{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T15:48:41Z","timestamp":1788364121996,"version":"build-2803163510"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T00:00:00Z","timestamp":1678492800000},"content-version":"vor","delay-in-days":3749,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["(R37-CA057030)"],"award-info":[{"award-number":["(R37-CA057030)"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004052","name":"King Abdullah University of Science and Technology","doi-asserted-by":"publisher","award":["KUS-CI-016-04"],"award-info":[{"award-number":["KUS-CI-016-04"]}],"id":[{"id":"10.13039\/501100004052","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000050","name":"National Heart, Lung and Blood Institute","doi-asserted-by":"publisher","award":["(RO1-HL091172-01)"],"award-info":[{"award-number":["(RO1-HL091172-01)"]}],"id":[{"id":"10.13039\/100000050","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["(DMS-0907014)"],"award-info":[{"award-number":["(DMS-0907014)"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["203650"],"award-info":[{"award-number":["203650"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Community\u2019s seventh framework programme","award":["(FP7\/2007-2013)"],"award-info":[{"award-number":["(FP7\/2007-2013)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,1,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Primary analysis of case\u2013control studies focuses on the relationship between disease D and a set of covariates of interest (Y, X). A secondary application of the case\u2013control study, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated owing to the case\u2013control sampling, where the regression of Y on X is different from what it is in the population. Previous work has assumed a parametric distribution for Y given X and derived semiparametric efficient estimation and inference without any distributional assumptions about X. We take up the issue of estimation of a regression function when Y given X follows a homoscedastic regression model, but otherwise the distribution of Y is unspecified. The semiparametric efficient approaches can be used to construct semiparametric efficient estimates, but they suffer from a lack of robustness to the assumed model for Y given X. We take an entirely different approach. We show how to estimate the regression parameters consistently even if the assumed model for Y given X is incorrect, and thus the estimates are model robust. For this we make the assumption that the disease rate is known or well estimated. The assumption can be dropped when the disease is rare, which is typically so for most case\u2013control studies, and the estimation algorithm simplifies. Simulations and empirical examples are used to illustrate the approach.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2012.01052.x","type":"journal-article","created":{"date-parts":[[2012,12,4]],"date-time":"2012-12-04T20:16:11Z","timestamp":1354652171000},"page":"185-206","source":"Crossref","is-referenced-by-count":22,"title":["Robust Estimation for Homoscedastic Regression in the Secondary Analysis of Case\u2013Control Data"],"prefix":"10.1093","volume":"75","author":[{"given":"Jiawei","family":"Wei","sequence":"first","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raymond J.","family":"Carroll","sequence":"additional","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ursula U.","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ingrid Van","family":"Keilegom","sequence":"additional","affiliation":[{"name":"Universit\u00e9 catholique de Louvain , Louvain-la-Neuve , Belgium"},{"name":"Tilburg University , The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nilanjan","family":"Chatterjee","sequence":"additional","affiliation":[{"name":"National Cancer Institute , Rockville , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2012,12,4]]},"reference":[{"key":"2023031201055524700_","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1093\/carcin\/bgp055","article-title":"Vitamin D-related genes, serum vitamin D concentrations and prostate cancer risk","volume":"30","author":"Ahn","year":"2009","journal-title":"Carcinogenesis"},{"key":"2023031201055524700_","doi-asserted-by":"crossref","DOI":"10.4135\/9781412985109","volume-title":"Modern Methods for Robust Regression","author":"Anderson","year":"2008"},{"key":"2023031201055524700_","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1214\/aos\/1176346267","article-title":"Inference on means using the bootstrap","volume":"11","author":"Babu","year":"1983","journal-title":"Ann. 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