Estimating the correlation between concentrations of two species of bacteria with censored microbial testing data

Indicator organisms, such as generic Escherichia coli (GEC) and coliforms, can be used to measure changes in microbial contamination during the production of food products. Large and consistent reductions in the concentration of these organisms demonstrates an effective and well-controlled production process. Nevertheless, it is unclear to what degree concentrations of indicator organisms are related to pathogenic organisms such as Campylobacter and Salmonella on a sample-by-sample basis. If a strong correlation exists between the concentrations of different organisms, then the monitoring of indicator organisms would be a cost-effective surrogate for the measurement of pathogenic organisms. Calculating the correlation between the concentrations of an indicator and pathogenic organism is complicated because microbial testing datasets typically contain a large proportion of censored observations (i.e., samples where the true concentration is not observable, with nondetects and samples that are only screen-test positive being examples). This study proposes a maximum likelihood estimator that can be used to estimate the correlation between the concentrations of indicator and pathogenic organisms. An example based on broiler chicken rinse samples demonstrates modest, but significant positive correlations between the concentration of the indicator organism GEC when compared to the concentration of both Campylobacter and Salmonella. A weak positive correlation was also observed between concentrations of Campylobacter and Salmonella, but it was not statistically significant.