Bayesian estimation of the total intake of chemical contaminants from multiple food products

The Bayesian model was built to estimate the acute as well as the chronic intake of chemical contaminants from food products. The model was applied to estimate the cadmium intake from several food products. The food consumption data (grains, meat, fish, and milk) were based on the 48-h dietary recall of 2038 adults, and cadmium concentration data were drawn from the control program.

The cadmium concentration in each food product was modeled using a log-normal distribution. The measurements below the limit of detection were treated as censored data in order to achieve optimum estimates. The long-term consumption of each food product was obtained as a combination of the estimated acute consumption (days when used) and consumption frequency. The consumption frequency was modeled using a binomial logit model with multinormal prior to take into account the correlation in consumption between different food products as well as the variation between different individuals. Finally, the chronic intake was achieved by the combination of the estimated mean concentration and long-term consumption. The computation of the model was performed in OpenBUGS via R software.

The proposed model provides a proper way to assess the chronic intake of chemical contaminants due to a single source as well as total diet taking into account individual variation. The model was made to be flexible for different requirements of research and data sets. The concentration model performs well even when the size of the data set is small, and a large proportion of the concentration measurements is below the limit of detection.

The proposed model could also be expanded to estimate the joint intake of several contaminants at once. The modeling of the possible correlation between the consumption amount and consumption frequency is another issue that needs to be further studied. In future, the model could also be converted into a tool that anyone can use.