Count data distributions and their zero-modified equivalents as a framework for modelling microbial data with a relatively high occurrence of zero counts

In many cases, microbial data are characterised by a relatively high proportion of zero counts, as occurs with some hygiene indicators and pathogens, which complicates the statistical treatment under the assumption of log normality. The objective of this work was to introduce an alternative Poisson-based distribution framework capable of representing this kind of data without incurring loss of information. The negative binomial, and two zero-modified parameterisations of the Poisson and negative binomial distributions (zero-inflated and hurdle) were fitted to actual zero-inflated bacterial data consisting of total coliforms (n = 590) and Escherichia coli (n = 677) present on beef carcasses sampled from nine Irish abattoirs. Improvement over the simple Poisson was shown by the simple negative binomial (p = 0.426 for χ2 test for the coliforms data) due to the added heterogeneity parameter, although it slightly overestimated the zero counts and underestimated the first few positive counts for both data sets. Whereas, the zero-modified Poisson could not cope with the data over-dispersion in any of its parameterisations (p < 0.001 for χ2 tests), the parameterisations of the zero-modified negative binomial presented differences in fit due to approximation errors. While the zero-inflated negative binomial parameterisation was apparently reduced to a negative binomial due to a non-convergence of the logit parameter estimate, the goodness of fit of the hurdle negative binomial parameterisation indicated that for the data sets under evaluation (coliforms data with ~ 13% zero counts and E.coli data with ~ 42% zero counts), the zero-modified negative binomial distribution was comparable to the simpler negative binomial distribution. Thus, bacterial data consisting of a considerable number of zero counts can be appropriately represented by using such count distributions, and this work serves as the starting point for an alternative statistical treatment of this kind of data and stochastic risk assessment modelling.