### Abstract

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 (Formula presented.) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, (Formula presented.), is proposed in which the minimum number of organisms required for causing infection, K_{min}, is not fixed, but a random variable following a geometric distribution with parameter (Formula presented.). The single-hit beta-Poisson model, (Formula presented.), is a special case of the generalized model with K_{min} = 1 (which implies (Formula presented.)). 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 (Formula presented.) estimates produced fall short of meeting the required condition of (Formula presented.) = 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.

Original language | English |
---|---|

Pages (from-to) | 1948-1958 |

Number of pages | 11 |

Journal | Risk Analysis |

Volume | 36 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1 Oct 2016 |

Externally published | Yes |

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### Cite this

*Risk Analysis*,

*36*(10), 1948-1958. https://doi.org/10.1111/risa.12561

}

*Risk Analysis*, vol. 36, no. 10, pp. 1948-1958. https://doi.org/10.1111/risa.12561

**A Generalized QMRA Beta-Poisson Dose-Response Model.** / Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K.; Mengersen, Kerrie.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Generalized QMRA Beta-Poisson Dose-Response Model

AU - Xie, Gang

AU - Roiko, Anne

AU - Stratton, Helen

AU - Lemckert, Charles

AU - Dunn, Peter K.

AU - Mengersen, Kerrie

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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 (Formula presented.) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, (Formula presented.), 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 (Formula presented.). The single-hit beta-Poisson model, (Formula presented.), is a special case of the generalized model with Kmin = 1 (which implies (Formula presented.)). 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 (Formula presented.) estimates produced fall short of meeting the required condition of (Formula presented.) = 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.

AB - 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 (Formula presented.) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, (Formula presented.), 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 (Formula presented.). The single-hit beta-Poisson model, (Formula presented.), is a special case of the generalized model with Kmin = 1 (which implies (Formula presented.)). 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 (Formula presented.) estimates produced fall short of meeting the required condition of (Formula presented.) = 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.

KW - A generalized beta-Poisson model

KW - approximate Bayesian computation

KW - QMRA

KW - single-hit beta-Poisson models

KW - Food Contamination

KW - Humans

KW - Probability

KW - Models, Statistical

KW - Healthy Volunteers

KW - Campylobacter Infections/microbiology

KW - Food Microbiology/methods

KW - Listeriosis/microbiology

KW - Likelihood Functions

KW - Sample Size

KW - Algorithms

KW - Animals

KW - Bayes Theorem

KW - Poisson Distribution

KW - Mice

KW - Risk Assessment/methods

KW - Water Microbiology

UR - http://www.scopus.com/inward/record.url?scp=84959255567&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/generalized-qmra-betapoisson-doseresponse-model

U2 - 10.1111/risa.12561

DO - 10.1111/risa.12561

M3 - Article

VL - 36

SP - 1948

EP - 1958

JO - Risk Analysis

JF - Risk Analysis

SN - 0272-4332

IS - 10

ER -