{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T01:21:34Z","timestamp":1787016094783,"version":"build-2736575974"},"reference-count":23,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2016,2,5]],"date-time":"2016-02-05T00:00:00Z","timestamp":1454630400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003550","name":"Queensland Government","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003550","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Risk Analysis"],"published-print":{"date-parts":[[2016,10]]},"abstract":"\n Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single\u2010hit dose\u2010response models are the most commonly used dose\u2010response models in QMRA. Denoting\n \n as the probability of infection at a given mean dose\n d<\/jats:italic>\n , a three\u2010parameter generalized QMRA beta\u2010Poisson dose\u2010response model,\n \n , is proposed in which the minimum number of organisms required for causing infection,\n K<\/jats:italic>\n min<\/jats:sub>\n , is not fixed, but a random variable following a geometric distribution with parameter\n \n . The single\u2010hit beta\u2010Poisson model,\n \n , is a special case of the generalized model with\n K<\/jats:italic>\n min<\/jats:sub>\n = 1 (which implies\n \n ). The generalized beta\u2010Poisson model is based on a conceptual model with greater detail in the dose\u2010response mechanism. Since a maximum likelihood solution is not easily available, a likelihood\u2010free approximate Bayesian computation (ABC) algorithm is employed for parameter estimation. By fitting the generalized model to four experimental data sets from the literature, this study reveals that the posterior median\n \n estimates produced fall short of meeting the required condition of\n \n = 1 for single\u2010hit assumption. However, three out of four data sets fitted by the generalized models could not achieve an improvement in goodness of fit. These combined results imply that, at least in some cases, a single\u2010hit assumption for characterizing the dose\u2010response process may not be appropriate, but that the more complex models may be difficult to support especially if the sample size is small. The three\u2010parameter generalized model provides a possibility to investigate the mechanism of a dose\u2010response process in greater detail than is possible under a single\u2010hit model.\n <\/jats:p>","DOI":"10.1111\/risa.12561","type":"journal-article","created":{"date-parts":[[2016,2,5]],"date-time":"2016-02-05T15:13:45Z","timestamp":1454685225000},"page":"1948-1958","source":"Crossref","is-referenced-by-count":16,"title":["A Generalized QMRA Beta\u2010Poisson Dose\u2010Response Model"],"prefix":"10.1111","volume":"36","author":[{"given":"Gang","family":"Xie","sequence":"first","affiliation":[{"name":"Faculty of Science, Health, Education and Engineering University of the Sunshine Coast Queensland Australia"},{"name":"Smart Water Research Centre Griffith University Queensland Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anne","family":"Roiko","sequence":"additional","affiliation":[{"name":"Smart Water Research Centre Griffith University Queensland Australia"},{"name":"Menzies Health Institute Queensland Griffith University Queensland Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Helen","family":"Stratton","sequence":"additional","affiliation":[{"name":"Smart Water Research Centre Griffith University Queensland Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles","family":"Lemckert","sequence":"additional","affiliation":[{"name":"Smart Water Research Centre Griffith University Queensland Australia"},{"name":"School of Engineering Griffith University Queensland Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter K.","family":"Dunn","sequence":"additional","affiliation":[{"name":"Faculty of Science, Health, Education and Engineering University of the Sunshine Coast Queensland Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kerrie","family":"Mengersen","sequence":"additional","affiliation":[{"name":"Science and Engineering Faculty Queensland University of Technology Queensland Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2016,2,5]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118910030"},{"key":"e_1_2_10_3_1","unstructured":"RoseJ HaasC GurianP MitchellJ WeirM. QMRA wiki: Center for Advancing Microbial Risk Assessment. Quantitative Microbial Risk Assessment (QMRA) Wiki 2015. Available at:http:\/\/qmrawiki.canr.msu.edu\/index.php\/Quantitative_Microbial_Risk_Assessment_%28QMRA%29_Wiki Accessed April 2015."},{"key":"e_1_2_10_4_1","unstructured":"The Interagency Microbiological Risk Assessment Guideline Workgroup.Microbial Risk Assessment Guideline Pathogenic Microorganisms with Focus on Food and Water. U.S. Environment Protection Agency (EPA) and U.S. Department of Agriculture\/Food Safety and Inspection Service (USDA\/FSIS) 2012."},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-011-9288-2"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/0272-4332.204048"},{"key":"e_1_2_10_7_1","unstructured":"TeunisP vander HeijdenOG vander GiessenJWB HavelaarA.The Dose\u2010Response Relation in Human Volunteers for Gastro\u2010Intestinal Pathogens. The Netherlands: National Institute of Public Health and the Environment (RIVM) 1996. Contract No.: Report no. 284550002."},{"key":"e_1_2_10_8_1","volume-title":"Quantitative Microbial Risk Assessment","author":"Haas CN","year":"1999"},{"key":"e_1_2_10_9_1","volume-title":"Advanced Engineering Mathematics","author":"Kreyszig E","year":"2011"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100285"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1031689021"},{"key":"e_1_2_10_12_1","volume-title":"Statistical Inference","author":"Casella G","year":"2002"},{"key":"e_1_2_10_13_1","volume-title":"Bayesian Data Analysis","author":"Gelman A","year":"2014"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/0272-4332.00035"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3242-6"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4539-6"},{"key":"e_1_2_10_17_1","unstructured":"R Development Core Team. 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