Fitting a lognormal distribution to enumeration and absence/presence data

To fit a lognormal distribution to a complex set of microbial data, including detection data (e.g. presence or absence in 25 g) and enumeration data (e.g. 30 cfu/g), we compared two models: a model called M CLD based on data expressed as concentrations (in cfu/g) or censored concentrations (e.g. < 10 cfu/g, or > 1 cfu/25 g) 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) = 1 cfu/25 g; limit of quantification (LOQ) = 10 cfu/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 .