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Guidelines for Use of the Approximate Beta‐Poisson Dose–Response Model

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  • Gang Xie
  • Anne Roiko
  • Helen Stratton
  • Charles Lemckert
  • Peter K. Dunn
  • Kerrie Mengersen

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 >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 (22α̂)0.50 for 0.02 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

Suggested Citation

  • Gang Xie & Anne Roiko & Helen Stratton & Charles Lemckert & Peter K. Dunn & Kerrie Mengersen, 2017. "Guidelines for Use of the Approximate Beta‐Poisson Dose–Response Model," Risk Analysis, John Wiley & Sons, vol. 37(7), pages 1388-1402, July.
    • Handle: RePEc:wly:riskan:v:37:y:2017:i:7:p:1388-1402
    DOI: 10.1111/risa.12682
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    References listed on IDEAS

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    1. Peter Teunis & Katsuhisa Takumi & Kunihiro Shinagawa, 2004. "Dose Response for Infection by Escherichia coli O157:H7 from Outbreak Data," Risk Analysis, John Wiley & Sons, vol. 24(2), pages 401-407, April.
    2. P. F. M. Teunis & A. H. Havelaar, 2000. "The Beta Poisson Dose‐Response Model Is Not a Single‐Hit Model," Risk Analysis, John Wiley & Sons, vol. 20(4), pages 513-520, August.
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