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Modern studies increasingly enjoy the ability to examine a large number of exposures in a comprehensive manner. However, several risk factors often tend to be related in a nontrivial way, undermining efforts to identify the risk factors using standard analytic methods due to inflated type-I errors and possible masking of effects. Epidemiologists often use data reduction techniques by grouping the prognostic factors using a thematic approach, with themes deriving from biological considerations. We propose shrinkage-type estimators based on Bayesian penalization methods to estimate the effects of the risk factors using these themes. The properties of the estimators are examined using extensive simulations. The methodology is illustrated using data from a matched case-control study of polychlorinated biphenyls in relation to the etiology of non-Hodgkin's lymphoma.<\/jats:p>","DOI":"10.1111\/biom.12444","type":"journal-article","created":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T20:58:50Z","timestamp":1447793930000},"page":"584-595","source":"Crossref","is-referenced-by-count":9,"title":["Bayes and Empirical Bayes Methods for Reduced Rank Regression Models in Matched Case-Control Studies"],"prefix":"10.1093","volume":"72","author":[{"given":"Jaya M.","family":"Satagopan","sequence":"first","affiliation":[{"name":"Department of Epidemiology and Biostatistics, Memorial Sloan Kettering Cancer Center , New York 10017 , U.S.A."}]},{"given":"Ananda","family":"Sen","sequence":"additional","affiliation":[{"name":"Departments of Family Medicine and Biostatistics, University of Michigan , Ann Arbor, Michigan 48104 , U.S.A."}]},{"given":"Qin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Epidemiology and Biostatistics, Memorial Sloan Kettering Cancer Center , New York 10017 , U.S.A."}]},{"given":"Qing","family":"Lan","sequence":"additional","affiliation":[{"name":"Division of Cancer Epidemiology and Genetics, National Cancer Insitute , Rockville, Maryland 20892 , U.S.A."}]},{"given":"Nathaniel","family":"Rothman","sequence":"additional","affiliation":[{"name":"Division of Cancer Epidemiology and Genetics, National Cancer Insitute , Rockville, Maryland 20892 , U.S.A."}]},{"given":"Hilde","family":"Langseth","sequence":"additional","affiliation":[{"name":"Cancer Registry of Norway, Institute of Population-Based Cancer Research , Oslo 0304 , Norway"}]},{"given":"Lawrence S.","family":"Engel","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, University of North Carolina , Chapel Hill, North Carolina 27599 , 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