Guidelines for Use of the Approximate Beta‐Poisson Dose–Response Model |
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| Authors: | Gang Xie Anne Roiko Helen Stratton Charles Lemckert Peter K. Dunn Kerrie Mengersen |
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| Affiliation: | 1. Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Queensland, Australia;2. Smart Water Research Centre, Griffith University, Queensland, Australia;3. Menzies Health Institute Queensland, Griffith University, Queensland, Australia;4. Griffith School of Engineering, Griffith University, Queensland, Australia;5. Science and Engineering Faculty, Queensland University of Technology, Queensland, Australia |
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| 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  and  , which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting  as the probability of infection at a given mean dose d, the widely used dose–response model  is an approximate formula for the exact beta‐Poisson model. Notwithstanding the required conditions  and  , 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 |  ,  ) as a validity measure (r is a random variable that follows a gamma distribution;  and  are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions  for  as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 |  ,  ) >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 |  ,  ), 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. |
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| Keywords: | A rule of thumb beta‐Poisson dose– response model experimental dose– response data QMRA |
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