{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T02:05:44Z","timestamp":1782439544811,"version":"3.54.5"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Background<\/jats:title>\n            <jats:p>The success achieved by genome-wide association (GWA) studies in the identification of candidate loci for complex diseases has been accompanied by an inability to explain the bulk of heritability. Here, we describe the algorithm V-Bay, a variational Bayes algorithm for multiple locus GWA analysis, which is designed to identify weaker associations that may contribute to this missing heritability.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>V-Bay provides a novel solution to the computational scaling constraints of most multiple locus methods and can complete a simultaneous analysis of a million genetic markers in a few hours, when using a desktop. Using a range of simulated genetic and GWA experimental scenarios, we demonstrate that V-Bay is highly accurate, and reliably identifies associations that are too weak to be discovered by single-marker testing approaches. V-Bay can also outperform a multiple locus analysis method based on the lasso, which has similar scaling properties for large numbers of genetic markers. For demonstration purposes, we also use V-Bay to confirm associations with gene expression in cell lines derived from the Phase II individuals of HapMap.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusions<\/jats:title>\n            <jats:p>V-Bay is a versatile, fast, and accurate multiple locus GWA analysis tool for the practitioner interested in identifying weaker associations without high false positive rates.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1471-2105-11-58","type":"journal-article","created":{"date-parts":[[2010,1,27]],"date-time":"2010-01-27T19:18:28Z","timestamp":1264619908000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":88,"title":["A variational Bayes algorithm for fast and accurate multiple locus genome-wide association analysis"],"prefix":"10.1186","volume":"11","author":[{"given":"Benjamin A","family":"Logsdon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gabriel E","family":"Hoffman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jason G","family":"Mezey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,1,27]]},"reference":[{"issue":"7223","key":"3515_CR1","doi-asserted-by":"publisher","first-page":"728","DOI":"10.1038\/nature07631","volume":"465","author":"P Donnelly","year":"2008","unstructured":"Donnelly P: Progress and challenges in genome-wide association studies in humans. Nature 2008, 465(7223):728\u2013731. 10.1038\/nature07631","journal-title":"Nature"},{"key":"3515_CR2","unstructured":"Hindorff L, Junkins H, Mehta J, Manolio T: A Catalog of Published Genome-Wide Association Studies.[http:\/\/www.genome.gov\/gwastudies] Accessed 2009"},{"issue":"5","key":"3515_CR3","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1038\/nrg2344","volume":"9","author":"M McCarthy","year":"2008","unstructured":"McCarthy M, Abecasis G, Cardon L, Goldstein D, Little J, Ioannidis J, Hirschhorn J: Genome-wide association studies for complex traits: consensus, uncertainty and challenges. Nature Reviews Genetics 2008, 9(5):356\u2013369. 10.1038\/nrg2344","journal-title":"Nature Reviews Genetics"},{"issue":"7","key":"3515_CR4","doi-asserted-by":"publisher","first-page":"e1000130","DOI":"10.1371\/journal.pgen.1000130","volume":"4","author":"C Hoggart","year":"2008","unstructured":"Hoggart C, Whittaker J, De lorio M, Balding D: Simultaneous analysis of all SNPs in genome-wide and re-sequencing association studies. PLoS Genetics 2008, 4(7):e1000130. 10.1371\/journal.pgen.1000130","journal-title":"PLoS Genetics"},{"key":"3515_CR5","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/978-1-59745-389-9_6","volume":"376","author":"S Iyengar","year":"2007","unstructured":"Iyengar S, Elston R: The genetic basis of complex traits: rare variants or \"common gene, common disease\"? Methods in molecular biology (Clifton, NJ) 2007, 376: 71. full_text","journal-title":"Methods in molecular biology (Clifton, NJ)"},{"issue":"3","key":"3515_CR6","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1038\/nrg2537","volume":"10","author":"W Cookson","year":"2009","unstructured":"Cookson W, Liang L, Abecasis G, Moffatt M, Lathrop M: Mapping complex disease traits with global gene expression. Nature Reviews Genetics 2009, 10(3):184\u2013194. 10.1038\/nrg2537","journal-title":"Nature Reviews Genetics"},{"issue":"7218","key":"3515_CR7","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1038\/456018a","volume":"456","author":"B Maher","year":"2008","unstructured":"Maher B: Personal genomes: The case of the missing heritability. Nature 2008, 456(7218):18. 10.1038\/456018a","journal-title":"Nature"},{"key":"3515_CR8","doi-asserted-by":"crossref","unstructured":"Zhang M, Zhang D, Wells M: Variable selection for large p small n regression models with incomplete data: mapping QTL with epistasis. BMC Bioinformatics 2008., 9(251):","DOI":"10.1186\/1471-2105-9-251"},{"issue":"3","key":"3515_CR9","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1534\/genetics.108.099556","volume":"181","author":"N Yi","year":"2009","unstructured":"Yi N, Banerjee S: Hierarchical generalized linear models for multiple quantitative trait locus mapping. Genetics 2009, 181(3):1101\u20131113. 10.1534\/genetics.108.099556","journal-title":"Genetics"},{"issue":"3","key":"3515_CR10","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1038\/sj.hdy.6801074","volume":"100","author":"N Yi","year":"2008","unstructured":"Yi N, Shriner D: Advances in Bayesian multiple quantitative trait loci mapping in experimental crosses. Heredity 2008, 100(3):240\u2013252. 10.1038\/sj.hdy.6801074","journal-title":"Heredity"},{"issue":"2","key":"3515_CR11","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1534\/genetics.107.085589","volume":"179","author":"N Yi","year":"2008","unstructured":"Yi N, Xu S: Bayesian Lasso for quantitative trait loci mapping. Genetics 2008, 179(2):1045\u20131055. 10.1534\/genetics.107.085589","journal-title":"Genetics"},{"issue":"2","key":"3515_CR12","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1086\/519495","volume":"81","author":"J Liu","year":"2007","unstructured":"Liu J, Liu Y, Liu X, Deng H: Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components. Am J Hum Genet 2007, 81(2):304\u2013320. 10.1086\/519495","journal-title":"Am J Hum Genet"},{"issue":"4","key":"3515_CR13","doi-asserted-by":"publisher","first-page":"2305","DOI":"10.1534\/genetics.104.034181","volume":"169","author":"M Zhang","year":"2005","unstructured":"Zhang M, Montooth K, Wells M, Clark A, Zhang D: Mapping multiple quantitative trait loci by Bayesian classification. Genetics 2005, 169(4):2305\u20132318. 10.1534\/genetics.104.034181","journal-title":"Genetics"},{"issue":"6","key":"3515_CR14","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1093\/bioinformatics\/btp041","volume":"25","author":"T Wu","year":"2009","unstructured":"Wu T, Chen Y, Hastie T, Sobel E, Lange K: Genome-wide association analysis by lasso penalized logistic regression. Bioinformatics 2009, 25(6):714. 10.1093\/bioinformatics\/btp041","journal-title":"Bioinformatics"},{"issue":"2","key":"3515_CR15","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1093\/genetics\/163.2.789","volume":"163","author":"S Xu","year":"2003","unstructured":"Xu S: Estimating polygenic effects using markers of the entire genome. Genetics 2003, 163(2):789\u2013801.","journal-title":"Genetics"},{"issue":"9","key":"3515_CR16","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1038\/ng2110","volume":"39","author":"Y Zhang","year":"2007","unstructured":"Zhang Y, Liu J: Bayesian inference of epistatic interactions in case-control studies. Nature Genetics 2007, 39(9):1167\u20131173. 10.1038\/ng2110","journal-title":"Nature Genetics"},{"key":"3515_CR17","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1086\/338007","volume":"70","author":"H Cordell","year":"2002","unstructured":"Cordell H, Clayton D: A unified stepwise regression procedure for evaluating the relative effects of polymorphisms within a gene using case\/control or family data: application to HLA in type 1 diabetes. The American Journal of Human Genetics 2002, 70: 124\u2013141. 10.1086\/338007","journal-title":"The American Journal of Human Genetics"},{"issue":"9","key":"3515_CR18","doi-asserted-by":"publisher","first-page":"e157","DOI":"10.1371\/journal.pgen.0020157","volume":"2","author":"D Evans","year":"2006","unstructured":"Evans D, Marchini J, Morris A, Cardon L: Two-stage two-locus models in genome-wide association. PLoS Genet 2006, 2(9):e157. 10.1371\/journal.pgen.0020157","journal-title":"PLoS Genet"},{"issue":"11","key":"3515_CR19","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1162\/089976601753196003","volume":"13","author":"M Girolami","year":"2001","unstructured":"Girolami M: A variational method for learning sparse and overcomplete representations. Neural Computation 2001, 13(11):2517\u20132532. 10.1162\/089976601753196003","journal-title":"Neural Computation"},{"issue":"3","key":"3515_CR20","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1023\/A:1020830525823","volume":"50","author":"G Hermosillo","year":"2002","unstructured":"Hermosillo G, Chefd'Hotel C, Faugeras O: Variational methods for multimodal image matching. International Journal of Computer Vision 2002, 50(3):329\u2013343. 10.1023\/A:1020830525823","journal-title":"International Journal of Computer Vision"},{"key":"3515_CR21","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1023\/A:1008932416310","volume":"10","author":"T Jaakkola","year":"2000","unstructured":"Jaakkola T, Jordan M: Bayesian parameter estimation via variational methods. Statistics and Computing 2000, 10: 25\u201337. 10.1023\/A:1008932416310","journal-title":"Statistics and Computing"},{"key":"3515_CR22","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1214\/06-BA104","volume":"1","author":"D Blei","year":"2006","unstructured":"Blei D, Jordan M: Variational inference for Dirichlet process mixtures. Bayesian Analysis 2006, 1: 121\u2013144. 10.1214\/06-BA104","journal-title":"Bayesian Analysis"},{"key":"3515_CR23","volume-title":"Pattern recognition and machine learning","author":"CM Bishop","year":"2006","unstructured":"Bishop CM: Pattern recognition and machine learning. New York: Springer Science; 2006."},{"issue":"2","key":"3515_CR24","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.ajhg.2007.10.012","volume":"82","author":"N Malo","year":"2008","unstructured":"Malo N, Libiger O, Schork N: Accommodating linkage disequilibrium in genetic-association analyses via ridge regression. The American Journal of Human Genetics 2008, 82(2):375\u2013385. 10.1016\/j.ajhg.2007.10.012","journal-title":"The American Journal of Human Genetics"},{"issue":"423","key":"3515_CR25","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1080\/01621459.1993.10476353","volume":"88","author":"E George","year":"1993","unstructured":"George E, McCulloch R: Variable selection via Gibbs sampling. Journal of the American Statistical Association 1993, 88(423):881\u2013889. 10.2307\/2290777","journal-title":"Journal of the American Statistical Association"},{"key":"3515_CR26","first-page":"138","volume-title":"New Directions in Statistical Signal Processing","author":"M Wainwright","year":"2003","unstructured":"Wainwright M, Jordan M: Graphical models, exponential families, and variational methods. In New Directions in Statistical Signal Processing. Volume 2005. MIT Press; 2003:138."},{"key":"3515_CR27","volume-title":"PhD thesis","author":"M Beal","year":"2003","unstructured":"Beal M: Variational algorithms for approximate Bayesian inference. PhD thesis. University of London; 2003."},{"key":"3515_CR28","volume-title":"Bayesian data analysis","author":"A Gelman","year":"2004","unstructured":"Gelman A, Carlin J, Stern H, Rubin D: Bayesian data analysis. Boca Raton, Florida: Chapman and Hall; 2004."},{"key":"3515_CR29","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1101\/gr.083634.108","volume":"19","author":"G Chen","year":"2009","unstructured":"Chen G, Marjoram P, Wall J: Fast and flexible simulation of DNA sequence data. Genome Res 2009, 19: 136\u2013142. 10.1101\/gr.083634.108","journal-title":"Genome Res"},{"key":"3515_CR30","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani R: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 1996, 58: 267\u2013288.","journal-title":"Journal of the Royal Statistical Society. Series B (Methodological)"},{"issue":"5813","key":"3515_CR31","doi-asserted-by":"publisher","first-page":"848","DOI":"10.1126\/science.1136678","volume":"315","author":"B Stranger","year":"2007","unstructured":"Stranger B, Forrest M, Dunning M, Ingle C, Beazley C, Thorne N, Redon R, Bird C, de Grassi A, Lee C, Tyler-Smith C, Carter N, Scherer S, Tavare S, Deloukas P, Hurles M, Dermitzakis E: Relative impact of nucleotide and copy number variation on gene expression phenotypes. Science 2007, 315(5813):848\u2013853. 10.1126\/science.1136678","journal-title":"Science"},{"issue":"7164","key":"3515_CR32","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1038\/nature06258","volume":"449","author":"International HapMap Consortium","year":"2007","unstructured":"International HapMap Consortium: A second generation human haplotype map of over 3.1 million SNPs. Nature 2007, 449(7164):851\u2013861. 10.1038\/nature06258","journal-title":"Nature"},{"key":"3515_CR33","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex opimization","author":"S Boyd","year":"2004","unstructured":"Boyd S, Vandenberghe L: Convex opimization. New York: Cambridge University Press New York; 2004."},{"key":"3515_CR34","first-page":"267","volume-title":"Journal of the Royal Statistical Society. Series B (Methodological)","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani R: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 1996, 267\u2013288."},{"key":"3515_CR35","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1214\/07-AOAS147","volume":"2","author":"T Wu","year":"2008","unstructured":"Wu T, Lange K: Coordinate descent algorithms for lasso penalized regression. Ann Appl Stat 2008, 2: 224\u2013244. 10.1214\/07-AOAS147","journal-title":"Ann Appl Stat"},{"issue":"2","key":"3515_CR36","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1214\/07-AOAS131","volume":"1","author":"J Friedman","year":"2007","unstructured":"Friedman J, Hastie T, Hofling H, Tibshirani R: Pathwise coordinate optimization. Annals of Applied Statistics 2007, 1(2):302\u2013332. 10.1214\/07-AOAS131","journal-title":"Annals of Applied Statistics"},{"issue":"51","key":"3515_CR37","doi-asserted-by":"publisher","first-page":"18508","DOI":"10.1073\/pnas.0507325102","volume":"102","author":"B Voight","year":"2005","unstructured":"Voight B, Adams A, Frisse L, Qian Y, Hudson R, Di Rienzo A: Interrogating multiple aspects of variation in a full resequencing data set to infer human population size changes. Proceedings of the National Academy of Sciences 2005, 102(51):18508\u201318513. 10.1073\/pnas.0507325102","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"7063","key":"3515_CR38","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1038\/nature04226","volume":"437","author":"D Altshuler","year":"2005","unstructured":"Altshuler D, Brooks L, Chakravarti A, Collins F, Daly M, Donnelly P: A haplotype map of the human genome. Nature 2005, 437(7063):1299\u20131320. 10.1038\/nature04226","journal-title":"Nature"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-11-58.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T12:08:05Z","timestamp":1630498085000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-11-58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,27]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["3515"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-11-58","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1,27]]},"assertion":[{"value":"10 August 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2010","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2010","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"58"}}