{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T15:20:08Z","timestamp":1772810408546,"version":"3.50.1"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"15","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,8,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivation: The genetic basis of complex traits often involves the function of multiple genetic factors, their interactions and the interaction between the genetic and environmental factors. Gene\u2013environment (G\u00d7E) interaction is considered pivotal in determining trait variations and susceptibility of many genetic disorders such as neurodegenerative diseases or mental disorders. Regression-based methods assuming a linear relationship between a disease response and the genetic and environmental factors as well as their interaction is the commonly used approach in detecting G\u00d7E interaction. The linearity assumption, however, could be easily violated due to non-linear genetic penetrance which induces non-linear G\u00d7E interaction.<\/jats:p><jats:p>Results: In this work, we propose to relax the linear G\u00d7E assumption and allow for non-linear G\u00d7E interaction under a varying coefficient model framework. We propose to estimate the varying coefficients with regression spline technique. The model allows one to assess the non-linear penetrance of a genetic variant under different environmental stimuli, therefore help us to gain novel insights into the etiology of a complex disease. Several statistical tests are proposed for a complete dissection of G\u00d7E interaction. A wild bootstrap method is adopted to assess the statistical significance. Both simulation and real data analysis demonstrate the power and utility of the proposed method. Our method provides a powerful and testable framework for assessing non-linear G\u00d7E interaction.<\/jats:p><jats:p>Contact: \u00a0cui@stt.msu.edu<\/jats:p><jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btr318","type":"journal-article","created":{"date-parts":[[2011,6,21]],"date-time":"2011-06-21T03:59:35Z","timestamp":1308628775000},"page":"2119-2126","source":"Crossref","is-referenced-by-count":39,"title":["Varying coefficient model for gene\u2013environment interaction: a non-linear look"],"prefix":"10.1093","volume":"27","author":[{"given":"Shujie","family":"Ma","sequence":"first","affiliation":[{"name":"1 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, 2Department of Statistics, University of California, Riverside, California 92507, USA, 3Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, 215006 China and 4Perinatology Research Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development\/National Institutes of Health\/Department of Health and Human Services, Bethesda, MD, and Detroit, Michigan 48201, USA"},{"name":"1 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, 2Department of Statistics, University of California, Riverside, California 92507, USA, 3Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, 215006 China and 4Perinatology Research Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development\/National Institutes of Health\/Department of Health and Human Services, Bethesda, MD, and Detroit, Michigan 48201, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lijian","family":"Yang","sequence":"additional","affiliation":[{"name":"1 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, 2Department of Statistics, University of California, Riverside, California 92507, USA, 3Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, 215006 China and 4Perinatology Research Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development\/National Institutes of Health\/Department of Health and Human Services, Bethesda, MD, and Detroit, Michigan 48201, USA"},{"name":"1 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, 2Department of Statistics, University of California, Riverside, California 92507, USA, 3Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, 215006 China and 4Perinatology Research Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development\/National Institutes of Health\/Department of Health and Human Services, Bethesda, MD, and Detroit, Michigan 48201, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"Romero","sequence":"additional","affiliation":[{"name":"1 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, 2Department of Statistics, University of California, Riverside, California 92507, USA, 3Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, 215006 China and 4Perinatology Research Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development\/National Institutes of Health\/Department of Health and Human Services, Bethesda, MD, and Detroit, Michigan 48201, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuehua","family":"Cui","sequence":"additional","affiliation":[{"name":"1 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, 2Department of Statistics, University of California, Riverside, California 92507, USA, 3Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, 215006 China and 4Perinatology Research Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development\/National Institutes of Health\/Department of Health and Human Services, Bethesda, MD, and Detroit, Michigan 48201, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2011,6,20]]},"reference":[{"key":"2023012511524025000_B1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J. Roy. Stat. Soc. B"},{"key":"2023012511524025000_B2","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1080\/01621459.2000.10474280","article-title":"Efficient estimation and inferences for varying-coefficient models","volume":"95","author":"Cai","year":"2000","journal-title":"J. Am. Stat. Asso."},{"key":"2023012511524025000_B3","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1038\/nrn1925","article-title":"Gene-environment interactions in psychiatry: joining forces with neuroscience","volume":"7","author":"Caspi","year":"2006","journal-title":"Nat. Rev. Neurosci."},{"key":"2023012511524025000_B4","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1126\/science.1083968","article-title":"Influence of life stress on depression: moderation by a polymorphism in the 5-HTT gene","volume":"301","author":"Caspi","year":"2003","journal-title":"Science"},{"key":"2023012511524025000_B5","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1093\/biomet\/92.2.399","article-title":"Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies","volume":"92","author":"Chatterjee","year":"2005","journal-title":"Biometrika"},{"key":"2023012511524025000_B6","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1198\/016214501753168280","article-title":"Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables","volume":"96","author":"Chiang","year":"2001","journal-title":"J. Am. Stat. Asso."},{"key":"2023012511524025000_B7","first-page":"309","article-title":"Local Regression Models","volume-title":"Statistical Models","author":"Cleveland","year":"1991"},{"key":"2023012511524025000_B8","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1093\/genetics\/39.6.859","article-title":"An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present","volume":"39","author":"Cockerham","year":"1954","journal-title":"Genetics"},{"key":"2023012511524025000_B9","volume-title":"Gene-Environment Interactions: Fundamentals of Ecogenetics","author":"Costa","year":"2006"},{"key":"2023012511524025000_B10","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1086\/281736","article-title":"The problem of environment and selection","volume":"86","author":"Falconer","year":"1952","journal-title":"Am. Natural."},{"key":"2023012511524025000_B11","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1214\/aos\/1017939139","article-title":"Statistical estimation in varying coefficient models","volume":"27","author":"Fan","year":"1999","journal-title":"Ann. Stat."},{"key":"2023012511524025000_B12","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1111\/1467-9469.00218","article-title":"Simultaneous confidence bands and hypothesis testing in varying-coefficient models","volume":"27","author":"Fan","year":"2000","journal-title":"Scand. J. Stat."},{"key":"2023012511524025000_B13","doi-asserted-by":"crossref","first-page":"179","DOI":"10.4310\/SII.2008.v1.n1.a15","article-title":"Statistical methods with varying coefficient models","volume":"1","author":"Fan","year":"2008","journal-title":"Stat. Interface"},{"key":"2023012511524025000_B14","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1159\/000022931","article-title":"Gene-environment interaction and the mapping of complex traits: some statistical models and their implications","volume":"50","author":"Guo","year":"2000","journal-title":"Hum. Hered."},{"key":"2023012511524025000_B15","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1214\/aos\/1176349403","article-title":"Comparing nonparametric versus parametric regression fits","volume":"21","author":"H\u00e4rdle","year":"1993","journal-title":"Ann. Stat."},{"key":"2023012511524025000_B16","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1111\/j.2517-6161.1993.tb01939.x","article-title":"Varying-coefficient models","volume":"55","author":"Hastie","year":"1993","journal-title":"J. Roy. Statist. Soc. B."},{"key":"2023012511524025000_B17","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1093\/bioinformatics\/btf869","article-title":"Multifactor dimensionality reduction software for detecting gene-gene and gene-environment interactions","volume":"19","author":"Hahn","year":"2003","journal-title":"Bioinformatics"},{"key":"2023012511524025000_B18","volume-title":"Evolutionary Genetics and Environmental Stress","author":"Hoffman","year":"1991"},{"key":"2023012511524025000_B19","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1093\/biomet\/85.4.809","article-title":"Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data","volume":"85","author":"Hoover","year":"1998","journal-title":"Biometrika"},{"key":"2023012511524025000_B20","first-page":"763","article-title":"Polynomial spline estimation and inference for varying coefficient models with longitudinal data","volume":"14","author":"Huang","year":"2004","journal-title":"Stat. Sinica"},{"key":"2023012511524025000_B21","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1159\/000099183","article-title":"Exploiting gene-environment interaction to detect genetic associations","volume":"63","author":"Kraft","year":"2007","journal-title":"Hum. Hered."},{"key":"2023012511524025000_B22","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1002\/(SICI)1098-2795(199810)51:2<218::AID-MRD12>3.0.CO;2-0","article-title":"Effects of differentiation on the transcriptional regulation of the FGF-4 gene: critical roles played by a distal enhancer","volume":"51","author":"Lamb","year":"1998","journal-title":"Mol. Reprod. Dev."},{"key":"2023012511524025000_B23","article-title":"A regularized regression approach for dissecting genetic conflicts that increase disease risk in pregnancy","volume":"8","author":"Li","year":"2009","journal-title":"Stat. Appl. Genet. Mol. 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