title: Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.
abstract: For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<<β and β>>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve.
authors.affiliation: Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Queensland, Australia.|Smart Water Research Centre, Griffith University, Queensland, Australia.
authors.forename: Gang
authors.initials: G
authors.lastname: Xie
authors.affiliation: Smart Water Research Centre, Griffith University, Queensland, Australia.|Menzies Health Institute Queensland, Griffith University, Queensland, Australia.
authors.forename: Anne
authors.initials: A
authors.lastname: Roiko
authors.affiliation: Smart Water Research Centre, Griffith University, Queensland, Australia.
authors.forename: Helen
authors.initials: H
authors.lastname: Stratton
authors.affiliation: Smart Water Research Centre, Griffith University, Queensland, Australia.|Griffith School of Engineering, Griffith University, Queensland, Australia.
authors.forename: Charles
authors.initials: C
authors.lastname: Lemckert
authors.affiliation: Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Queensland, Australia.
authors.forename: Peter K
authors.initials: PK
authors.lastname: Dunn
authors.affiliation: Science and Engineering Faculty, Queensland University of Technology, Queensland, Australia.
authors.forename: Kerrie
authors.initials: K
authors.lastname: Mengersen
mesh_terms: D002169:Campylobacter Infections / Q000453:epidemiology* / Q000382:microbiology; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016012:Poisson Distribution; D011336:Probability; D018570:Risk Assessment / Q000379:methods*; D014871:Water Microbiology
keywords: A rule of thumb; QMRA; beta-Poisson dose-response model; experimental dose-response data