Fitting a distribution to microbial counts: Making sense of zeroes

The accurate estimation of true prevalence and concentration of microorganisms in foods is an important element of quantitative microbiological risk assessment (QMRA). This estimation is often based on microbial detection and enumeration data. Among such data are artificial zero counts, that originated by chance from contaminated food products. When these products are not differentiated from uncontaminated products that originate true zero counts, the estimates of true prevalence and concentration may be inaccurate. This inaccuracy is especially relevant in situations where highly pathogenic bacteria are involved and where growth can occur along the food pathway. Our aim was to develop a method that provides accurate estimates of concentration parameters and differentiates between artificial and true zeroes, thus also accurately estimating true prevalence.

We first show the disadvantages of using a limit of quantification (LOQ) threshold for the analysis of microbial enumeration data. We show that, depending on the original distribution of concentrations and the LOQ value, it may be incorrect to treat artificial zeroes as censored below a quantification threshold.

Next, a method is developed that estimates the true prevalence of contamination within a food lot and the parameters characterizing the within-lot distribution of concentrations, without assuming a LOQ, and using raw plate count data as an input. Counts resulting both from contaminated and uncontaminated sample units are analysed together. This procedure allows the estimation of the proportion of artificial zeroes among the total of zero counts, and therefore the estimation of true prevalence from enumeration results.

We observe that this method yields best estimates of mean, standard deviation and prevalence at low true prevalence levels and low expected standard deviation. Furthermore, we conclude that the estimation of prevalence and the estimation of the distribution of concentrations are interrelated and therefore should be estimated simultaneously. We also conclude that one of the keys to an accurate characterization of the overall microbial contamination is the correct identification and separation of true and artificial zeroes.

Our method for the analysis of quantitative microbial data shows a good performance in the estimation of true prevalence and the parameters of the distribution of concentrations, which indicates that it is a useful data analysis tool in the field of QMRA.