Modeling prevalence and counts from most probable number in a bayesian framework: an application to Salmonella...

Prevalence and counts of Salmonella Typhimurium in fresh pork sausage packs at the point of retail were modeled by using Irish and United Kingdom retail surveys' data. A methodology for modeling a second-order distribution for the initial Salmonella concentration (lambda0) in pork sausage at retail was presented considering the uncertainty originated from the most probable-number (MPN) serial dilutions. A conditional probability of observing the tube counts given true Salmonella concentration in a contaminated pack was built from the MPN triplets of every sausage tested. A posterior distribution was then modeled under the assumption that the counts from each of the portions of sausage mix stuffed into casings (and subsequently packed) are Poisson distributed. In order to model the variability of lambda0 among contaminated sausage packs, MPN uncertainties were propagated to a predefined lognormal distribution. Because the sausage samples from the Irish survey were frozen prior to MPN analysis (which is expected to cause reduction in viable cells), the resulting distribution for lambda0 appeared greatly underestimated (mean: 0.514 CFU/g; 95% confidence interval [CI]: 0.02 to 2.74 CFU/g). The lambda0 distribution produced with the United Kingdom survey data (mean: 69.7 CFU/g; 95% CI: 15 to 200 CFU/g) was, however, more conservative, and is to be used along with the fitted distribution for prevalence of Salmonella Typhimurium in pork sausage packs in Ireland (gamma[37.997, 0.0013]; mean: 0.046; 95% CI: 0.032 to 0.064) as the main inputs of a stochastic consumer-phase exposure assessment model.