Estimating probability distributions of bacterial concentrations in food based on data generated using the most probable number (MPN) method for use in risk assessment

Estimating probability distributions that describe bacterial concentrations in food products is a key element of quantitative microbial risk assessments. Standard bacteriological protocols for bacterial enumeration first apply a detection test to a set of samples. For samples that test positive, bacterial concentrations are quantified using a serial dilution assay such as the most probable number (MPN) method. Estimation of bacterial concentration distributions based on a set of such data, however, represents a considerable statistical challenge. A maximum likelihood approach has been published to estimate bacterial concentrations from this type of data while accounting for the censored nature of the data. In this study, we derived an alternative method, based on complete likelihood maximization from observed MPN pattern data. Both methods were first evaluated in simulation studies, which showed that the latter method generated unbiased estimates of the parameters of the bacterial concentration distribution, while the former method generated biased results. The bias was particularly pronounced when bacterial concentrations were low. Both methods fail to predict accurately low contamination levels at low prevalence (e.g. mean of −7 log10 for contaminated products and prevalence of 0.2). The methods were then applied to bacteriological data from a food survey of Listeria monocytogenes in the United States. The former method led to approximately 1 log10 cfu higher estimated mean bacterial concentration compared to estimates generated using the alternative method. The alternative method is preferable, in particular if bacterial concentrations are low.