Methods for fitting a parametric probability distribution to most probable number data.

Area of Science:

• Microbiology
• Statistics
• Food Safety

Background:

• Microbial contamination in food and water requires sensitive detection methods.
• The most probable number (MPN) technique estimates low pathogen concentrations using dilution experiments.
• Existing methods for fitting MPN data to distributions often overlook MPN's inherent data characteristics.

Purpose of the Study:

• To propose and evaluate two novel methods for fitting most probable number (MPN) data to probability distributions.
• To address the bias in existing methods when dealing with real-valued estimates from MPN, rather than direct measurements.
• To compare the performance of a maximum likelihood estimator with a Bayesian latent variable method using real-world food safety data.

Main Methods:

• Developed a maximum likelihood estimator using average concentration values as input.
• Developed a Bayesian latent variable method utilizing positive tube counts at each dilution.
• Compared both methods using datasets of Salmonella and Campylobacter concentrations on chicken carcasses.

Main Results:

• The maximum likelihood estimator showed increasing bias as average concentrations decreased.
• The Bayesian latent variable method provided unbiased estimates across all tested datasets.
• The Bayesian approach proved more robust for fitting microbial contamination data derived from MPN.

Conclusions:

• The Bayesian latent variable method is recommended for fitting MPN data due to its unbiased estimation.
• Accurate microbial contamination estimates are crucial for reliable food-safety risk assessments.
• The study provides computational code for the proposed Bayesian fitting method.