Nonparametric modeling of the left censorship of analytical data in food risk assessment

Contaminants and natural toxicants such as mycotoxins may be present in various food items that may be considered dangerous to human health if the cumulative intake remains above the toxicologic safe references. This intake or exposure can be estimated using both consumption surveys and analytical data that record the contamination levels of food. Analytical data often present some left censorship, that is, data below some limit of detection or quantification. This article proposes the integration of a nonparametric modeling of the left censorship of analytical data in a model aiming at giving a quantitative evaluation of the risk due to the presence of some particular contaminants in food. We focus on the estimation of the "risk," defined as the probability for exposure to exceed the so-called "provisional tolerable weekly intake" (PTWI), when both consumption data and contamination data are independently available. To account for the left censorship of the contamination data (due to the existence of detection/quantification limits), we propose using a Kaplan-Meier estimator instead of the empirical cumulative distribution function generally used in nonparametric procedures. We give the asymptotic behavior of our estimator and derive the asymptotic properties of the associated risk estimator. Several confidence intervals are obtained using a double-bootstrap procedure. A detailed algorithm is proposed. As an illustration, we present an evaluation of the risk exposure to ochratoxin A in France and use our risk estimator to show that children under age 10 years are a population at particular risk. Imposing some maximum limits on particular food items, namely cereals and wine, would not significantly reduce the risk.