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Risk Anal. 2016 Oct;36(10):1948-1958. doi: 10.1111/risa.12561. Epub 2016 Feb 5.

A Generalized QMRA Beta-Poisson Dose-Response Model.

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Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Queensland, Australia.
Smart Water Research Centre, Griffith University, Queensland, Australia.
Menzies Health Institute Queensland, Griffith University, Queensland, Australia.
School of Engineering, Griffith University, Queensland Australia.
Science and Engineering Faculty, Queensland University of Technology, Queensland, Australia.


Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single-hit dose-response models are the most commonly used dose-response models in QMRA. Denoting PI(d) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, PI(d|α,β,r*), is proposed in which the minimum number of organisms required for causing infection, Kmin , is not fixed, but a random variable following a geometric distribution with parameter 0<r*≤1. The single-hit beta-Poisson model, PI(d|α,β), is a special case of the generalized model with Kmin = 1 (which implies r*=1). The generalized beta-Poisson model is based on a conceptual model with greater detail in the dose-response mechanism. Since a maximum likelihood solution is not easily available, a likelihood-free approximate Bayesian computation (ABC) algorithm is employed for parameter estimation. By fitting the generalized model to four experimental data sets from the literature, this study reveals that the posterior median r* estimates produced fall short of meeting the required condition of r* = 1 for single-hit assumption. However, three out of four data sets fitted by the generalized models could not achieve an improvement in goodness of fit. These combined results imply that, at least in some cases, a single-hit assumption for characterizing the dose-response process may not be appropriate, but that the more complex models may be difficult to support especially if the sample size is small. The three-parameter generalized model provides a possibility to investigate the mechanism of a dose-response process in greater detail than is possible under a single-hit model.


A generalized beta-Poisson model; QMRA; approximate Bayesian computation; single-hit beta-Poisson models

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