Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models
We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machin...
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| Veröffentlicht in: | Biometrics 2007-12, Vol.63 (4), p.1079-1088 |
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| container_title | Biometrics |
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| creator | Liu, Dawei Lin, Xihong Ghosh, Debashis |
| description | We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations. |
| doi_str_mv | 10.1111/j.1541-0420.2007.00799.x |
| format | Article |
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This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations.</description><identifier>ISSN: 0006-341X</identifier><identifier>EISSN: 1541-0420</identifier><identifier>DOI: 10.1111/j.1541-0420.2007.00799.x</identifier><identifier>PMID: 18078480</identifier><identifier>CODEN: BIOMA5</identifier><language>eng</language><publisher>Malden, USA: Blackwell Publishing Inc</publisher><subject>Algorithms ; Biometrics ; biometry ; Biometry - methods ; BLUPs ; Computer Simulation ; computer software ; data collection ; Data Interpretation, Statistical ; Data smoothing ; gene expression ; Gene Expression Profiling - methods ; genes ; Genetics ; Kernel function ; Kernel functions ; least squares ; Linear Models ; Linear regression ; Measurement techniques ; Medical genetics ; Model/variable selection ; Modeling ; Models, Biological ; Nonparametric models ; Nonparametric regression ; Parametric models ; Penalized likelihood ; Prostate cancer ; prostatic neoplasms ; Proteome - metabolism ; Regression Analysis ; REML ; Research methodology ; Sample Size ; Score test ; Sensitivity and Specificity ; Signal Transduction - physiology ; Simulations ; Smoothing parameter ; statistical models ; Support vector machines ; variance</subject><ispartof>Biometrics, 2007-12, Vol.63 (4), p.1079-1088</ispartof><rights>Copyright 2007 The International Biometric Society</rights><rights>2007, The International Biometric Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c6139-eafe1f55c5839711be164213ed3df6848e7c73149ea682ddde424cba6f3d87d13</citedby><cites>FETCH-LOGICAL-c6139-eafe1f55c5839711be164213ed3df6848e7c73149ea682ddde424cba6f3d87d13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/4541462$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/4541462$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,776,780,799,828,881,1411,27901,27902,45550,45551,57992,57996,58225,58229</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/18078480$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Dawei</creatorcontrib><creatorcontrib>Lin, Xihong</creatorcontrib><creatorcontrib>Ghosh, Debashis</creatorcontrib><title>Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models</title><title>Biometrics</title><addtitle>Biometrics</addtitle><description>We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations.</description><subject>Algorithms</subject><subject>Biometrics</subject><subject>biometry</subject><subject>Biometry - methods</subject><subject>BLUPs</subject><subject>Computer Simulation</subject><subject>computer software</subject><subject>data collection</subject><subject>Data Interpretation, Statistical</subject><subject>Data smoothing</subject><subject>gene expression</subject><subject>Gene Expression Profiling - methods</subject><subject>genes</subject><subject>Genetics</subject><subject>Kernel function</subject><subject>Kernel functions</subject><subject>least squares</subject><subject>Linear Models</subject><subject>Linear regression</subject><subject>Measurement techniques</subject><subject>Medical genetics</subject><subject>Model/variable selection</subject><subject>Modeling</subject><subject>Models, Biological</subject><subject>Nonparametric models</subject><subject>Nonparametric regression</subject><subject>Parametric models</subject><subject>Penalized likelihood</subject><subject>Prostate cancer</subject><subject>prostatic neoplasms</subject><subject>Proteome - metabolism</subject><subject>Regression Analysis</subject><subject>REML</subject><subject>Research methodology</subject><subject>Sample Size</subject><subject>Score test</subject><subject>Sensitivity and Specificity</subject><subject>Signal Transduction - physiology</subject><subject>Simulations</subject><subject>Smoothing parameter</subject><subject>statistical models</subject><subject>Support vector machines</subject><subject>variance</subject><issn>0006-341X</issn><issn>1541-0420</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqNktuO0zAQhiMEYsvCGyCwuOAuxY6dxEECCRa2rGhYlrJixY01jSetSw5dO2Hbt8clVTncgCXLh__7Rx7PBAFhdMz8eLYas1iwkIqIjiNK07GfWTbe3ApGB-F2MKKUJiEX7OoouOfcyh-zmEZ3gyMmaSqFpKNgO8ParMFCjZ01BfmEC4vOmbYhbUnyvuqMNjU2uxuoyAQb7Dz2EbrlDWzJG-jgOZkiuC6cXffgveQ92gYrkkOxNI0_Q6PJ1O_AktxsUJO81Vi5-8GdEiqHD_brcXB5-vbzybtwej45O3k1DYuE8SxEKJGVcVzEkmcpY3NkiYgYR811mfgkMC1SzkSGkMhIa40iEsUckpJrmWrGj4OXQ9x1P69RF9h0Fiq1tqYGu1UtGPWn0pilWrTfVZQksaTUB3i6D2Db6x5dp2rjCqwqaLDtnUoy6l8UyX-CQjIRD-CTv8BV21v_v075zCSPUxp7SA5QYVvnLJaHJzOqdl2gVmpXbLUrttp1gfrZBWrjrY9-T_mXcV92D7wYgBtT4fa_A6vXZ-e533n_w8G_cl1rD37hXSKJvBwOsnEdbg4y2G8qSXkaqy8fJuqK5heTr_xUXXj-8cCX0CpYWOPU5SyijFMqeZRKxn8A2rLkTA</recordid><startdate>200712</startdate><enddate>200712</enddate><creator>Liu, Dawei</creator><creator>Lin, Xihong</creator><creator>Ghosh, Debashis</creator><general>Blackwell Publishing Inc</general><general>International Biometric Society</general><general>Blackwell Publishing Ltd</general><scope>FBQ</scope><scope>BSCLL</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>7S9</scope><scope>L.6</scope><scope>7X8</scope><scope>5PM</scope></search><sort><creationdate>200712</creationdate><title>Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models</title><author>Liu, Dawei ; Lin, Xihong ; Ghosh, Debashis</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c6139-eafe1f55c5839711be164213ed3df6848e7c73149ea682ddde424cba6f3d87d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Algorithms</topic><topic>Biometrics</topic><topic>biometry</topic><topic>Biometry - methods</topic><topic>BLUPs</topic><topic>Computer Simulation</topic><topic>computer software</topic><topic>data collection</topic><topic>Data Interpretation, Statistical</topic><topic>Data smoothing</topic><topic>gene expression</topic><topic>Gene Expression Profiling - methods</topic><topic>genes</topic><topic>Genetics</topic><topic>Kernel function</topic><topic>Kernel functions</topic><topic>least squares</topic><topic>Linear Models</topic><topic>Linear regression</topic><topic>Measurement techniques</topic><topic>Medical genetics</topic><topic>Model/variable selection</topic><topic>Modeling</topic><topic>Models, Biological</topic><topic>Nonparametric models</topic><topic>Nonparametric regression</topic><topic>Parametric models</topic><topic>Penalized likelihood</topic><topic>Prostate cancer</topic><topic>prostatic neoplasms</topic><topic>Proteome - metabolism</topic><topic>Regression Analysis</topic><topic>REML</topic><topic>Research methodology</topic><topic>Sample Size</topic><topic>Score test</topic><topic>Sensitivity and Specificity</topic><topic>Signal Transduction - physiology</topic><topic>Simulations</topic><topic>Smoothing parameter</topic><topic>statistical models</topic><topic>Support vector machines</topic><topic>variance</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Dawei</creatorcontrib><creatorcontrib>Lin, Xihong</creatorcontrib><creatorcontrib>Ghosh, Debashis</creatorcontrib><collection>AGRIS</collection><collection>Istex</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><collection>AGRICOLA</collection><collection>AGRICOLA - Academic</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Biometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Dawei</au><au>Lin, Xihong</au><au>Ghosh, Debashis</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models</atitle><jtitle>Biometrics</jtitle><addtitle>Biometrics</addtitle><date>2007-12</date><risdate>2007</risdate><volume>63</volume><issue>4</issue><spage>1079</spage><epage>1088</epage><pages>1079-1088</pages><issn>0006-341X</issn><eissn>1541-0420</eissn><coden>BIOMA5</coden><abstract>We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations.</abstract><cop>Malden, USA</cop><pub>Blackwell Publishing Inc</pub><pmid>18078480</pmid><doi>10.1111/j.1541-0420.2007.00799.x</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Biometrics, 2007-12, Vol.63 (4), p.1079-1088 |
| issn | 0006-341X 1541-0420 |
| language | eng |
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| source | Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current); MEDLINE; Wiley Online Library Journals Frontfile Complete; JSTOR Mathematics & Statistics |
| subjects | Algorithms Biometrics biometry Biometry - methods BLUPs Computer Simulation computer software data collection Data Interpretation, Statistical Data smoothing gene expression Gene Expression Profiling - methods genes Genetics Kernel function Kernel functions least squares Linear Models Linear regression Measurement techniques Medical genetics Model/variable selection Modeling Models, Biological Nonparametric models Nonparametric regression Parametric models Penalized likelihood Prostate cancer prostatic neoplasms Proteome - metabolism Regression Analysis REML Research methodology Sample Size Score test Sensitivity and Specificity Signal Transduction - physiology Simulations Smoothing parameter statistical models Support vector machines variance |
| title | Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models |
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