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

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

Risk Analysis, 2017, vol. 37, issue 7, 1388-1402

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

Date: 2017
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