Hierarchical Bayesian models to assess between- and within-batch variability of pathogen contamination in food

Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked.