Uncertainty distribution associated with estimating a proportion in microbial risk assessment

Area of Science:

• Quantitative risk assessment
• Microbial risk assessment
• Statistical modeling

Background:

• Uncertainty quantification is crucial for risk assessment.
• Estimating low proportions from small sample sizes presents challenges.
• Prevalence estimation in food safety often involves limited testing.

Purpose of the Study:

• To compare Bayesian and frequentist methods for estimating low proportions with small sample sizes.
• To evaluate the impact of different prior distributions in Bayesian approaches.
• To assess the performance of these methods in a realistic food safety scenario.

Main Methods:

• Comparison of four statistical methods: three Bayesian (beta(0,0), beta(1/2,1/2), beta(1,1) priors) and one frequentist (confidence distribution).
• Monte Carlo simulations were used to evaluate method performance.
• Application to estimate Listeria monocytogenes contamination in cold smoked salmon using two-dimensional simulations.

Main Results:

• Differences were observed between the four methods, particularly for small sample sizes.
• The optimal method's performance is dependent on the unknown true proportion of contamination.
• Two-dimensional Monte Carlo simulations highlighted practical differences in risk estimation.

Conclusions:

• No single method is universally superior for estimating low proportions from small samples.
• When prior information is absent, the beta (1/2, 1/2) prior or the frequentist confidence distribution are recommended.
• Accurate uncertainty estimation is vital for reliable microbial risk assessment in food products.