Estimating correlation of prevalence at two locations in the farm-to-table continuum using qualitative test data

- Presence/absence testing is used to assess microbial and chemical contamination.
- The proportion of positive samples estimates the prevalence of contaminated units.
- Samples are collected at multiple locations in the farm-to-table continuum.
- Pearson's estimator of the correlation of prevalence at two locations is biased.
- Three methods for unbiased estimation of correlation of prevalence are presented.

The presence or absence of contaminants in food samples changes as a commodity moves along the farm-to-table continuum. Interest lies in the degree to which the prevalence (i.e., infected animals or contaminated sample units) at one location in the continuum, as measured by the proportion of test-positive samples, is correlated with the prevalence at a location later in the continuum. If prevalence of a contaminant at one location in the continuum is strongly correlated with the prevalence of the contaminant later in the continuum, then the effect of changes in contamination on overall food safety can be better understood. Pearson's correlation coefficient is one of the simplest metrics of association between two measurements of prevalence but it is biased when data consisting of presence/absence testing results are used to directly estimate the correlation. This study demonstrates the potential magnitude of this bias and explores the utility of three methods for unbiased estimation of the degree of correlation in prevalence. An example, based on testing broiler chicken carcasses for Salmonella at re-hang and post-chill, is used to demonstrate the methods.