{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:39:50Z","timestamp":1773103190687,"version":"3.50.1"},"reference-count":24,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T00:00:00Z","timestamp":1666656000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Reference intervals are widely used in the interpretation of results of biochemical and physiological tests of patients. When there are multiple biochemical analytes measured from each subject, a multivariate reference region is needed. Because of their greater specificity against false positives, such reference regions are more desirable than separate univariate reference intervals that disregard the cross\u2010correlations between variables. Traditionally, under multivariate normality, reference regions have been constructed as ellipsoidal regions. This approach suffers from a major drawback: it cannot detect component\u2010wise extreme observations. In the present work, procedures are developed to construct rectangular reference regions in the multivariate normal setup. The construction is based on the criteria for tolerance intervals. The problems addressed include the computation of a rectangular tolerance region and simultaneous tolerance intervals. Also addressed is the computation of mixed reference intervals that include both two\u2010sided and one\u2010sided limits, simultaneously. A parametric bootstrap approach is used in the computations, and the accuracy of the proposed methodology is assessed using estimated coverage probabilities. The problem of sample size determination is also addressed, and the results are illustrated using examples that call for the computation of reference\u00a0regions.<\/jats:p>","DOI":"10.1002\/bimj.202100180","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T05:51:02Z","timestamp":1666763462000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Rectangular tolerance regions and multivariate normal reference regions in laboratory medicine"],"prefix":"10.1002","volume":"65","author":[{"given":"Michael Daniel","family":"Lucagbo","sequence":"first","affiliation":[{"name":"Department of Mathematics &amp; Statistics University of Maryland Baltimore County Baltimore Maryland USA"},{"name":"School of Statistics University of the Philippines Diliman Quezon City Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4152-3628","authenticated-orcid":false,"given":"Thomas","family":"Mathew","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics University of Maryland Baltimore County Baltimore Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,10,25]]},"reference":[{"key":"e_1_2_10_2_1","volume-title":"Multivariate interpretation of clinical laboratory data","author":"Albert A.","year":"1987"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.3174\/ajnr.A2529"},{"key":"e_1_2_10_4_1","unstructured":"Cleveland Clinic. (2020).https:\/\/my.clevelandclinic.org\/health\/diagnostics\/17684\u2010blood\u2010urea\u2010nitrogen\u2010bun\u2010test\/results\u2010and\u2010follow\u2010up"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2014.10.009"},{"key":"e_1_2_10_6_1","first-page":"45","volume-title":"Progress in clinical pathology","author":"Harris E. K.","year":"1981"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781482273151"},{"key":"e_1_2_10_8_1","volume-title":"Reference intervals: A users guide","author":"Horn P. S.","year":"2005"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2177"},{"key":"e_1_2_10_10_1","doi-asserted-by":"crossref","unstructured":"Katki H. A. Engels E. A. & Rosenberg P. S. (2005).\u00a0 Assessing uncertainty in reference intervals via tolerance intervals: application to a mixed model describing HIV infection.Statistics in Medicine 24 599 \u2013 601.","DOI":"10.1002\/sim.2171"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1161\/STROKEAHA.110.591818"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470473900"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280220961793"},{"key":"e_1_2_10_14_1","doi-asserted-by":"crossref","unstructured":"Lucagbo M. D. 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