Estimating distributions of numbers of organisms in food products

Procedures of sampling and measurement contribute variability and uncertainty to exposure models that predict incidence and levels of organisms in food products. This paper focuses on methods that account for sampling and measurement error in fitting distributions of organisms in food products for use in exposure models for microbial risk assessment. Define y to be a measured density on a sample selected with stipulated probability from a population, and define x to be the "true" density for that sample. Designate the conditional distribution of y given the sample with "true" value x as g(y/x), and let F(x) be the unknown cumulative density of x. The distribution of the observed values y, h(y), can be expressed through the integral equation h(y) = integral of g(y/x) dF(x). Knowledge of g(y/x) and h(y) enables an estimate of the unknown distribution of the organism's F(x). In applications to risk assessment, use of continuous distributions described by a few parameters is desirable. Also desirable may be imputation or assignment of possible nonzero values for nondetect observations--those results below the limit of detection of the methodology--that may not be truly zero. This paper explores the use of the above formulation for estimating distributions of organisms used for microbial risk assessment and presents some simple examples.