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1.  Comparison of Methods for Competitive Tests of Pathway Analysis 
PLoS ONE  2012;7(7):e41018.
It has been suggested that pathway analysis can complement single-SNP analysis in exploring genomewide association data. Pathway analysis incorporates the available biological knowledge of genes and SNPs and is expected to improve the chances of revealing the underlying genetic architecture of complex traits. Methods for pathway analysis can be classified as competitive (enrichment) or self-contained (association) according to the hypothesis tested. Although association tests are statistically more powerful than enrichment tests they can be difficult to calibrate because biases in analysis accumulate across multiple SNPs or genes. Furthermore, enrichment tests can be more scientifically relevant than association tests, as they detect pathways with relatively more evidence for association than the remaining genes. Here we show how some well known association tests can be simply adapted to test for enrichment, and compare their performance to some established enrichment tests. We propose versions of the Adaptive Rank Truncated Product (ARTP), Tail Strength Measure and Fisher’s combination of p-values for testing the enrichment null hypothesis. We compare the behaviour of these proposed methods with the established Hypergeometric Test and Gene-Set Enrichment Analysis (GSEA). The results of the simulation study show that the modified version of the ARTP method has generally the best performance across the situations considered. The methods were also applied for finding enriched pathways for body mass index (BMI) and platelet function phenotypes. The pathway analysis of BMI identified the Vasoactive Intestinal Peptide pathway as significantly associated with BMI. This pathway has been previously reported as associated with BMI and the risk of obesity. The ARTP method was the method that identified the largest number of enriched pathways across all tested pathway databases and phenotypes. The simulation and data application results are in agreement with previous work on association tests and suggests that the ARTP should be preferred for both enrichment and association testing.
doi:10.1371/journal.pone.0041018
PMCID: PMC3409204  PMID: 22859961
2.  SNP-based pathway enrichment analysis for genome-wide association studies 
BMC Bioinformatics  2011;12:99.
Background
Recently we have witnessed a surge of interest in using genome-wide association studies (GWAS) to discover the genetic basis of complex diseases. Many genetic variations, mostly in the form of single nucleotide polymorphisms (SNPs), have been identified in a wide spectrum of diseases, including diabetes, cancer, and psychiatric diseases. A common theme arising from these studies is that the genetic variations discovered by GWAS can only explain a small fraction of the genetic risks associated with the complex diseases. New strategies and statistical approaches are needed to address this lack of explanation. One such approach is the pathway analysis, which considers the genetic variations underlying a biological pathway, rather than separately as in the traditional GWAS studies. A critical challenge in the pathway analysis is how to combine evidences of association over multiple SNPs within a gene and multiple genes within a pathway. Most current methods choose the most significant SNP from each gene as a representative, ignoring the joint action of multiple SNPs within a gene. This approach leads to preferential identification of genes with a greater number of SNPs.
Results
We describe a SNP-based pathway enrichment method for GWAS studies. The method consists of the following two main steps: 1) for a given pathway, using an adaptive truncated product statistic to identify all representative (potentially more than one) SNPs of each gene, calculating the average number of representative SNPs for the genes, then re-selecting the representative SNPs of genes in the pathway based on this number; and 2) ranking all selected SNPs by the significance of their statistical association with a trait of interest, and testing if the set of SNPs from a particular pathway is significantly enriched with high ranks using a weighted Kolmogorov-Smirnov test. We applied our method to two large genetically distinct GWAS data sets of schizophrenia, one from European-American (EA) and the other from African-American (AA). In the EA data set, we found 22 pathways with nominal P-value less than or equal to 0.001 and corresponding false discovery rate (FDR) less than 5%. In the AA data set, we found 11 pathways by controlling the same nominal P-value and FDR threshold. Interestingly, 8 of these pathways overlap with those found in the EA sample. We have implemented our method in a JAVA software package, called SNP Set Enrichment Analysis (SSEA), which contains a user-friendly interface and is freely available at http://cbcl.ics.uci.edu/SSEA.
Conclusions
The SNP-based pathway enrichment method described here offers a new alternative approach for analysing GWAS data. By applying it to schizophrenia GWAS studies, we show that our method is able to identify statistically significant pathways, and importantly, pathways that can be replicated in large genetically distinct samples.
doi:10.1186/1471-2105-12-99
PMCID: PMC3102637  PMID: 21496265
3.  Uncovering Networks from Genome-Wide Association Studies via Circular Genomic Permutation 
G3: Genes|Genomes|Genetics  2012;2(9):1067-1075.
Genome-wide association studies (GWAS) aim to detect single nucleotide polymorphisms (SNP) associated with trait variation. However, due to the large number of tests, standard analysis techniques impose highly stringent significance thresholds, leaving potentially associated SNPs undetected, and much of the trait genetic variation unexplained. Pathway- and network-based methodologies applied to GWAS aim to detect associations missed by standard single-marker approaches. The complex and non-random architecture of the genome makes it a challenge to derive an appropriate testing framework for such methodologies. We developed a rapid and simple permutation approach that uses GWAS SNP association results to establish the significance of pathway associations while accounting for the linkage disequilibrium structure of SNPs and the clustering of functionally related elements in the genome. All SNPs used in the GWAS are placed in a “circular genome” according to their location. Then the complete set of SNP association P values are permuted by rotation with respect to the genomic locations of the SNPs. Once these “simulated” P values are assigned, the joint gene P values are calculated using Fisher’s combination test, and the association of pathways is tested using the hypergeometric test. The circular genomic permutation approach was applied to a human genome-wide association dataset. The data consists of 719 individuals from the ORCADES study genotyped for ∼300,000 SNPs and measured for 51 traits ranging from physical to biochemical measurements. KEGG pathways (n = 225) were used as the sets of pathways to be tested. Our results demonstrate that the circular genomic permutations provide robust association P values. The non-permuted hypergeometric analysis generates ∼1400 pathway-trait combination results with an association P value more significant than P ≤ 0.05, whereas applying circular genomic permutation reduces the number of significant results to a more credible 40% of that value. The circular permutation software (“genomicper”) is available as an R package at http://cran.r-project.org/.
doi:10.1534/g3.112.002618
PMCID: PMC3429921  PMID: 22973544
GWAS; pathway-based; permutation method; genomicper R package; cardiac disease
4.  Finding type 2 diabetes causal single nucleotide polymorphism combinations and functional modules from genome-wide association data 
Background
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.
Methods
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.
Results
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.
Conclusions
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.
doi:10.1186/1472-6947-13-S1-S3
PMCID: PMC3618247  PMID: 23566118
5.  Hormone metabolism pathway genes and mammographic density change after quitting estrogen and progestin combined hormone therapy in the California Teachers Study 
Introduction
Mammographic density (MD) is a strong biomarker of breast cancer risk. MD increases after women start estrogen plus progestin therapy (EPT) and decreases after women quit EPT. A large interindividual variation in EPT-associated MD change has been observed, but few studies have investigated genetic predictors of the EPT-associated MD change. Here, we evaluate the association between polymorphisms in hormone metabolism pathway genes and MD changes when women quit EPT.
Methods
We collected mammograms before and after women quit EPT and genotyped 405 tagging single nucleotide polymorphisms (SNPs) in 30 hormone metabolism pathway genes in 284 non-Hispanic white participants of the California Teachers Study (CTS). Participants were ages 49 to 71 years at time of mammography taken after quitting EPT. We assessed percent MD using a computer-assisted method. MD change was calculated by subtracting MD of an ‘off-EPT’ mammogram from MD of an ‘on-EPT’ (that is baseline) mammogram. Linear regression analysis was used to investigate the SNP-MD change association, adjusting for the baseline ‘on-EPT’ MD, age and BMI at time of baseline mammogram, and time interval and BMI change between the two mammograms. An overall pathway and gene-level summary was obtained using the adaptive rank truncated product (ARTP) test. We calculated ‘P values adjusted for correlated tests (PACT)’ to account for multiple testing within a gene.
Results
The strongest associations were observed for rs7489119 in SLCO1B1, and rs5933863 in ARSC. SLCO1B1 and ARSC are involved in excretion and activation of estrogen metabolites of EPT, respectively. MD change after quitting was 4.2% smaller per minor allele of rs7489119 (P = 0.0008; PACT = 0.018) and 1.9% larger per minor allele of rs5933863 (P = 0.013; PACT = 0.025). These individual SNP associations did not reach statistical significance when we further used Bonferroni correction to consider the number of tested genes. The pathway level summary ARTP P value was not statistically significant.
Conclusions
Data from this longitudinal study of EPT quitters suggest that genetic variation in two hormone metabolism pathway genes, SLCO1B1 and ARSC, may be associated with change in MD after women stop using EPT. Larger longitudinal studies are needed to confirm our findings.
Electronic supplementary material
The online version of this article (doi:10.1186/s13058-014-0477-8) contains supplementary material, which is available to authorized users.
doi:10.1186/s13058-014-0477-8
PMCID: PMC4318222  PMID: 25499601
6.  RS-SNP: a random-set method for genome-wide association studies 
BMC Genomics  2011;12:166.
Background
The typical objective of Genome-wide association (GWA) studies is to identify single-nucleotide polymorphisms (SNPs) and corresponding genes with the strongest evidence of association (the 'most-significant SNPs/genes' approach). Borrowing ideas from micro-array data analysis, we propose a new method, named RS-SNP, for detecting sets of genes enriched in SNPs moderately associated to the phenotype. RS-SNP assesses whether the number of significant SNPs, with p-value P ≤ α, belonging to a given SNP set is statistically significant. The rationale of proposed method is that two kinds of null hypotheses are taken into account simultaneously. In the first null model the genotype and the phenotype are assumed to be independent random variables and the null distribution is the probability of the number of significant SNPs in greater than observed by chance. The second null model assumes the number of significant SNPs in depends on the size of and not on the identity of the SNPs in . Statistical significance is assessed using non-parametric permutation tests.
Results
We applied RS-SNP to the Crohn's disease (CD) data set collected by the Wellcome Trust Case Control Consortium (WTCCC) and compared the results with GENGEN, an approach recently proposed in literature. The enrichment analysis using RS-SNP and the set of pathways contained in the MSigDB C2 CP pathway collection highlighted 86 pathways rich in SNPs weakly associated to CD. Of these, 47 were also indicated to be significant by GENGEN. Similar results were obtained using the MSigDB C5 pathway collection. Many of the pathways found to be enriched by RS-SNP have a well-known connection to CD and often with inflammatory diseases.
Conclusions
The proposed method is a valuable alternative to other techniques for enrichment analysis of SNP sets. It is well founded from a theoretical and statistical perspective. Moreover, the experimental comparison with GENGEN highlights that it is more robust with respect to false positive findings.
doi:10.1186/1471-2164-12-166
PMCID: PMC3079664  PMID: 21450072
7.  Gene ontology analysis of pairwise genetic associations in two genome-wide studies of sporadic ALS 
BioData Mining  2012;5:9.
Background
It is increasingly clear that common human diseases have a complex genetic architecture characterized by both additive and nonadditive genetic effects. The goal of the present study was to determine whether patterns of both additive and nonadditive genetic associations aggregate in specific functional groups as defined by the Gene Ontology (GO).
Results
We first estimated all pairwise additive and nonadditive genetic effects using the multifactor dimensionality reduction (MDR) method that makes few assumptions about the underlying genetic model. Statistical significance was evaluated using permutation testing in two genome-wide association studies of ALS. The detection data consisted of 276 subjects with ALS and 271 healthy controls while the replication data consisted of 221 subjects with ALS and 211 healthy controls. Both studies included genotypes from approximately 550,000 single-nucleotide polymorphisms (SNPs). Each SNP was mapped to a gene if it was within 500 kb of the start or end. Each SNP was assigned a p-value based on its strongest joint effect with the other SNPs. We then used the Exploratory Visual Analysis (EVA) method and software to assign a p-value to each gene based on the overabundance of significant SNPs at the α = 0.05 level in the gene. We also used EVA to assign p-values to each GO group based on the overabundance of significant genes at the α = 0.05 level. A GO category was determined to replicate if that category was significant at the α = 0.05 level in both studies. We found two GO categories that replicated in both studies. The first, ‘Regulation of Cellular Component Organization and Biogenesis’, a GO Biological Process, had p-values of 0.010 and 0.014 in the detection and replication studies, respectively. The second, ‘Actin Cytoskeleton’, a GO Cellular Component, had p-values of 0.040 and 0.046 in the detection and replication studies, respectively.
Conclusions
Pathway analysis of pairwise genetic associations in two GWAS of sporadic ALS revealed a set of genes involved in cellular component organization and actin cytoskeleton, more specifically, that were not reported by prior GWAS. However, prior biological studies have implicated actin cytoskeleton in ALS and other motor neuron diseases. This study supports the idea that pathway-level analysis of GWAS data may discover important associations not revealed using conventional one-SNP-at-a-time approaches.
doi:10.1186/1756-0381-5-9
PMCID: PMC3463436  PMID: 22839596
8.  Gene, pathway and network frameworks to identify epistatic interactions of single nucleotide polymorphisms derived from GWAS data 
BMC Systems Biology  2012;6(Suppl 3):S15.
Background
Interactions among genomic loci (also known as epistasis) have been suggested as one of the potential sources of missing heritability in single locus analysis of genome-wide association studies (GWAS). The computational burden of searching for interactions is compounded by the extremely low threshold for identifying significant p-values due to multiple hypothesis testing corrections. Utilizing prior biological knowledge to restrict the set of candidate SNP pairs to be tested can alleviate this problem, but systematic studies that investigate the relative merits of integrating different biological frameworks and GWAS data have not been conducted.
Results
We developed four biologically based frameworks to identify pairwise interactions among candidate SNP pairs as follows: (1) for each human protein-coding gene, a set of SNPs associated with that gene was constructed providing a gene-based interaction model, (2) for each known biological pathway, a set of SNPs associated with the genes in the pathway was constructed providing a pathway-based interaction model, (3) a set of SNPs associated with genes in a disease-related subnetwork provides a network-based interaction model, and (4) a framework is based on the function of SNPs. The last approach uses expression SNPs (eSNPs or eQTLs), which are SNPs or loci that have defined effects on the abundance of transcripts of other genes. We constructed pairs of eSNPs and SNPs located in the target genes whose expression is regulated by eSNPs. For all four frameworks the SNP sets were exhaustively tested for pairwise interactions within the sets using a traditional logistic regression model after excluding genes that were previously identified to associate with the trait. Using previously published GWAS data for type 2 diabetes (T2D) and the biologically based pair-wise interaction modeling, we identify twelve genes not seen in the previous single locus analysis.
Conclusion
We present four approaches to detect interactions associated with complex diseases. The results show our approaches outperform the traditional single locus approaches in detecting genes that previously did not reach significance; the results also provide novel drug targets and biomarkers relevant to the underlying mechanisms of disease.
doi:10.1186/1752-0509-6-S3-S15
PMCID: PMC3524014  PMID: 23281810
9.  Large-Scale Pathway-Based Analysis of Bladder Cancer Genome-Wide Association Data from Five Studies of European Background 
PLoS ONE  2012;7(1):e29396.
Pathway analysis of genome-wide association studies (GWAS) offer a unique opportunity to collectively evaluate genetic variants with effects that are too small to be detected individually. We applied a pathway analysis to a bladder cancer GWAS containing data from 3,532 cases and 5,120 controls of European background (n = 5 studies). Thirteen hundred and ninety-nine pathways were drawn from five publicly available resources (Biocarta, Kegg, NCI-PID, HumanCyc, and Reactome), and we constructed 22 additional candidate pathways previously hypothesized to be related to bladder cancer. In total, 1421 pathways, 5647 genes and ∼90,000 SNPs were included in our study. Logistic regression model adjusting for age, sex, study, DNA source, and smoking status was used to assess the marginal trend effect of SNPs on bladder cancer risk. Two complementary pathway-based methods (gene-set enrichment analysis [GSEA], and adapted rank-truncated product [ARTP]) were used to assess the enrichment of association signals within each pathway. Eighteen pathways were detected by either GSEA or ARTP at P≤0.01. To minimize false positives, we used the I2 statistic to identify SNPs displaying heterogeneous effects across the five studies. After removing these SNPs, seven pathways (‘Aromatic amine metabolism’ [PGSEA = 0.0100, PARTP = 0.0020], ‘NAD biosynthesis’ [PGSEA = 0.0018, PARTP = 0.0086], ‘NAD salvage’ [PARTP = 0.0068], ‘Clathrin derived vesicle budding’ [PARTP = 0.0018], ‘Lysosome vesicle biogenesis’ [PGSEA = 0.0023, PARTP<0.00012], ’Retrograde neurotrophin signaling’ [PGSEA = 0.00840], and ‘Mitotic metaphase/anaphase transition’ [PGSEA = 0.0040]) remained. These pathways seem to belong to three fundamental cellular processes (metabolic detoxification, mitosis, and clathrin-mediated vesicles). Identification of the aromatic amine metabolism pathway provides support for the ability of this approach to identify pathways with established relevance to bladder carcinogenesis.
doi:10.1371/journal.pone.0029396
PMCID: PMC3251580  PMID: 22238607
10.  Comparison of Pathway Analysis Approaches Using Lung Cancer GWAS Data Sets 
PLoS ONE  2012;7(2):e31816.
Pathway analysis has been proposed as a complement to single SNP analyses in GWAS. This study compared pathway analysis methods using two lung cancer GWAS data sets based on four studies: one a combined data set from Central Europe and Toronto (CETO); the other a combined data set from Germany and MD Anderson (GRMD). We searched the literature for pathway analysis methods that were widely used, representative of other methods, and had available software for performing analysis. We selected the programs EASE, which uses a modified Fishers Exact calculation to test for pathway associations, GenGen (a version of Gene Set Enrichment Analysis (GSEA)), which uses a Kolmogorov-Smirnov-like running sum statistic as the test statistic, and SLAT, which uses a p-value combination approach. We also included a modified version of the SUMSTAT method (mSUMSTAT), which tests for association by averaging χ2 statistics from genotype association tests. There were nearly 18000 genes available for analysis, following mapping of more than 300,000 SNPs from each data set. These were mapped to 421 GO level 4 gene sets for pathway analysis. Among the methods designed to be robust to biases related to gene size and pathway SNP correlation (GenGen, mSUMSTAT and SLAT), the mSUMSTAT approach identified the most significant pathways (8 in CETO and 1 in GRMD). This included a highly plausible association for the acetylcholine receptor activity pathway in both CETO (FDR≤0.001) and GRMD (FDR = 0.009), although two strong association signals at a single gene cluster (CHRNA3-CHRNA5-CHRNB4) drive this result, complicating its interpretation. Few other replicated associations were found using any of these methods. Difficulty in replicating associations hindered our comparison, but results suggest mSUMSTAT has advantages over the other approaches, and may be a useful pathway analysis tool to use alongside other methods such as the commonly used GSEA (GenGen) approach.
doi:10.1371/journal.pone.0031816
PMCID: PMC3283683  PMID: 22363742
11.  Genome-wide Gene and Pathway Analysis 
Current GWAS have primarily focused on testing association of single SNPs. To only test for association of single SNPs has limited utility and is insufficient to dissect the complex genetic structure of many common diseases. To meet conceptual and technical challenges raised by GWAS, we propose gene and pathway-based GWAS as complementary to the current single SNP-based GWAS. This publication develops three statistics for testing association of genes and pathways with disease: linear combination test, quadratic test and decorrelation test which take correlations among SNPs within a gene or genes within a pathway into account. The null distribution of the proposed statistics is examined and the statistics are applied to GWAS of rheumatoid arthritis in the Wellcome Trust Case Control Consortium and the North American Rheumatoid Arthritis Consortium studies. The preliminary results show that the proposed gene and pathway-based GWAS offer several remarkable features. First, not only can they identify the genes that have large genetic effects, but also they can detect new genes in which each single SNP conferred a small amount of disease risk, and their joint actions can be implicated in the development of diseases. Second, gene and pathway-based analysis can allow the formation of the core of pathway definition of complex diseases and unravel the functional bases of an association finding. Third, replication of association findings at the gene or pathway level is much easier than replication at the individual SNP level.
doi:10.1038/ejhg.2010.62
PMCID: PMC2924916  PMID: 20442747
GWAS; gene association analysis; pathway association analysis; complex diseases
12.  JOINT ANALYSIS OF SNP AND GENE EXPRESSION DATA IN GENETIC ASSOCIATION STUDIES OF COMPLEX DISEASES 
The annals of applied statistics  2014;8(1):352-376.
Genetic association studies have been a popular approach for assessing the association between common Single Nucleotide Polymorphisms (SNPs) and complex diseases. However, other genomic data involved in the mechanism from SNPs to disease, e.g., gene expressions, are usually neglected in these association studies. In this paper, we propose to exploit gene expression information to more powerfully test the association between SNPs and diseases by jointly modeling the relations among SNPs, gene expressions and diseases. We propose a variance component test for the total effect of SNPs and a gene expression on disease risk. We cast the test within the causal mediation analysis framework with the gene expression as a potential mediator. For eQTL SNPs, the use of gene expression information can enhance power to test for the total effect of a SNP-set, which are the combined direct and indirect effects of the SNPs mediated through the gene expression, on disease risk. We show that the test statistic under the null hypothesis follows a mixture of χ2 distributions, which can be evaluated analytically or empirically using the resampling-based perturbation method. We construct tests for each of three disease models that is determined by SNPs only, SNPs and gene expression, or includes also their interactions. As the true disease model is unknown in practice, we further propose an omnibus test to accommodate different underlying disease models. We evaluate the finite sample performance of the proposed methods using simulation studies, and show that our proposed test performs well and the omnibus test can almost reach the optimal power where the disease model is known and correctly specified. We apply our method to re-analyze the overall effect of the SNP-set and expression of the ORMDL3 gene on the risk of asthma.
doi:10.1214/13-AOAS690
PMCID: PMC3981558  PMID: 24729824
Causal Inference; Data Integration; Mediation Analysis; Mixed Models; Score Test; SNP Set Analysis; Variance Component Test
13.  A System-Level Pathway-Phenotype Association Analysis Using Synthetic Feature Random Forest 
Genetic epidemiology  2014;38(3):209-219.
As the cost of genome-wide genotyping decreases, the number of genome-wide association studies (GWAS) has increased considerably. However, the transition from GWAS findings to the underlying biology of various phenotypes remains challenging. As a result, due to its system-level interpretability, pathway analysis has become a popular tool for gaining insights on the underlying biology from high-throughput genetic association data. In pathway analyses, gene sets representing particular biological processes are tested for significant associations with a given phenotype. Most existing pathway analysis approaches rely on single-marker statistics and assume that pathways are independent of each other. As biological systems are driven by complex biomolecular interactions, embracing the complex relationships between single-nucleotide polymorphisms (SNPs) and pathways needs to be addressed. To incorporate the complexity of gene-gene interactions and pathway-pathway relationships, we propose a system-level pathway analysis approach, synthetic feature random forest (SF-RF), which is designed to detect pathway-phenotype associations without making assumptions about the relationships among SNPs or pathways. In our approach, the genotypes of SNPs in a particular pathway are aggregated into a synthetic feature representing that pathway via Random Forest (RF). Multiple synthetic features are analyzed using RF simultaneously and the significance of a synthetic feature indicates the significance of the corresponding pathway. We further complement SF-RF with pathway-based Statistical Epistasis Network (SEN) analysis that evaluates interactions among pathways. By investigating the pathway SEN, we hope to gain additional insights into the genetic mechanisms contributing to the pathway-phenotype association. We apply SF-RF to a population-based genetic study of bladder cancer and further investigate the mechanisms that help explain the pathway-phenotype associations using SEN. The bladder cancer associated pathways we found are both consistent with existing biological knowledge and reveal novel and plausible hypotheses for future biological validations.
doi:10.1002/gepi.21794
PMCID: PMC4327826  PMID: 24535726
interactions; epistasis; pathway analysis; synthetic feature random forest (SF-RF); statistical epistasis network (SEN)
14.  Gene-Based Tests of Association 
PLoS Genetics  2011;7(7):e1002177.
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.
Author Summary
Genome-wide association studies (GWAS) have successfully identified genetic variants associated with complex human phenotypes. Despite a proliferation of analysis methods, most studies rely on simple, robust SNP–by–SNP univariate tests with ever-larger population sizes. Here we introduce a new test motivated by the biological hypothesis that a single gene may contain multiple variants that contribute independently to a trait. Applied to simulated phenotypes with real genotypes, our new method, Gene-Wide Significance (GWiS), has better power to identify true associations than traditional univariate methods, previous Bayesian methods, popular L1 regularized (LASSO) multivariate regression, and other approaches. GWiS retains power for low-frequency alleles that are increasingly important for personal genetics, and it is the only method tested that accurately estimates the number of independent effects within a gene. When applied to human data for multiple ECG traits, GWiS identifies more genome-wide significant loci (verified by meta-analyses of much larger populations) than any other method. We estimate that 35%–50% of ECG trait loci are likely to have multiple independent effects, suggesting that our method will reveal previously unidentified associations when applied to existing data and will improve power for future association studies.
doi:10.1371/journal.pgen.1002177
PMCID: PMC3145613  PMID: 21829371
15.  Pathways-Driven Sparse Regression Identifies Pathways and Genes Associated with High-Density Lipoprotein Cholesterol in Two Asian Cohorts 
PLoS Genetics  2013;9(11):e1003939.
Standard approaches to data analysis in genome-wide association studies (GWAS) ignore any potential functional relationships between gene variants. In contrast gene pathways analysis uses prior information on functional structure within the genome to identify pathways associated with a trait of interest. In a second step, important single nucleotide polymorphisms (SNPs) or genes may be identified within associated pathways. The pathways approach is motivated by the fact that genes do not act alone, but instead have effects that are likely to be mediated through their interaction in gene pathways. Where this is the case, pathways approaches may reveal aspects of a trait's genetic architecture that would otherwise be missed when considering SNPs in isolation. Most pathways methods begin by testing SNPs one at a time, and so fail to capitalise on the potential advantages inherent in a multi-SNP, joint modelling approach. Here, we describe a dual-level, sparse regression model for the simultaneous identification of pathways and genes associated with a quantitative trait. Our method takes account of various factors specific to the joint modelling of pathways with genome-wide data, including widespread correlation between genetic predictors, and the fact that variants may overlap multiple pathways. We use a resampling strategy that exploits finite sample variability to provide robust rankings for pathways and genes. We test our method through simulation, and use it to perform pathways-driven gene selection in a search for pathways and genes associated with variation in serum high-density lipoprotein cholesterol levels in two separate GWAS cohorts of Asian adults. By comparing results from both cohorts we identify a number of candidate pathways including those associated with cardiomyopathy, and T cell receptor and PPAR signalling. Highlighted genes include those associated with the L-type calcium channel, adenylate cyclase, integrin, laminin, MAPK signalling and immune function.
Author Summary
Genes do not act in isolation, but interact in complex networks or pathways. By accounting for such interactions, pathways analysis methods hope to identify aspects of a disease or trait's genetic architecture that might be missed using more conventional approaches. Most existing pathways methods take a univariate approach, in which each variant within a pathway is separately tested for association with the phenotype of interest. These statistics are then combined to assess pathway significance. As a second step, further analysis can reveal important genetic variants within significant pathways. We have previously shown that a joint-modelling approach using a sparse regression model can increase the power to detect pathways influencing a quantitative trait. Here we extend this approach, and describe a method that is able to simultaneously identify pathways and genes that may be driving pathway selection. We test our method using simulations, and apply it to a study searching for pathways and genes associated with high-density lipoprotein cholesterol in two separate East Asian cohorts.
doi:10.1371/journal.pgen.1003939
PMCID: PMC3836716  PMID: 24278029
16.  Set-Based Joint Test of Interaction Between SNPs in the VEGF Pathway and Exogenous Estrogen Finds Association With Age-Related Macular Degeneration 
Purpose.
Age-related macular degeneration (AMD) is the leading cause of irreversible visual loss in developed countries. Its etiology includes genetic and environmental factors. Although VEGFA variants are associated with AMD, the joint action of variants within the VEGF pathway and their interaction with nongenetic factors have not been investigated.
Methods.
Affymetrix 6.0 chipsets were used to genotype 668,238 single nucleotide polymorphisms (SNPs) in 1207 AMD cases and 686 controls. Environmental exposures were collected by questionnaire. A set-based test was conducted using the χ2 statistic at each SNP derived from Kraft's two degree of freedom (2df) joint test. Pathway- and gene-based test statistics were calculated as the mean of all independent SNP statistics. Phenotype labels were permuted 10,000 times to generate an empirical P value.
Results.
While a main effect of the VEGF pathway was not identified, the pathway was associated with neovascular AMD in women when accounting for birth control pill (BCP) use (P = 0.017). Analysis of VEGF's subpathways showed that SNPs in the proliferation subpathway were associated with neovascular AMD (P = 0.029) when accounting for BCP use. Nominally significant genes within this subpathway were also observed. Stratification by BCP use revealed novel significant genetic effects in women who had taken BCPs.
Conclusions.
These results illustrate that some AMD genetic risk factors may be revealed only when complex relationships among risk factors are considered. This shows the utility of exploring pathways of previously associated genes to find novel effects. It also demonstrates the importance of incorporating environmental exposures in tests of genetic association at the SNP, gene, or pathway level.
Analysis using a set-based joint test of genetic main effects and environmental interaction found that SNPs in VEGF's proliferation subpathway were associated with neovascular AMD when exogenous estrogen use in women was accounted for.
doi:10.1167/iovs.14-14494
PMCID: PMC4126792  PMID: 25015356
age-related macular degeneration; case-control study; epidemiology; statistics; candidate genes
17.  Detecting purely epistatic multi-locus interactions by an omnibus permutation test on ensembles of two-locus analyses 
BMC Bioinformatics  2009;10:294.
Background
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.
Results
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.
Conclusion
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.
doi:10.1186/1471-2105-10-294
PMCID: PMC2759961  PMID: 19761607
18.  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.
Background
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.
Results
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.
Conclusions
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.
doi:10.1186/1752-0509-8-S2-S5
PMCID: PMC4101698  PMID: 25032480
19.  Genetic variants in Fas signaling pathway genes and risk of gastric cancer 
Populations in north central China are at high risk for gastric cancers (GC), and altered FAS-mediated cell signaling and/or apoptosis may contribute to this risk. We examined the association of 554 single nucleotide polymorphisms (SNPs) in 53 Fas signaling-related genes using a pathway-based approach in 1758 GC cases (1126 gastric cardia adenocarcinomas (GCA) and 632 gastric noncardia adenocarcinomas (GNCA)), and 2111 controls from a genome-wide association study (GWAS) of GC in ethnic Chinese. SNP associations with risk of overall GC, GCA and GNCA were evaluated using unconditional logistic regressions controlling for age, sex and study. Gene- and pathway-based associations were tested using the adaptive rank-truncated product (ARTP) method. Statistical significance was evaluated empirically by permutation. Significant pathway-based associations were observed for Fas signaling with risk of overall GC (P = 5.5E-04) and GCA (P = 6.3E-03), but not GNCA (P = 8.1E-02). Among examined genes in the Fas signaling pathway, MAP2K4, FAF1, MAPK8, CASP10, CASP8, CFLAR, MAP2K1, CAP8AP2, PAK2 and IKBKB were associated with risk of GC (nominal P < 0.05), and FAF1 and MAPK8 were significantly associated with risk of both GCA and GNCA (nominal P < 0.05). Our examination of genetic variation in the Fas signaling pathway is consistent with an association of altered Fas signaling and/or apoptosis with risk of GC. As one of the first attempts to investigate a pathway-level association, our results suggest that these genes and the Fas signaling pathway warrant further evaluation in relation to GC risk in other populations.
doi:10.1002/ijc.28415
PMCID: PMC3858487  PMID: 23921907
Gastric cancer; gastric cardia; gastric noncardia; Fas signaling; genetic variants; GWAS; single nucleotide polymorphisms; pathway genes
20.  Systematic permutation testing in GWAS pathway analyses: identification of genetic networks in dilated cardiomyopathy and ulcerative colitis 
BMC Genomics  2014;15:622.
Background
Genome wide association studies (GWAS) are applied to identify genetic loci, which are associated with complex traits and human diseases. Analogous to the evolution of gene expression analyses, pathway analyses have emerged as important tools to uncover functional networks of genome-wide association data. Usually, pathway analyses combine statistical methods with a priori available biological knowledge. To determine significance thresholds for associated pathways, correction for multiple testing and over-representation permutation testing is applied.
Results
We systematically investigated the impact of three different permutation test approaches for over-representation analysis to detect false positive pathway candidates and evaluate them on genome-wide association data of Dilated Cardiomyopathy (DCM) and Ulcerative Colitis (UC). Our results provide evidence that the gold standard - permuting the case–control status – effectively improves specificity of GWAS pathway analysis. Although permutation of SNPs does not maintain linkage disequilibrium (LD), these permutations represent an alternative for GWAS data when case–control permutations are not possible. Gene permutations, however, did not add significantly to the specificity. Finally, we provide estimates on the required number of permutations for the investigated approaches.
Conclusions
To discover potential false positive functional pathway candidates and to support the results from standard statistical tests such as the Hypergeometric test, permutation tests of case control data should be carried out. The most reasonable alternative was case–control permutation, if this is not possible, SNP permutations may be carried out. Our study also demonstrates that significance values converge rapidly with an increasing number of permutations. By applying the described statistical framework we were able to discover axon guidance, focal adhesion and calcium signaling as important DCM-related pathways and Intestinal immune network for IgA production as most significant UC pathway.
doi:10.1186/1471-2164-15-622
PMCID: PMC4223581  PMID: 25052024
DCM; UC; GWAS; Permutation tests; Pathway analysis
21.  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.
doi:10.1186/2043-9113-3-4
PMCID: PMC3626712  PMID: 23410245
22.  Association tests using kernel-based measures of multi-locus genotype similarity between individuals 
Genetic Epidemiology  2010;34(3):213-221.
In a genetic association study, it is often desirable to perform an overall test of whether any or all single-nucleotide polymorphisms (SNPs) in a gene are associated with a phenotype. Several such tests exist, but most of them are powerful only under very specific assumptions about the genetic effects of the individual SNPs. In addition, some of the existing tests assume that the direction of the effect of each SNP is known, which is a highly unlikely scenario. Here we propose a new kernel-based association test (KBAT) of joint association of several SNPs. Our test is non-parametric and robust, and does not make any assumption about the directions of individual SNP effects. It can be used to test multiple correlated SNPs within a gene and can also be used to test independent SNPs or genes in a biological pathway. Our test uses an analysis of variance (ANOVA) paradigm to compare variation between cases and controls to the variation within the groups. The variation is measured using kernel functions for each marker, and then a composite statistic is constructed to combine the markers into a single test. We present simulation results comparing our statistic to the U-statistic based method by Schaid et al. and another statistic by Wessel and Schork. We consider a variety of different disease models and assumptions about how many SNPs within the gene are actually associated with disease. Our results indicate that our statistic has higher power than other statistics under most realistic conditions.
doi:10.1002/gepi.20451
PMCID: PMC3272581  PMID: 19697357
genetic similarity; association study; multilocus association
23.  Pathway-Based Analysis Using Genome-wide Association Data from a Korean Non-Small Cell Lung Cancer Study 
PLoS ONE  2013;8(6):e65396.
Pathway-based analysis, used in conjunction with genome-wide association study (GWAS) techniques, is a powerful tool to detect subtle but systematic patterns in genome that can help elucidate complex diseases, like cancers. Here, we stepped back from genetic polymorphisms at a single locus and examined how multiple association signals can be orchestrated to find pathways related to lung cancer susceptibility. We used single-nucleotide polymorphism (SNP) array data from 869 non-small cell lung cancer (NSCLC) cases from a previous GWAS at the National Cancer Center and 1,533 controls from the Korean Association Resource project for the pathway-based analysis. After mapping single-nucleotide polymorphisms to genes, considering their coding region and regulatory elements (±20 kbp), multivariate logistic regression of additive and dominant genetic models were fitted against disease status, with adjustments for age, gender, and smoking status. Pathway statistics were evaluated using Gene Set Enrichment Analysis (GSEA) and Adaptive Rank Truncated Product (ARTP) methods. Among 880 pathways, 11 showed relatively significant statistics compared to our positive controls (PGSEA≤0.025, false discovery rate≤0.25). Candidate pathways were validated using the ARTP method and similarities between pathways were computed against each other. The top-ranked pathways were ABC Transporters (PGSEA<0.001, PARTP = 0.001), VEGF Signaling Pathway (PGSEA<0.001, PARTP = 0.008), G1/S Check Point (PGSEA = 0.004, PARTP = 0.013), and NRAGE Signals Death through JNK (PGSEA = 0.006, PARTP = 0.001). Our results demonstrate that pathway analysis can shed light on post-GWAS research and help identify potential targets for cancer susceptibility.
doi:10.1371/journal.pone.0065396
PMCID: PMC3675130  PMID: 23762359
24.  Genome-wide gene and pathway analysis 
European Journal of Human Genetics  2010;18(9):1045-1053.
Current GWAS have primarily focused on testing association of single SNPs. To only test for association of single SNPs has limited utility and is insufficient to dissect the complex genetic structure of many common diseases. To meet conceptual and technical challenges raised by GWAS, we suggest gene and pathway-based GWAS as complementary to the current single SNP-based GWAS. This publication develops three statistics for testing association of genes and pathways with disease: linear combination test, quadratic test and decorrelation test, which take correlations among SNPs within a gene or genes within a pathway into account. The null distribution of the suggested statistics is examined and the statistics are applied to GWAS of rheumatoid arthritis in the Wellcome Trust Case–Control Consortium and the North American Rheumatoid Arthritis Consortium studies. The preliminary results show that the suggested gene and pathway-based GWAS offer several remarkable features. First, not only can they identify the genes that have large genetic effects, but also they can detect new genes in which each single SNP conferred a small amount of disease risk, and their joint actions can be implicated in the development of diseases. Second, gene and pathway-based analysis can allow the formation of the core of pathway definition of complex diseases and unravel the functional bases of an association finding. Third, replication of association findings at the gene or pathway level is much easier than replication at the individual SNP level.
doi:10.1038/ejhg.2010.62
PMCID: PMC2924916  PMID: 20442747
GWAS; gene association analysis; pathway association analysis; complex diseases
25.  A Genomic Pathway Approach to a Complex Disease: Axon Guidance and Parkinson Disease 
PLoS Genetics  2007;3(6):e98.
While major inroads have been made in identifying the genetic causes of rare Mendelian disorders, little progress has been made in the discovery of common gene variations that predispose to complex diseases. The single gene variants that have been shown to associate reproducibly with complex diseases typically have small effect sizes or attributable risks. However, the joint actions of common gene variants within pathways may play a major role in predisposing to complex diseases (the paradigm of complex genetics). The goal of this study was to determine whether polymorphism in a candidate pathway (axon guidance) predisposed to a complex disease (Parkinson disease [PD]). We mined a whole-genome association dataset and identified single nucleotide polymorphisms (SNPs) that were within axon-guidance pathway genes. We then constructed models of axon-guidance pathway SNPs that predicted three outcomes: PD susceptibility (odds ratio = 90.8, p = 4.64 × 10−38), survival free of PD (hazards ratio = 19.0, p = 5.43 × 10−48), and PD age at onset (R2 = 0.68, p = 1.68 × 10−51). By contrast, models constructed from thousands of random selections of genomic SNPs predicted the three PD outcomes poorly. Mining of a second whole-genome association dataset and mining of an expression profiling dataset also supported a role for many axon-guidance pathway genes in PD. These findings could have important implications regarding the pathogenesis of PD. This genomic pathway approach may also offer insights into other complex diseases such as Alzheimer disease, diabetes mellitus, nicotine and alcohol dependence, and several cancers.
Author Summary
Complex diseases are common disorders that are believed to have many causes. Examples include Alzheimer disease, diabetes mellitus, nicotine and alcohol dependence, and several cancers. This study represents a paradigm shift from single gene to pathway studies of complex diseases. We present the example of Parkinson disease (PD) and a complex array of chemical signals that wires the brain during fetal development (the axon guidance pathway). We mined a dataset that studied hundreds of thousands of DNA variations (single nucleotide polymorphisms [SNPs]) in persons with and without PD and identified SNPs that were assigned to axon-guidance pathway genes. We then identified sets of SNPs that were highly predictive of PD susceptibility, survival free of PD, and age at onset of PD. The effect sizes and the statistical significance observed for the pathway were far greater than for any single gene. We validated our findings for the pathway using a second SNP dataset for PD and also a dataset for PD that studied RNA variations. There is prior evidence that the axon guidance pathway might play a role in other brain disorders (e.g., Alzheimer disease, Tourette syndrome, dyslexia, epilepsy, and schizophrenia). A genomic pathway approach may lead to important breakthroughs for many complex diseases.
doi:10.1371/journal.pgen.0030098
PMCID: PMC1904362  PMID: 17571925

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