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This article introduces an original methodology based on empirical likelihood, which aims at combining different food contamination and consumption surveys to provide risk managers with a risk measure, taking into account all the available information. This risk index is defined as the probability that exposure to a contaminant exceeds a safe dose. It is naturally expressed as a nonlinear functional of the different consumption and contamination distributions, more precisely as a generalized U-statistic. This nonlinearity and the huge size of the data sets make direct computation of the problem unfeasible. Using linearization techniques and incomplete versions of the U-statistic, a tractable "approximated" empirical likelihood program is solved yielding asymptotic confidence intervals for the risk index. An alternative "Euclidean likelihood program" is also considered, replacing the Kullback-Leibler distance involved in the empirical likelihood by the Euclidean distance. Both methodologies are tested on simulated data and applied to assess the risk due to the presence of methyl mercury in fish and other seafood.

This paper presents new statistical methods in the field of exposure assessment. We focus on the estimation of the probability for the exposure to exceed a fixed safe level such as the provisional tolerable weekly intake (PTWI), when both consumption data and contamination data are independently available. Various calculations of exposure are proposed and compared. For many contaminants, PTWI belongs to the exposure tail distribution, which suggests the use of extreme value theory (EVT) to evaluate the risk. Our approach consists in modelling the exposure tail by a Pareto type distribution characterized by a Pareto index which may be seen as a measure of the risk of exceeding the PTWI. Using propositions by EVT specialists, we correct the bias of the usual Hill estimator to accurately estimate this risk index. We compare the results with an empirical plug-in method and show that the Pareto adjustment is relevant and efficient when exposure is low compared to the PTWI while the plug-in method should be used when exposure is higher. To illustrate our approach, we present some exposure assessment for heavy metals (lead, cadmium, mercury) via sea product consumption.