Fitting a lognormal distribution to enumeration and absence/presence data.

To fit a lognormal distribution to a complex set of microbial data, including detection data (e.g. presence or absence in 25g) and enumeration data (e.g. 30cfu/g), we compared two models: a model called M(CLD) based on data expressed as concentrations (in cfu/g) or censored concentrations (e.g. <10cfu/g, or >1cfu/25g) versus a model called M(RD) that directly uses raw data (presence/absence in test portions, and plate colony counts). We used these two models to simulated data sets, under standard conditions (limit of detection (LOD)=1cfu/25g; limit of quantification (LOQ)=10cfu/g) and used a maximum likelihood estimation method (directly for the model M(CLD) and via the Expectation-Maximisation (EM) algorithm for the model M(RD). The comparison suggests that in most cases estimates provided by the proposed model M(RD) are similar to those obtained by model M(CLD) accounting for censorship. Nevertheless, in some cases, the proposed model M(RD) leads to less biased and more precise estimates than model M(CLD).

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.