Conducting inferential statistics for low microbial counts in foods using the Poisson-gamma regression

Abstract

Mixed Poisson distributions have been shown to be able to represent low microbial counts more efficiently than the lognormal distribution because of its greater flexibility to model microbial clustering even when data consist of a large proportion of zero counts. The objective of this study was to develop an alternative modelling framework for low microbial counts based on heterogeneous Poisson regressions. As an illustration, Poisson-gamma regression models were used to assess the effect of chilling on the concentration of total coliforms from beef carcasses (n = 600) sampled at eight large Irish abattoirs. Three Poisson-gamma and three zero-modified (hurdle and zero-inflated) models were appraised with a series of random-effects variants in order to extract any variability in microbial mean concentration, dispersion and/or proportion of zero counts. Models were compared and validated in their ability to predict the coliforms counts on carcasses after chilling. In all five test batches, the hurdle Poisson-gamma distributions predicted the observed post-chill counts closer than the Poisson-gamma distributions. This is justified by the better capacity of the hurdle model to represent a higher proportion of zero counts, which were in fact observed in the post-chill batches. Thus, with a coded variable (pre-chill/post-chill) as treatment, and extracting the significant variability of batches nested in abattoirs for the coliforms mean concentration (σ2u = 2.68), the dispersion measure (σ2v = 2.39) and the probability of zero counts (σ2w = 0.89), the validated hurdle Poisson-gamma model confirmed that chilling has a decreasing effect on the viability of coliforms from beef carcasses, and that the concentration is reduced by an average (pre-chill to post-chill) factor of 2.2 (95% CI: 2.15–2.24) at batch level. The model also indicated that chilling increases the odds of producing a zero count from a carcass swab in about 13.5 times, and that the higher the coliforms concentration in a batch, the weaker the effect that chilling has to reduce such contamination on the beef carcasses.