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

Gang Xie; Anne H Roiko; Helen Stratton; Charles Lemckert; Peter K Dunn; Kerrie Mengersen

doi:10.1111/risa.12682

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

Journal article

Peer reviewed

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

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

Risk Analysis, Vol.37(7), pp.1388-1402

2017

DOI: https://doi.org/10.1111/risa.12682

PMID: 27704592

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Abstract

a rule of thumb

beta-Poisson dose-response model

experimental dose-response data

QMRA

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 inline image and inline image, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting inline image as the probability of infection at a given mean dose d, the widely used dose-response model inline image is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions inline image and inline image, 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 | inline image, inline image) as a validity measure (r is a random variable that follows a gamma distribution; inline image and inline image are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions inline image for inline image as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | inline image, inline image) >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 | inline image, inline image), 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.

Details

Title: Guidelines for Use of the Approximate Beta-Poisson Dose–Response Model
Authors: Gang Xie (Author) - University of the Sunshine Coast - Faculty of Science, Health, Education and Engineering
Anne H Roiko (Author) - Griffith University
Helen Stratton (Author) - Griffith University
Charles Lemckert (Author) - Griffith University
Peter K Dunn (Author) - University of the Sunshine Coast - Faculty of Science, Health, Education and Engineering
Kerrie Mengersen (Author) - Queensland University of Technology
Publication details: Risk Analysis, Vol.37(7), pp.1388-1402
Publisher: Wiley-Blackwell Publishing Inc.
Date published: 2017
DOI: 10.1111/risa.12682
ISSN: 0272-4332
PMID: 27704592
Organisation Unit: School of Health and Sport Sciences - Legacy; School of Science, Technology and Engineering; Sustainability Research Cluster
Language: English
Record Identifier: 99450320402621
Output Type: Journal article

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Collaboration types: Domestic collaboration
Web Of Science research areas: Mathematics, Interdisciplinary Applications; Public, Environmental & Occupational Health; Social Sciences, Mathematical Methods

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