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1.  Comparative analysis of methods for detecting interacting loci 
BMC Genomics  2011;12:344.
Interactions among genetic loci are believed to play an important role in disease risk. While many methods have been proposed for detecting such interactions, their relative performance remains largely unclear, mainly because different data sources, detection performance criteria, and experimental protocols were used in the papers introducing these methods and in subsequent studies. Moreover, there have been very few studies strictly focused on comparison of existing methods. Given the importance of detecting gene-gene and gene-environment interactions, a rigorous, comprehensive comparison of performance and limitations of available interaction detection methods is warranted.
We report a comparison of eight representative methods, of which seven were specifically designed to detect interactions among single nucleotide polymorphisms (SNPs), with the last a popular main-effect testing method used as a baseline for performance evaluation. The selected methods, multifactor dimensionality reduction (MDR), full interaction model (FIM), information gain (IG), Bayesian epistasis association mapping (BEAM), SNP harvester (SH), maximum entropy conditional probability modeling (MECPM), logistic regression with an interaction term (LRIT), and logistic regression (LR) were compared on a large number of simulated data sets, each, consistent with complex disease models, embedding multiple sets of interacting SNPs, under different interaction models. The assessment criteria included several relevant detection power measures, family-wise type I error rate, and computational complexity. There are several important results from this study. First, while some SNPs in interactions with strong effects are successfully detected, most of the methods miss many interacting SNPs at an acceptable rate of false positives. In this study, the best-performing method was MECPM. Second, the statistical significance assessment criteria, used by some of the methods to control the type I error rate, are quite conservative, thereby limiting their power and making it difficult to fairly compare them. Third, as expected, power varies for different models and as a function of penetrance, minor allele frequency, linkage disequilibrium and marginal effects. Fourth, the analytical relationships between power and these factors are derived, aiding in the interpretation of the study results. Fifth, for these methods the magnitude of the main effect influences the power of the tests. Sixth, most methods can detect some ground-truth SNPs but have modest power to detect the whole set of interacting SNPs.
This comparison study provides new insights into the strengths and limitations of current methods for detecting interacting loci. This study, along with freely available simulation tools we provide, should help support development of improved methods. The simulation tools are available at:
PMCID: PMC3161015  PMID: 21729295
2.  A Markov blanket-based method for detecting causal SNPs in GWAS 
BMC Bioinformatics  2010;11(Suppl 3):S5.
Detecting epistatic interactions associated with complex and common diseases can help to improve prevention, diagnosis and treatment of these diseases. With the development of genome-wide association studies (GWAS), designing powerful and robust computational method for identifying epistatic interactions associated with common diseases becomes a great challenge to bioinformatics society, because the study of epistatic interactions often deals with the large size of the genotyped data and the huge amount of combinations of all the possible genetic factors. Most existing computational detection methods are based on the classification capacity of SNP sets, which may fail to identify SNP sets that are strongly associated with the diseases and introduce a lot of false positives. In addition, most methods are not suitable for genome-wide scale studies due to their computational complexity.
We propose a new Markov Blanket-based method, DASSO-MB (Detection of ASSOciations using Markov Blanket) to detect epistatic interactions in case-control GWAS. Markov blanket of a target variable T can completely shield T from all other variables. Thus, we can guarantee that the SNP set detected by DASSO-MB has a strong association with diseases and contains fewest false positives. Furthermore, DASSO-MB uses a heuristic search strategy by calculating the association between variables to avoid the time-consuming training process as in other machine-learning methods. We apply our algorithm to simulated datasets and a real case-control dataset. We compare DASSO-MB to other commonly-used methods and show that our method significantly outperforms other methods and is capable of finding SNPs strongly associated with diseases.
Our study shows that DASSO-MB can identify a minimal set of causal SNPs associated with diseases, which contains less false positives compared to other existing methods. Given the huge size of genomic dataset produced by GWAS, this is critical in saving the potential costs of biological experiments and being an efficient guideline for pathogenesis research.
PMCID: PMC2863064  PMID: 20438652
3.  An algorithm for learning maximum entropy probability models of disease risk that efficiently searches and sparingly encodes multilocus genomic interactions 
Bioinformatics  2009;25(19):2478-2485.
Motivation: In both genome-wide association studies (GWAS) and pathway analysis, the modest sample size relative to the number of genetic markers presents formidable computational, statistical and methodological challenges for accurately identifying markers/interactions and for building phenotype-predictive models.
Results: We address these objectives via maximum entropy conditional probability modeling (MECPM), coupled with a novel model structure search. Unlike neural networks and support vector machines (SVMs), MECPM makes explicit and is determined by the interactions that confer phenotype-predictive power. Our method identifies both a marker subset and the multiple k-way interactions between these markers. Additional key aspects are: (i) evaluation of a select subset of up to five-way interactions while retaining relatively low complexity; (ii) flexible single nucleotide polymorphism (SNP) coding (dominant, recessive) within each interaction; (iii) no mathematical interaction form assumed; (iv) model structure and order selection based on the Bayesian Information Criterion, which fairly compares interactions at different orders and automatically sets the experiment-wide significance level; (v) MECPM directly yields a phenotype-predictive model. MECPM was compared with a panel of methods on datasets with up to 1000 SNPs and up to eight embedded penetrance function (i.e. ground-truth) interactions, including a five-way, involving less than 20 SNPs. MECPM achieved improved sensitivity and specificity for detecting both ground-truth markers and interactions, compared with previous methods.
Supplementary information:Supplementary data are available at Bioinformatics online.
PMCID: PMC3140808  PMID: 19608708
4.  Finding type 2 diabetes causal single nucleotide polymorphism combinations and functional modules from genome-wide association data 
Due to the low statistical power of individual markers from a genome-wide association study (GWAS), detecting causal single nucleotide polymorphisms (SNPs) for complex diseases is a challenge. SNP combinations are suggested to compensate for the low statistical power of individual markers, but SNP combinations from GWAS generate high computational complexity.
We aim to detect type 2 diabetes (T2D) causal SNP combinations from a GWAS dataset with optimal filtration and to discover the biological meaning of the detected SNP combinations. Optimal filtration can enhance the statistical power of SNP combinations by comparing the error rates of SNP combinations from various Bonferroni thresholds and p-value range-based thresholds combined with linkage disequilibrium (LD) pruning. T2D causal SNP combinations are selected using random forests with variable selection from an optimal SNP dataset. T2D causal SNP combinations and genome-wide SNPs are mapped into functional modules using expanded gene set enrichment analysis (GSEA) considering pathway, transcription factor (TF)-target, miRNA-target, gene ontology, and protein complex functional modules. The prediction error rates are measured for SNP sets from functional module-based filtration that selects SNPs within functional modules from genome-wide SNPs based expanded GSEA.
A T2D causal SNP combination containing 101 SNPs from the Wellcome Trust Case Control Consortium (WTCCC) GWAS dataset are selected using optimal filtration criteria, with an error rate of 10.25%. Matching 101 SNPs with known T2D genes and functional modules reveals the relationships between T2D and SNP combinations. The prediction error rates of SNP sets from functional module-based filtration record no significance compared to the prediction error rates of randomly selected SNP sets and T2D causal SNP combinations from optimal filtration.
We propose a detection method for complex disease causal SNP combinations from an optimal SNP dataset by using random forests with variable selection. Mapping the biological meanings of detected SNP combinations can help uncover complex disease mechanisms.
PMCID: PMC3618247  PMID: 23566118
5.  Cloud computing for detecting high-order genome-wide epistatic interaction via dynamic clustering 
BMC Bioinformatics  2014;15:102.
Taking the advan tage of high-throughput single nucleotide polymorphism (SNP) genotyping technology, large genome-wide association studies (GWASs) have been considered to hold promise for unravelling complex relationships between genotype and phenotype. At present, traditional single-locus-based methods are insufficient to detect interactions consisting of multiple-locus, which are broadly existing in complex traits. In addition, statistic tests for high order epistatic interactions with more than 2 SNPs propose computational and analytical challenges because the computation increases exponentially as the cardinality of SNPs combinations gets larger.
In this paper, we provide a simple, fast and powerful method using dynamic clustering and cloud computing to detect genome-wide multi-locus epistatic interactions. We have constructed systematic experiments to compare powers performance against some recently proposed algorithms, including TEAM, SNPRuler, EDCF and BOOST. Furthermore, we have applied our method on two real GWAS datasets, Age-related macular degeneration (AMD) and Rheumatoid arthritis (RA) datasets, where we find some novel potential disease-related genetic factors which are not shown up in detections of 2-loci epistatic interactions.
Experimental results on simulated data demonstrate that our method is more powerful than some recently proposed methods on both two- and three-locus disease models. Our method has discovered many novel high-order associations that are significantly enriched in cases from two real GWAS datasets. Moreover, the running time of the cloud implementation for our method on AMD dataset and RA dataset are roughly 2 hours and 50 hours on a cluster with forty small virtual machines for detecting two-locus interactions, respectively. Therefore, we believe that our method is suitable and effective for the full-scale analysis of multiple-locus epistatic interactions in GWAS.
PMCID: PMC4021249  PMID: 24717145
Cloud computing; Genome-wide association studies; Dynamic clustering
6.  LEAP: Biomarker Inference Through Learning and Evaluating Association Patterns 
Genetic epidemiology  2015;39(3):173-184.
Single nucleotide polymorphism (SNP) high-dimensional datasets are available due to 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 several genes combined 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 1000 SNP simulated datasets, each of which contains 15 SNPs involved in interactions. When learning interacting SNPs from these datasets, LEAP outperformed 7 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.
PMCID: PMC4366363  PMID: 25677188
Bayesian network; GWAS; epistasis; biomarker; high-dimensional; interaction; SNP; LOAD; Alzheimer's disease; breast cancer
7.  An efficient weighted tag SNP-set analytical method in genome-wide association studies 
BMC Genetics  2015;16:25.
Single-nucleotide polymorphism (SNP)-set analysis in Genome-wide association studies (GWAS) has emerged as a research hotspot for identifying genetic variants associated with disease susceptibility. But most existing methods of SNP-set analysis are affected by the quality of SNP-set, and poor quality of SNP-set can lead to low power in GWAS.
In this research, we propose an efficient weighted tag-SNP-set analytical method to detect the disease associations. In our method, we first design a fast algorithm to select a subset of SNPs (called tag SNP-set) from a given original SNP-set based on the linkage disequilibrium (LD) between SNPs, then assign a proper weight to each of the selected tag SNP respectively and test the joint effect of these weighted tag SNPs. The intensive simulation results show that the power of weighted tag SNP-set-based test is much higher than that of weighted original SNP-set-based test and that of un-weighted tag SNP-set-based test. We also compare the powers of the weighted tag SNP-set-based test based on four types of tag SNP-sets. The simulation results indicate the method of selecting tag SNP-set impacts the power greatly and the power of our proposed method is the highest.
From the analysis of simulated replicated data sets, we came to a conclusion that weighted tag SNP-set-based test is a powerful SNP-set test in GWAS. We also designed a faster algorithm of selecting tag SNPs which include most of information of original SNP-set, and a better weighted function which can describe the status of each tag SNP in GWAS.
PMCID: PMC4373116  PMID: 25879733
Association test; GWAS; Linkage disequilibrium; SNP-set; Tag SNP
8.  Epistatic Gene-Based Interaction Analyses for Glaucoma in eMERGE and NEIGHBOR Consortium 
PLoS Genetics  2016;12(9):e1006186.
Primary open angle glaucoma (POAG) is a complex disease and is one of the major leading causes of blindness worldwide. Genome-wide association studies have successfully identified several common variants associated with glaucoma; however, most of these variants only explain a small proportion of the genetic risk. Apart from the standard approach to identify main effects of variants across the genome, it is believed that gene-gene interactions can help elucidate part of the missing heritability by allowing for the test of interactions between genetic variants to mimic the complex nature of biology. To explain the etiology of glaucoma, we first performed a genome-wide association study (GWAS) on glaucoma case-control samples obtained from electronic medical records (EMR) to establish the utility of EMR data in detecting non-spurious and relevant associations; this analysis was aimed at confirming already known associations with glaucoma and validating the EMR derived glaucoma phenotype. Our findings from GWAS suggest consistent evidence of several known associations in POAG. We then performed an interaction analysis for variants found to be marginally associated with glaucoma (SNPs with main effect p-value <0.01) and observed interesting findings in the electronic MEdical Records and GEnomics Network (eMERGE) network dataset. Genes from the top epistatic interactions from eMERGE data (Likelihood Ratio Test i.e. LRT p-value <1e-05) were then tested for replication in the NEIGHBOR consortium dataset. To replicate our findings, we performed a gene-based SNP-SNP interaction analysis in NEIGHBOR and observed significant gene-gene interactions (p-value <0.001) among the top 17 gene-gene models identified in the discovery phase. Variants from gene-gene interaction analysis that we found to be associated with POAG explain 3.5% of additional genetic variance in eMERGE dataset above what is explained by the SNPs in genes that are replicated from previous GWAS studies (which was only 2.1% variance explained in eMERGE dataset); in the NEIGHBOR dataset, adding replicated SNPs from gene-gene interaction analysis explain 3.4% of total variance whereas GWAS SNPs alone explain only 2.8% of variance. Exploring gene-gene interactions may provide additional insights into many complex traits when explored in properly designed and powered association studies.
Author Summary
The complex nature of primary-open angle glaucoma (POAG) has left researchers exploring the genetic architecture and searching for the missing heritability using a number of different study designs. Over the past decade, many studies have been conducted to explain the etiology of POAG; however, a high proportion of estimated heritability still remains unexplained. GWA studies for POAG have identified significant associations but these associations have only explained a small proportion of the genetic risk (odds ratios range between 1–3). In this paper, we sought to confirm the primary genome-wide significant associations that have been discovered so far for glaucoma in phenotypes developed from EMR data in an effort to show that EMR data can be a powerful resource for finding genetic variants influencing POAG susceptibility. Next, we tested for statistical interactions, which can be presented as an important tool in an attempt to explain POAG heritability. We used a reduced list of variants filtered by marginal main effect analysis to look for epistatic interactions. We present our results from replication of gene-based interaction analyses performed in eMERGE and the NEIGHBOR consortium data. Using expression data and annotations from various publicly available databases, the most significant genes that replicated in our analyses show expression in the eye and trabecular meshwork. Analysis for estimation of genetic variance explained by significant associations from previous GWAS and replicated variants from gene-based interactions suggest that these explain 5.6% of variance in eMERGE dataset and also explain 3.4% variance in NEIGHBOR dataset.
PMCID: PMC5021356  PMID: 27623284
9.  Simultaneous Analysis of All SNPs in Genome-Wide and Re-Sequencing Association Studies 
PLoS Genetics  2008;4(7):e1000130.
Testing one SNP at a time does not fully realise the potential of genome-wide association studies to identify multiple causal variants, which is a plausible scenario for many complex diseases. We show that simultaneous analysis of the entire set of SNPs from a genome-wide study to identify the subset that best predicts disease outcome is now feasible, thanks to developments in stochastic search methods. We used a Bayesian-inspired penalised maximum likelihood approach in which every SNP can be considered for additive, dominant, and recessive contributions to disease risk. Posterior mode estimates were obtained for regression coefficients that were each assigned a prior with a sharp mode at zero. A non-zero coefficient estimate was interpreted as corresponding to a significant SNP. We investigated two prior distributions and show that the normal-exponential-gamma prior leads to improved SNP selection in comparison with single-SNP tests. We also derived an explicit approximation for type-I error that avoids the need to use permutation procedures. As well as genome-wide analyses, our method is well-suited to fine mapping with very dense SNP sets obtained from re-sequencing and/or imputation. It can accommodate quantitative as well as case-control phenotypes, covariate adjustment, and can be extended to search for interactions. Here, we demonstrate the power and empirical type-I error of our approach using simulated case-control data sets of up to 500 K SNPs, a real genome-wide data set of 300 K SNPs, and a sequence-based dataset, each of which can be analysed in a few hours on a desktop workstation.
Author Summary
Tests of association with disease status are normally conducted one SNP at a time, ignoring the effects of all other genotyped SNPs. We developed a computationally efficient method to simultaneously analyse all SNPs, either in a genome-wide association (GWA) study, or a fine-mapping study based on re-sequencing and/or imputation. The method selects a subset of SNPs that best predicts disease status, while controlling the type-I error of the selected SNPs. This brings many advantages over standard single-SNP approaches, because the signal from a particular SNP can be more clearly assessed when other SNPs associated with disease status are already included in the model. Thus, in comparison with single-SNP analyses, power is increased and the false positive rate is reduced because of reduced residual variation. Localisation is also greatly improved. We demonstrate these advantages over the widely used single-SNP Armitage Trend Test using GWA simulation studies, a real GWA dataset, and a sequence-based fine-mapping simulation study.
PMCID: PMC2464715  PMID: 18654633
10.  Weighted Interaction SNP Hub (WISH) network method for building genetic networks for complex diseases and traits using whole genome genotype data 
BMC Systems Biology  2014;8(Suppl 2):S5.
High-throughput genotype (HTG) data has been used primarily in genome-wide association (GWA) studies; however, GWA results explain only a limited part of the complete genetic variation of traits. In systems genetics, network approaches have been shown to be able to identify pathways and their underlying causal genes to unravel the biological and genetic background of complex diseases and traits, e.g., the Weighted Gene Co-expression Network Analysis (WGCNA) method based on microarray gene expression data. The main objective of this study was to develop a scale-free weighted genetic interaction network method using whole genome HTG data in order to detect biologically relevant pathways and potential genetic biomarkers for complex diseases and traits.
We developed the Weighted Interaction SNP Hub (WISH) network method that uses HTG data to detect genome-wide interactions between single nucleotide polymorphism (SNPs) and its relationship with complex traits. Data dimensionality reduction was achieved by selecting SNPs based on its: 1) degree of genome-wide significance and 2) degree of genetic variation in a population. Network construction was based on pairwise Pearson's correlation between SNP genotypes or the epistatic interaction effect between SNP pairs. To identify modules the Topological Overlap Measure (TOM) was calculated, reflecting the degree of overlap in shared neighbours between SNP pairs. Modules, clusters of highly interconnected SNPs, were defined using a tree-cutting algorithm on the SNP dendrogram created from the dissimilarity TOM (1-TOM). Modules were selected for functional annotation based on their association with the trait of interest, defined by the Genome-wide Module Association Test (GMAT). We successfully tested the established WISH network method using simulated and real SNP interaction data and GWA study results for carcass weight in a pig resource population; this resulted in detecting modules and key functional and biological pathways related to carcass weight.
We developed the WISH network method which is a novel 'systems genetics' approach to study genetic networks underlying complex trait variation. The WISH network method reduces data dimensionality and statistical complexity in associating genotypes with phenotypes in GWA studies and enables researchers to identify biologically relevant pathways and potential genetic biomarkers for any complex trait of interest.
PMCID: PMC4101698  PMID: 25032480
11.  Genome-wide association data classification and SNPs selection using two-stage quality-based Random Forests 
BMC Genomics  2015;16(Suppl 2):S5.
Single-nucleotide polymorphisms (SNPs) selection and identification are the most important tasks in Genome-wide association data analysis. The problem is difficult because genome-wide association data is very high dimensional and a large portion of SNPs in the data is irrelevant to the disease. Advanced machine learning methods have been successfully used in Genome-wide association studies (GWAS) for identification of genetic variants that have relatively big effects in some common, complex diseases. Among them, the most successful one is Random Forests (RF). Despite of performing well in terms of prediction accuracy in some data sets with moderate size, RF still suffers from working in GWAS for selecting informative SNPs and building accurate prediction models. In this paper, we propose to use a new two-stage quality-based sampling method in random forests, named ts-RF, for SNP subspace selection for GWAS. The method first applies p-value assessment to find a cut-off point that separates informative and irrelevant SNPs in two groups. The informative SNPs group is further divided into two sub-groups: highly informative and weak informative SNPs. When sampling the SNP subspace for building trees for the forest, only those SNPs from the two sub-groups are taken into account. The feature subspaces always contain highly informative SNPs when used to split a node at a tree.
This approach enables one to generate more accurate trees with a lower prediction error, meanwhile possibly avoiding overfitting. It allows one to detect interactions of multiple SNPs with the diseases, and to reduce the dimensionality and the amount of Genome-wide association data needed for learning the RF model. Extensive experiments on two genome-wide SNP data sets (Parkinson case-control data comprised of 408,803 SNPs and Alzheimer case-control data comprised of 380,157 SNPs) and 10 gene data sets have demonstrated that the proposed model significantly reduced prediction errors and outperformed most existing the-state-of-the-art random forests. The top 25 SNPs in Parkinson data set were identified by the proposed model including four interesting genes associated with neurological disorders.
The presented approach has shown to be effective in selecting informative sub-groups of SNPs potentially associated with diseases that traditional statistical approaches might fail. The new RF works well for the data where the number of case-control objects is much smaller than the number of SNPs, which is a typical problem in gene data and GWAS. Experiment results demonstrated the effectiveness of the proposed RF model that outperformed the state-of-the-art RFs, including Breiman's RF, GRRF and wsRF methods.
PMCID: PMC4331719  PMID: 25708662
Genome-wide association study; SNPs Selection; Random Forests; Data mining
12.  Comparison of multimarker logistic regression models, with application to a genomewide scan of schizophrenia 
BMC Genetics  2010;11:80.
Genome-wide association studies (GWAS) are a widely used study design for detecting genetic causes of complex diseases. Current studies provide good coverage of common causal SNPs, but not rare ones. A popular method to detect rare causal variants is haplotype testing. A disadvantage of this approach is that many parameters are estimated simultaneously, which can mean a loss of power and slower fitting to large datasets.
Haplotype testing effectively tests both the allele frequencies and the linkage disequilibrium (LD) structure of the data. LD has previously been shown to be mostly attributable to LD between adjacent SNPs. We propose a generalised linear model (GLM) which models the effects of each SNP in a region as well as the statistical interactions between adjacent pairs. This is compared to two other commonly used multimarker GLMs: one with a main-effect parameter for each SNP; one with a parameter for each haplotype.
We show the haplotype model has higher power for rare untyped causal SNPs, the main-effects model has higher power for common untyped causal SNPs, and the proposed model generally has power in between the two others. We show that the relative power of the three methods is dependent on the number of marker haplotypes the causal allele is present on, which depends on the age of the mutation. Except in the case of a common causal variant in high LD with markers, all three multimarker models are superior in power to single-SNP tests.
Including the adjacent statistical interactions results in lower inflation in test statistics when a realistic level of population stratification is present in a dataset.
Using the multimarker models, we analyse data from the Molecular Genetics of Schizophrenia study. The multimarker models find potential associations that are not found by single-SNP tests. However, multimarker models also require stricter control of data quality since biases can have a larger inflationary effect on multimarker test statistics than on single-SNP test statistics.
Analysing a GWAS with multimarker models can yield candidate regions which may contain rare untyped causal variants. This is useful for increasing prior odds of association in future whole-genome sequence analyses.
PMCID: PMC2949738  PMID: 20828390
13.  GWIS - model-free, fast and exhaustive search for epistatic interactions in case-control GWAS 
BMC Genomics  2013;14(Suppl 3):S10.
It has been hypothesized that multivariate analysis and systematic detection of epistatic interactions between explanatory genotyping variables may help resolve the problem of "missing heritability" currently observed in genome-wide association studies (GWAS). However, even the simplest bivariate analysis is still held back by significant statistical and computational challenges that are often addressed by reducing the set of analysed markers. Theoretically, it has been shown that combinations of loci may exist that show weak or no effects individually, but show significant (even complete) explanatory power over phenotype when combined. Reducing the set of analysed SNPs before bivariate analysis could easily omit such critical loci.
We have developed an exhaustive bivariate GWAS analysis methodology that yields a manageable subset of candidate marker pairs for subsequent analysis using other, often more computationally expensive techniques. Our model-free filtering approach is based on classification using ROC curve analysis, an alternative to much slower regression-based modelling techniques. Exhaustive analysis of studies containing approximately 450,000 SNPs and 5,000 samples requires only 2 hours using a desktop CPU or 13 minutes using a GPU (Graphics Processing Unit). We validate our methodology with analysis of simulated datasets as well as the seven Wellcome Trust Case-Control Consortium datasets that represent a wide range of real life GWAS challenges. We have identified SNP pairs that have considerably stronger association with disease than their individual component SNPs that often show negligible effect univariately. When compared against previously reported results in the literature, our methods re-detect most significant SNP-pairs and additionally detect many pairs absent from the literature that show strong association with disease. The high overlap suggests that our fast analysis could substitute for some slower alternatives.
We demonstrate that the proposed methodology is robust, fast and capable of exhaustive search for epistatic interactions using a standard desktop computer. First, our implementation is significantly faster than timings for comparable algorithms reported in the literature, especially as our method allows simultaneous use of multiple statistical filters with low computing time overhead. Second, for some diseases, we have identified hundreds of SNP pairs that pass formal multiple test (Bonferroni) correction and could form a rich source of hypotheses for follow-up analysis.
A web-based version of the software used for this analysis is available at
PMCID: PMC3665501  PMID: 23819779
14.  A novel survival multifactor dimensionality reduction method for detecting gene–gene interactions with application to bladder cancer prognosis 
Human Genetics  2010;129(1):101-110.
The widespread use of high-throughput methods of single nucleotide polymorphism (SNP) genotyping has created a number of computational and statistical challenges. The problem of identifying SNP–SNP interactions in case–control studies has been studied extensively, and a number of new techniques have been developed. Little progress has been made, however, in the analysis of SNP–SNP interactions in relation to time-to-event data, such as patient survival time or time to cancer relapse. We present an extension of the two class multifactor dimensionality reduction (MDR) algorithm that enables detection and characterization of epistatic SNP–SNP interactions in the context of survival analysis. The proposed Survival MDR (Surv-MDR) method handles survival data by modifying MDR’s constructive induction algorithm to use the log-rank test. Surv-MDR replaces balanced accuracy with log-rank test statistics as the score to determine the best models. We simulated datasets with a survival outcome related to two loci in the absence of any marginal effects. We compared Surv-MDR with Cox-regression for their ability to identify the true predictive loci in these simulated data. We also used this simulation to construct the empirical distribution of Surv-MDR’s testing score. We then applied Surv-MDR to genetic data from a population-based epidemiologic study to find prognostic markers of survival time following a bladder cancer diagnosis. We identified several two-loci SNP combinations that have strong associations with patients’ survival outcome. Surv-MDR is capable of detecting interaction models with weak main effects. These epistatic models tend to be dropped by traditional Cox regression approaches to evaluating interactions. With improved efficiency to handle genome wide datasets, Surv-MDR will play an important role in a research strategy that embraces the complexity of the genotype–phenotype mapping relationship since epistatic interactions are an important component of the genetic basis of disease.
PMCID: PMC3255326  PMID: 20981448
15.  Genome-wide association study combined with biological context can reveal more disease-related SNPs altering microRNA target seed sites 
BMC Genomics  2014;15(1):669.
Emerging studies demonstrate that single nucleotide polymorphisms (SNPs) resided in the microRNA recognition element seed sites (MRESSs) in 3′UTR of mRNAs are putative biomarkers for human diseases and cancers. However, exhaustively experimental validation for the causality of MRESS SNPs is impractical. Therefore bioinformatics have been introduced to predict causal MRESS SNPs. Genome-wide association study (GWAS) provides a way to detect susceptibility of millions of SNPs simultaneously by taking linkage disequilibrium (LD) into account, but the multiple-testing corrections implemented to suppress false positive rate always sacrificed the sensitivity. In our study, we proposed a method to identify candidate causal MRESS SNPs from 12 GWAS datasets without performing multiple-testing corrections. Alternatively, we used biological context to ensure credibility of the selected SNPs.
In 11 out of the 12 GWAS datasets, MRESS SNPs were over-represented in SNPs with p-value ≤ 0.05 (odds ratio (OR) ranged from 1.1 to 2.4). Moreover, host genes of susceptible MRESS SNPs in each of the 11 GWAS dataset shared biological context with reported causal genes. There were 286 MRESS SNPs identified by our method, while only 13 SNPs were identified by multiple-testing corrections with a given threshold of 1 × 10−5, which is a common cutoff used in GWAS. 27 out of the 286 candidate SNPs have been reported to be deleterious while only 2 out of 13 multiple-testing corrected SNPs were documented in PubMed. MicroRNA-mRNA interactions affected by the 286 candidate SNPs were likely to present negatively correlated expression. These SNPs introduced greater alternation of binding free energy than other MRESS SNPs, especially when grouping by haplotypes (4210 vs. 4105 cal/mol by mean, 9781 vs. 8521 cal/mol by mean, respectively).
MRESS SNPs are promising disease biomarkers in multiple GWAS datasets. The method of integrating GWAS p-value and biological context is stable and effective for selecting candidate causal MRESS SNPs, it reduces the loss of sensitivity compared to multiple-testing corrections. The 286 candidate causal MRESS SNPs provide researchers a credible source to initialize their design of experimental validations in the future.
Electronic supplementary material
The online version of this article (doi:10.1186/1471-2164-15-669) contains supplementary material, which is available to authorized users.
PMCID: PMC4246476  PMID: 25106527
microRNA; Genome-wide association study; Single nucleotide polymorphisms; Human diseases and cancers
16.  Pathways of Distinction Analysis: A New Technique for Multi–SNP Analysis of GWAS Data 
PLoS Genetics  2011;7(6):e1002101.
Genome-wide association studies (GWAS) have become increasingly common due to advances in technology and have permitted the identification of differences in single nucleotide polymorphism (SNP) alleles that are associated with diseases. However, while typical GWAS analysis techniques treat markers individually, complex diseases (cancers, diabetes, and Alzheimers, amongst others) are unlikely to have a single causative gene. Thus, there is a pressing need for multi–SNP analysis methods that can reveal system-level differences in cases and controls. Here, we present a novel multi–SNP GWAS analysis method called Pathways of Distinction Analysis (PoDA). The method uses GWAS data and known pathway–gene and gene–SNP associations to identify pathways that permit, ideally, the distinction of cases from controls. The technique is based upon the hypothesis that, if a pathway is related to disease risk, cases will appear more similar to other cases than to controls (or vice versa) for the SNPs associated with that pathway. By systematically applying the method to all pathways of potential interest, we can identify those for which the hypothesis holds true, i.e., pathways containing SNPs for which the samples exhibit greater within-class similarity than across classes. Importantly, PoDA improves on existing single–SNP and SNP–set enrichment analyses, in that it does not require the SNPs in a pathway to exhibit independent main effects. This permits PoDA to reveal pathways in which epistatic interactions drive risk. In this paper, we detail the PoDA method and apply it to two GWAS: one of breast cancer and the other of liver cancer. The results obtained strongly suggest that there exist pathway-wide genomic differences that contribute to disease susceptibility. PoDA thus provides an analytical tool that is complementary to existing techniques and has the power to enrich our understanding of disease genomics at the systems-level.
Author Summary
We present a novel method for multi–SNP analysis of genome-wide association studies. The method is motivated by the intuition that, if a set of SNPs is associated with disease, cases and controls will exhibit more within-group similarity than across-group similarity for the SNPs in the set of interest. Our method, Pathways of Distinction Analysis (PoDA), uses GWAS data and known pathway–gene and gene–SNP associations to identify pathways that permit the distinction of cases from controls. By systematically applying the method to all pathways of potential interest, we can identify pathways containing SNPs for which the cases and controls are distinguished and infer those pathways' role in disease. We detail the PoDA method and describe its results in breast and liver cancer GWAS data, demonstrating its utility as a method for systems-level analysis of GWAS data.
PMCID: PMC3111473  PMID: 21695280
17.  Detecting purely epistatic multi-locus interactions by an omnibus permutation test on ensembles of two-locus analyses 
BMC Bioinformatics  2009;10:294.
Purely epistatic multi-locus interactions cannot generally be detected via single-locus analysis in case-control studies of complex diseases. Recently, many two-locus and multi-locus analysis techniques have been shown to be promising for the epistasis detection. However, exhaustive multi-locus analysis requires prohibitively large computational efforts when problems involve large-scale or genome-wide data. Furthermore, there is no explicit proof that a combination of multiple two-locus analyses can lead to the correct identification of multi-locus interactions.
The proposed 2LOmb algorithm performs an omnibus permutation test on ensembles of two-locus analyses. The algorithm consists of four main steps: two-locus analysis, a permutation test, global p-value determination and a progressive search for the best ensemble. 2LOmb is benchmarked against an exhaustive two-locus analysis technique, a set association approach, a correlation-based feature selection (CFS) technique and a tuned ReliefF (TuRF) technique. The simulation results indicate that 2LOmb produces a low false-positive error. Moreover, 2LOmb has the best performance in terms of an ability to identify all causative single nucleotide polymorphisms (SNPs) and a low number of output SNPs in purely epistatic two-, three- and four-locus interaction problems. The interaction models constructed from the 2LOmb outputs via a multifactor dimensionality reduction (MDR) method are also included for the confirmation of epistasis detection. 2LOmb is subsequently applied to a type 2 diabetes mellitus (T2D) data set, which is obtained as a part of the UK genome-wide genetic epidemiology study by the Wellcome Trust Case Control Consortium (WTCCC). After primarily screening for SNPs that locate within or near 372 candidate genes and exhibit no marginal single-locus effects, the T2D data set is reduced to 7,065 SNPs from 370 genes. The 2LOmb search in the reduced T2D data reveals that four intronic SNPs in PGM1 (phosphoglucomutase 1), two intronic SNPs in LMX1A (LIM homeobox transcription factor 1, alpha), two intronic SNPs in PARK2 (Parkinson disease (autosomal recessive, juvenile) 2, parkin) and three intronic SNPs in GYS2 (glycogen synthase 2 (liver)) are associated with the disease. The 2LOmb result suggests that there is no interaction between each pair of the identified genes that can be described by purely epistatic two-locus interaction models. Moreover, there are no interactions between these four genes that can be described by purely epistatic multi-locus interaction models with marginal two-locus effects. The findings provide an alternative explanation for the aetiology of T2D in a UK population.
An omnibus permutation test on ensembles of two-locus analyses can detect purely epistatic multi-locus interactions with marginal two-locus effects. The study also reveals that SNPs from large-scale or genome-wide case-control data which are discarded after single-locus analysis detects no association can still be useful for genetic epidemiology studies.
PMCID: PMC2759961  PMID: 19761607
18.  Association Test Based on SNP Set: Logistic Kernel Machine Based Test vs. Principal Component Analysis 
PLoS ONE  2012;7(9):e44978.
GWAS has facilitated greatly the discovery of risk SNPs associated with complex diseases. Traditional methods analyze SNP individually and are limited by low power and reproducibility since correction for multiple comparisons is necessary. Several methods have been proposed based on grouping SNPs into SNP sets using biological knowledge and/or genomic features. In this article, we compare the linear kernel machine based test (LKM) and principal components analysis based approach (PCA) using simulated datasets under the scenarios of 0 to 3 causal SNPs, as well as simple and complex linkage disequilibrium (LD) structures of the simulated regions. Our simulation study demonstrates that both LKM and PCA can control the type I error at the significance level of 0.05. If the causal SNP is in strong LD with the genotyped SNPs, both the PCA with a small number of principal components (PCs) and the LKM with kernel of linear or identical-by-state function are valid tests. However, if the LD structure is complex, such as several LD blocks in the SNP set, or when the causal SNP is not in the LD block in which most of the genotyped SNPs reside, more PCs should be included to capture the information of the causal SNP. Simulation studies also demonstrate the ability of LKM and PCA to combine information from multiple causal SNPs and to provide increased power over individual SNP analysis. We also apply LKM and PCA to analyze two SNP sets extracted from an actual GWAS dataset on non-small cell lung cancer.
PMCID: PMC3441747  PMID: 23028716
19.  Re-Ranking Sequencing Variants in the Post-GWAS Era for Accurate Causal Variant Identification 
PLoS Genetics  2013;9(8):e1003609.
Next generation sequencing has dramatically increased our ability to localize disease-causing variants by providing base-pair level information at costs increasingly feasible for the large sample sizes required to detect complex-trait associations. Yet, identification of causal variants within an established region of association remains a challenge. Counter-intuitively, certain factors that increase power to detect an associated region can decrease power to localize the causal variant. First, combining GWAS with imputation or low coverage sequencing to achieve the large sample sizes required for high power can have the unintended effect of producing differential genotyping error among SNPs. This tends to bias the relative evidence for association toward better genotyped SNPs. Second, re-use of GWAS data for fine-mapping exploits previous findings to ensure genome-wide significance in GWAS-associated regions. However, using GWAS findings to inform fine-mapping analysis can bias evidence away from the causal SNP toward the tag SNP and SNPs in high LD with the tag. Together these factors can reduce power to localize the causal SNP by more than half. Other strategies commonly employed to increase power to detect association, namely increasing sample size and using higher density genotyping arrays, can, in certain common scenarios, actually exacerbate these effects and further decrease power to localize causal variants. We develop a re-ranking procedure that accounts for these adverse effects and substantially improves the accuracy of causal SNP identification, often doubling the probability that the causal SNP is top-ranked. Application to the NCI BPC3 aggressive prostate cancer GWAS with imputation meta-analysis identified a new top SNP at 2 of 3 associated loci and several additional possible causal SNPs at these loci that may have otherwise been overlooked. This method is simple to implement using R scripts provided on the author's website.
Author Summary
As next-generation sequencing (NGS) costs continue to fall and genome-wide association study (GWAS) platform coverage improves, the human genetics community is positioned to identify potentially causal variants. However, current NGS or imputation-based studies of either the whole genome or regions previously identified by GWAS have not yet been very successful in identifying causal variants. A major hurdle is the development of methods to distinguish disease-causing variants from their highly-correlated proxies within an associated region. We show that various common factors, such as differential sequencing or imputation accuracy rates and linkage disequilibrium patterns, with or without GWAS-informed region selection, can substantially decrease the probability of identifying the correct causal SNP, often by more than half. We then describe a novel and easy-to-implement re-ranking procedure that can double the probability that the causal SNP is top-ranked in many settings. Application to the NCI Breast and Prostate Cancer (BPC3) Cohort Consortium aggressive prostate cancer data identified new top SNPs within two associated loci previously established via GWAS, as well as several additional possible causal SNPs that had been previously overlooked.
PMCID: PMC3738448  PMID: 23950724
20.  SNP- and haplotype-based genome-wide association studies for growth, carcass, and meat quality traits in a Duroc multigenerational population 
BMC Genetics  2016;17:60.
The aim of the present study was to compare the power of single nucleotide polymorphism (SNP)-based genome-wide association study (GWAS) and haplotype-based GWAS for quantitative trait loci (QTL) detection, and to detect novel candidate genes affecting economically important traits in a purebred Duroc population comprising seven-generation pedigree. First, we performed a simulation analysis using real genotype data of this population to compare the power (based on the null hypothesis) of the two methods. We then performed GWAS using both methods and real phenotype data comprising 52 traits, which included growth, carcass, and meat quality traits.
In total, 836 animals were genotyped using the Illumina PorcineSNP60 BeadChip and 14 customized SNPs from regions of known candidate genes related to the traits of interest. The power of SNP-based GWAS was greater than that of haplotype-based GWAS in a simulation analysis. In real data analysis, a larger number of significant regions was obtained by SNP-based GWAS than by haplotype-based GWAS. For SNP-based GWAS, 23 genome-wide significant SNP regions were detected for 17 traits, and 120 genome-wide suggestive SNP regions were detected for 27 traits. For haplotype-based GWAS, 6 genome-wide significant SNP regions were detected for four traits, and 11 genome-wide suggestive SNP regions were detected for eight traits. All genome-wide significant SNP regions detected by haplotype-based GWAS were located in regions also detected by SNP-based GWAS. Four regions detected by SNP-based GWAS were significantly associated with multiple traits: on Sus scrofa chromosome (SSC) 1 at 304 Mb; and on SSC7 at 35–39 Mb, 41–42 Mb, and 103 Mb. The vertnin gene (VRTN) in particular, was located on SSC7 at 103 Mb and was significantly associated with vertebrae number and carcass lengths. Mapped QTL regions contain some candidate genes involved in skeletal formation (FUBP3; far upstream element binding protein 3) and fat deposition (METTL3; methyltransferase like 3).
Our results show that a multigenerational pig population is useful for detecting QTL, which are typically segregated in a purebred population. In addition, a novel significant region could be detected by SNP-based GWAS as opposed to haplotype-based GWAS.
Electronic supplementary material
The online version of this article (doi:10.1186/s12863-016-0368-3) contains supplementary material, which is available to authorized users.
PMCID: PMC4837538  PMID: 27094516
Duroc pigs; Haplotype-based GWAS; Known candidate genes; Production traits; SNP-based GWAS
21.  Single Nucleotide Polymorphism (SNP)-Strings: An Alternative Method for Assessing Genetic Associations 
PLoS ONE  2014;9(4):e90034.
Genome-wide association studies (GWAS) identify disease-associations for single-nucleotide-polymorphisms (SNPs) from scattered genomic-locations. However, SNPs frequently reside on several different SNP-haplotypes, only some of which may be disease-associated. This circumstance lowers the observed odds-ratio for disease-association.
Methodology/Principal Findings
Here we develop a method to identify the two SNP-haplotypes, which combine to produce each person’s SNP-genotype over specified chromosomal segments. Two multiple sclerosis (MS)-associated genetic regions were modeled; DRB1 (a Class II molecule of the major histocompatibility complex) and MMEL1 (an endopeptidase that degrades both neuropeptides and β-amyloid). For each locus, we considered sets of eleven adjacent SNPs, surrounding the putative disease-associated gene and spanning ∼200 kb of DNA. The SNP-information was converted into an ordered-set of eleven-numbers (subject-vectors) based on whether a person had zero, one, or two copies of particular SNP-variant at each sequential SNP-location. SNP-strings were defined as those ordered-combinations of eleven-numbers (0 or 1), representing a haplotype, two of which combined to form the observed subject-vector. Subject-vectors were resolved using probabilistic methods. In both regions, only a small number of SNP-strings were present. We compared our method to the SHAPEIT-2 phasing-algorithm. When the SNP-information spanning 200 kb was used, SHAPEIT-2 was inaccurate. When the SHAPEIT-2 window was increased to 2,000 kb, the concordance between the two methods, in both of these eleven-SNP regions, was over 99%, suggesting that, in these regions, both methods were quite accurate. Nevertheless, correspondence was not uniformly high over the entire DNA-span but, rather, was characterized by alternating peaks and valleys of concordance. Moreover, in the valleys of poor-correspondence, SHAPEIT-2 was also inconsistent with itself, suggesting that the SNP-string method is more accurate across the entire region.
Accurate haplotype identification will enhance the detection of genetic-associations. The SNP-string method provides a simple means to accomplish this and can be extended to cover larger genomic regions, thereby improving a GWAS’s power, even for those published previously.
PMCID: PMC3984082  PMID: 24727690
22.  A random forest approach to the detection of epistatic interactions in case-control studies 
BMC Bioinformatics  2009;10(Suppl 1):S65.
The key roles of epistatic interactions between multiple genetic variants in the pathogenesis of complex diseases notwithstanding, the detection of such interactions remains a great challenge in genome-wide association studies. Although some existing multi-locus approaches have shown their successes in small-scale case-control data, the "combination explosion" course prohibits their applications to genome-wide analysis. It is therefore indispensable to develop new methods that are able to reduce the search space for epistatic interactions from an astronomic number of all possible combinations of genetic variants to a manageable set of candidates.
We studied case-control data from the viewpoint of binary classification. More precisely, we treated single nucleotide polymorphism (SNP) markers as categorical features and adopted the random forest to discriminate cases against controls. On the basis of the gini importance given by the random forest, we designed a sliding window sequential forward feature selection (SWSFS) algorithm to select a small set of candidate SNPs that could minimize the classification error and then statistically tested up to three-way interactions of the candidates. We compared this approach with three existing methods on three simulated disease models and showed that our approach is comparable to, sometimes more powerful than, the other methods. We applied our approach to a genome-wide case-control dataset for Age-related Macular Degeneration (AMD) and successfully identified two SNPs that were reported to be associated with this disease.
Besides existing pure statistical approaches, we demonstrated the feasibility of incorporating machine learning methods into genome-wide case-control studies. The gini importance offers yet another measure for the associations between SNPs and complex diseases, thereby complementing existing statistical measures to facilitate the identification of epistatic interactions and the understanding of epistasis in the pathogenesis of complex diseases.
PMCID: PMC2648748  PMID: 19208169
23.  High-throughput analysis of epistasis in genome-wide association studies with BiForce 
Bioinformatics  2012;28(15):1957-1964.
Motivation: Gene–gene interactions (epistasis) are thought to be important in shaping complex traits, but they have been under-explored in genome-wide association studies (GWAS) due to the computational challenge of enumerating billions of single nucleotide polymorphism (SNP) combinations. Fast screening tools are needed to make epistasis analysis routinely available in GWAS.
Results: We present BiForce to support high-throughput analysis of epistasis in GWAS for either quantitative or binary disease (case–control) traits. BiForce achieves great computational efficiency by using memory efficient data structures, Boolean bitwise operations and multithreaded parallelization. It performs a full pair-wise genome scan to detect interactions involving SNPs with or without significant marginal effects using appropriate Bonferroni-corrected significance thresholds. We show that BiForce is more powerful and significantly faster than published tools for both binary and quantitative traits in a series of performance tests on simulated and real datasets. We demonstrate BiForce in analysing eight metabolic traits in a GWAS cohort (323 697 SNPs, >4500 individuals) and two disease traits in another (>340 000 SNPs, >1750 cases and 1500 controls) on a 32-node computing cluster. BiForce completed analyses of the eight metabolic traits within 1 day, identified nine epistatic pairs of SNPs in five metabolic traits and 18 SNP pairs in two disease traits. BiForce can make the analysis of epistasis a routine exercise in GWAS and thus improve our understanding of the role of epistasis in the genetic regulation of complex traits.
Availability and implementation: The software is free and can be downloaded from
Supplementary information: Supplementary data are available at Bioinformatics online.
PMCID: PMC3400955  PMID: 22618535
24.  Assessing SNP-SNP Interactions among DNA Repair, Modification and Metabolism Related Pathway Genes in Breast Cancer Susceptibility 
PLoS ONE  2013;8(6):e64896.
Genome-wide association studies (GWASs) have identified low-penetrance common variants (i.e., single nucleotide polymorphisms, SNPs) associated with breast cancer susceptibility. Although GWASs are primarily focused on single-locus effects, gene-gene interactions (i.e., epistasis) are also assumed to contribute to the genetic risks for complex diseases including breast cancer. While it has been hypothesized that moderately ranked (P value based) weak single-locus effects in GWASs could potentially harbor valuable information for evaluating epistasis, we lack systematic efforts to investigate SNPs showing consistent associations with weak statistical significance across independent discovery and replication stages. The objectives of this study were i) to select SNPs showing single-locus effects with weak statistical significance for breast cancer in a GWAS and/or candidate-gene studies; ii) to replicate these SNPs in an independent set of breast cancer cases and controls; and iii) to explore their potential SNP-SNP interactions contributing to breast cancer susceptibility. A total of 17 SNPs related to DNA repair, modification and metabolism pathway genes were selected since these pathways offer a priori knowledge for potential epistatic interactions and an overall role in breast carcinogenesis. The study design included predominantly Caucasian women (2,795 cases and 4,505 controls) from Alberta, Canada. We observed two two-way SNP-SNP interactions (APEX1-rs1130409 and RPAP1-rs2297381; MLH1-rs1799977 and MDM2-rs769412) in logistic regression that conferred elevated risks for breast cancer (Pinteraction<7.3×10−3). Logic regression identified an interaction involving four SNPs (MBD2-rs4041245, MLH1-rs1799977, MDM2-rs769412, BRCA2-rs1799943) (Ppermutation = 2.4×10−3). SNPs involved in SNP-SNP interactions also showed single-locus effects with weak statistical significance, while BRCA2-rs1799943 showed stronger statistical significance (Pcorrelation/trend = 3.2×10−4) than the others. These single-locus effects were independent of body mass index. Our results provide a framework for evaluating SNPs showing statistically weak but reproducible single-locus effects for epistatic effects contributing to disease susceptibility.
PMCID: PMC3670937  PMID: 23755158
The annals of applied statistics  2014;8(4):2292-2318.
With the recent advent of high-throughput genotyping techniques, genetic data for genome-wide association studies (GWAS) have become increasingly available, which entails the development of efficient and effective statistical approaches. Although many such approaches have been developed and used to identify single-nucleotide polymorphisms (SNPs) that are associated with complex traits or diseases, few are able to detect gene–gene interactions among different SNPs. Genetic interactions, also known as epistasis, have been recognized to play a pivotal role in contributing to the genetic variation of phenotypic traits. However, because of an extremely large number of SNP–SNP combinations in GWAS, the model dimensionality can quickly become so overwhelming that no prevailing variable selection methods are capable of handling this problem. In this paper, we present a statistical framework for characterizing main genetic effects and epistatic interactions in a GWAS study. Specifically, we first propose a two-stage sure independence screening (TS-SIS) procedure and generate a pool of candidate SNPs and interactions, which serve as predictors to explain and predict the phenotypes of a complex trait. We also propose a rates adjusted thresholding estimation (RATE) approach to determine the size of the reduced model selected by an independence screening. Regularization regression methods, such as LASSO or SCAD, are then applied to further identify important genetic effects. Simulation studies show that the TS-SIS procedure is computationally efficient and has an outstanding finite sample performance in selecting potential SNPs as well as gene–gene interactions. We apply the proposed framework to analyze an ultrahigh-dimensional GWAS data set from the Framingham Heart Study, and select 23 active SNPs and 24 active epistatic interactions for the body mass index variation. It shows the capability of our procedure to resolve the complexity of genetic control.
PMCID: PMC4595934  PMID: 26457126
Gene–gene interaction; GWAS; high-dimensional data; sure independence screening; variable selection

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