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1.  Accounting for multiple comparisons in a genome-wide association study (GWAS) 
BMC Genomics  2010;11:724.
Background
As we enter an era when testing millions of SNPs in a single gene association study will become the standard, consideration of multiple comparisons is an essential part of determining statistical significance. Bonferroni adjustments can be made but are conservative due to the preponderance of linkage disequilibrium (LD) between genetic markers, and permutation testing is not always a viable option. Three major classes of corrections have been proposed to correct the dependent nature of genetic data in Bonferroni adjustments: permutation testing and related alternatives, principal components analysis (PCA), and analysis of blocks of LD across the genome. We consider seven implementations of these commonly used methods using data from 1514 European American participants genotyped for 700,078 SNPs in a GWAS for AIDS.
Results
A Bonferroni correction using the number of LD blocks found by the three algorithms implemented by Haploview resulted in an insufficiently conservative threshold, corresponding to a genome-wide significance level of α = 0.15 - 0.20. We observed a moderate increase in power when using PRESTO, SLIDE, and simpleℳ when compared with traditional Bonferroni methods for population data genotyped on the Affymetrix 6.0 platform in European Americans (α = 0.05 thresholds between 1 × 10-7 and 7 × 10-8).
Conclusions
Correcting for the number of LD blocks resulted in an anti-conservative Bonferroni adjustment. SLIDE and simpleℳ are particularly useful when using a statistical test not handled in optimized permutation testing packages, and genome-wide corrected p-values using SLIDE, are much easier to interpret for consumers of GWAS studies.
doi:10.1186/1471-2164-11-724
PMCID: PMC3023815  PMID: 21176216
2.  ParaHaplo: A program package for haplotype-based whole-genome association study using parallel computing 
Background
Since more than a million single-nucleotide polymorphisms (SNPs) are analyzed in any given genome-wide association study (GWAS), performing multiple comparisons can be problematic. To cope with multiple-comparison problems in GWAS, haplotype-based algorithms were developed to correct for multiple comparisons at multiple SNP loci in linkage disequilibrium. A permutation test can also control problems inherent in multiple testing; however, both the calculation of exact probability and the execution of permutation tests are time-consuming. Faster methods for calculating exact probabilities and executing permutation tests are required.
Methods
We developed a set of computer programs for the parallel computation of accurate P-values in haplotype-based GWAS. Our program, ParaHaplo, is intended for workstation clusters using the Intel Message Passing Interface (MPI). We compared the performance of our algorithm to that of the regular permutation test on JPT and CHB of HapMap.
Results
ParaHaplo can detect smaller differences between 2 populations than SNP-based GWAS. We also found that parallel-computing techniques made ParaHaplo 100-fold faster than a non-parallel version of the program.
Conclusion
ParaHaplo is a useful tool in conducting haplotype-based GWAS. Since the data sizes of such projects continue to increase, the use of fast computations with parallel computing--such as that used in ParaHaplo--will become increasingly important. The executable binaries and program sources of ParaHaplo are available at the following address:
doi:10.1186/1751-0473-4-7
PMCID: PMC2774321  PMID: 19845960
3.  A general method for controlling the genome-wide type I error rate in linkage and association mapping experiments in plants 
Heredity  2010;106(5):825-831.
Control of the genome-wide type I error rate (GWER) is an important issue in association mapping and linkage mapping experiments. For the latter, different approaches, such as permutation procedures or Bonferroni correction, were proposed. The permutation test, however, cannot account for population structure present in most association mapping populations. This can lead to false positive associations. The Bonferroni correction is applicable, but usually on the conservative side, because correlation of tests cannot be exploited. Therefore, a new approach is proposed, which controls the genome-wide error rate, while accounting for population structure. This approach is based on a simulation procedure that is equally applicable in a linkage and an association-mapping context. Using the parameter settings of three real data sets, it is shown that the procedure provides control of the GWER and the generalized genome-wide type I error rate (GWERk).
doi:10.1038/hdy.2010.125
PMCID: PMC3186238  PMID: 20959861
association mapping; genome-wide type I error rate; linkage mapping; mixed model; Monte Carlo simulation; parametric bootstrap
4.  The null distributions of test statistics in genomewide association studies 
Statistics in biosciences  2009;1(2):214-227.
SUMMARY
Genomewide association (GWA) studies assay hundreds of thousands of single nucleotide polymorphisms (SNPs) simultaneously across the entire genome and associate them with diseases, other biological or clinical traits. The association analysis usually tests each SNP as an independent entity and ignores the biological information such as linkage disequilibrium. Although the Bonferroni correction and other approaches have been proposed to address the issue of multiple comparisons as a result of testing many SNPs, there is a lack of understanding of the distribution of an association test statistic when an entire genome is considered together. In other words, there are extensive efforts in hypothesis testing, and almost no attempt in estimating the density under the null hypothesis. By estimating the true null distribution, we can apply the result directly to hypothesis testing; better assess the existing approaches of multiple comparisons; and evaluate the impact of linkage disequilibrium on the GWA studies. To this end, we estimate the empirical null distribution of an association test statistic in GWA studies using simulated population data. We further propose a convenient and accurate method based on adaptive spline to estimate the empirical value in GWA studies and validate our findings using a real data set. Our method enables us to fully characterize the null distribution of an association test that not only can be used to test the null hypothesis of no association, but also provide important information about the impact of density of the genetic markers on the significance of the tests. Our method does not require users to perform computationally intensive permutations, and hence provides a timely solution to an important and difficult problem in GWA studies.
doi:10.1007/s12561-009-9011-4
PMCID: PMC2826849  PMID: 20190869
critical value; generalized extreme-value distribution; genomewide association
5.  Genome-wide association studies of rheumatoid arthritis data via multiple hypothesis testing methods for correlated tests 
BMC Proceedings  2009;3(Suppl 7):S38.
Genome-wide association studies often involve testing hundreds of thousands of single-nucleotide polymorphisms (SNPs). These tests may be highly correlated because of linkage disequilibrium among SNPs. Multiple testing correction ignoring the correlation among markers, as is done in the Bonferroni procedure, can cause loss of power. Several multiple testing adjustment methods accounting for correlations among tests have been developed and have shown improved power compared to the Bonferroni procedure. These methods include a Monte Carlo (MC) method and a method of computing p-values adjusted for correlated tests. The objective of this study is to apply these two multiple testing methods to genome-wide association study of the Genetic Analysis Workshop 16 rheumatoid arthritis data from the North American Rheumatoid Arthritis Consortium, to compare the performance of these two methods to the Bonferroni procedure in identifying susceptibility loci underlying rheumatoid arthritis, and to discuss the strengths and weaknesses of these methods. The results show that both the MC method and p-values adjusted for correlated tests method identified more significant SNPs, thus potentially have higher power than the corresponding Bonferroni methods using the same test statistics as in the MC method and p-values adjusted for correlated tests, respectively. Simulation studies demonstrate that the MC method may have slightly higher power than the p-values adjusted for correlated tests method.
PMCID: PMC2795936  PMID: 20018029
6.  Fast and Accurate Approximation to Significance Tests in Genome-Wide Association Studies 
Genome-wide association studies commonly involve simultaneous tests of millions of single nucleotide polymorphisms (SNP) for disease association. The SNPs in nearby genomic regions, however, are often highly correlated due to linkage disequilibrium (LD, a genetic term for correlation). Simple Bonferonni correction for multiple comparisons is therefore too conservative. Permutation tests, which are often employed in practice, are both computationally expensive for genome-wide studies and limited in their scopes. We present an accurate and computationally efficient method, based on Poisson de-clumping heuristics, for approximating genome-wide significance of SNP associations. Compared with permutation tests and other multiple comparison adjustment approaches, our method computes the most accurate and robust p-value adjustments for millions of correlated comparisons within seconds. We demonstrate analytically that the accuracy and the efficiency of our method are nearly independent of the sample size, the number of SNPs, and the scale of p-values to be adjusted. In addition, our method can be easily adopted to estimate false discovery rate. When applied to genome-wide SNP datasets, we observed highly variable p-value adjustment results evaluated from different genomic regions. The variation in adjustments along the genome, however, are well conserved between the European and the African populations. The p-value adjustments are significantly correlated with LD among SNPs, recombination rates, and SNP densities. Given the large variability of sequence features in the genome, we further discuss a novel approach of using SNP-specific (local) thresholds to detect genome-wide significant associations. This article has supplementary material online.
doi:10.1198/jasa.2011.ap10657
PMCID: PMC3226809  PMID: 22140288
Genome-wide association study; Multiple comparison; Poisson approximation
7.  FastANOVA: an Efficient Algorithm for Genome-Wide Association Study 
Studying the association between quantitative phenotype (such as height or weight) and single nucleotide polymorphisms (SNPs) is an important problem in biology. To understand underlying mechanisms of complex phenotypes, it is often necessary to consider joint genetic effects across multiple SNPs. ANOVA (analysis of variance) test is routinely used in association study. Important findings from studying gene-gene (SNP-pair) interactions are appearing in the literature. However, the number of SNPs can be up to millions. Evaluating joint effects of SNPs is a challenging task even for SNP-pairs. Moreover, with large number of SNPs correlated, permutation procedure is preferred over simple Bonferroni correction for properly controlling family-wise error rate and retaining mapping power, which dramatically increases the computational cost of association study.
In this paper, we study the problem of finding SNP-pairs that have significant associations with a given quantitative phenotype. We propose an efficient algorithm, FastANOVA, for performing ANOVA tests on SNP-pairs in a batch mode, which also supports large permutation test. We derive an upper bound of SNP-pair ANOVA test, which can be expressed as the sum of two terms. The first term is based on single-SNP ANOVA test. The second term is based on the SNPs and independent of any phenotype permutation. Furthermore, SNP-pairs can be organized into groups, each of which shares a common upper bound. This allows for maximum reuse of intermediate computation, efficient upper bound estimation, and effective SNP-pair pruning. Consequently, FastANOVA only needs to perform the ANOVA test on a small number of candidate SNP-pairs without the risk of missing any significant ones. Extensive experiments demonstrate that FastANOVA is orders of magnitude faster than the brute-force implementation of ANOVA tests on all SNP pairs.
PMCID: PMC2951741  PMID: 20945829
Association study; ANOVA test
8.  Mass Univariate Analysis of Event-Related Brain Potentials/Fields II: Simulation Studies 
Psychophysiology  2011;48(12):1726-1737.
Mass univariate analysis is a relatively new approach for the study of ERPs/ERFs. It consists of many statistical tests and one of several powerful corrections for multiple comparisons. Multiple comparison corrections differ in their power and permissiveness. Moreover, some methods are not guaranteed to work or may be overly sensitive to uninteresting deviations from the null hypothesis. Here we report the results of simulations assessing the accuracy, permissiveness, and power of six popular multiple comparison corrections (permutation-based control of the family-wise error rate: FWER, weak control of FWER via cluster-based permutation tests, permutation based control of the generalized FWER, and three false discovery rate control procedures) using realistic ERP data. In addition, we look at the sensitivity of permutation tests to differences in population variance. These results will help researchers apply and interpret these procedures.
doi:10.1111/j.1469-8986.2011.01272.x
PMCID: PMC4059014  PMID: 21895684
9.  Multiple testing corrections for imputed SNPs 
Genetic epidemiology  2011;35(3):154-158.
Multiple testing corrections are an active research topic in genetic association studies, especially for genome-wide association studies (GWAS), where tests of association with traits are conducted at millions of imputed SNPs with estimated allelic dosages now. Failure to address multiple comparisons appropriately can introduce excess false positive results and make subsequent studies following up those results inefficient. Permutation tests are considered the gold standard in multiple testing adjustment; however, this procedure is computationally demanding, especially for GWAS. Notably, the permutation thresholds for the huge number of estimated allelic dosages in real data sets have not been reported. Although many researchers have recently developed algorithms to rapidly approximate the permutation thresholds with accuracy similar to the permutation test, these methods have not been verified with estimated allelic dosages. In this study, we compare recently published multiple testing correction methods using 2.5M estimated allelic dosages. We also derive permutation significance levels based on 10,000 GWAS results under the null hypothesis of no association. Our results show that the simpleM method works well with estimated allelic dosages and gives the closest approximation to the permutation threshold while requiring the least computation time.
doi:10.1002/gepi.20563
PMCID: PMC3055936  PMID: 21254223
multiple testing; genome-wide association studies; imputed SNPs; allelic dosages
10.  Testing Haplotype-Environment Interactions Using Case-Parent Triads 
Human Heredity  2010;70(1):23-33.
Objective
Joint analysis of multiple SNP markers can be informative, but studying joint effects of haplotypes and environmental exposures is challenging. Population structure can involve both genes and exposures and a case-control study is susceptible to bias from either source of stratification. We propose a procedure that uses case-parent triad data and, though not fully robust, resists bias from population structure.
Methods
Our procedure assumes that haplotypes under study have no influence on propensity to exposure. Then, under a no-interaction null hypothesis (multiplicative scale), transmission of a causative haplotype from parents to affected offspring might show distortion from Mendelian proportions but should be independent of exposure. We used this insight to develop a permutation test of no haplotype-by-exposure interaction.
Results
Simulations showed that our proposed test respects the nominal Type I error rate and provides good power under a variety of scenarios. We illustrate by examining whether SNP variants in GSTP1 modify the association between maternal smoking and oral clefting.
Conclusion
Our procedure offers desirable features: no need for haplotype estimation, validity under unspecified genetic main effects, tolerance to Hardy-Weinberg disequilibrium, ability to handle missing genotypes and a relatively large number of SNPs. Simulations suggest resistance to bias due to exposure-related population stratification.
doi:10.1159/000298326
PMCID: PMC2912643  PMID: 20413979
Haplotype-environment interaction; Gene-environment interaction; Case-parent triad; Permutation test; Non-parametreic test; Population stratification
11.  A New Approach to Account for the Correlations among Single Nucleotide Polymorphisms in Genome-Wide Association Studies 
Human Heredity  2011;72(1):1-9.
In genetic association studies, such as genome-wide association studies (GWAS), the number of single nucleotide polymorphisms (SNPs) can be as large as hundreds of thousands. Due to linkage disequilibrium, many SNPs are highly correlated; assuming they are independent is not valid. The commonly used multiple comparison methods, such as Bonferroni correction, are not appropriate and are too conservative when applied to GWAS. To overcome these limitations, many approaches have been proposed to estimate the so-called effective number of independent tests to account for the correlations among SNPs. However, many current effective number estimation methods are based on eigenvalues of the correlation matrix. When the dimension of the matrix is large, the numeric results may be unreliable or even unobtainable. To circumvent this obstacle and provide better estimates, we propose a new effective number estimation approach which is not based on the eigenvalues. We compare the new method with others through simulated and real data. The comparison results show that the proposed method has very good performance.
doi:10.1159/000330135
PMCID: PMC3171280  PMID: 21849789
Effective number; Genome-wide association studies; Multiple comparisons; Single nucleotide polymorphisms
12.  PRESTO: Rapid calculation of order statistic distributions and multiple-testing adjusted P-values via permutation for one and two-stage genetic association studies 
BMC Bioinformatics  2008;9:309.
Background
Large-scale genetic association studies can test hundreds of thousands of genetic markers for association with a trait. Since the genetic markers may be correlated, a Bonferroni correction is typically too stringent a correction for multiple testing. Permutation testing is a standard statistical technique for determining statistical significance when performing multiple correlated tests for genetic association. However, permutation testing for large-scale genetic association studies is computationally demanding and calls for optimized algorithms and software. PRESTO is a new software package for genetic association studies that performs fast computation of multiple-testing adjusted P-values via permutation of the trait.
Results
PRESTO is an order of magnitude faster than other existing permutation testing software, and can analyze a large genome-wide association study (500 K markers, 5 K individuals, 1 K permutations) in approximately one hour of computing time. PRESTO has several unique features that are useful in a wide range of studies: it reports empirical null distributions for the top-ranked statistics (i.e. order statistics), it performs user-specified combinations of allelic and genotypic tests, it performs stratified analysis when sampled individuals are from multiple populations and each individual's population of origin is specified, and it determines significance levels for one and two-stage genotyping designs. PRESTO is designed for case-control studies, but can also be applied to trio data (parents and affected offspring) if transmitted parental alleles are coded as case alleles and untransmitted parental alleles are coded as control alleles.
Conclusion
PRESTO is a platform-independent software package that performs fast and flexible permutation testing for genetic association studies. The PRESTO executable file, Java source code, example data, and documentation are freely available at .
doi:10.1186/1471-2105-9-309
PMCID: PMC2483288  PMID: 18620604
13.  META-ANALYSIS OF GENETIC ASSOCIATION STUDIES AND ADJUSTMENT FOR MULTIPLE TESTING OF CORRELATED SNPS AND TRAITS 
Genetic epidemiology  2010;34(7):739-746.
Meta-analysis has become a key component of well-designed genetic association studies due to the boost in statistical power achieved by combining results across multiple samples of individuals and the need to validate observed associations in independent studies. Meta-analyses of genetic association studies based on multiple SNPs and traits are subject to the same multiple testing issues as single-sample studies, but it is often difficult to adjust accurately for the multiple tests. Procedures such as Bonferroni may control the type I error rate but will generally provide an overly harsh correction if SNPs or traits are correlated. Depending on study design, availability of individual-level data, and computational requirements, permutation testing may not be feasible in a meta-analysis framework. In this paper we present methods for adjusting for multiple correlated tests under several study designs commonly employed in meta-analyses of genetic association tests. Our methods are applicable to both prospective meta-analyses in which several samples of individuals are analyzed with the intent to combine results, and retrospective meta-analyses, in which results from published studies are combined, including situations in which 1) individual-level data are unavailable, and 2) different sets of SNPs are genotyped in different studies due to random missingness or two-stage design. We show through simulation that our methods accurately control the rate of type I error and achieve improved power over multiple testing adjustments that do not account for correlation between SNPs or traits.
doi:10.1002/gepi.20538
PMCID: PMC3070606  PMID: 20878715
meta-analysis; association study; multiple testing; SNPs
14.  Olfactory Receptor Gene Polymorphisms and Nonallergic Vasomotor Rhinitis 
We sought a genotype-phenotype association: between single-nucleotide polymorphisms (SNPs) in olfactory receptor (OR) genes from the two largest OR gene clusters and odor-triggered nonallergic vasomotor rhinitis (nVMR). In the initial pedigree screen, using transmission disequilibrium test (TDT) analysis, six SNPs showed “significant” p-values between 0.0449 and 0.0043. In a second case-control population, the previously identified six SNPs did not re-emerge, whereas four new SNPs showed p-values between 0.0490 and 0.0001. Combining both studies, none of the SNPs in the TDT analysis survived the Bonferroni correction. In the population study, one SNP showed an empirical p-value of 0.0066 by shuffling cases and controls with 105 replicates; however, the p-value for this SNP was 0.83 in the pedigree study. This study emphasizes that underpowered studies having p-values between <0.05 and 0.0001 should be regarded as inconclusive and require further replication before concluding the study is “informative.” However, we believe that our hypothesis that an association between OR genotypes and the nVMR phenotype remains feasible. Future studies using either a genomewide association study of all OR gene-pseudogene regions throughout the genome—at the current recommended density of 2.5 to 5 kb per tag SNP—or studies incorporating microarray analyses of the entire “OR genome” in well-characterized nVMR patients are required.
doi:10.1080/02770900701867579
PMCID: PMC2752410  PMID: 18446592
vasomotor rhinitis; olfactory receptor genes; genotype-phenotype association study; transmission disequilibrium test; case-control study; multiple-testing; Bonferroni correction; idiopathic environmental intolerance
15.  A hidden Markov random field model for genome-wide association studies 
Biostatistics (Oxford, England)  2009;11(1):139-150.
Genome-wide association studies (GWAS) are increasingly utilized for identifying novel susceptible genetic variants for complex traits, but there is little consensus on analysis methods for such data. Most commonly used methods include single single nucleotide polymorphism (SNP) analysis or haplotype analysis with Bonferroni correction for multiple comparisons. Since the SNPs in typical GWAS are often in linkage disequilibrium (LD), at least locally, Bonferroni correction of multiple comparisons often leads to conservative error control and therefore lower statistical power. In this paper, we propose a hidden Markov random field model (HMRF) for GWAS analysis based on a weighted LD graph built from the prior LD information among the SNPs and an efficient iterative conditional mode algorithm for estimating the model parameters. This model effectively utilizes the LD information in calculating the posterior probability that an SNP is associated with the disease. These posterior probabilities can then be used to define a false discovery controlling procedure in order to select the disease-associated SNPs. Simulation studies demonstrated the potential gain in power over single SNP analysis. The proposed method is especially effective in identifying SNPs with borderline significance at the single-marker level that nonetheless are in high LD with significant SNPs. In addition, by simultaneously considering the SNPs in LD, the proposed method can also help to reduce the number of false identifications of disease-associated SNPs. We demonstrate the application of the proposed HMRF model using data from a case–control GWAS of neuroblastoma and identify 1 new SNP that is potentially associated with neuroblastoma.
doi:10.1093/biostatistics/kxp043
PMCID: PMC2800164  PMID: 19822692
Empirical Bayes; False discovery; Iterative conditional model; Linkage disequilibrium
16.  Screening and Replication using the Same Data Set: Testing Strategies for Family-Based Studies in which All Probands Are Affected 
PLoS Genetics  2008;4(9):e1000197.
For genome-wide association studies in family-based designs, we propose a powerful two-stage testing strategy that can be applied in situations in which parent-offspring trio data are available and all offspring are affected with the trait or disease under study. In the first step of the testing strategy, we construct estimators of genetic effect size in the completely ascertained sample of affected offspring and their parents that are statistically independent of the family-based association/transmission disequilibrium tests (FBATs/TDTs) that are calculated in the second step of the testing strategy. For each marker, the genetic effect is estimated (without requiring an estimate of the SNP allele frequency) and the conditional power of the corresponding FBAT/TDT is computed. Based on the power estimates, a weighted Bonferroni procedure assigns an individually adjusted significance level to each SNP. In the second stage, the SNPs are tested with the FBAT/TDT statistic at the individually adjusted significance levels. Using simulation studies for scenarios with up to 1,000,000 SNPs, varying allele frequencies and genetic effect sizes, the power of the strategy is compared with standard methodology (e.g., FBATs/TDTs with Bonferroni correction). In all considered situations, the proposed testing strategy demonstrates substantial power increases over the standard approach, even when the true genetic model is unknown and must be selected based on the conditional power estimates. The practical relevance of our methodology is illustrated by an application to a genome-wide association study for childhood asthma, in which we detect two markers meeting genome-wide significance that would not have been detected using standard methodology.
Author Summary
The current state of genotyping technology has enabled researchers to conduct genome-wide association studies of up to 1,000,000 SNPs, allowing for systematic scanning of the genome for variants that might influence the development and progression of complex diseases. One of the largest obstacles to the successful detection of such variants is the multiple comparisons/testing problem in the genetic association analysis. For family-based designs in which all offspring are affected with the disease/trait under study, we developed a methodology that addresses this problem by partitioning the family-based data into two statistically independent components. The first component is used to screen the data and determine the most promising SNPs. The second component is used to test the SNPs for association, where information from the screening is used to weight the SNPs during testing. This methodology is more powerful than standard procedures for multiple comparisons adjustment (i.e., Bonferroni correction). Additionally, as only one data set is required for screening and testing, our testing strategy is less susceptible to study heterogeneity. Finally, as many family-based studies collect data only from affected offspring, this method addresses a major limitation of previous methodologies for multiple comparisons in family-based designs, which require variation in the disease/trait among offspring.
doi:10.1371/journal.pgen.1000197
PMCID: PMC2529406  PMID: 18802462
17.  INRICH: interval-based enrichment analysis for genome-wide association studies 
Bioinformatics  2012;28(13):1797-1799.
Summary: Here we present INRICH (INterval enRICHment analysis), a pathway-based genome-wide association analysis tool that tests for enriched association signals of predefined gene-sets across independent genomic intervals. INRICH has wide applicability, fast running time and, most importantly, robustness to potential genomic biases and confounding factors. Such factors, including varying gene size and single-nucleotide polymorphism density, linkage disequilibrium within and between genes and overlapping genes with similar annotations, are often not accounted for by existing gene-set enrichment methods. By using a genomic permutation procedure, we generate experiment-wide empirical significance values, corrected for the total number of sets tested, implicitly taking overlap of sets into account. By simulation we confirm a properly controlled type I error rate and reasonable power of INRICH under diverse parameter settings. As a proof of principle, we describe the application of INRICH on the NHGRI GWAS catalog.
Availability: A standalone C++ program, user manual and datasets can be freely downloaded from: http://atgu.mgh.harvard.edu/inrich/.
Contact: shaun@atgu.mgh.harvard.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/bts191
PMCID: PMC3381960  PMID: 22513993
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.
doi:10.1371/journal.pone.0044978
PMCID: PMC3441747  PMID: 23028716
19.  Assessment of transmission distortion on chromosome 6p in healthy individuals using tagSNPs 
European Journal of Human Genetics  2009;17(9):1182-1189.
The best-documented example for transmission distortion (TD) to normal offspring are the t haplotypes on mouse chromosome 17. In healthy humans, TD has been described for whole chromosomes and for particular loci, but multiple comparisons have presented a statistical obstacle in wide-ranging analyses. Here we provide six high-resolution TD maps of the short arm of human chromosome 6 (Hsa6p), based on single-nucleotide polymorphism (SNP) data from 60 trio families belonging to two ethnicities that are available through the International HapMap Project. We tested all approximately 70 000 previously genotyped SNPs within Hsa6p by the transmission disequilibrium test. TagSNP selection followed by permutation testing was performed to adjust for multiple testing. A statistically significant evidence for TD was observed among male parents of European ancestry, due to strong and wide-ranging skewed segregation in a 730 kb long region containing the transcription factor-encoding genes SUPT3H and RUNX2, as well as the microRNA locus MIRN586. We also observed that this chromosomal segment coincides with pronounced linkage disequilibrium (LD), suggesting a relationship between TD and LD. The fact that TD may be taking place in samples not selected for a genetic disease implies that linkage studies must be assessed with particular caution in chromosomal segments with evidence of TD.
doi:10.1038/ejhg.2009.16
PMCID: PMC2986600  PMID: 19259136
transmission distortion; linkage disequilibrium; human chromosome 6p; SUPT3H; MIRN586; RUNX2
20.  Association study between a polymorphism at the 3'-untranslated region of CLOCK gene and attention deficit hyperactivity disorder 
Background
The circadian locomotor output cycles kaput (CLOCK) gene encodes protein regulation circadian rhythm and also plays some roles in neural transmitter systems including the dopamine system. Several lines of evidence implicate a relationship between attention-deficit hyperactivity disorder (ADHD), circadian rythmicity and sleeping disturbances. A recent study has reported that a polymorphism (rs1801260) at the 3'-untranslated region of the CLOCK gene is associated with adult ADHD.
Methods
To investigate the association between the polymorphism (rs1801260) in ADHD, two samples of ADHD probands from the United Kingdom (n = 180) and Taiwan (n = 212) were genotyped and analysed using within-family transmission disequilibrium test (TDT). Bonferroni correction procedures were used to just for multiple comparisons.
Results
We found evidence of increased transmission of the T allele of the rs1801260 polymorphism in Taiwanese samples (P = 0.010). There was also evidence of preferential transmission of the T allele of the rs1801260 polymorphism in combined samples from the Taiwan and UK (P = 0.008).
Conclusion
This study provides evidence for the possible involvement of CLOCK in susceptibility to ADHD.
doi:10.1186/1744-9081-6-48
PMCID: PMC2925327  PMID: 20704703
21.  Establishing an adjusted p-value threshold to control the family-wide type 1 error in genome wide association studies 
BMC Genomics  2008;9:516.
Background
By assaying hundreds of thousands of single nucleotide polymorphisms, genome wide association studies (GWAS) allow for a powerful, unbiased review of the entire genome to localize common genetic variants that influence health and disease. Although it is widely recognized that some correction for multiple testing is necessary, in order to control the family-wide Type 1 Error in genetic association studies, it is not clear which method to utilize. One simple approach is to perform a Bonferroni correction using all n single nucleotide polymorphisms (SNPs) across the genome; however this approach is highly conservative and would "overcorrect" for SNPs that are not truly independent. Many SNPs fall within regions of strong linkage disequilibrium (LD) ("blocks") and should not be considered "independent".
Results
We proposed to approximate the number of "independent" SNPs by counting 1 SNP per LD block, plus all SNPs outside of blocks (interblock SNPs). We examined the effective number of independent SNPs for Genome Wide Association Study (GWAS) panels. In the CEPH Utah (CEU) population, by considering the interdependence of SNPs, we could reduce the total number of effective tests within the Affymetrix and Illumina SNP panels from 500,000 and 317,000 to 67,000 and 82,000 "independent" SNPs, respectively. For the Affymetrix 500 K and Illumina 317 K GWAS SNP panels we recommend using 10-5, 10-7 and 10-8 and for the Phase II HapMap CEPH Utah and Yoruba populations we recommend using 10-6, 10-7 and 10-9 as "suggestive", "significant" and "highly significant" p-value thresholds to properly control the family-wide Type 1 error.
Conclusion
By approximating the effective number of independent SNPs across the genome we are able to 'correct' for a more accurate number of tests and therefore develop 'LD adjusted' Bonferroni corrected p-value thresholds that account for the interdepdendence of SNPs on well-utilized commercially available SNP "chips". These thresholds will serve as guides to researchers trying to decide which regions of the genome should be studied further.
doi:10.1186/1471-2164-9-516
PMCID: PMC2621212  PMID: 18976480
22.  Handling Missing Data in Transmission Disequilibrium Test in Nuclear Families with One Affected Offspring 
PLoS ONE  2012;7(10):e46100.
The Transmission Disequilibrium Test (TDT) compares frequencies of transmission of two alleles from heterozygote parents to an affected offspring. This test requires all genotypes to be known from all members of the nuclear families. However, obtaining all genotypes in a study might not be possible for some families, in which case, a data set results in missing genotypes. There are many techniques of handling missing genotypes in parents but only a few in offspring. The robust TDT (rTDT) is one of the methods that handles missing genotypes for all members of nuclear families [with one affected offspring]. Even though all family members can be imputed, the rTDT is a conservative test with low power. We propose a new method, Mendelian Inheritance TDT (MITDT-ONE), that controls type I error and has high power. The MITDT-ONE uses Mendelian Inheritance properties, and takes population frequencies of the disease allele and marker allele into account in the rTDT method. One of the advantages of using the MITDT-ONE is that the MITDT-ONE can identify additional significant genes that are not found by the rTDT. We demonstrate the performances of both tests along with Sib-TDT (S-TDT) in Monte Carlo simulation studies. Moreover, we apply our method to the type 1 diabetes data from the Warren families in the United Kingdom to identify significant genes that are related to type 1 diabetes.
doi:10.1371/journal.pone.0046100
PMCID: PMC3466247  PMID: 23056239
23.  Fast Association Tests for Genes with FAST 
PLoS ONE  2013;8(7):e68585.
Gene-based tests of association can increase the power of a genome-wide association study by aggregating multiple independent effects across a gene or locus into a single stronger signal. Recent gene-based tests have distinct approaches to selecting which variants to aggregate within a locus, modeling the effects of linkage disequilibrium, representing fractional allele counts from imputation, and managing permutation tests for p-values. Implementing these tests in a single, efficient framework has great practical value. Fast ASsociation Tests (Fast) addresses this need by implementing leading gene-based association tests together with conventional SNP-based univariate tests and providing a consolidated, easily interpreted report. Fast scales readily to genome-wide SNP data with millions of SNPs and tens of thousands of individuals, provides implementations that are orders of magnitude faster than original literature reports, and provides a unified framework for performing several gene based association tests concurrently and efficiently on the same data. Availability: https://bitbucket.org/baderlab/fast/downloads/FAST.tar.gz, with documentation at https://bitbucket.org/baderlab/fast/wiki/Home
doi:10.1371/journal.pone.0068585
PMCID: PMC3720833  PMID: 23935874
24.  Genome-wide association analyses of the 15th QTL-MAS workshop data using mixed model based single locus regression analysis 
BMC Proceedings  2012;6(Suppl 2):S5.
Background
The mixed model based single locus regression analysis (MMRA) method was used to analyse the common simulated dataset of the 15th QTL-MAS workshop to detect potential significant association between single nucleotide polymorphisms (SNPs) and the simulated trait. A Wald chi-squared statistic with df =1 was employed as test statistic and the permutation test was performed. For adjusting multiple testing, phenotypic observations were permutated 10,000 times against the genotype and pedigree data to obtain the threshold for declaring genome-wide significant SNPs. Linkage disequilibrium (LD) in term of D' between significant SNPs was quantified and LD blocks were defined to indicate quantitative trait loci (QTL) regions.
Results
The estimated heritability of the simulated trait is approximately 0.30. 82 genome-wide significant SNPs (P < 0.05) on chromosomes 1, 2 and 3 were detected. Through the LD blocks of the significant SNPs, we confirmed 5 and 1 QTL regions on chromosomes 1 and 3, respectively. No block was detected on chromosome 2, and no significant SNP was detected on chromosomes 4 and 5.
Conclusion
MMRA is a suitable method for detecting additive QTL and a fast method with feasibility of performing permutation test. Using LD blocks can effectively detect QTL regions.
doi:10.1186/1753-6561-6-S2-S5
PMCID: PMC3363159  PMID: 22640694
25.  Comparison of type I error for multiple test corrections in large single-nucleotide polymorphism studies using principal components versus haplotype blocking algorithms 
BMC Genetics  2005;6(Suppl 1):S78.
Although permutation testing has been the gold standard for assessing significance levels in studies using multiple markers, it is time-consuming. A Bonferroni correction to the nominal p-value that uses the underlying pair-wise linkage disequilibrium (LD) structure among the markers to determine the number of effectively independent tests has recently been proposed. We propose using the number of independent LD blocks plus the number of independent single-nucleotide polymorphisms for correction. Using the Collaborative Study on the Genetics of Alcoholism LD data for chromosome 21, we simulated 1,000 replicates of parent-child trio data under the null hypothesis with two levels of LD: moderate and high. Assuming haplotype blocks were independent, we calculated the number of independent statistical tests using 3 haplotype blocking algorithms. We then compared the type I error rates using a principal components-based method, the three blocking methods, a traditional Bonferroni correction, and the unadjusted p-values obtained from FBAT. Under high LD conditions, the PC method and one of the blocking methods were slightly conservative, whereas the 2 other blocking methods exceeded the target type I error rate. Under conditions of moderate LD, we show that the blocking algorithm corrections are closest to the desired type I error, although still slightly conservative, with the principal components-based method being almost as conservative as the traditional Bonferroni correction.
doi:10.1186/1471-2156-6-S1-S78
PMCID: PMC1866703  PMID: 16451692

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