Fitting a lognormal distribution to enumeration and absence/presence data

Abstract

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).