Bayesian variable and model selection methods for genetic association studies

Using the Bayesian variational spike and slab model in a genome-wide association study for finding associated loci with bipolar disorder

OBJECTIVE

The genome-wide association studies (GWAS) analysis, the most successful technique for discovering disease-related genetic variation, has some statistical concerns, including multiple testing, the correlation among variants (single-nucleotide polymorphisms) based on linkage disequilibrium and omitting the important variants when fitting the model with just one variant. To eliminate these problems in a small sample-size study, we used a sparse Bayesian learning model for finding bipolar disorder (BD) genetic variants.

METHODS

This study used the Wellcome Trust Case Control Consortium data set, including 1998 BD cases and 1500 control samples, and after quality control, 380,628 variants were analysed. In this GWAS, a Bayesian logistic model with hierarchical shrinkage spike and slab priors was used, with all variants considered simultaneously in one model. In order to decrease the computational burden, an alternative inferential method, Bayesian variational inference, has been used.

RESULTS

Thirteen variants were selected as associated with BD. The three of them (rs7572953, rs1378850 and rs4148944) were reported in previous GWAS. Eight of which were related to hemogram parameters, such as lymphocyte percentage, plateletcrit and haemoglobin concentration. Among selected related genes, GABPA, ELF3 and JAM2 were enriched in the platelet-derived growth factor pathway. These three genes, along with APP, ARL8A, CDH23 and GPR37L1, could be differential diagnostic variants for BD.

CONCLUSIONS

By reducing the statistical restrictions of GWAS analysis, the application of the Bayesian variational spike and slab models can offer insight into the genetic link with BD even with a small sample size. To uncover related variations with other traits, this model needs to be further examined.

Bayesian approaches to variable selection: a comparative study from practical perspectives

In many clinical studies, researchers are interested in parsimonious models that simultaneously achieve consistent variable selection and optimal prediction. The resulting parsimonious models will facilitate meaningful biological interpretation and scientific findings. Variable selection via Bayesian inference has been receiving significant advancement in recent years. Despite its increasing popularity, there is limited practical guidance for implementing these Bayesian approaches and evaluating their comparative performance in clinical datasets. In this paper, we review several commonly used Bayesian approaches to variable selection, with emphasis on application and implementation through R software. These approaches can be roughly categorized into four classes: namely the Bayesian model selection, spike-and-slab priors, shrinkage priors, and the hybrid of both. To evaluate their variable selection performance under various scenarios, we compare these four classes of approaches using real and simulated datasets. These results provide practical guidance to researchers who are interested in applying Bayesian approaches for the purpose of variable selection.

Improving Practices for Selecting a Subset of Important Predictors in Psychology: An Application to Predicting Pain

Frequently, researchers in psychology are faced with the challenge of narrowing down a large set of predictors to a smaller subset. There are a variety of ways to do this, but commonly it is done by choosing predictors with the strongest bivariate correlations with the outcome. However, when predictors are correlated, bivariate relationships may not translate into multivariate relationships. Further, any attempts to control for multiple testing are likely to result in extremely low power. Here we introduce a Bayesian variable-selection procedure frequently used in other disciplines, stochastic search variable selection (SSVS). We apply this technique to choosing the best set of predictors of the perceived unpleasantness of an experimental pain stimulus from among a large group of sociocultural, psychological, and neurobiological (functional MRI) individual-difference measures. Using SSVS provides information about which variables predict the outcome, controlling for uncertainty in the other variables of the model. This approach yields new, useful information to guide the choice of relevant predictors. We have provided Web-based open-source software for performing SSVS and visualizing the results.

A Bayesian approach to Mendelian randomisation with dependent instruments

Mendelian randomisation (MR) is a method for establishing causality between a risk factor and an outcome by using genetic variants as instrumental variables. In practice, the association between individual genetic variants and the risk factor is often weak, which may lead to a lack of precision in the MR and even biased MR estimates. Usually, the most significant variant within a genetic region is selected to represent the association with the risk factor, but there is no guarantee that this variant will be causal or that it will capture all of the genetic association within the region. It may be advantageous to use extra variants selected from the same region in the MR. The problem is to decide which variants to select. Rather than selecting a specific set of variants, we investigate the use of Bayesian model averaging (BMA) to average the MR over all possible combinations of genetic variants. Our simulations demonstrate that the BMA version of MR outperforms classical estimation with many dependent variants and performs much better than an MR based on variants selected by penalised regression. In further simulations, we investigate robustness to violations in the model assumptions and demonstrate sensitivity to the inclusion of invalid instruments. The method is illustrated by applying it to an MR of the effect of body mass index on blood pressure using SNPs in the FTO gene.

Salt stress under the scalpel - dissecting the genetics of salt tolerance

Salt stress limits the productivity of crops grown under saline conditions, leading to substantial losses of yield in saline soils and under brackish and saline irrigation. Salt tolerant crops could alleviate these losses while both increasing irrigation opportunities and reducing agricultural demands on dwindling freshwater resources. However, despite significant efforts, progress towards this goal has been limited, largely because of the genetic complexity of salt tolerance for agronomically important yield-related traits. Consequently, the focus is shifting to the study of traits that contribute to overall tolerance, thus breaking down salt tolerance into components that are more genetically tractable. Greater consideration of the plasticity of salt tolerance mechanisms throughout development and across environmental conditions furthers this dissection. The demand for more sophisticated and comprehensive methodologies is being met by parallel advances in high-throughput phenotyping and sequencing technologies that are enabling the multivariate characterisation of vast germplasm resources. Alongside steady improvements in statistical genetics models, forward genetics approaches for elucidating salt tolerance mechanisms are gaining momentum. Subsequent quantitative trait locus and gene validation has also become more accessible, most recently through advanced techniques in molecular biology and genomic analysis, facilitating the translation of findings to the field. Besides fuelling the improvement of established crop species, this progress also facilitates the domestication of naturally salt tolerant orphan crops. Taken together, these advances herald a promising era of discovery for research into the genetics of salt tolerance in plants.

Bayesian inference for the genetic control of water deficit tolerance in spring wheat by stochastic search variable selection

Drought is the main abiotic stress seriously influencing wheat production. Information about the inheritance of drought tolerance is necessary to determine the most appropriate strategy to develop tolerant cultivars and populations. In this study, generation means analysis to identify the genetic effects controlling grain yield inheritance in water deficit and normal conditions was considered as a model selection problem in a Bayesian framework. Stochastic search variable selection (SSVS) was applied to identify the most important genetic effects and the best fitted models using different generations obtained from two crosses applying two water regimes in two growing seasons. The SSVS is used to evaluate the effect of each variable on the dependent variable via posterior variable inclusion probabilities. The model with the highest posterior probability is selected as the best model. In this study, the grain yield was controlled by the main effects (additive and non-additive effects) and epistatic. The results demonstrate that breeding methods such as recurrent selection and subsequent pedigree method and hybrid production can be useful to improve grain yield.

Fine-mapping of prostate cancer susceptibility loci in a large meta-analysis identifies candidate causal variants

Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling.

Bayesian and frequentist analysis of an Austrian genome-wide association study of colorectal cancer and advanced adenomas

Most genome-wide association studies (GWAS) were analyzed using single marker tests in combination with stringent correction procedures for multiple testing. Thus, a substantial proportion of associated single nucleotide polymorphisms (SNPs) remained undetected and may account for missing heritability in complex traits. Model selection procedures present a powerful alternative to identify associated SNPs in high-dimensional settings. In this GWAS including 1060 colorectal cancer cases, 689 cases of advanced colorectal adenomas and 4367 controls we pursued a dual approach to investigate genome-wide associations with disease risk applying both, single marker analysis and model selection based on the modified Bayesian information criterion, mBIC2, implemented in the software package MOSGWA. For different case-control comparisons, we report models including between 1-14 candidate SNPs. A genome-wide significant association of rs17659990 (P=5.43×10^-9, DOCK3, chromosome 3p21.2) with colorectal cancer risk was observed. Furthermore, 56 SNPs known to influence susceptibility to colorectal cancer and advanced adenoma were tested in a hypothesis-driven approach and several of them were found to be relevant in our Austrian cohort. After correction for multiple testing (α=8.9×10^-4), the most significant associations were observed for SNPs rs10505477 (P=6.08×10^-4) and rs6983267 (P=7.35×10^-4) of CASC8, rs3802842 (P=8.98×10^-5, COLCA1,2), and rs12953717 (P=4.64×10^-4, SMAD7). All previously unreported SNPs demand replication in additional samples. Reanalysis of existing GWAS datasets using model selection as tool to detect SNPs associated with a complex trait may present a promising resource to identify further genetic risk variants not only for colorectal cancer.

A pharmacogenetic signature of high response to Copaxone in late-phase clinical-trial cohorts of multiple sclerosis

Background

Copaxone is an efficacious and safe therapy that has demonstrated clinical benefit for over two decades in patients with relapsing forms of multiple sclerosis (MS). On an individual level, patients show variability in their response to Copaxone, with some achieving significantly higher response levels. The involvement of genes (e.g., HLA-DRB1*1501) with high inter-individual variability in Copaxone’s mechanism of action (MoA) suggests the potential contribution of genetics to treatment response. This study aimed to identify genetic variants associated with Copaxone response in patient cohorts from late-phase clinical trials.

Methods

Single nucleotide polymorphisms (SNPs) associated with high and low levels of response to Copaxone were identified using genome-wide SNP data in a discovery cohort of 580 patients from two phase III clinical trials of Copaxone. Multivariable Bayesian modeling on the resulting SNPs in an expanded discovery cohort with 1171 patients identified a multi-SNP signature of Copaxone response. This signature was examined in 941 Copaxone-treated MS patients from seven independent late-phase trials of Copaxone and assessed for specificity to Copaxone in 310 Avonex-treated and 311 placebo-treated patients, also from late-phase trials.

Results

A four-SNP signature consisting of rs80191572 (in UVRAG), rs28724893 (in HLA-DQB2), rs1789084 (in MBP), and rs139890339 (in ZAK(CDCA7)) was identified as significantly associated with Copaxone response. Copaxone-treated signature-positive patients had a greater reduction in annualized relapse rate (ARR) compared to signature-negative patients in both discovery and independent cohorts, an effect not observed in Avonex-treated patients. Additionally, signature-positive placebo-treated cohorts did not show a reduction in ARR, demonstrating the predictive as opposed to prognostic nature of the signature. A 10% subset of patients, delineated by the signature, showed marked improvements across multiple clinical parameters, including ARR, MRI measures, and higher proportion with no evidence of disease activity (NEDA).

Conclusions

This study is the largest pharmacogenetic study in MS reported to date. Gene regions underlying the four-SNP signature have been linked with pathways associated with either Copaxone’s MoA or the pathophysiology of MS. The pronounced association of the four-SNP signature with clinical improvements in a ~10% subset of the MS patient population demonstrates the complex interplay of immune mechanisms and the individualized nature of response to Copaxone.

Electronic supplementary material

The online version of this article (doi:10.1186/s13073-017-0436-y) contains supplementary material, which is available to authorized users.

Accurate phenotyping: Reconciling approaches through Bayesian model averaging

Genetic research into complex diseases is frequently hindered by a lack of clear biomarkers for phenotype ascertainment. Phenotypes for such diseases are often identified on the basis of clinically defined criteria; however such criteria may not be suitable for understanding the genetic composition of the diseases. Various statistical approaches have been proposed for phenotype definition; however our previous studies have shown that differences in phenotypes estimated using different approaches have substantial impact on subsequent analyses. Instead of obtaining results based upon a single model, we propose a new method, using Bayesian model averaging to overcome problems associated with phenotype definition. Although Bayesian model averaging has been used in other fields of research, this is the first study that uses Bayesian model averaging to reconcile phenotypes obtained using multiple models. We illustrate the new method by applying it to simulated genetic and phenotypic data for Kofendred personality disorder-an imaginary disease with several sub-types. Two separate statistical methods were used to identify clusters of individuals with distinct phenotypes: latent class analysis and grade of membership. Bayesian model averaging was then used to combine the two clusterings for the purpose of subsequent linkage analyses. We found that causative genetic loci for the disease produced higher LOD scores using model averaging than under either individual model separately. We attribute this improvement to consolidation of the cores of phenotype clusters identified using each individual method.

Looking Beyond Respiratory Cultures: Microbiome-Cytokine Signatures of Bacterial Pneumonia and Tracheobronchitis in Lung Transplant Recipients

Bacterial pneumonia and tracheobronchitis are diagnosed frequently following lung transplantation. The diseases share clinical signs of inflammation and are often difficult to differentiate based on culture results. Microbiome and host immune-response signatures that distinguish between pneumonia and tracheobronchitis are undefined. Using a retrospective study design, we selected 49 bronchoalveolar lavage fluid samples from 16 lung transplant recipients associated with pneumonia (n = 8), tracheobronchitis (n = 12) or colonization without respiratory infection (n = 29). We ensured an even distribution of Pseudomonas aeruginosa or Staphylococcus aureus culture-positive samples across the groups. Bayesian regression analysis identified non-culture-based signatures comprising 16S ribosomal RNA microbiome profiles, cytokine levels and clinical variables that characterized the three diagnoses. Relative to samples associated with colonization, those from pneumonia had significantly lower microbial diversity, decreased levels of several bacterial genera and prominent multifunctional cytokine responses. In contrast, tracheobronchitis was characterized by high microbial diversity and multifunctional cytokine responses that differed from those of pneumonia-colonization comparisons. The dissimilar microbiomes and cytokine responses underlying bacterial pneumonia and tracheobronchitis following lung transplantation suggest that the diseases result from different pathogenic processes. Microbiomes and cytokine responses had complementary features, suggesting that they are closely interconnected in the pathogenesis of both diseases.

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.

A Bayesian Partitioning Model for the Detection of Multilocus Effects in Case-Control Studies

BACKGROUND

Genome-wide association studies (GWASs) have identified hundreds of genetic variants associated with complex diseases, but these variants appear to explain very little of the disease heritability. The typical single-locus association analysis in a GWAS fails to detect variants with small effect sizes and to capture higher-order interaction among these variants. Multilocus association analysis provides a powerful alternative by jointly modeling the variants within a gene or a pathway and by reducing the burden of multiple hypothesis testing in a GWAS.

METHODS

Here, we propose a powerful and flexible dimension reduction approach to model multilocus association. We use a Bayesian partitioning model which clusters SNPs according to their direction of association, models higher-order interactions using a flexible scoring scheme and uses posterior marginal probabilities to detect association between the SNP set and the disease.

RESULTS

We illustrate our method using extensive simulation studies and applying it to detect multilocus interaction in Atherosclerosis Risk in Communities (ARIC) GWAS with type 2 diabetes.

CONCLUSION

We demonstrate that our approach has better power to detect multilocus interactions than several existing approaches. When applied to the ARIC study dataset with 9,328 individuals to study gene-based associations for type 2 diabetes, our method identified some novel variants not detected by conventional single-locus association analyses.

Air toxics and birth defects: a Bayesian hierarchical approach to evaluate multiple pollutants and spina bifida

BACKGROUND

While there is evidence that maternal exposure to benzene is associated with spina bifida in offspring, to our knowledge there have been no assessments to evaluate the role of multiple hazardous air pollutants (HAPs) simultaneously on the risk of this relatively common birth defect. In the current study, we evaluated the association between maternal exposure to HAPs identified by the United States Environmental Protection Agency (U.S. EPA) and spina bifida in offspring using hierarchical Bayesian modeling that includes Stochastic Search Variable Selection (SSVS).

METHODS

The Texas Birth Defects Registry provided data on spina bifida cases delivered between 1999 and 2004. The control group was a random sample of unaffected live births, frequency matched to cases on year of birth. Census tract-level estimates of annual HAP levels were obtained from the U.S. EPA's 1999 Assessment System for Population Exposure Nationwide. Using the distribution among controls, exposure was categorized as high exposure (>95(th) percentile), medium exposure (5(th)-95(th) percentile), and low exposure (<5(th) percentile, reference). We used hierarchical Bayesian logistic regression models with SSVS to evaluate the association between HAPs and spina bifida by computing an odds ratio (OR) for each HAP using the posterior mean, and a 95% credible interval (CI) using the 2.5(th) and 97.5(th) quantiles of the posterior samples. Based on previous assessments, any pollutant with a Bayes factor greater than 1 was selected for inclusion in a final model.

RESULTS

Twenty-five HAPs were selected in the final analysis to represent "bins" of highly correlated HAPs (ρ > 0.80). We identified two out of 25 HAPs with a Bayes factor greater than 1: quinoline (ORhigh = 2.06, 95% CI: 1.11-3.87, Bayes factor = 1.01) and trichloroethylene (ORmedium = 2.00, 95% CI: 1.14-3.61, Bayes factor = 3.79).

CONCLUSIONS

Overall there is evidence that quinoline and trichloroethylene may be significant contributors to the risk of spina bifida. Additionally, the use of Bayesian hierarchical models with SSVS is an alternative approach in the evaluation of multiple environmental pollutants on disease risk. This approach can be easily extended to environmental exposures, where novel approaches are needed in the context of multi-pollutant modeling.

Integrative Bayesian variable selection with gene-based informative priors for genome-wide association studies

Background

Genome-wide Association Studies (GWAS) are typically designed to identify phenotype-associated single nucleotide polymorphisms (SNPs) individually using univariate analysis methods. Though providing valuable insights into genetic risks of common diseases, the genetic variants identified by GWAS generally account for only a small proportion of the total heritability for complex diseases. To solve this “missing heritability” problem, we implemented a strategy called integrative Bayesian Variable Selection (iBVS), which is based on a hierarchical model that incorporates an informative prior by considering the gene interrelationship as a network. It was applied here to both simulated and real data sets.

Results

Simulation studies indicated that the iBVS method was advantageous in its performance with highest AUC in both variable selection and outcome prediction, when compared to Stepwise and LASSO based strategies. In an analysis of a leprosy case–control study, iBVS selected 94 SNPs as predictors, while LASSO selected 100 SNPs. The Stepwise regression yielded a more parsimonious model with only 3 SNPs. The prediction results demonstrated that the iBVS method had comparable performance with that of LASSO, but better than Stepwise strategies.

Conclusions

The proposed iBVS strategy is a novel and valid method for Genome-wide Association Studies, with the additional advantage in that it produces more interpretable posterior probabilities for each variable unlike LASSO and other penalized regression methods.

Electronic supplementary material

The online version of this article (doi:10.1186/s12863-014-0130-7) contains supplementary material, which is available to authorized users.

Bayesian systems-based genetic association analysis with effect strength estimation and omic wide interpretation: a case study in rheumatoid arthritis

Rich dependency structures are often formed in genetic association studies between the phenotypic, clinical, and environmental descriptors. These descriptors may not be standardized, and may encompass various disease definitions and clinical endpoints which are only weakly influenced by various (e.g., genetic) factors. Such loosely defined complex intermediate clinical phenotypes are typically used in follow-up candidate gene association studies, e.g., after genome-wide analysis, to deepen the understanding of the associations and to estimate effect strength. This chapter discusses a solid methodology, which is useful in such a scenario, by using probabilistic graphical models, namely, Bayesian networks in the Bayesian statistical framework. This method offers systematically scalable, comprehensive hierarchical hypotheses about multivariate relevance. We discuss its workflow: from data engineering to semantic publication of the results. We overview the construction, visualization, and interpretation of complex hypotheses related to the structural analysis of relevance. Furthermore, we illustrate the use of a dependency model-based relevance measure, which takes into account the structural properties of the model, for quantifying the effect strength. Finally, we discuss the "interpretational" or translational challenge of a genetic association study, with a focus on the fusion of heterogeneous omic knowledge to reintegrate the results into a genome-wide context.

Bayesian model selection in complex linear systems, as illustrated in genetic association studies

Motivated by examples from genetic association studies, this article considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent a priori information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems.

Integrated enrichment analysis of variants and pathways in genome-wide association studies indicates central role for IL-2 signaling genes in type 1 diabetes, and cytokine signaling genes in Crohn's disease

Pathway analyses of genome-wide association studies aggregate information over sets of related genes, such as genes in common pathways, to identify gene sets that are enriched for variants associated with disease. We develop a model-based approach to pathway analysis, and apply this approach to data from the Wellcome Trust Case Control Consortium (WTCCC) studies. Our method offers several benefits over existing approaches. First, our method not only interrogates pathways for enrichment of disease associations, but also estimates the level of enrichment, which yields a coherent way to promote variants in enriched pathways, enhancing discovery of genes underlying disease. Second, our approach allows for multiple enriched pathways, a feature that leads to novel findings in two diseases where the major histocompatibility complex (MHC) is a major determinant of disease susceptibility. Third, by modeling disease as the combined effect of multiple markers, our method automatically accounts for linkage disequilibrium among variants. Interrogation of pathways from eight pathway databases yields strong support for enriched pathways, indicating links between Crohn's disease (CD) and cytokine-driven networks that modulate immune responses; between rheumatoid arthritis (RA) and "Measles" pathway genes involved in immune responses triggered by measles infection; and between type 1 diabetes (T1D) and IL2-mediated signaling genes. Prioritizing variants in these enriched pathways yields many additional putative disease associations compared to analyses without enrichment. For CD and RA, 7 of 8 additional non-MHC associations are corroborated by other studies, providing validation for our approach. For T1D, prioritization of IL-2 signaling genes yields strong evidence for 7 additional non-MHC candidate disease loci, as well as suggestive evidence for several more. Of the 7 strongest associations, 4 are validated by other studies, and 3 (near IL-2 signaling genes RAF1, MAPK14, and FYN) constitute novel putative T1D loci for further study.

Variable selection methods for developing a biomarker panel for prediction of dengue hemorrhagic fever

BACKGROUND

The choice of selection methods to identify important variables for binary classification modeling is critical to produce stable models that are interpretable, that generate accurate predictions and have minimum bias. This work is motivated by data on clinical and laboratory features of severe dengue infections (dengue hemorrhagic fever, DHF) obtained from 51 individuals enrolled in a prospective observational study of acute human dengue infections.

RESULTS

We carry out a comprehensive performance comparison using several classification models for DHF over the dengue data set. We compared variable selection results by Multivariate Adaptive Regression Splines, Learning Ensemble, Random Forest, Bayesian Moving Averaging, Stochastic Search Variable Selection, and Generalized Regularized Logistics Regression. Model averaging methods (bagging, boosting and ensemble learners) have higher accuracy, but the generalized regularized regression model has the highest predictive power because the linearity assumptions of candidate predictors are strongly satisfied via deviance chi-square testing procedures. Bootstrapping applications for evaluating predictive regression coefficients in regularized regression model are performed.

CONCLUSIONS

Feature reduction methods introduce inherent biases and therefore are data-type dependent. We propose that these limitations can be overcome using an exhaustive approach for searching feature space. Using this approach, our results suggest that IL-10, platelet and lymphocyte counts are the major features for predicting dengue DHF on the basis of blood chemistries and cytokine measurements.

Improved branch and bound algorithm for detecting SNP-SNP interactions in breast cancer

BACKGROUND

Single nucleotide polymorphisms (SNPs) in genes derived from distinct pathways are associated with a breast cancer risk. Identifying possible SNP-SNP interactions in genome-wide case-control studies is an important task when investigating genetic factors that influence common complex traits; the effects of SNP-SNP interaction need to be characterized. Furthermore, observations of the complex interplay (interactions) between SNPs for high-dimensional combinations are still computationally and methodologically challenging. An improved branch and bound algorithm with feature selection (IBBFS) is introduced to identify SNP combinations with a maximal difference of allele frequencies between the case and control groups in breast cancer, i.e., the high/low risk combinations of SNPs.

RESULTS

A total of 220 real case and 334 real control breast cancer data are used to test IBBFS and identify significant SNP combinations. We used the odds ratio (OR) as a quantitative measure to estimate the associated cancer risk of multiple SNP combinations to identify the complex biological relationships underlying the progression of breast cancer, i.e., the most likely SNP combinations. Experimental results show the estimated odds ratio of the best SNP combination with genotypes is significantly smaller than 1 (between 0.165 and 0.657) for specific SNP combinations of the tested SNPs in the low risk groups. In the high risk groups, predicted SNP combinations with genotypes are significantly greater than 1 (between 2.384 and 6.167) for specific SNP combinations of the tested SNPs.

CONCLUSIONS

This study proposes an effective high-speed method to analyze SNP-SNP interactions in breast cancer association studies. A number of important SNPs are found to be significant for the high/low risk group. They can thus be considered a potential predictor for breast cancer association.

Improved branch and bound algorithm for detecting SNP-SNP interactions in breast cancer

Background

Single nucleotide polymorphisms (SNPs) in genes derived from distinct pathways are associated with a breast cancer risk. Identifying possible SNP-SNP interactions in genome-wide case–control studies is an important task when investigating genetic factors that influence common complex traits; the effects of SNP-SNP interaction need to be characterized. Furthermore, observations of the complex interplay (interactions) between SNPs for high-dimensional combinations are still computationally and methodologically challenging. An improved branch and bound algorithm with feature selection (IBBFS) is introduced to identify SNP combinations with a maximal difference of allele frequencies between the case and control groups in breast cancer, i.e., the high/low risk combinations of SNPs.

Results

A total of 220 real case and 334 real control breast cancer data are used to test IBBFS and identify significant SNP combinations. We used the odds ratio (OR) as a quantitative measure to estimate the associated cancer risk of multiple SNP combinations to identify the complex biological relationships underlying the progression of breast cancer, i.e., the most likely SNP combinations. Experimental results show the estimated odds ratio of the best SNP combination with genotypes is significantly smaller than 1 (between 0.165 and 0.657) for specific SNP combinations of the tested SNPs in the low risk groups. In the high risk groups, predicted SNP combinations with genotypes are significantly greater than 1 (between 2.384 and 6.167) for specific SNP combinations of the tested SNPs.

Conclusions

This study proposes an effective high-speed method to analyze SNP-SNP interactions in breast cancer association studies. A number of important SNPs are found to be significant for the high/low risk group. They can thus be considered a potential predictor for breast cancer association.

Investigating multiple candidate genes and nutrients in the folate metabolism pathway to detect genetic and nutritional risk factors for lung cancer

PURPOSE

Folate metabolism, with its importance to DNA repair, provides a promising region for genetic investigation of lung cancer risk. This project investigates genes (MTHFR, MTR, MTRR, CBS, SHMT1, TYMS), folate metabolism related nutrients (B vitamins, methionine, choline, and betaine) and their gene-nutrient interactions.

METHODS

We analyzed 115 tag single nucleotide polymorphisms (SNPs) and 15 nutrients from 1239 and 1692 non-Hispanic white, histologically-confirmed lung cancer cases and controls, respectively, using stochastic search variable selection (a Bayesian model averaging approach). Analyses were stratified by current, former, and never smoking status.

RESULTS

Rs6893114 in MTRR (odds ratio [OR] = 2.10; 95% credible interval [CI]: 1.20-3.48) and alcohol (drinkers vs. non-drinkers, OR = 0.48; 95% CI: 0.26-0.84) were associated with lung cancer risk in current smokers. Rs13170530 in MTRR (OR = 1.70; 95% CI: 1.10-2.87) and two SNP*nutrient interactions [betaine*rs2658161 (OR = 0.42; 95% CI: 0.19-0.88) and betaine*rs16948305 (OR = 0.54; 95% CI: 0.30-0.91)] were associated with lung cancer risk in former smokers. SNPs in MTRR (rs13162612; OR = 0.25; 95% CI: 0.11-0.58; rs10512948; OR = 0.61; 95% CI: 0.41-0.90; rs2924471; OR = 3.31; 95% CI: 1.66-6.59), and MTHFR (rs9651118; OR = 0.63; 95% CI: 0.43-0.95) and three SNP*nutrient interactions (choline*rs10475407; OR = 1.62; 95% CI: 1.11-2.42; choline*rs11134290; OR = 0.51; 95% CI: 0.27-0.92; and riboflavin*rs8767412; OR = 0.40; 95% CI: 0.15-0.95) were associated with lung cancer risk in never smokers.

CONCLUSIONS

This study identified possible nutrient and genetic factors related to folate metabolism associated with lung cancer risk, which could potentially lead to nutritional interventions tailored by smoking status to reduce lung cancer risk.

Bayesian Variable Selection to identify QTL affecting a simulated quantitative trait

BACKGROUND

Recent developments in genetic technology and methodology enable accurate detection of QTL and estimation of breeding values, even in individuals without phenotypes. The QTL-MAS workshop offers the opportunity to test different methods to perform a genome-wide association study on simulated data with a QTL structure that is unknown beforehand. The simulated data contained 3,220 individuals: 20 sires and 200 dams with 3,000 offspring. All individuals were genotyped, though only 2,000 offspring were phenotyped for a quantitative trait. QTL affecting the simulated quantitative trait were identified and breeding values of individuals without phenotypes were estimated using Bayesian Variable Selection, a multi-locus SNP model in association studies.

RESULTS

Estimated heritability of the simulated quantitative trait was 0.30 (SD = 0.02). Mean posterior probability of SNP modelled having a large effect (p ^i) was 0.0066 (95%HPDR: 0.0014-0.0132). Mean posterior probability of variance of second distribution was 0.409 (95%HPDR: 0.286-0.589). The genome-wide association analysis resulted in 14 significant and 43 putative SNP, comprising 7 significant QTL on chromosome 1, 2 and 3 and putative QTL on all chromosomes. Assigning single or multiple QTL to significant SNP was not obvious, especially for SNP in the same region that were more or less in LD. Correlation between the simulated and estimated breeding values of 1,000 offspring without phenotypes was 0.91.

CONCLUSIONS

Bayesian Variable Selection using thousands of SNP was successfully applied to genome-wide association analysis of a simulated dataset with unknown QTL structure. Simulated QTL with Mendelian inheritance were accurately identified, while imprinted and epistatic QTL were only putatively detected. The correlation between simulated and estimated breeding values of offspring without phenotypes was high.

Stochastic model search with binary outcomes for genome-wide association studies

Objective

The spread of case–control genome-wide association studies (GWASs) has stimulated the development of new variable selection methods and predictive models. We introduce a novel Bayesian model search algorithm, Binary Outcome Stochastic Search (BOSS), which addresses the model selection problem when the number of predictors far exceeds the number of binary responses.

Materials and methods

Our method is based on a latent variable model that links the observed outcomes to the underlying genetic variables. A Markov Chain Monte Carlo approach is used for model search and to evaluate the posterior probability of each predictor.

Results

BOSS is compared with three established methods (stepwise regression, logistic lasso, and elastic net) in a simulated benchmark. Two real case studies are also investigated: a GWAS on the genetic bases of longevity, and the type 2 diabetes study from the Wellcome Trust Case Control Consortium. Simulations show that BOSS achieves higher precisions than the reference methods while preserving good recall rates. In both experimental studies, BOSS successfully detects genetic polymorphisms previously reported to be associated with the analyzed phenotypes.

Discussion

BOSS outperforms the other methods in terms of F-measure on simulated data. In the two real studies, BOSS successfully detects biologically relevant features, some of which are missed by univariate analysis and the three reference techniques.

Conclusion

The proposed algorithm is an advance in the methodology for model selection with a large number of features. Our simulated and experimental results showed that BOSS proves effective in detecting relevant markers while providing a parsimonious model.

A Bayesian integrative genomic model for pathway analysis of complex traits

With new technologies, multiple types of genomic data are commonly collected on a single set of samples. However, standard analysis methods concentrate on a single data type at a time and ignore the relationships between genes, proteins, and biochemical reactions that give rise to complex phenotypes. In this paper, we propose a novel integrative model to incorporate multiple types of genomic data into an association analysis with a complex phenotype. The method combines path analysis and stochastic search variable selection into a Bayesian hierarchical model that simultaneously identifies both direct and indirect genomic effects on the phenotype. Results from a simulation study and application of the Bayesian model to a pharmacogenomic study of the drug gemcitabine demonstrate greater sensitivity to detect genomic effects in some simulation scenarios, when compared to the standard single data type analysis. Further research is required to extend and modify this integrative modeling framework to increase computational efficiency to best capitalize on the wealth of information available across multiple genomic data types.

Identifying rare variants using a Bayesian regression approach

Recent advances in next-generation sequencing technologies have made it possible to generate large amounts of sequence data with rare variants in a cost-effective way. Statistical methods that test variants individually are underpowered to detect rare variants, so it is desirable to perform association analysis of rare variants by combining the information from all variants. In this study, we use a Bayesian regression method to model all variants simultaneously to identify rare variants in a data set from Genetic Analysis Workshop 17. We studied the association between the quantitative risk traits Q1, Q2, and Q4 and the single-nucleotide polymorphisms and identified several positive single-nucleotide polymorphisms for traits Q1 and Q2. However, the model also generated several apparent false positives and missed many true positives, suggesting that there is room for improvement in this model.

Methods for identifying SNP interactions: a review on variations of Logic Regression, Random Forest and Bayesian logistic regression

Due to advancements in computational ability, enhanced technology and a reduction in the price of genotyping, more data are being generated for understanding genetic associations with diseases and disorders. However, with the availability of large data sets comes the inherent challenges of new methods of statistical analysis and modeling. Considering a complex phenotype may be the effect of a combination of multiple loci, various statistical methods have been developed for identifying genetic epistasis effects. Among these methods, logic regression (LR) is an intriguing approach incorporating tree-like structures. Various methods have built on the original LR to improve different aspects of the model. In this study, we review four variations of LR, namely Logic Feature Selection, Monte Carlo Logic Regression, Genetic Programming for Association Studies, and Modified Logic Regression-Gene Expression Programming, and investigate the performance of each method using simulated and real genotype data. We contrast these with another tree-like approach, namely Random Forests, and a Bayesian logistic regression with stochastic search variable selection.

Gene-based tests of association

Genome-wide association studies (GWAS) are now used routinely to identify SNPs associated with complex human phenotypes. In several cases, multiple variants within a gene contribute independently to disease risk. Here we introduce a novel Gene-Wide Significance (GWiS) test that uses greedy Bayesian model selection to identify the independent effects within a gene, which are combined to generate a stronger statistical signal. Permutation tests provide p-values that correct for the number of independent tests genome-wide and within each genetic locus. When applied to a dataset comprising 2.5 million SNPs in up to 8,000 individuals measured for various electrocardiography (ECG) parameters, this method identifies more validated associations than conventional GWAS approaches. The method also provides, for the first time, systematic assessments of the number of independent effects within a gene and the fraction of disease-associated genes housing multiple independent effects, observed at 35%-50% of loci in our study. This method can be generalized to other study designs, retains power for low-frequency alleles, and provides gene-based p-values that are directly compatible for pathway-based meta-analysis.

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.

Bayesian model averaging for evaluation of candidate gene effects

Statistical assessment of candidate gene effects can be viewed as a problem of variable selection and model comparison. Given a certain number of genes to be considered, many possible models may fit to the data well, each including a specific set of gene effects and possibly their interactions. The question arises as to which of these models is most plausible. Inference about candidate gene effects based on a specific model ignores uncertainty about model choice. Here, a Bayesian model averaging approach is proposed for evaluation of candidate gene effects. The method is implemented through simultaneous sampling of multiple models. By averaging over a set of competing models, the Bayesian model averaging approach incorporates model uncertainty into inferences about candidate gene effects. Features of the method are demonstrated using a simulated data set with ten candidate genes under consideration.

Bayesian statistical methods for genetic association studies

Bayesian statistical methods have recently made great inroads into many areas of science, and this advance is now extending to the assessment of association between genetic variants and disease or other phenotypes. We review these methods, focusing on single-SNP tests in genome-wide association studies. We discuss the advantages of the Bayesian approach over classical (frequentist) approaches in this setting and provide a tutorial on basic analysis steps, including practical guidelines for appropriate prior specification. We demonstrate the use of Bayesian methods for fine mapping in candidate regions, discuss meta-analyses and provide guidance for refereeing manuscripts that contain Bayesian analyses.

Mapping in structured populations by resample model averaging

Highly recombinant populations derived from inbred lines, such as advanced intercross lines and heterogeneous stocks, can be used to map loci far more accurately than is possible with standard intercrosses. However, the varying degrees of relatedness that exist between individuals complicate analysis, potentially leading to many false positive signals. We describe a method to deal with these problems that does not require pedigree information and accounts for model uncertainty through model averaging. In our method, we select multiple quantitative trait loci (QTL) models using forward selection applied to resampled data sets obtained by nonparametric bootstrapping and subsampling. We provide model-averaged statistics about the probability of loci or of multilocus regions being included in model selection, and this leads to more accurate identification of QTL than by single-locus mapping. The generality of our approach means it can potentially be applied to any population of unknown structure.