{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:45:46Z","timestamp":1740185146822,"version":"3.37.3"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"20","license":[{"start":{"date-parts":[[2022,9,2]],"date-time":"2022-09-02T00:00:00Z","timestamp":1662076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971292","11771267","12271329"],"award-info":[{"award-number":["11971292","11771267","12271329"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>The joint analysis of multiple phenotypes is important in many biological studies, such as plant and animal breeding. The heritability estimation for a linear combination of phenotypes is designed to account for correlation information. Existing methods for estimating heritability mainly focus on single phenotypes under random-effect models. These methods also require some stringent conditions, which calls for a more flexible and interpretable method for estimating heritability. Fixed-effect models emerge as a useful alternative.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>In this article, we propose a novel heritability estimator based on multivariate ridge regression for linear combinations of phenotypes, yielding accurate estimates in both sparse and dense cases. Under mild conditions in the high-dimensional setting, the proposed estimator appears to be consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator is promising under different scenarios. Compared with independently combined heritability estimates in the case of multiple phenotypes, the proposed method significantly improves the performance by considering correlations among those phenotypes. We further demonstrate its application in heritability estimation and correlation analysis for the Oryza sativa rice dataset.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>An R package implementing the proposed method is available at https:\/\/github.com\/xg-SUFE1\/MultiRidgeVar, where covariance estimates are also given together with heritability estimates.<\/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\/btac587","type":"journal-article","created":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T12:53:57Z","timestamp":1661950437000},"page":"4687-4696","source":"Crossref","is-referenced-by-count":0,"title":["Heritability estimation for a linear combination of phenotypes via ridge regression"],"prefix":"10.1093","volume":"38","author":[{"given":"Xiaoguang","family":"Li","sequence":"first","affiliation":[{"name":"School of Statistics and Management, Shanghai University of Finance and Economics , Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingdong","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Statistics and Management, Shanghai University of Finance and Economics , Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3829-1715","authenticated-orcid":false,"given":"Xu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Statistics and Management, Shanghai University of Finance and Economics , Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,9,2]]},"reference":[{"volume-title":"Principles of Plant Genetics and Breeding","year":"2009","author":"Acquaah","key":"2022101415191346400_btac587-B1"},{"key":"2022101415191346400_btac587-B2","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1142\/9789812793096_0018","volume-title":"Advances in Statistics","author":"Bai","year":"2008"},{"key":"2022101415191346400_btac587-B3","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.tplants.2010.05.004","article-title":"Molecular basis of trait correlations","volume":"15","author":"Chen","year":"2010","journal-title":"Trends Plant Sci"},{"key":"2022101415191346400_btac587-B4","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1093\/biomet\/ast065","article-title":"Variance estimation in high-dimensional linear models","volume":"101","author":"Dicker","year":"2014","journal-title":"Biometrika"},{"key":"2022101415191346400_btac587-B5","first-page":"159","volume-title":"Artificial Intelligence and Statistics","author":"Dicker","year":"2016"},{"volume-title":"Introduction to Quantitative Genetics","year":"1996","author":"Falconer","key":"2022101415191346400_btac587-B6"},{"key":"2022101415191346400_btac587-B7","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1534\/genetics.114.171447","article-title":"Efficient multiple-trait association and estimation of genetic correlation using the matrix-variate linear mixed model","volume":"200","author":"Furlotte","year":"2015","journal-title":"Genetics"},{"key":"2022101415191346400_btac587-B8","doi-asserted-by":"crossref","first-page":"13291","DOI":"10.1038\/ncomms13291","article-title":"Multidimensional heritability analysis of neuroanatomical shape","volume":"7","author":"Ge","year":"2016","journal-title":"Nat. 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