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

Area of Science:

• Microbial risk assessment
• Statistical modeling
• Computational toxicology

Background:

• The exact beta-Poisson model is crucial for dose-response analysis in quantitative microbial risk assessment (QMRA).
• Evaluating the Kummer confluent hypergeometric function in the exact model presents computational challenges.
• The approximate formula PI(d)=1-(1+dβ)-α is widely used but its validity and accuracy are often overlooked.

Purpose of the Study:

• To propose a novel probability measure, Pr(0 < r < 1 | α̂, β̂), as a validity metric for the approximate beta-Poisson model.
• To establish constraint conditions, β̂>(22α̂)0.50 for 0.02<α̂<2, as a rule of thumb for ensuring approximation accuracy.
• To validate the proposed measure and rule of thumb using existing QMRA data sets.

Main Methods:

• Development of a probability measure Pr(0 < r < 1 | α̂, β̂) based on maximum likelihood estimates (α̂, β̂) of the approximate model parameters.
• Definition of a rule of thumb (β̂>(22α̂)0.50) for parameter values within a specified range (0.02<α̂<2).
• Application and validation of the proposed methods to 85 completed beta-Poisson models from the QMRA Wiki.

Main Results:

• A higher probability Pr(0 < r < 1 | α̂, β̂) correlates with improved approximation accuracy of the beta-Poisson model.
• Sixty-eight out of 85 examined models met the criteria for valid approximate model applications.
• Validated models demonstrated a near-perfect match between the approximate and exact beta-Poisson dose-response curves.

Conclusions:

• The proposed probability measure and rule of thumb provide reliable criteria for assessing the validity and accuracy of approximate beta-Poisson models in QMRA.
• The findings confirm the utility of the approximate model when specific conditions are met, enhancing QMRA practices.
• This work offers practical guidance for researchers and practitioners in selecting and applying appropriate dose-response models for microbial risk assessment.