{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:03:04Z","timestamp":1790665384513,"version":"4.1.0"},"reference-count":21,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Interval estimation of a proportion estimated from testing of pooled samples has been studied by a variety of researchers, who have examined both exact and asymptotic methods. Recent work in point estimation has seen the use of Firth's correction to maximum likelihood estimation to reduce bias effectively. We consider the Firth\u2010corrected score statistic, using either expected or observed information, as the first derivative function of a penalized likelihood and develop score\u2010based confidence intervals wholly within this framework. We evaluate their performance, comparing them by information type and to the existing, recommended asymptotic method of Gart. The methods are illustrated using data on West Nile virus infection in field\u2010collected mosquitoes and on yellow fever virus infection in mosquitoes reported in Walter et\u00a0al. The penalized likelihood approach using expected information is found to unify previously recommended point and interval estimates under one inferential framework. Detailed evaluation of coverage properties of the intervals over a range of pooling designs show improved performance for the intervals using observed information and skewness\u2010correction to the score. We derive simple, interpretable expressions for the score and skewness\u2010corrected score statistics, and give a quadratic formula for the skewness\u2010corrected score interval for the case that all pools are the same size, which reduces to a skewness\u2010correction for the standard Wilson interval in the standard binomial\u00a0case.<\/jats:p>","DOI":"10.1002\/bimj.70185","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T06:25:15Z","timestamp":1790663115000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Confidence Intervals for a Proportion Estimated From Pooled Samples Based on Firth's Corrected Score"],"prefix":"10.1002","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3105-3530","authenticated-orcid":false,"given":"Brad J.","family":"Biggerstaff","sequence":"first","affiliation":[{"name":"Division of Vector\u2010Borne Diseases Centers for Disease Control and Prevention Fort Collins, Colorado USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Graham","family":"Hepworth","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics The University of Melbourne Melbourne, Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1093\/biomet\/40.1-2.12","article-title":"Approximate Confidence Intervals","volume":"40","author":"Bartlett M. 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