GATES: A Rapid and Powerful Gene-Based Association Test Using Extended Simes Procedure

The gene has been proposed as an attractive unit of analysis for association studies, but a simple yet valid, powerful, and sufficiently fast method of evaluating the statistical significance of all genes in large, genome-wide datasets has been lacking. Here we propose the use of an extended Simes test that integrates functional information and association evidence to combine the p values of the single nucleotide polymorphisms within a gene to obtain an overall p value for the association of the entire gene. Our computer simulations demonstrate that this test is more powerful than the SNP-based test, offers effective control of the type 1 error rate regardless of gene size and linkage-disequilibrium pattern among markers, and does not need permutation or simulation to evaluate empirical significance. Its statistical power in simulated data is at least comparable, and often superior, to that of several alternative gene-based tests. When applied to real genome-wide association study (GWAS) datasets on Crohn disease, the test detected more significant genes than SNP-based tests and alternative gene-based tests. The proposed test, implemented in an open-source package, has the potential to identify additional novel disease-susceptibility genes for complex diseases from large GWAS datasets. The gene has been proposed as an attractive unit of analysis for association studies, but a simple yet valid, powerful, and sufficiently fast method of evaluating the statistical significance of all genes in large, genome-wide datasets has been lacking. Here we propose the use of an extended Simes test that integrates functional information and association evidence to combine the p values of the single nucleotide polymorphisms within a gene to obtain an overall p value for the association of the entire gene. Our computer simulations demonstrate that this test is more powerful than the SNP-based test, offers effective control of the type 1 error rate regardless of gene size and linkage-disequilibrium pattern among markers, and does not need permutation or simulation to evaluate empirical significance. Its statistical power in simulated data is at least comparable, and often superior, to that of several alternative gene-based tests. When applied to real genome-wide association study (GWAS) datasets on Crohn disease, the test detected more significant genes than SNP-based tests and alternative gene-based tests. The proposed test, implemented in an open-source package, has the potential to identify additional novel disease-susceptibility genes for complex diseases from large GWAS datasets. Genome-wide association studies (GWASs) are being used for identification of susceptibility loci for complex diseases.1McCarthy M.I. Abecasis G.R. Cardon L.R. Goldstein D.B. Little J. Ioannidis J.P. Hirschhorn J.N. Genome-wide association studies for complex traits: Consensus, uncertainty and challenges.Nat. Rev. Genet. 2008; 9: 356-369Crossref PubMed Scopus (2023) Google Scholar These studies typically use the single nucleotide polymorphism (SNP) as the basic unit of analysis, which is a convenient strategy and has led to the discovery of many important genetic loci for human diseases.2Manolio T.A. Brooks L.D. Collins F.S. A HapMap harvest of insights into the genetics of common disease.J. Clin. Invest. 2008; 118: 1590-1605Crossref PubMed Scopus (714) Google Scholar However, the statistically significant variants detected so far explain only a modest proportion of the total variance in liability to disease, and inadequate statistical power is likely to have contributed to the failure to detect true effects.3Altshuler D. Daly M. Guilt beyond a reasonable doubt.Nat. Genet. 2007; 39: 813-815Crossref PubMed Scopus (122) Google Scholar, 4Frazer K.A. Murray S.S. Schork N.J. Topol E.J. Human genetic variation and its contribution to complex traits.Nat. Rev. Genet. 2009; 10: 241-251Crossref PubMed Scopus (727) Google Scholar The problem of statistical power is exacerbated by the necessity of adopting stringent p value thresholds for significance (typically 5 × 10−8) in order to control false-positive association from the large number of SNPs tested. In addition, many significant SNPs are likely to represent surrogate markers in linkage disequilibrium (LD) with the variants causing diseases, and differences in LD patterns across populations can lead to nonreplication of the same SNP in another population but significant association for some other surrogate SNPs.5Kraft P. Zeggini E. Ioannidis J.P. Replication in genome-wide association studies.Stat. Sci. 2009; 24: 561-573Crossref PubMed Scopus (173) Google Scholar Shifting from SNP-based association analysis to gene-based analysis is one possible way to improve the power of GWASs. In a gene-based analysis, one jointly analyzes all variants within a putative gene to obtain a single p value representing the significance of association of the entire gene. Analysis using the gene as the basic unit has several attractive features. First, the gene is the functional unit of the human genome. Unlike genetic variants that have different allele frequencies, LD structure, and heterogeneity across diverse human populations, the gene itself is highly consistent across populations.6Neale B.M. Sham P.C. The future of association studies: Gene-based analysis and replication.Am. J. Hum. Genet. 2004; 75: 353-362Abstract Full Text Full Text PDF PubMed Scopus (505) Google Scholar Gene-based analysis might therefore lead to more consistent results and alleviates difficulties in replication. Second, gene-based analysis reduces the multiple-testing burden substantially; it requires correction for approximately 20,000–30,000 genes rather than potentially millions of SNPs. Finally, with the gene as the unit of analysis, extension of the findings to further functional analyses, such as protein-protein interactions (PPIs) and biological pathways, is more straightforward. The integration of association evidence and functional information might facilitate the unraveling of the pathogenic mechanisms of complex diseases. A number of gene-based association tests have been proposed. Linear regression (for quantitative traits) and logistic regression (for binary traits) are straightforward methods of evaluating the overall association between a gene and a trait. In these tests, all the SNPs or haplotypes in the gene are entered as predictor variables simultaneously, except for redundant SNPs, whose inclusion would result in collinearity.6Neale B.M. Sham P.C. The future of association studies: Gene-based analysis and replication.Am. J. Hum. Genet. 2004; 75: 353-362Abstract Full Text Full Text PDF PubMed Scopus (505) Google Scholar However, a simple regression analysis might suffer from low statistical power if many SNPs or haplotypes are included, resulting in a test with many degrees. Many methods reduce the dimensionality of the test by compressing the information in the multiple correlated SNPs, for example by Fourier transformation,7Wang T. Elston R.C. Improved power by use of a weighted score test for linkage disequilibrium mapping.Am. J. Hum. Genet. 2007; 80: 353-360Abstract Full Text Full Text PDF PubMed Scopus (91) Google Scholar principal-components analysis,8Gauderman W.J. Murcray C. Gilliland F. Conti D.V. Testing association between disease and multiple SNPs in a candidate gene.Genet. Epidemiol. 2007; 31: 383-395Crossref PubMed Scopus (160) Google Scholar, 9Wang K. Abbott D. A principal components regression approach to multilocus genetic association studies.Genet. Epidemiol. 2008; 32: 108-118Crossref PubMed Scopus (104) Google Scholar the use of fixed SNP weights based on the LD pattern across the gene,10Li M. Wang K. Grant S.F. Hakonarson H. Li C. ATOM: A powerful gene-based association test by combining optimally weighted markers.Bioinformatics. 2009; 25: 497-503Crossref PubMed Scopus (40) Google Scholar and cluster analysis.11Buil A. Martinez-Perez A. Perera-Lluna A. Rib L. Caminal P. Soria J.M. A new gene-based association test for genome-wide association studies.BMC Proc. 2009; 3: S130Crossref PubMed Google Scholar All these regression-based methods require the availability of the raw, individual phenotype and genotype data. Methods involving the combination of the SNP-based test statistics or p values have also been proposed. The largest test statistic from all the SNP-based tests in a gene has been proposed as a gene-based test statistic.12Wang K. Li M. Bucan M. Pathway-based approaches for analysis of genomewide association studies.Am. J. Hum. Genet. 2007; 81: 1278-1283Abstract Full Text Full Text PDF PubMed Scopus (656) Google Scholar However, the value of this statistic is expected to be positively correlated with the number of SNPs in the gene, and although adjustment for gene size by a permutation procedure is possible, this is time consuming for large datasets.12Wang K. Li M. Bucan M. Pathway-based approaches for analysis of genomewide association studies.Am. J. Hum. Genet. 2007; 81: 1278-1283Abstract Full Text Full Text PDF PubMed Scopus (656) Google Scholar Another possible method is to combine the p values of the SNPs in a gene by Fisher's combination test.13Curtis D. Vine A.E. Knight J. A simple method for assessing the strength of evidence for association at the level of the whole gene.Advances and Applications in Bioinformatics and Chemistry. 2008; 2008: 1Google Scholar However, this method assumes that the constituent p values should be based on independent tests, which is unlikely to be true for SNPs in the same gene. Violation of this assumption is likely to inflate the type I error rate, unless use of a permutation procedure provides empirical statistical significance. A variant of the Fisher's method is the truncated-product p value method,14Yang H.C. Liang Y.J. Chung C.M. Chen J.W. Pan W.H. Genome-wide gene-based association study.BMC Proc. 2009; 3: S135Crossref PubMed Google Scholar which was originally developed to deal with “publication bias” in meta-analysis.15Zaykin D.V. Zhivotovsky L.A. Westfall P.H. Weir B.S. Truncated product method for combining P-values.Genet. Epidemiol. 2002; 22: 170-185Crossref PubMed Scopus (372) Google Scholar However, like the Fisher's combination method, this test is also sensitive to LD among the SNPs in a gene and therefore requires a permutation procedure if an empirical p value is to be obtained. Instead of permutation, which requires raw genotype data, a recent variation of the Fisher's combination test uses a simulation approach based on normal variables with correlations that are assigned values according to the LD structure between SNPs.16Liu J.Z. McRae A.F. Nyholt D.R. Medland S.E. Wray N.R. Brown K.M. Hayward N.K. Montgomery G.W. Visscher P.M. Martin N.G. Macgregor S. AMFS InvestigatorsA versatile gene-based test for genome-wide association studies.Am. J. Hum. Genet. 2010; 87: 139-145Abstract Full Text Full Text PDF PubMed Scopus (586) Google Scholar The p values of this method are highly correlated with those obtained from a permutation procedure. The simulation method, although faster than permutation, is still computationally intensive when applied to genome-wide datasets. A separate issue for the design of gene-based tests is the possibility of improving the power of the test by imposing weights on the SNPs according to prior information on their likely relative importance. The idea of p value weights was introduced in the context of a sequential step-down test for maintaining the family-wise type 1 error rate17Holm S. A simple sequentially rejective multiple test procedure.Scand. J. Stat. 1979; 6: 65-70Crossref Google Scholar and was subsequently incorporated into a false-discovery rate (FDR) procedure.18Benjamini Y. Hochberg Y. Multiple hypotheses testing with weights.Scand. J. Stat. 1997; 24: 407-418Crossref Scopus (173) Google Scholar A procedure for assigning prior p value weights based on a mixture model for p values has been suggested.19Genovese C.R. Roeder K. Wasserman L. False discovery control with p-value weighting.Biometrika. 2006; 93: 509-524Crossref Scopus (169) Google Scholar Indeed, given the observed p values, it is possible to optimize the choice of p value weights to be applied to tests grouped by prior information.20Roeder K. Devlin B. Wasserman L. Improving power in genome-wide association studies: Weights tip the scale.Genet. Epidemiol. 2007; 31: 741-747Crossref PubMed Scopus (69) Google Scholar However, because the observed dataset might contain limited information, it might be desirable to also make use of established functional information and prior data in the assignment of p value weights. In this paper, we propose a rapid gene-based association test that uses extended Simes procedure (GATES) to assess the gene-level statistical association significance that can efficiently handle results based on millions of SNPs (possibly from imputation and meta-analysis) in the later stages of GWASs and next-generation sequencing studies. This test can rapidly combine the p values of SNPs within a gene, without relying on raw, individual phenotype and genotype data, to produce valid gene-based p values. This gene-based test can also incorporate functional information on SNPs by the use of prior weights to increase statistical power. After introducing the test, we present a series of computer simulations that are useful in investigating the test's type 1 error rate, and we compare the test's statistical power with that of alternative gene-based tests. To assess its performance in real datasets, we applied the method to GWAS data on Crohn disease (CD [MIM 266600]). We assume that a test of association between the disease and each of the available SNPs within a gene has been carried out and that the resulting p values and pair-wise correlation coefficients r for all the SNPs are available. The proposed method, GATES, a modification of the Simes test, combines these available p values to give a gene-based p value. Let p(1), …, p(m) be the ascending p values of m SNPs within a gene. We propose combining the m SNP-based p values to obtain an overall p value for the gene as follows:PG=Min(mep(j)me(j)),where me is the effective number of independent p values among the m SNPs and me(j) is the effective number of independent p values among the top j SNPs. The null hypothesis of this gene-based test is that no SNP within the gene is associated with the disease, whereas the alternative is that at least one SNP in the gene is associated with the disease. In the test proposed above, we used a measure that is more robust than those currently available21Galwey N.W. A new measure of the effective number of tests, a practical tool for comparing families of non-independent significance tests.Genet. Epidemiol. 2009; 33: 559-568Crossref PubMed Scopus (70) Google Scholar, 22Gao X. Starmer J. Martin E.R. A multiple testing correction method for genetic association studies using correlated single nucleotide polymorphisms.Genet. Epidemiol. 2008; 32: 361-369Crossref PubMed Scopus (422) Google Scholar, 23Moskvina V. Schmidt K.M. On multiple-testing correction in genome-wide association studies.Genet. Epidemiol. 2008; 32: 567-573Crossref PubMed Scopus (174) Google Scholar, 24Nyholt D.R. A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with each other.Am. J. Hum. Genet. 2004; 74: 765-769Abstract Full Text Full Text PDF PubMed Scopus (1314) Google Scholar (unpublished data) to obtain me. The value of me is estimated to be equal to M−∑i=1M[I(λi>1)(λi−1)]λi>0, where I(x) is an indicator function and λi is the ith eigenvalue of the p value correlation coefficient matrix [ρi,j] of SNP-based statistic tests. The negative eigenvalues are set as zero and ignored. Negative eigenvalues should only arise in the presence of missing data, and they are usually relatively few in number and close to zero.21Galwey N.W. A new measure of the effective number of tests, a practical tool for comparing families of non-independent significance tests.Genet. Epidemiol. 2009; 33: 559-568Crossref PubMed Scopus (70) Google Scholar When the SNPs are independent, the eigenvalues are all 1, so that me is equal to the number of SNPs. When all the SNPs are in complete LD, the first eigenvalue is equal to the number of SNPs and the rest are 0, so that me = 1. For intermediate situations, we have performed simulation and permutation studies (see below) to show that the formula also provides an appropriate effective number of SNP p values and that PG will thus have an approximate uniform (0,1) distribution.18Benjamini Y. Hochberg Y. Multiple hypotheses testing with weights.Scand. J. Stat. 1997; 24: 407-418Crossref Scopus (173) Google Scholar, 25Simes R.J. An improved Bonferroni procedure for multiple tests of significance.Biometrika. 1986; 73: 751-754Crossref Scopus (1423) Google Scholar For a simple case-control study, the pair-wise SNP p value correlation coefficient ρ is expected to be mainly determined by the pair-wise LD between the two corresponding SNPs, as measured by the allelic correlation coefficient r, although it could also be influenced by the allele frequencies of the two SNPs and the numbers of cases and controls in the study. We explored the relationship ρ and r, for different allele frequencies and sample sizes, empirically by simulation. Genotype data of two biallelic SNPs were simulated for 1,500 cases and 1,500 controls, for a particular set of values of r and allele frequencies, under Hardy-Weinberg equilibrium. We then performed an allelic association test for each of the two SNP to obtain two p values. Repeating this procedure 100,000 times resulted in 100,000 sets of p values, from which the correlation coefficient of the p values of the two SNPs,ρ, was calculated. We increased the allele frequencies and r in steps of 0.05 from their minimum to their maximum values to generate a series of data points. It turned out that the p value correlation coefficient ρ could be accurately approximated by a sixth-order polynomial function of the pair-wise allelic correlation coefficient r (coefficient of determination R2 = 0.9986), regardless of allele frequencies (see Figure 1). Repeated simulations using samples of different sizes and quantitative traits (analyzed by linear regression) also yielded the same polynomial approximation. The gene-based test can be further extended to incorporate differential SNP weights as follows:PG=Min(mep(j)∑k=1jw(k)),where w(1), …, w(m) are non-negative and sum to me. These weights are calculated from prior weights r(1), …, r(m), set according to the relative functional importance of the SNP to non-negative values but otherwise unconstrained. The procedure takes in turn the sorted SNPs, according w(i) = c(me(i) − me(i-1))r(i), where me(0) = 0 and c is defined such that the weights sum to me:c=me∑i=1m(me(i)−me(i−1))r(i)The use of weights is expected to increase statistical power if SNPs with higher weights are more likely to be associated with disease than SNPs with lower weights. In the absence of information, equal weights can be used. We performed simulation studies to compare the type 1 error rate and statistical power of GATES with those of the following alternative gene-based tests:•Logistic regression. Each SNP is entered as an explanatory variable, coded as 0, 1, or 2 for the number of copies of the minor allele in the genotype, and case-control status is coded as the response variable. A gene-based p value is provided by the likelihood ratio test comparing the full model with all available SNPs and the null model without any SNP.•Fisher combination test. The gene-based test statistic is given by T=−2∑j=1mlnp(j), which has a chi-square distribution with 2m degrees of freedom under the null hypothesis when the m tests are independent.26Fisher R.A. Statistical methods for research workers.Twelfth Edition. Hafner, New York1954Google Scholar The test is expected to be liberal for positively correlated tests, such that a permutation procedure is needed if a valid p value is to be obtained.13Curtis D. Vine A.E. Knight J. A simple method for assessing the strength of evidence for association at the level of the whole gene.Advances and Applications in Bioinformatics and Chemistry. 2008; 2008: 1Google Scholar•Original Simes test. The gene-based p value is PS=min(mp(j)/j). For independent tests, PS is uniform (0,1) under the null hypothesis. For positively correlated tests, PS is expected to be conservative.•A versatile gene-based test for genome-wide association studies (VEGAS) proposed recently by Liu et al. (2010).16Liu J.Z. McRae A.F. Nyholt D.R. Medland S.E. Wray N.R. Brown K.M. Hayward N.K. Montgomery G.W. Visscher P.M. Martin N.G. Macgregor S. AMFS InvestigatorsA versatile gene-based test for genome-wide association studies.Am. J. Hum. Genet. 2010; 87: 139-145Abstract Full Text Full Text PDF PubMed Scopus (586) Google Scholar The test allows the SNP-based chi-square test statistics within a gene to be combined in a flexible manner to give a gene-based test statistic (e.g., it can take the sum of all the statistics, or the sum of the several top statistics, or simply the largest statistic). An empirical null distribution for this gene-based test statistic is obtained through a simulation of multivariate standard normal random vectors with correlations equal to those between the SNPs in the gene; the component variables are squared to give correlated chi-square random variables, and then appropriate variables are summed as dictated by how the gene-based test statistic was calculated. In our simulations, we calculated two versions of the test, one based on the sum of all the SNP-based chi-square statistics in the gene (VEGAS-Sum) and one based on just the largest statistic (VEGAS-Max). Note that only logistic regression requires the raw phenotype and genotype data, whereas the other tests require only the SNP-based p values. However, a permutation procedure, which is necessary to ensure the correct type 1 error rates for the Fisher and original Simes tests when the SNPs are correlated, also requires the raw data. The VEGAS method does not require raw data but instead requires only the correlation matrix of the SNPs. The simulation involved the generation of genotype data on 30 SNPs, which were all biallelic and under Hardy-Weinberg equilibrium. We considered three different scenarios in terms of LD structure: (1) the SNPs are situated in six strong LD blocks (see Table S1), (2) the SNPs are situated in six moderate LD blocks (see Table S2), or (3) the SNPs are in linkage equilibrium. Given the LD pattern and the allele frequencies of the 30 SNPs, we used a program based on the HapSim algorithm27Montana G. HapSim: A simulation tool for generating haplotype data with pre-specified allele frequencies and LD coefficients.Bioinformatics. 2005; 21: 4309-4311Crossref PubMed Scopus (48) Google Scholar to generate genotype data. We then considered three different scenarios in terms of gene size: (1) a three-SNP gene containing the first three SNPs, (2) a ten-SNP gene containing the first ten SNPs, and (3) a 30-SNP gene containing all 30 SNPs. Finally, we considered three scenarios in terms of disease model: (1) a null model where no SNP has any effect on disease risk, (2) an additive model where one SNP in each LD block has a minor allele that increases the risk ratio additively by 0.14, and (3) a multiplicative model where one SNP in each LD block has a minor allele that increases the risk ratio multiplicatively by a factor of 1.14 (see Tables S1 and S2).28Risch N. Linkage strategies for genetically complex traits. I. Multilocus models.Am. J. Hum. Genet. 1990; 46: 222-228PubMed Google Scholar Because three-SNP, ten-SNP, and 30-SNP genes contain one, two, and six LD blocks, respectively, the number of susceptibility SNPs they contain are correspondingly one, two, and six. The baseline risk corresponding to the absence of any risk-increasing alleles is calculated from the allele frequencies and risk ratios of the susceptibility SNPs and gives a population disease prevalence of 0.1. For each combination of scenarios, a population of 1,000,000 individuals was generated. A random sample of 1500 cases and 1500 controls was drawn, without replacement, from the population and subjected to the different methods of gene-based association. Type 1 error rates and statistical power estimates under the different scenarios were obtained from the proportion of simulated datasets, out of 1,000 simulated populations, that resulted in significant p values (set at 0.05). To evaluate the impact of weighting the SNPs in the construction of the gene-based test, we assigned some SNP with a high weight (wi > 1) and the others with a low weight (0 < wi < 1) in simulated data generated as described above. We considered two scenarios of weight assignment: (1) the SNPs assigned to have the high weight are the true susceptibility SNPs, whereas the SNPs assigned to have the low weight have no direct causal effect, and (2) the assignment of weight is random. Although the first scenario is expected to increase statistical power, the latter scenario is expected to have no effect or to result in reduced statistical power. Although random assignment is not the worst possible scenario, it might be the worst that is likely to occur in real data analyses. We also varied the ratio of high to low weights from 1 to 16 to see the impact on type 1 error rates and statistical power. The above evaluation of type 1 error rates in simulation was based on arbitrary LD structure and might not represent realistic examples of the actual LD structure of genes in real populations. In order to assess the genome-wide type 1 error rates under realistic situations, we calculated the various gene-based test statistics for genotype data from a real GWAS, where the phenotypes were reassigned at random. The real GWAS data used were on a sample of 2514 Chinese subjects typed by the Illumina Human610-Quad BeadChip from projects in Hong Kong with Institutional Review Board approval. After standard quality-control procedures, 473,931 SNPs were left for analysis; among these, 209,784 SNPs were in 23,672 genes. SNP-based association analysis was carried out with a genotypic association test in Plink.29Purcell S. Neale B. Todd-Brown K. Thomas L. Ferreira M.A. Bender D. Maller J. Sklar P. de Bakker P.I. Daly M.J. Sham P.C. PLINK: A tool set for whole-genome association and population-based linkage analyses.Am. J. Hum. Genet. 2007; 81: 559-575Abstract Full Text Full Text PDF PubMed Scopus (16836) Google Scholar Two LD datasets from different sources were prepared: the pair-wise r-squares estimated through Plink29Purcell S. Neale B. Todd-Brown K. Thomas L. Ferreira M.A. Bender D. Maller J. Sklar P. de Bakker P.I. Daly M.J. Sham P.C. PLINK: A tool set for whole-genome association and population-based linkage analyses.Am. J. Hum. Genet. 2007; 81: 559-575Abstract Full Text Full Text PDF PubMed Scopus (16836) Google Scholar from the genotype data of the actual case-control sample and the r-squares from the latest HapMap LD dataset (CHB panel) released on April 19, 2009. We used GATES to combine SNP-level p values to obtain gene-based p values. We assessed type 1 error rates for the gene-based tests by examining the proportion of genes for which the gene-based p value is lower than various threshold values (0.05., 0.01, 0.001, 0.0001). In addition, we used a quantile-quantile (Q-Q) plot to compare the overall distribution of the gene-based p values to a uniform (0,1) distribution. To further evaluate the performance of GATES under realistic situations, we used it to reanalyze the data from a published meta-analysis of three CD GWASs with a total of 3,230 cases and 4,829 controls.30Barrett J.C. Hansoul S. Nicolae D.L. Cho J.H. Duerr R.H. Rioux J.D. Brant S.R. Silverberg M.S. Taylor K.D. Barmada M.M. et al.NIDDK IBD Genetics ConsortiumBelgian-French IBD ConsortiumWellcome Trust Case Control ConsortiumGenome-wide association defines more than 30 distinct susceptibility loci for Crohn's disease.Nat. Genet. 2008; 40: 955-962Crossref PubMed Scopus (2029) Google Scholar We used the r-square values from the HapMap CEU sample to adjust for marker dependency. Prior to applying GATES, we subjected the SNP-based p values to genomic control correction31Devlin B. Roeder K. Genomic control for association studies.Biometrics. 1999; 55: 997-1004Crossref PubMed Scopus (2155) Google Scholar to avoid inflated significance levels. SNPs were mapped onto genes according to the gene coordinate information from NCBI. SNPs within 5 kilobase pairs of each gene were also assigned into the gene. In the very rare case where a SNP was in the overlapping region of two genes, the SNP was assigned into both genes. We compared the results of the SNP-based tests, the original Simes test and GATES, in terms of the number of significant hits after Bonferroni correction. The empirical type 1 error rates and statistical powers of GATES and the five alternative methods at a nominal type 1 error rate (α) of 0.05 are given in Table 1. When the markers within a gene are independent, the empirical type 1 error rates of all tests are approximately 0.05. For dependent markers, however, the Fisher combination test is a liberal test with an inflated type 1 error rate. In contrast, the original Simes test becomes conservative for a gene with multiple SNPs in strong LD. The type 1 error rates of the other five tests (including the one we propose) are all correct regardless of the marker dependency.Table 1Empirical Type 1 Errors and Power of Alternative Approaches (in percentage)#SNP (#DSL)Logistic RegressionFisherVEGAS –SumOriginal SimesVEGAS −MaxGATESLEError Rate (no disease)3(0)4.664.674.704.614.624.6110(0)5.105.005.045.065.075.063