{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T09:40:59Z","timestamp":1784108459487,"version":"3.55.0"},"reference-count":17,"publisher":"The Royal Society","issue":"57","license":[{"start":{"date-parts":[[2010,11,10]],"date-time":"2010-11-10T00:00:00Z","timestamp":1289347200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["J. R. Soc. Interface."],"published-print":{"date-parts":[[2011,4,6]]},"abstract":"<jats:p>The most commonly used dose\u2013response models implicitly assume that accumulation of dose is a time-independent process where each pathogen has a fixed risk of initiating infection. Immune particle neutralization of pathogens, however, may create strong time dependence; i.e. temporally clustered pathogens have a better chance of overwhelming the immune particles than pathogen exposures that occur at lower levels for longer periods of time. In environmental transmission systems, we expect different routes of transmission to elicit different dose\u2013timing patterns and thus potentially different realizations of risk. We present a dose\u2013response model that captures time dependence in a manner that incorporates the dynamics of initial immune response. We then demonstrate the parameter estimation of our model in a dose\u2013response survival analysis using empirical time-series data of inhalational anthrax in monkeys in which we find slight dose\u2013timing effects. Future dose\u2013response experiments should include varying the time pattern of exposure in addition to varying the total doses delivered. Ultimately, the dynamic dose\u2013response paradigm presented here will improve modelling of environmental transmission systems where different systems have different time patterns of exposure.<\/jats:p>","DOI":"10.1098\/rsif.2010.0491","type":"journal-article","created":{"date-parts":[[2010,11,10]],"date-time":"2010-11-10T20:31:44Z","timestamp":1289421104000},"page":"506-517","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["A dynamic dose\u2013response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax"],"prefix":"10.1098","volume":"8","author":[{"given":"Bryan T.","family":"Mayer","sequence":"first","affiliation":[{"name":"Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James S.","family":"Koopman","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109, USA"},{"name":"Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edward L.","family":"Ionides","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Michigan, Ann Arbor, MI 48104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Josep M.","family":"Pujol","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109, USA"},{"name":"Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48104, USA"},{"name":"Telefonica Research, Augusta 177, Barcelona 08021, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph N. 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