Abstract
This chapter discusses the statistical analysis of genome-wide association studies. After briefly alluding to the topics of genotype calling and imputation of missing data, we will be mainly concerned with downstream analysis of association, where the genotypes of each individual at each SNP have been established. The classical approach of single marker tests combined with multiple testing correction is contrasted with different strategies of model selection, which tend to perform much better in terms of correctly identifying causal SNPs in the case of complex traits. Specific methods of handling rare SNPs, as well as population stratification, are discussed. The analysis of admixture mapping and gene–gene interactions are amongst the more advanced topics also considered here.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Affymetrix, Inc.: BRLMM: an Improved Genotype Calling Method for the GeneChip Human Mapping 500K Array Set. http://www.affymetrix.com/support/technical/whitepapers/brlmm_whitepaper.pdf (2006)
Alexander, D.H., Lange, K.: Enhancements to the ADMIXTURE algorithm for individual ancestry estimation. BMC Bioinform. 12, 246 (2011)
Alexander, D., Novembre, J., Lange, K.: Fast model-based estimation of ancestry in unrelated individuals. Genome Res. 19, 1655–1664 (2009)
Andrew, A.S., Nelson, H.H., Kelsey, K.T., et al.: Concordance of multiple analytical approaches demonstrates a complex relationship between DNA repair gene SNPs, smoking and bladder cancer susceptibility. Carcinogenesis 27(5), 1030–1037 (2006)
Asimit, J., Zeggini, E.: Rare variant association analysis methods for complex traits. Annu. Rev. Genet. 44, 293–308 (2010)
Armitage, P.: Tests for linear trends in proportions and frequencies. Biometrics 11(3), 375–386 (1955)
Balding, D.J.: A tutorial on statistical methods for population association studies. Nat. Rev. Gen. 7, 781–791 (2006)
de Bakker, P.I., Yelensky, R., Pe’er, I., Gabriel, S.B., Daly, M.J., Altshuler, D.: Efficiency and power in genetic association studies. Nat. Genet. 37, 1217–1223 (2005)
Bansal, V., Libiger, O., Torkamani, A., Schork, N.J.: Statistical analysis strategies for association studies involving rare variants. Nat. Rev. Genet. 11(11), 773–785 (2010)
Barlow, R.E., Bartholomew, D.J., Bremner, J.M., Brunk, H.D.: Statistical Inference under Order Restrictions; the Theory and Application of Isotonic Regression. Wiley, New York (1972)
Barrett, J.C., Fry, B., Maller, J., Daly, M.J.: Haploview: analysis and visualization of LD and haplotype maps. Bioinformatics 21, 263–265 (2005)
Bazaraa, M., Shetty, C.: Nonlinear Programming: Theory and Algorithms. Wiley, New York (1979)
Beben, B., Visscher, P.M., McRae, A.F.: Family-based genome-wide association studies. Pharmacogenomics 20(2), 181–190 (2009)
Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57, 289–300 (1995)
Bogdan, M., Frommlet, F., Biecek, P., Cheng, R., Ghosh, J.K., Doerge, R.W.: Extending the modified Bayesian Information Criterion (mBIC) to dense markers and multiple interval mapping. Biometrics 64, 1162–1169 (2008)
Bogdan, M., Żak-Szatkowska, M., Ghosh, J.K.: Selecting explanatory variables with the modified version of Bayesian Information Criterion. Qual. Reliab. Eng. Int. 24, 627–641 (2008)
Browning, S.R.: Missing data imputation and haplotype phase inference for genome-wide association studies. Hum. Genet. 124, 439–450 (2008)
Browning, B.L., Yu, Z.: Simultaneous genotype calling and haplotype phase inference improves genotype accuracy and reduces false positive associations for genome-wide association studies. Am. J. Hum. Genet. 85, 847–861 (2009)
Browning, B.L., Browning, S.R.: A unified approach to genotype imputation and haplotype phase inference for large data sets of trios and unrelated individuals. Am. J. Hum. Genet. 84, 210–223 (2009)
Cantor, R.M., Lange, K., Sinsheimer, J.S.: Prioritizing GWAS results: A review of statistical methods and recommendations for their application. Am. J. Hum. Genet. 86(1), 6–22 (2010)
Carlson, C.S., Eberle, M.A., Rieder, M.J., Yi, Q., Kruglyak, L., Nickerson, D.A.: Selecting a maximally informative set of single-nucleotide polymorphisms for association analyses using linkage disequilibrium. Am. J. Hum. Genet. 74(1), 106–120 (2004)
Carvalho, B., Bengtsson, H., Speed, T.P., Irizarry, R.A.: Exploration, normalization, and genotype calls of high-density oligonucleotide SNP array data. Biostatistics 8, 485–499 (2007)
Carvalho, B.S., Irizarry, R.A.: A framework for oligonucleotide microarray preprocessing. Bioinformatics 26, 2363–2367 (2010)
Chakraborty, R., Weiss, K.M.: Admixture as a tool for finding linked genes and detecting that difference from allelic association between loci. Proc. Nat. Acad. Sci. 85(23), 9119–9123 (1988)
Chen, C.C.M., Schwender, H., Keith, J., Nunkesser, R., Mengersen, K., Macrossan, P.: Methods for identifying SNP interactions: a review on variations of logic regression, random forest and Bayesian logistic regression. IEEE/ACM Trans. Comput. Biol. Bioinf. 8(6), 1580–1591 (2011)
Chen, J., Chen, Z.: Extended Bayesian Information criteria for model selection with large model spaces. Biometrika 95(3), 759–771 (2008)
Chen, J., Chen, Z.: Extended BIC for small \(n\)-large-\(P\) sparse GLM. www.stat.nus.edu.sg/~stachenz/ChenChen.pdf (2010)
Chen, J., Chen, Z.: Tournament screening cum EBIC for feature selection with high-dimensional feature spaces. Sci. China A: Math. 52(6), 1327–1341 (2009)
Chen, L., Yu, G., Langefeld, C.D., et al.: Comparative analysis of methods for detecting interacting loci. BMC Genomics 12(1), 344 (2011)
Chipman, H., George, E.I., McCulloch, R.E.: The practical implementation of Bayesian model selection (with discussion). In: Lahiri, P. (ed.) Model Selection, pp. 66–134. IMS, Beachwood, OH (2001)
Colditz, G.A., Hankinson, S.E.: The nurses’ health study: lifestyle and health among women. Nat. Rev. Cancer 5, 388–396 (2005)
Consortium WTCCC: Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 447, 661–678 (2007)
Cordell, H.J.: Detecting gene-gene interactions that underlie human diseases. Nat. Rev. Genet. 10(6), 392–404 (2009)
Dai, H., Bhandary, M., Becker, M., Leeder, J.S., Gaedigk, R., Motsinger-Reif, A.A.: Global tests of p-values for multifactor dimensionality reduction models in selection of optimal number of target genes biodata mining 5(1), 1–17 (2012)
De, R., Verma, S.S., Holmes, M.V. et al.: Dissecting the obesity disease landscape: identifying gene-gene interactions that are highly associated with body mass index. In: 2014 8th International Conference on Systems Biology (ISB), 124–131. IEEE (2014)
de Bakker, P.I., Yelensky, R., Pe’er, I., Gabriel, S.B., Daly, M.J., Altshuler, D.: Efficiency and power in genetic association studies. Nat. Genet. 37(11), 1217–1223 (2005)
Devlin, B., Roeder, K.: Genomic control for association studies. Biometrics 55, 997–1004 (1999)
Di, X., Matsuzaki, H., Webster, T.A., Hubbell, E., Liu, G., Dong, S., Bartell, D., Huang, J., Chiles, R., Yang, G., Shen, M., Kulp, D., Kennedy, G.C., Mei, R., Jones, K.W., Cawley, S.: Dynamic model based algorithms for screening and genotyping over 100K SNPs on oligonucleotide microarrays. Bioinformatics 21, 1958–1963 (2005)
Dolejsi, E., Bodenstorfer, B., Frommlet, F.: Analyzing genome-wide association studies with an FDR controlling modification of the Bayesian Information Criterion. PLoS One e103322 (2014)
Dudbridge, F., Gusnanto, A.: Estimation of significance thresholds for genomewide association scans. Genet. Epid. 32, 227–234 (2008)
Eichler, E.E., et al.: Missing heritability and strategies for finding the underlying causes of complex disease. Nat. Rev. Genet. 11, 446–450 (2010)
Emily, M., Mailund, T., Hein, J., Schauser, L., Schierup, M.H.: Using biological networks to search for interacting loci in genome-wide association studies. Eur. J. Hum. Genet. 17(10), 1231–1240 (2009)
Fan, J., Lv, J.: Sure independence screening for ultrahigh dimensional feature space. J. R. Statist. Soc. B 70, 849–911 (2008)
Freidlin, B., Zheng, G., Li, Z., Gastwirth, J.L.: Trend tests for case-control studies of genetic markers: power, sample size and robustness. Hum. Hered. 53, 146–152 (2002)
Friedman, N., Linial, M., Nachman, I., Pe’er, D.: Using Bayesian networks to analyze expression data. J. Comput. Biol. 7(3–4), 601–620 (2000)
Frommlet, F.: Tag SNP selection based on clustering according to dominant sets found using replicator dynamics. Adv. Data Anal. Classif. 4, 65–83 (2010)
Frommlet, F., Chakrabarti, A., Murawska, M., Bogdan, M.: Asymptotic Bayes optimality under sparsity of selection rules for general priors. arXiv:1005.4753 (2010)
Frommlet, F., Ruhaltinger, F., Twarog, P., Bogdan, M.: Modified versions of Bayesian information criterion for genome-wide association studies. CSDA 56, 1038–1051 (2012)
George, E.I., Foster, D.P.: Calibration and empirical Bayes variable selection. Biometrika 87, 731–747 (2000)
Griffin, J.E., Brown, P.J.: Bayesian adaptive lasso with non-convex penalization. Technical Report, University of Kent (2007)
Gui, J., Moore, J.H., Williams, S.M., Andrews, P., Hillege, H.L., van der Harst, P., Navis, G., Van Gilst, W.H., Asselbergs, F.W., Gilbert-Diamond, D.: A simple and computationally efficient approach to multifactor dimensionality reduction analysis of gene-gene interactions for quantitative traits. PLoS One 8(6), e66545 (2013)
Nature Consortium.: A second generation human haplotype map of over 3.1 million SNPs. Nature 449, 851–862 (2007)
Han, F., Pan, W.: A data-adaptive sum test for disease association with multiple common or rare variants. Hum. Hered. 70(1), 42–54 (2010)
Hansen, M.H., Kooperberg, C.: Spline adaptation in extended linear models (with discussion). Stat. Sci. 17, 2–51 (2002)
He, Q., Lin, D.: A variable selection method for genome-wide association studies. Bioinformatics 27(1), 1–8 (2011)
Hindorff, L.A., Junkins, H.A., Hall, P.N., Mehta, J.P., Manolio, T.A.: A Catalog of Published Genome-Wide Association Studies. www.genome.gov/gwastudies
Hirschhorn, J.N., Daly, M.J.: Genome-wide association studies for common diseases and complex traits. Nat. Rev. Genet. 6(2), 95–108 (2005)
Hoggart, C.J., Whittaker, J.C., De Iorio, M., Balding, D.J.: Simultaneous analysis of all SNPs in genome-wide and re-sequencing association studies. PLOS Genet. 4(7), e1000130 (2008). doi:10.1371/journal.pgen.1000130
Hothorn, L.A., Hothorn, T.: Order-restricted scores test for the evaluation of population-based case-control studies when the genetic model is unknown. Biometrical J. 51(4), 659–669 (2009)
Iyengar, S.K., Elston, R.C.: The genetic basis of complex traits: rare variants or “common gene, common disease”? Methods Mol. Biol. 376, 71–84 (2007)
Kang, H.M., Zaitlen, N.A., Wade, C.M., Kirby, A., Heckerman, D., Daly, M.J., Eskin, E.: Efficient control of population structure in model organism association mapping. Genetics 178(3), 1709–1723 (2008)
Kang, H.M., Sul, J.H., Service, S.K., Zaitlen, N.A., Kong, S.Y., Freimer, N.B., Sabatti C., Eskin, E.: Variance component model to account for sample structure in genome-wide association studies. Nat. Genet. 42(4), 348–354 (2010)
Kennedy, G.C., Matsuzaki, H., Dong, S., Liu, W.M., Huang, J., Liu, G., Su, X., Cao, M., Chen, W., Zhang, J., Liu, W., Yang, G., Di, X., Ryder, T., He, Z., Surti, U., Phillips, M.S., Boyce-Jacino, M.T., Fodor, S.P., Jones, K.W.: Large-scale genotyping of complex DNA. Nat. Biotechnol. 21, 1233–1237 (2003)
Kooperberg, C., LeBlanc, M., Obenchain, V.: Risk prediction using genome-wide association studies. Genet. Epidem. 34, 643–652 (2010)
Kooperberg, C., Ruczinski, I.: Identifying interacting SNPs using Monte Carlo logic regression. Genet. Epidemiol. 28(2), 157–170 (2005)
Koren, M., Kimmel, G., Ben-Asher, E., Gal, I., Papa, M.Z., Beckmann, J.S., Lancet, D., Shamir, R., Friedman, E.: ATM haplotypes and breast cancer risk in Jewish high-risk women. Br. J. Cancer. 94(10), 1537–1543 (2006)
Lao, O., et al.: Genome-wide association studies for complex traits: consensus, uncertainty and challenges. Curr. Biol. 18(16), 1241–1248 (2008)
Laurie, C.L., et al.: Quality control and quality assurance in genotypic data for genome-wide association studies. Genet. Epidemiol. 34, 591–602 (2010)
Li, J., Das, K., Fu, G., Li, R., Wu, R.: The Bayesian Lasso for genome-wide association studies. Bioinformatics 27(4), 516–523 (2010)
Li, B., Leal, S.M.: Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. Am. J. Hum. Genet. 83(3), 311–321 (2008)
Lin, S., Carvalho, B., Cutler, D.J., Arking, D.E., Chakravarti, A., Irizarry, R.A.: Validation and extension of an empirical Bayes method for SNP calling on affymetrix microarrays. Genome Biol. 9, R63 (2008)
Lippert, C., Listgarten, J., Liu, Y., Kadie, C.M., Davidson, R.I., Heckerman, D.: FaST linear mixed models for genome-wide association studies. Nat. Methods 8(10), 833–835 (2011)
Liu, W., Di, X., Yang, G., Matsuzaki, H., Huang, J., Mei, R., Ryder, T.B., Webster, T.A., Dong, S., Liu, G., Jones, K.W., Kennedy, G.C., Kulp, D.: Algorithms for large-scale genotyping microarrays. Bioinformatics 19, 2397–2403 (2003)
Long, J.C.: The genetic structure of admixed populations. Genetics 127, 417–428 (1991)
Lou, X.Y., Chen, G.B., Yan, L., Ma, J.Z., Zhu, J., et al.: A generalized combinatorial approach for detecting gene-by-gene and gene-by-environment interactions with application to nicotine dependence. Am. J. Hum. Genet. 80, 1125–1137 (2007)
Manolio, T.A., et al.: Finding the missing heritability of complex diseases. Nature 461(7265), 747–753 (2009)
Marchini, J., Donnelly, P., Cardon, L.R.: Genome-wide strategies for detecting multiple loci that influence complex diseases. Nat. Genet. 37(4), 413–417 (2005)
Marchini, J., Howie, B.: Genotype imputation for genome-wide association studies. Nat. Rev. Genet. 11, 499–511 (2010)
McCarthy, 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. 9(5), 356–369 (2008)
McCarthy, M.I., Hirschhorn, J.N.: Genome-wide association studies: potential next steps on a genetic journey. Hum. Mol. Genet. 17, R156–R165 (2008)
McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Chapman and Hall/CRC, Boca Raton (1989)
McKeigue, P.M.: Mapping genes underlying ethnic differences in disease risk by linkage disequilibrium in recently admixed populations. Am. J. Hum. Genet. 60(1), 188 (1997)
Meinshausen, N., Bhlmann, P.: Stability selection. JRSSB 72, 417–448 (2010)
Menozzi, P., Piazza, A., Cavalli-Sforza, L.: Synthetic maps of human gene frequencies in Europeans. Science 201, 786–792 (1978)
Miller, D.J., Zhang, Y., Yu, G.: An algorithm for learning maximum entropy probability models of disease risk that efficiently searches and sparingly encodes multilocus genomic interactions. Bioinformatics 25(19), 2478–2485 (2009)
Moore, J.H.: The ubiquitous nature of epistasis in determining susceptibility to common human diseases. Hum. Hered. 56, 73–82 (2003)
Moore, J.H., Gilbert, J.C., Tsai, C.T., Chiang, F.T., Holden, T., Barney, N., White, B.C.: A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility. J. Theor. Biol. 241(2), 252–261 (2006)
Morgenthaler, S., Thilly, W.G.: A strategy to discover genes that carry multi-allelic or mono-allelic risk for common diseases: a cohort allelic sums test (CAST). Mutat. Res. 615(1–2), 28–56 (2007)
National Center for Biotechnology Information, United States National Library of Medicine. NCBI dbSNP build 144 for human. Summary Page. http://www.ncbi.nlm.nih.gov/projects/SNP/snp_summary.cgi?view+summary=view+summary&build_id=144. Accessed 26 Aug 2015
Nelson, M.R., et al.: The population reference sample, POPRES: a resource for population, disease, and pharmacological genetics research. Am. J. Hum. Genet. 83, 347–358 (2008)
Ouwehand, W.H.: The discovery of genes implicated in myocardial infarction. J. Thromb. Haemost. 7(Suppl 1), 305–307 (2009)
Park, T., Casella, G.: The Bayesian Lasso. JASA 103, 681–686 (2008)
Pattin, K.A., White, B.C., Barney, N., et al.: A computationally efficient hypothesis testing method for epistasis analysis using multifactor dimensionality reduction. Genet. Epidemi. 33(1), 87–94 (2009)
Pierce, J.R.: An Introduction to Information Theory: Symbols, Signals, and Noise. Dover, New York (1980)
Potkin, S.G., Turner, J.A., Guffanti, G., Lakatos, A., Torri, F., Keator, D.B., Macciardi, F.: Genome-wide strategies for discovering genetic influences on cognition and cognitive disorders: methodological considerations. Cogn. Neuropsychiatry 14(4/5), 391–418 (2009)
Pritchard, J.K., Rosenberg, N.A.: Use of unlinked genetic markers to detect population stratification in association studies. Am. J. Hum. Genet. 65, 220–228 (1999)
Pritchard, J., Stephens, M., Donnelly, P.: Inference of population structure using multilocus genotype data. Genetics 155(2), 945 (2000)
Price, A.L., et al.: Principal components analysis corrects for stratification in genome-wide association studies. Nat. Genet. 38, 904–909 (2006)
Price, A.L., Patterson, N., Yu, F., et al.: A genomewide admixture map for Latino populations. Am. J. Hum. Genet. 80(6), 1024–1036 (2007)
Price, A.L., Tandon, A., Patterson, N., Barnes, K.C., Rafaels, N., Ruczinski, I., Beatty, T.H., Mathias, R., Reich, D., Myers, S.: Sensitive detection of chromosomal segments of distinct ancestry in admixed populations. PLoS Genet. 5(6), e1000519 (2009)
Price, A.L., Zaitlen, N.A., Reich, D., Patterson, N.: New approaches to population stratification in genome-wide association studies. Nat. Rev. Genet. 11(7), 459–463 (2010)
Purcell, S., Neale, B., Todd-Brown, K., et al.: PLINK: a tool set for whole-genome association and population-based linkage analyses. Am. J. Hum. Genet. 81(3), 559–575 (2007)
Rabbee, N., Speed, T.P.: A genotype calling algorithm for affymetrix SNP arrays. Bioinformatics 22, 7–12 (2006)
Redden, D.T., Divers, J., Vaughan, L.K., et al.: Regional admixture mapping and structured association testing: conceptual unification and an extensible general linear model. PLoS Genet. 2, e137 (2006)
Reich, D.E., Goldstein, D.B.: Detecting association in a case-control study while correcting for population stratification. Genet. Epidemiol. 20, 4–16 (2001)
Ritchie, M.E., Carvalho, B.S., Hetrick, K.N., Tavaré, S., Irizarry, R.A.: R/Bioconductor software for Illumina’s Infinium whole-genome genotyping BeadChips. Bioinformatics 25, 2621–2623 (2009)
Ritchie, M.D., Hahn, L.W., Roodi, N., Bailey, L.R., Dupont, W.D., Parl, F.F., Moore, J.H.: Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. Am. J. Hum. Genet. 69(1), 138–147 (2001)
Riveros, C., Vimieiro, R., Holliday, E.G.: Identification of Genome-Wide SNP-SNP and SNP-Clinical Boolean Interactions in Age-Related Macular Degeneration In Epistasis, 217–255. Springer, New York (2015)
Robertson, T., Wright, F.T., Dykstra, R.L.: Order Restricted Statistical Inference. Wiley, New York (1988)
Nature Genetics Genome-wide association analysis of metabolic traits in a birth cohort from a founder population. 41(1), 35–46 (2009)
Sampson, J.N., Zhao, H.: Genotyping and inflated type I error rate in genome-wide association case/control studies. BMC Bioinform. 10, 68 (2009)
Sasieni, P.D.: From genotypes to genes: doubling the sample size. Biometrics 53, 1253–1261 (1997)
Scheet, P., Stephens, M.: A fast and flexible statistical model for large-scale population genotype data: applications to inferring missing genotypes and haplotypic phase. Am. J. Hum. Genet. 78, 629–644 (2006)
Schwender, H., Ickstadt, K.: Identification of SNP interactions using logic regression. Biostatistics 9(1), 187–198 (2008)
Schwender, H., Ruczinski, I., Ickstadt, K.: Testing SNPs and sets of SNPs for importance in association studies. Biostatistics (2010). doi:10.1093/biostatistics/kxq042
Segura, V., Vilhjalmsson, B.J., Platt, A., Korte, A., Seren, Ü., Long, Q., Nordborg, M.: An efficient multi-locus mixed-model approach for genome-wide association studies in structured populations. Nat. Genet. 44(7), 825–830 (2012)
Setakis, E., Stirnadel, H., Balding, D.J.: Logistic regression protects against population structure in genetic association studies. Genome Res. 16, 290–296 (2006)
Spielman, R.S., McGinnis, R.E., Ewens, W.J.: Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM). Am. J. Hum. Genet. 52(3), 506–516 (1993)
Stranger, B.E., Nica, A.C., Forrest, M.S., Dimas, A., Bird, C.P., Beazley, C., Ingle, C.E., Dunning, M., Flicek, P., Montgomery, S., Tavaré, S., Deloukas, P., Dermitzakis, E.T.: Population genomics of human gene expression. Nat. Genet. 39, 1217–1224 (2007)
Szulc, P., Bogdan, M., Frommlet, F., Tang H.: Joint Genotype- and Ancestry-based Genome-wide Association Studies in Admixed Populations. Working Paper (2015)
Tang, H., Siegmund, D.O., Johnson, N.A., Romieu, I., London, S.J.: Joint testing of genotype and ancestry association in admixed families. Genet. Epidemiol. 34(8), 783–791 (2010)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc. B 58(1), 267–288 (1996)
Via, M., Gignoux, C., Burchard, E.G.: The 1000 genomes project: new opportunities for research and social challenges. Genome Med. 2, 3 (2010)
Wei, Z., Sun, W., Wang, K., Hakonarson, H.: Multiple testing in genome-wide association studies via hidden Markov models. Bioinformatics 25(21), 2802–2808 (2009)
Wolf, B.J., Hill, E.G., Slate, E.H.: Logic forest: an ensemble classifier for discovering logical combinations of binary markers. Bioinformatics 26(17), 2183–2189 (2010)
Wu, T.T., Chen, Y.F., Hastie, T., Sobel, E., Lange, K.: Genome-wide association analysis by lasso penalized logistic regression. Bioinformatics 25(6), 714–721 (2009)
Yang, C., He, Z., Wan, X., Yang, Q., Xue, H., Yu, W.: SNPHarvester: a filtering-based approach for detecting epistatic interactions in genome-wide association studies. Bioinformatics 25(4), 504–511 (2009)
Yang, J., et al.: Common SNPs explain a large proportion of heritability for human height. Nat. Genet. 42, 565–569 (2010)
Yu, J., Pressoir, G., Briggs, W.H., Vroh Bi, I., Yamasaki, M., Doebley, J.F., McMullen, M.D., Gaut, B.S., Nielsen, D.M., Holland, J.B., Kresovich, S., Buckler, E.S.: A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nat. Genet. 38(2), 203–208 (2006)
Żak-Szatkowska, M., Bogdan, M.: Modified versions of Bayesian information criterion for sparse generalized linear models. CSDA. In Press, Accepted Manuscript (2012)
Zehetmayer, S., Posch, M.: False discovery rate control in two-stage designs. BMC Bioinform. 613, 81 (2012). doi:10.1186/1471-2105-13-81
Zhang, Y., Liu, J.S.: Bayesian inference of epistatic interactions in case-control studies. Nat. Genet. 39(9), 1167–1173 (2007)
Zhao, J., Chen, Z.: A two-stage penalized logistic regression approach to case-control genome-wide association studies. www.stat.nus.edu.sg/~stachenz/MS091221PR.pdf (2010)
Ziegler, A., König, I.R., Thompson, J.R.: Biostatistical aspects of genome-wide association studies. Biometrical J. 50(1), 8–28 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer-Verlag London
About this chapter
Cite this chapter
Frommlet, F., Bogdan, M., Ramsey, D. (2016). Statistical Analysis of GWAS. In: Phenotypes and Genotypes. Computational Biology, vol 18. Springer, London. https://doi.org/10.1007/978-1-4471-5310-8_5
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5310-8_5
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5309-2
Online ISBN: 978-1-4471-5310-8
eBook Packages: Computer ScienceComputer Science (R0)