Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model

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

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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 | αˆ, βˆ) as a validity measure (r is a random variable that follows a gamma distribution; αˆ and βˆ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions βˆ>(22αˆ)0.50 for 0.02<αˆ<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | αˆ, βˆ) >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 | αˆ, βˆ), 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.

Original languageEnglish
Pages (from-to)1388-1402
Number of pages15
JournalRisk Analysis
Issue number7
Publication statusPublished - 1 Jul 2017
Externally publishedYes


Dive into the research topics of 'Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model'. Together they form a unique fingerprint.

Cite this