Methodology for Determining the Appropriateness of a Linear Dose-Response Function

Authors

  • Michael S. Williams,

    Corresponding author
    1. Risk Assessment Division, Office of Public Health Science, Food Safety Inspection Service, USDA, CO, USA.
      Address correspondence to Michael S. Williams, Risk Assessment Division, Office of Public Health Science, Food Safety Inspection Service, USDA 2150, Centre Avenue, Building D, Fort Collins, CO 80526, USA; tel: 970-492-7189; mike.williams@fsis.usda.gov.
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  • Eric D. Ebel,

    1. Risk Assessment Division, Office of Public Health Science, Food Safety Inspection Service, USDA, CO, USA.
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  • David Vose

    1. Vose Consulting (US) LLC, USA.
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Address correspondence to Michael S. Williams, Risk Assessment Division, Office of Public Health Science, Food Safety Inspection Service, USDA 2150, Centre Avenue, Building D, Fort Collins, CO 80526, USA; tel: 970-492-7189; mike.williams@fsis.usda.gov.

Abstract

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose-response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose-response functions are approximately linear when the dose is low. Nevertheless, what constitutes “low” is dependent on the parameters of the dose-response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose-response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose-response approximation, for example, the expected value for exposure doses is two to three logs10 smaller than the upper bound of the linear portion of the dose-response function, then predicting the risk-reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.

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