{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:54:53Z","timestamp":1761897293720},"reference-count":59,"publisher":"Oxford University Press (OUP)","issue":"14","license":[{"start":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T00:00:00Z","timestamp":1588809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"United States National Science Foundation Collaborative Research","award":["473 DBI-1458515"],"award-info":[{"award-number":["473 DBI-1458515"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,7,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Genome-wide association studies (GWAS) are still the primary steps toward gene discovery. The urgency is more obvious in the big data era when GWAS are conducted simultaneously for thousand traits, e.g. transcriptomic and metabolomic traits. Efficient mixed model association (EMMA) and genome-wide efficient mixed model association (GEMMA) are the widely used methods for GWAS. An algorithm with high computational efficiency is badly needed. It is interesting to note that the test statistics of the ordinary ridge regression (ORR) have the same patterns across the genome as those obtained from the EMMA method. However, ORR has never been used for GWAS due to its severe shrinkage on the estimated effects and the test statistics.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>We introduce a degree of freedom for each marker effect obtained from ORR and use it to deshrink both the estimated effect and the standard error so that the Wald test of ORR is brought back to the same level as that of EMMA. The new method is called deshrinking ridge regression (DRR). By evaluating the methods under three different model sizes (small, medium and large), we demonstrate that DRR is more generalized for all model sizes than EMMA, which only works for medium and large models. Furthermore, DRR detect all markers in a simultaneous manner instead of scanning one marker at a time. As a result, the computational time complexity of DRR is much simpler than EMMA and about m (number of genetic variants) times simpler than that of GEMMA when the sample size is way smaller than the number of markers.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Contact<\/jats:title>\n                  <jats:p>shizhong.xu@ucr.edu<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btaa345","type":"journal-article","created":{"date-parts":[[2020,4,29]],"date-time":"2020-04-29T20:23:04Z","timestamp":1588191784000},"page":"4154-4162","source":"Crossref","is-referenced-by-count":9,"title":["Deshrinking ridge regression for genome-wide association studies"],"prefix":"10.1093","volume":"36","author":[{"given":"Meiyue","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Botany and Plant Sciences , University of California, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruidong","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Botany and Plant Sciences , University of California, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shizhong","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Botany and Plant Sciences , University of California, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,5,7]]},"reference":[{"key":"2023062213540753800_btaa345-B1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1186\/s12711-019-0469-3","article-title":"Frequentist p-values for large-scale-single step genome-wide association, with an application to birth weight in American Angus cattle","volume":"51","author":"Aguilar","year":"2019","journal-title":"Genet. Select. Evol"},{"key":"2023062213540753800_btaa345-B2","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1534\/genetics.107.075614","article-title":"Genomewide rapid association using mixed model and regression: a fast and simple method for genomewide pedigree-based quantitative trait loci association analysis","volume":"177","author":"Aulchenko","year":"2007","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B3","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1111\/age.12378","article-title":"Meta-analysis of genome-wide association from genomic prediction models","volume":"47","author":"Bernal Rubio","year":"2016","journal-title":"Anim. Genet"},{"key":"2023062213540753800_btaa345-B4","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1038\/ng.3007","article-title":"Genome-wide association analyses provide genetic and biochemical insights into natural variation in rice metabolism","volume":"46","author":"Chen","year":"2014","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B5","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1534\/genetics.112.143313","article-title":"Whole-genome regression and prediction methods applied to plant and animal breeding","volume":"193","author":"de los Campos","year":"2013","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B6","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1186\/1471-2105-15-246","article-title":"Rapid screening for phenotype-genotype associations by linear transformations of genomic evaluations","volume":"15","author":"Duarte","year":"2014","journal-title":"BMC Bioinformatics"},{"key":"2023062213540753800_btaa345-B7","doi-asserted-by":"crossref","first-page":"250","DOI":"10.3835\/plantgenome2011.08.0024","article-title":"Ridge regression and other kernels for genomic selection with R package rrBLUP","volume":"4","author":"Endelman","year":"2011","journal-title":"Plant Genome"},{"key":"2023062213540753800_btaa345-B8","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1007\/s00122-006-0218-1","article-title":"GS3, a major QTL for grain length and weight and minor QTL for grain width and thickness in rice, encodes a putative transmembrane protein","volume":"112","author":"Fan","year":"2006","journal-title":"Theor. Appl. Genet"},{"key":"2023062213540753800_btaa345-B9","doi-asserted-by":"crossref","first-page":"22","DOI":"10.18637\/jss.v033.i01","article-title":"Regularization paths for generalized linear models via coordinate descent","volume":"33","author":"Friedman","year":"2010","journal-title":"J. Stat. Softw"},{"key":"2023062213540753800_btaa345-B10","volume-title":"Matrix Computations","author":"Golub","year":"1996"},{"key":"2023062213540753800_btaa345-B11","doi-asserted-by":"crossref","first-page":"20320","DOI":"10.1073\/pnas.1319681110","article-title":"Genetic analysis of the metabolome exemplified using a rice population","volume":"110","author":"Gong","year":"2013","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2023062213540753800_btaa345-B12","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1093\/biostatistics\/kxh010","article-title":"Efficient quadratic regularization for expression arrays","volume":"5","author":"Hastie","year":"2004","journal-title":"Biostatistics"},{"key":"2023062213540753800_btaa345-B13","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21606-5","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"Hastie","year":"2001"},{"key":"2023062213540753800_btaa345-B14","doi-asserted-by":"crossref","first-page":"423","DOI":"10.2307\/2529430","article-title":"Best linear unbiased estimation and prediction under a selection model","volume":"31","author":"Henderson","year":"1975","journal-title":"Biometrics"},{"key":"2023062213540753800_btaa345-B15","first-page":"54","article-title":"Application of ridge analysis to regression problems","volume":"58","author":"Hoerl","year":"1962","journal-title":"Chem. Eng. Progress"},{"key":"2023062213540753800_btaa345-B16","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","article-title":"Ridge regression: biased estimation for nonorthogonal problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"2023062213540753800_btaa345-B17","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1038\/ng.1018","article-title":"Genome-wide association study of flowering time and grain yield traits in a worldwide collection of rice germplasm","volume":"44","author":"Huang","year":"2012","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B18","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1093\/genetics\/135.1.205","article-title":"Interval mapping of multiple quantitative trait loci","volume":"135","author":"Jansen","year":"1993","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B19","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1093\/genetics\/136.4.1447","article-title":"High resolution of quantitative traits into multiple loci via interval mapping","volume":"136","author":"Jansen","year":"1994","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B20","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1186\/1471-2164-11-724","article-title":"Accounting for multiple comparisons in a genome-wide association study (GWAS)","volume":"11","author":"Johnson","year":"2010","journal-title":"BMC Genomics"},{"key":"2023062213540753800_btaa345-B21","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1038\/ng.548","article-title":"Variance component model to account for sample structure in genome-wide association studies","volume":"42","author":"Kang","year":"2010","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B22","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1534\/genetics.107.080101","article-title":"Efficient control of population structure in model organism association mapping","volume":"178","author":"Kang","year":"2008","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B23","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1093\/genetics\/152.3.1203","article-title":"Multiple interval mapping for quantitative trait loci","volume":"152","author":"Kao","year":"1999","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B24","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1093\/genetics\/121.1.185","article-title":"Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps","volume":"121","author":"Lander","year":"1989","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B25","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1534\/g3.118.200336","article-title":"GWAS by GBLUP: single and multimarker EMMAX and Bayes factors, with an example in detection of a major gene for horse gait","volume":"8","author":"Legarra","year":"2018","journal-title":"G3 Genes Genomes Genet"},{"key":"2023062213540753800_btaa345-B26","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1038\/nmeth.1681","article-title":"FaST linear mixed models for genome-wide association studies","volume":"8","author":"Lippert","year":"2011","journal-title":"Nat. Methods"},{"key":"2023062213540753800_btaa345-B27","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1038\/nmeth.2037","article-title":"Improved linear mixed models for genome-wide association studies","volume":"9","author":"Listgarten","year":"2012","journal-title":"Nat. Methods"},{"key":"2023062213540753800_btaa345-B28","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1038\/ng.3190","article-title":"Efficient Bayesian mixed-model analysis increases association power in large cohorts","volume":"47","author":"Loh","year":"2015","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B29","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s00122-009-1166-3","article-title":"Accuracy of genotypic value predictions for marker-based selection in biparental plant populations","volume":"120","author":"Lorenzana","year":"2009","journal-title":"Theor. Appl. Genet"},{"key":"2023062213540753800_btaa345-B30","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1162\/neco.1992.4.3.415","article-title":"Bayesian interpolation","volume":"4","author":"Mackay","year":"1992","journal-title":"Neural Comput"},{"key":"2023062213540753800_btaa345-B31","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.ajhg.2007.10.012","article-title":"Accommodating linkage disequilibrium in genetic-association analyses via ridge regression","volume":"82","author":"Malo","year":"2008","journal-title":"Am. J. Hum. Genet"},{"key":"2023062213540753800_btaa345-B32","doi-asserted-by":"crossref","first-page":"19579","DOI":"10.1073\/pnas.1014419107","article-title":"Linking differential domain functions of the GS3 protein to natural variation of grain size in rice","volume":"107","author":"Mao","year":"2010","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2023062213540753800_btaa345-B33","doi-asserted-by":"crossref","first-page":"1819","DOI":"10.1093\/genetics\/157.4.1819","article-title":"Prediction of total genetic value using genome-wide dense marker maps","volume":"157","author":"Meuwissen","year":"2001","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B34","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1002\/gepi.20331","article-title":"On multiple-testing correction in genome-wide association studies","volume":"32","author":"Moskvina","year":"2008","journal-title":"Genet. Epidemiol"},{"key":"2023062213540753800_btaa345-B35","doi-asserted-by":"crossref","first-page":"1817","DOI":"10.1093\/bioinformatics\/bty017","article-title":"A rapid epistatic mixed-model association analysis by linear retransformations of genomic estimated values","volume":"34","author":"Ning","year":"2018","journal-title":"Bioinformatics"},{"key":"2023062213540753800_btaa345-B36","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.2135\/cropsci2008.10.0595","article-title":"Ridge regression and extensions for genomewide selection in maize","volume":"49","author":"Piepho","year":"2009","journal-title":"Crop Sci"},{"key":"2023062213540753800_btaa345-B37","doi-asserted-by":"crossref","first-page":"335","DOI":"10.5194\/aab-60-335-2017","article-title":"Invited review: genome-wide association analysis for quantitative traits in livestock\u2014a selective review of statistical models and experimental designs","volume":"60","author":"Schmid","year":"2017","journal-title":"Arch. Anim. Breed"},{"key":"2023062213540753800_btaa345-B38","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1534\/genetics.112.146720","article-title":"A novel generalized ridge regression method for quantitative genetics","volume":"193","author":"Shen","year":"2013","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B39","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1038\/ng.169","article-title":"Deletion in a gene associated with grain size increased yields during rice domestication","volume":"40","author":"Shomura","year":"2008","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B40","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1093\/jxb\/ert464","article-title":"An expression quantitative trait loci-guided co-expression analysis for constructing regulatory network using a rice recombinant inbred line population","volume":"65","author":"Wang","year":"2014","journal-title":"J. Exp. Bot"},{"key":"2023062213540753800_btaa345-B41","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.semcancer.2018.04.008","article-title":"Statistical methods for genome-wide association studies","volume":"55","author":"Wang","year":"2019","journal-title":"Sem. Cancer Biol"},{"key":"2023062213540753800_btaa345-B42","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1111\/jbg.12191","article-title":"An efficient empirical Bayes method for genomewide association studies","volume":"133","author":"Wang","year":"2016","journal-title":"J. Anim. Breed. Genet"},{"key":"2023062213540753800_btaa345-B43","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1038\/s41437-017-0032-3","article-title":"Metabolome-wide association studies for agronomic traits of rice","volume":"120","author":"Wei","year":"2018","journal-title":"Heredity"},{"key":"2023062213540753800_btaa345-B44","doi-asserted-by":"crossref","first-page":"3438","DOI":"10.1038\/ncomms4438","article-title":"Metabolome-based genome-wide association study of maize kernel leads to novel biochemical insights","volume":"5","author":"Wen","year":"2014","journal-title":"Nat. Commun"},{"key":"2023062213540753800_btaa345-B45","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1038\/cr.2008.307","article-title":"Isolation and initial characterization of GW5, a major QTL associated with rice grain width and weight","volume":"18","author":"Weng","year":"2008","journal-title":"Cell Res"},{"key":"2023062213540753800_btaa345-B46","first-page":"336","article-title":"Inverting modified matrices","volume":"42","author":"Woodbury","year":"1950","journal-title":"Memo. Rep"},{"key":"2023062213540753800_btaa345-B47","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1534\/genetics.113.155309","article-title":"Genetic mapping and genomic selection using recombination breakpoint data","volume":"195","author":"Xu","year":"2013","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B48","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1534\/genetics.113.157032","article-title":"Mapping quantitative trait loci by controlling polygenic background effects","volume":"195","author":"Xu","year":"2013","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B49","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1111\/tpj.13242","article-title":"Metabolomic prediction of yield in hybrid rice","volume":"88","author":"Xu","year":"2016","journal-title":"Plant J"},{"key":"2023062213540753800_btaa345-B50","doi-asserted-by":"crossref","first-page":"12456","DOI":"10.1073\/pnas.1413750111","article-title":"Predicting hybrid performance in rice using genomic best linear unbiased prediction","volume":"111","author":"Xu","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2023062213540753800_btaa345-B51","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.cj.2016.06.003","article-title":"Genetic mapping of quantitative trait loci in crops","volume":"5","author":"Xu","year":"2017","journal-title":"Crop J"},{"key":"2023062213540753800_btaa345-B52","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1038\/hdy.2017.27","article-title":"Prediction and association mapping of agronomic traits in maize using multiple omic data","volume":"119","author":"Xu","year":"2017","journal-title":"Heredity"},{"key":"2023062213540753800_btaa345-B53","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1038\/ng.2876","article-title":"Advantages and pitfalls in the application of mixed-model association methods","volume":"46","author":"Yang","year":"2014","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B54","article-title":"Gains in QTL detection using an ultra-high density SNP map based on population sequencing relative to traditional RFLP\/SSR markers","author":"Yu","year":"2011","journal-title":"PLoS One"},{"key":"2023062213540753800_btaa345-B55","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1038\/ng1702","article-title":"A unified mixed-model method for association mapping that accounts for multiple levels of relatedness","volume":"38","author":"Yu","year":"2006","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B56","doi-asserted-by":"crossref","first-page":"10972","DOI":"10.1073\/pnas.90.23.10972","article-title":"Theoretical basis for separation of multiple linked gene effects in mapping quantitative trait loci","volume":"90","author":"Zeng","year":"1993","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2023062213540753800_btaa345-B57","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1093\/genetics\/136.4.1457","article-title":"Precision mapping of quantitative trait loci","volume":"136","author":"Zeng","year":"1994","journal-title":"Genetics"},{"key":"2023062213540753800_btaa345-B58","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1038\/ng.546","article-title":"Mixed linear model approach adapted for genome-wide association studies","volume":"42","author":"Zhang","year":"2010","journal-title":"Nat. Genet"},{"key":"2023062213540753800_btaa345-B59","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1038\/ng.2310","article-title":"Genome-wide efficient mixed-model analysis for association studies","volume":"44","author":"Zhou","year":"2012","journal-title":"Nat. Genet"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/bioinformatics\/advance-article-pdf\/doi\/10.1093\/bioinformatics\/btaa345\/33445146\/btaa345.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/36\/14\/4154\/50676463\/btaa345.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/36\/14\/4154\/50676463\/btaa345.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T14:32:02Z","timestamp":1687530722000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/36\/14\/4154\/5831829"}},"subtitle":[],"editor":[{"given":"Russell","family":"Schwartz","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2020,5,7]]},"references-count":59,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2020,7,30]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btaa345","relation":{},"ISSN":["1367-4803","1367-4811"],"issn-type":[{"value":"1367-4803","type":"print"},{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,7,15]]},"published":{"date-parts":[[2020,5,7]]}}}