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 25g) and enumeration data (e.g. 30cfu/g), we compared two models: a model called MCLD based on data expressed as concentrations (in cfu/g) or censored concentrations (e.g. 1cfu/25g) versus a model called MRD 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 MCLD and via the Expectation–Maximisation (EM) algorithm for the model MRD. The comparison suggests that in most cases estimates provided by the proposed model MRD are similar to those obtained by model MCLD accounting for censorship. Nevertheless, in some cases, the proposed model MRD leads to less biased and more precise estimates than model MCLD. ► Two pathogens concentration models are compared. ► One is based on concentration data and uses censorship while the other is based on raw data. ► Both are based on the MLE to assess parameters but the EM algorithm is used for one of them. ► In some cases, the model with raw data leads to more precise estimates.