{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T04:46:00Z","timestamp":1745901960472,"version":"3.37.3"},"reference-count":32,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T00:00:00Z","timestamp":1608768000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004295","name":"Shandong University of Science and Technology","doi-asserted-by":"publisher","award":["2019RCJJ021","71501114"],"award-info":[{"award-number":["2019RCJJ021","71501114"]}],"id":[{"id":"10.13039\/501100004295","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2019RCJJ021","71501114"],"award-info":[{"award-number":["2019RCJJ021","71501114"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,12,24]]},"abstract":"<jats:p>Case-cohort design is a biased sampling method. Due to its cost-effective and theoretical significance, this design has extensive application value in many large cohort studies. The case-cohort data includes a subcohort sampled randomly from the entire cohort and all the failed subjects outside the subcohort. In this paper, the adjustment for the distorted covariates is considered to case-cohort data in Cox\u2019s model. According to the existing adjustable methods of distorted covariates for linear and nonlinear models, we propose estimating the distorting functions by nonparametrically regressing the distorted covariates on the distorting factors; then, the estimators for the parameters are obtained using the estimated covariates. The proof of consistency and being asymptotically normal is completed. For calculating the maximum likelihood estimates of the regression coefficients subject in Cox\u2019s model, a minorization-maximization (MM) algorithm is developed. Simulation studies are performed to compare the estimations with the covariates undistorted, distorted, and adjusted to illustrate the proposed methods.<\/jats:p>","DOI":"10.1155\/2020\/8884665","type":"journal-article","created":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:20:25Z","timestamp":1608855625000},"page":"1-16","source":"Crossref","is-referenced-by-count":1,"title":["The Adjustment of Covariates in Cox\u2019s Model under Case-Cohort Design"],"prefix":"10.1155","volume":"2020","author":[{"given":"Guocai","family":"Rong","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"}]},{"given":"Luwei","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanning Normal University, Nanning 530001, Guangxi, China"}]},{"given":"Wenting","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanning Normal University, Nanning 530001, Guangxi, China"}]},{"given":"Qing","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3356-7383","authenticated-orcid":true,"given":"Lifeng","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/73.1.1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1093\/jn\/nxz156"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1093\/eurheartj\/ehx448"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.2307\/2530199"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1001\/jamaoncol.2016.4188"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1093\/jnci\/djz065"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-019-09466-0"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-020-09492-3"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/s0140-6736(84)90818-3"},{"issue":"13","key":"10","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1056\/NEJM199403313301301","article-title":"The effffects of dietary protein restriction and blood pressure control on the progression of renal disease","volume":"330","author":"S. Klahr","year":"1994","journal-title":"New England Journal of Medicine"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.1.75"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1214\/08-aos627"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s10198-015-0731-8"},{"issue":"5","key":"14","first-page":"441","article-title":"Adjusting for high-dimensional covariates in sparse precision matrix estimation by lasso penalized D-trace loss","volume":"35","author":"X. D. Huang","year":"2019","journal-title":"Chinese Applied Probability Statistics"},{"issue":"2","key":"15","first-page":"155","article-title":"A powerful procedure for multiple outcomes comparison with covariate adjustment and its application to genomic data","volume":"36","author":"S. H. Zhang","year":"2019","journal-title":"Journal of University of Chinese Academy of Sciences"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2014.11.005"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2017.08.013"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1972.tb00899.x"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00062"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345976"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350691"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000083"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1032526955"},{"key":"24","unstructured":"HjortN. L.Bootstrapping cox\u2019s regression model1985Stanford, CA, USADepartment of Statistics, Stanford UniversityTechnical report NSF-241"},{"key":"25","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-4541-9","volume-title":"An Introduction to the Bootstrap","author":"B. Efron","year":"1993"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476869"},{"volume-title":"Spline Smoothing and Nonparametric Regression","year":"1988","author":"R. L. Eubank","key":"27"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.3.605"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324320"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2000.10474236"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2007.00838.x"},{"key":"32","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316436","volume-title":"Linear Statistical Inference and its Applications","author":"C. R. Rao","year":"1973","edition":"2nd"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8884665.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8884665.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8884665.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:20:34Z","timestamp":1608855634000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/8884665\/"}},"subtitle":[],"editor":[{"given":"Songbai","family":"Guo","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,12,24]]},"references-count":32,"alternative-id":["8884665","8884665"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8884665","relation":{},"ISSN":["1099-0526","1076-2787"],"issn-type":[{"type":"electronic","value":"1099-0526"},{"type":"print","value":"1076-2787"}],"subject":[],"published":{"date-parts":[[2020,12,24]]}}}