North Karelia in LDLR gene with three carriers in 1,155 individuals, which is missed by both SKAT and Granvil.     

Prioritizing individual genetic variants after kernel machine testing using variable selection

Kernel machine learning methods, such as the SNP‐set kernel association test (SKAT), have been widely used to test associations between traits and genetic polymorphisms. In contrast to traditional single‐SNP analysis methods, these methods are designed to examine the joint effect of a set of related SNPs (such as a group of SNPs within a gene or a pathway) and are able to identify sets of SNPs that are associated with the trait of interest. However, as with many multi‐SNP testing approaches, kernel machine testing can draw conclusion only at the SNP‐set level, and does not directly inform on which one(s) of the identified SNP set is actually driving the associations. A recently proposed procedure, KerNel Iterative Feature Extraction (KNIFE), provides a general framework for incorporating variable selection into kernel machine methods. In this article, we focus on quantitative traits and relatively common SNPs, and adapt the KNIFE procedure to genetic association studies and propose an approach to identify driver SNPs after the application of SKAT to gene set analysis. Our approach accommodates several kernels that are widely used in SNP analysis, such as the linear kernel and the Identity by State (IBS) kernel. The proposed approach provides practically useful utilities to prioritize SNPs, and fills the gap between SNP set analysis and biological functional studies. Both simulation studies and real data application are used to demonstrate the proposed approach.     

Statistical Testing of Shared Genetic Control for Potentially Related Traits

Integration of data from genome‐wide single nucleotide polymorphism (SNP) association studies of different traits should allow researchers to disentangle the genetics of potentially related traits within individually associated regions. Formal statistical colocalisation testing of individual regions requires selection of a set of SNPs summarising the association in a region. We show that the SNP selection method greatly affects type 1 error rates, with published studies having used methods expected to result in substantially inflated type 1 error rates. We show that either avoiding variable selection and instead testing the most informative principal components or integrating over variable selection using Bayesian model averaging can help control type 1 error rates. Application to data from Graves' disease and Hashimoto's thyroiditis reveals a common genetic signature across seven regions shared between the diseases, and indicates that in five of six regions associated with Graves' disease and not Hashimoto's thyroiditis, this more likely reflects genuine absence of association with the latter rather than lack of power. Our examination, by simulation, of the performance of colocalisation tests and associated software will foster more widespread adoption of formal colocalisation testing. Given the increasing availability of large expression and genetic association datasets from disease‐relevant tissue and purified cell populations, coupled with identification of regulatory sequences by projects such as ENCODE, colocalisation analysis has the potential to reveal both shared genetic signatures of related traits and causal disease genes and tissues.     

LEAP: Biomarker Inference Through Learning and Evaluating Association Patterns

Single nucleotide polymorphism (SNP) high‐dimensional datasets are available from Genome Wide Association Studies (GWAS). Such data provide researchers opportunities to investigate the complex genetic basis of diseases. Much of genetic risk might be due to undiscovered epistatic interactions, which are interactions in which combination of several genes affect disease. Research aimed at discovering interacting SNPs from GWAS datasets proceeded in two directions. First, tools were developed to evaluate candidate interactions. Second, algorithms were developed to search over the space of candidate interactions. Another problem when learning interacting SNPs, which has not received much attention, is evaluating how likely it is that the learned SNPs are associated with the disease. A complete system should provide this information as well. We develop such a system. Our system, called LEAP, includes a new heuristic search algorithm for learning interacting SNPs, and a Bayesian network based algorithm for computing the probability of their association. We evaluated the performance of LEAP using 100 1,000‐SNP simulated datasets, each of which contains 15 SNPs involved in interactions. When learning interacting SNPs from these datasets, LEAP outperformed seven others methods. Furthermore, only SNPs involved in interactions were found to be probable. We also used LEAP to analyze real Alzheimer's disease and breast cancer GWAS datasets. We obtained interesting and new results from the Alzheimer's dataset, but limited results from the breast cancer dataset. We conclude that our results support that LEAP is a useful tool for extracting candidate interacting SNPs from high‐dimensional datasets and determining their probability.     

Principal component analysis for selection of optimal SNP-sets that capture intragenic genetic variation

Candidate gene association studies often utilize one single nucleotide polymorphism (SNP) for analysis, with an initial report typically not being replicated by subsequent studies. The failure to replicate may result from incomplete or poor identification of disease-related variants or haplotypes, possibly due to naive SNP selection. A method for identification of linkage disequilibrium (LD) groups and selection of SNPs that capture sufficient intra-genic genetic diversity is described. We assume all SNPs with minor allele frequency above a pre-determined frequency have been identified. Principal component analysis (PCA) is applied to evaluate multivariate SNP correlations to infer groups of SNPs in LD (LD-groups) and to establish an optimal set of group-tagging SNPs (gtSNPs) that provide the most comprehensive coverage of intra-genic diversity while minimizing the resources necessary to perform an informative association analysis. This PCA method differs from haplotype block (HB) and haplotype-tagging SNP (htSNP) methods, in that an LD-group of SNPs need not be a contiguous DNA fragment. Results of the PCA method compared well with existing htSNP methods while also providing advantages over those methods, including an indication of the optimal number of SNPs needed. Further, evaluation of the method over multiple replicates of simulated data indicated PCA to be a robust method for SNP selection. Our findings suggest that PCA may be a powerful tool for establishing an optimal SNP set that maximizes the amount of genetic variation captured for a candidate gene using a minimal number of SNPs.     

The Single‐Nucleotide Polymorphism Lottery: How Useful are a Few Common SNPs in Identifying Disease‐Associated Alleles?

It has been proposed that using association analysis of single nucleotide polymorphism (SNP) markers in candidate genes may be more successful in identifying disease susceptibility genes for complex diseases. Finding all the SNPs within a candidate gene and genotyping a large case‐control cohort is a resource‐intensive process. As linkage disequilibrium extends across small regions of the genome, the expectation is that a few common anonymous SNPs will be sufficient to detect functional disease‐associated alleles. The aim of this investigation was to compare the ability of a number of family‐ and population‐based association methods to identify known susceptibility loci using the Genetic Analysis Workshop 12 simulated data set. As expected, case‐control methods were more likely to detect association with individual SNPs but family‐based haplotyping methods appeared better able to localize the position of functional polymorphism. © 2001 Wiley‐Liss, Inc.     

Modeling disease‐state transition heterogeneity through Bayesian variable selection

In many diseases, Markov transition models are useful in describing transitions between discrete disease states. Often the probability of transitioning from one state to another varies widely across subjects. This heterogeneity is driven, in part, by a possibly unknown number of previous disease states and by potentially complex relationships between clinical data and these states. We propose use of Bayesian variable selection in Markov transition models to allow estimation of subject‐specific transition probabilities. Our approach simultaneously estimates the order of the Markov process and the transition‐specific covariate effects. The methods are assessed using simulation studies and applied to model disease‐state transition on the expanded disability status scale (EDSS) in multiple sclerosis (MS) patients from the Partners MS Center in Boston, MA. The proposed methodology is shown to accurately identify complex covariate–transition relationships in simulations and identifies a clinically significant interaction between relapse history and EDSS history in MS patients. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical methods for cis-Mendelian randomization with two-sample summary-level data

Mendelian randomization (MR) is the use of genetic variants to assess the existence of a causal relationship between a risk factor and an outcome of interest. Here, we focus on two-sample summary-data MR analyses with many correlated variants from a single gene region, particularly on cis-MR studies which use protein expression as a risk factor. Such studies must rely on a small, curated set of variants from the studied region; using all variants in the region requires inverting an ill-conditioned genetic correlation matrix and results in numerically unstable causal effect estimates. We review methods for variable selection and estimation in cis-MR with summary-level data, ranging from stepwise pruning and conditional analysis to principal components analysis, factor analysis, and Bayesian variable selection. In a simulation study, we show that the various methods have comparable performance in analyses with large sample sizes and strong genetic instruments. However, when weak instrument bias is suspected, factor analysis and Bayesian variable selection produce more reliable inferences than simple pruning approaches, which are often used in practice. We conclude by examining two case studies, assessing the effects of low-density lipoprotein-cholesterol and serum testosterone on coronary heart disease risk using variants in the HMGCR and SHBG gene regions, respectively.     

Two-phase stratified sampling designs for regional sequencing

By systematic examination of common tag single-nucleotide polymorphisms (SNPs) across the genome, the genome-wide association study (GWAS) has proven to be a successful approach to identify genetic variants that are associated with complex diseases and traits. Although the per base pair cost of sequencing has dropped dramatically with the advent of the next-generation technologies, it may still only be feasible to obtain DNA sequence data for a portion of available study subjects due to financial constraints. Two-phase sampling designs have been used frequently in large-scale surveys and epidemiological studies where certain variables are too costly to be measured on all subjects. We consider two-phase stratified sampling designs for genetic association, in which tag SNPs for candidate genes or regions are genotyped on all subjects in phase 1, and a proportion of subjects are selected into phase 2 based on genotypes at one or more tag SNPs. Deep sequencing in the region is then applied to genotype phase 2 subjects at sequence SNPs. We investigate alternative sampling designs for selection of phase 2 subjects within strata defined by tag SNP genotypes and develop methods of inference for sequence SNP variant associations using data from both phases. In comparison to methods that use data from phase 2 alone, the combined analysis improves efficiency.     

Fine‐Mapping Additive and Dominant SNP Effects Using Group‐LASSO and Fractional Resample Model Averaging

Genomewide association studies (GWAS) sometimes identify loci at which both the number and identities of the underlying causal variants are ambiguous. In such cases, statistical methods that model effects of multiple single‐nucleotide polymorphisms (SNPs) simultaneously can help disentangle the observed patterns of association and provide information about how those SNPs could be prioritized for follow‐up studies. Current multi‐SNP methods, however, tend to assume that SNP effects are well captured by additive genetics; yet when genetic dominance is present, this assumption translates to reduced power and faulty prioritizations. We describe a statistical procedure for prioritizing SNPs at GWAS loci that efficiently models both additive and dominance effects. Our method, LLARRMA‐dawg, combines a group LASSO procedure for sparse modeling of multiple SNP effects with a resampling procedure based on fractional observation weights. It estimates for each SNP the robustness of association with the phenotype both to sampling variation and to competing explanations from other SNPs. In producing an SNP prioritization that best identifies underlying true signals, we show the following: our method easily outperforms a single‐marker analysis; when additive‐only signals are present, our joint model for additive and dominance is equivalent to or only slightly less powerful than modeling additive‐only effects; and when dominance signals are present, even in combination with substantial additive effects, our joint model is unequivocally more powerful than a model assuming additivity. We also describe how performance can be improved through calibrated randomized penalization, and discuss how dominance in ungenotyped SNPs can be incorporated through either heterozygote dosage or multiple imputation.     

Candidate single nucleotide polymorphism selection using publicly available tools: a guide for epidemiologists

Single nucleotide polymorphisms (SNPs) are the most common form of human genetic variation, with millions present in the human genome. Because only 1% might be expected to confer more than modest individual effects in association studies, the selection of predictive candidate variants for complex disease analyses is formidable. Technologic advances in SNP discovery and the ever-changing annotation of the genome have led to massive informational resources that can be difficult to master across disciplines. A simplified guide is needed. Although methods for evaluating nonsynonymous coding SNPs are known, several other publicly available computational tools can be utilized to assess polymorphic variants in noncoding regions. As an example, the authors applied multiple methods to select SNPs in DNA double-strand break repair genes. They chose to evaluate SNPs that occurred among a preexisting set of 57 validated assays and to justify new assay development for 83 potential SNPs in the DNA-dependent protein kinase catalytic subunit. Of the 140 SNPs, the authors eliminated 119 variants with low or neutral predictions. The existing computational methods they used and the semiquantitative relative ranking strategy they developed can be adapted to a priori SNP selection or post hoc evaluation of variants identified in whole genome scans or within haplotype blocks associated with disease. The authors show a "real world" application of some existing bioinformatics tools for use in large epidemiologic studies and genetic analyses. They also reviewed alternative approaches that provide related information.     

Multiple hypothesis testing strategies for genetic case-control association studies

The genetic case-control association study of unrelated subjects is a leading method to identify single nucleotide polymorphisms (SNPs) and SNP haplotypes that modulate the risk of complex diseases. Association studies often genotype several SNPs in a number of candidate genes; we propose a two-stage approach to address the inherent statistical multiple comparisons problem. In the first stage, each gene's association with disease is summarized by a single p-value that controls a familywise error rate. In the second stage, summary p-values are adjusted for multiplicity using a false discovery rate (FDR) controlling procedure. For the first stage, we consider marginal and joint tests of SNPs and haplotypes within genes, and we construct an omnibus test that combines SNP and haplotype analysis. Simulation studies show that when disease susceptibility is conferred by a SNP, and all common SNPs in a gene are genotyped, marginal analysis of SNPs using the Simes test has similar or higher power than marginal or joint haplotype analysis. Conversely, haplotype analysis can be more powerful when disease susceptibility is conferred by a haplotype. The omnibus test tracks the more powerful of the two approaches, which is generally unknown. Multiple testing balances the desire for statistical power against the implicit costs of false positive results, which up to now appear to be common in the literature.     

Using biological knowledge to discover higher order interactions in genetic association studies

The recent successes of genome-wide association studies (GWAS) have revealed that many of the replicated findings have explained only a small fraction of the heritability of common diseases. One hypothesis that investigators have suggested is that higher order interactions between SNPs or SNPs and environmental risk factors may account for some of this missing heritability. Searching for these interactions poses great statistical and computational challenges. In this article, we propose a novel method that addresses these challenges by incorporating external biological knowledge into a fully Bayesian analysis. The method is designed to be scalable for high-dimensional search spaces (where it supports interactions of any order) because priors that use such knowledge focus the search in regions that are more biologically plausible and avoid having to enumerate all possible interactions. We provide several examples based on simulated data demonstrating how external information can enhance power, specificity, and effect estimates in comparison to conventional approaches based on maximum likelihood estimates. We also apply the method to data from a GWAS for breast cancer, revealing a set of interactions enriched for the Gene Ontology terms growth, metabolic process, and biological regulation.     

Inclusion of biological knowledge in a Bayesian shrinkage model for joint estimation of SNP effects

With the aim of improving detection of novel single‐nucleotide polymorphisms (SNPs) in genetic association studies, we propose a method of including prior biological information in a Bayesian shrinkage model that jointly estimates SNP effects. We assume that the SNP effects follow a normal distribution centered at zero with variance controlled by a shrinkage hyperparameter. We use biological information to define the amount of shrinkage applied on the SNP effects distribution, so that the effects of SNPs with more biological support are less shrunk toward zero, thus being more likely detected. The performance of the method was tested in a simulation study (1,000 datasets, 500 subjects with ～200 SNPs in 10 linkage disequilibrium (LD) blocks) using a continuous and a binary outcome. It was further tested in an empirical example on body mass index (continuous) and overweight (binary) in a dataset of 1,829 subjects and 2,614 SNPs from 30 blocks. Biological knowledge was retrieved using the bioinformatics tool Dintor, which queried various databases. The joint Bayesian model with inclusion of prior information outperformed the standard analysis: in the simulation study, the mean ranking of the true LD block was 2.8 for the Bayesian model versus 3.6 for the standard analysis of individual SNPs; in the empirical example, the mean ranking of the six true blocks was 8.5 versus 9.3 in the standard analysis. These results suggest that our method is more powerful than the standard analysis. We expect its performance to improve further as more biological information about SNPs becomes available.