Pesticide residues in fruit and vegetables vary both between batches (e.g. from different farms) and between items within batches. This variability is critical in determining the likelihood of consumers encountering a high enough residue to exceed a safe level of acute intake (the Acute Reference Dose, ARfD). In dietary intake assessment, variation in residues is often assumed to follow a lognormal distribution. A lognormal distribution extends to infinity and therefore implies a small proportion of very high residues. Although these are relatively rare (e.g. 1 in 100 or 1000), when considering a frequently consumed commodity (e.g. apples) in a national population they may imply sufficient cases of exceeding the ARfD to cause concern. It is therefore very important to ensure that the upper tails of residue distributions used in dietary intake assessment are realistic. Unfortunately, the number of residue measurements in a typical field trial (8) or market survey (<100) is too small to estimate these upper tails with any certainty. In addition, commodities in the marketplace usually comprise a mixture of untreated batches and batches treated at different rates, which may need to be modelled with a mixture of distributions.
These difficulties are one of the most important sources of uncertainty in dietary intake assessment. It is therefore proposed to investigate ways of pooling data from multiple trials and surveys to test the applicability of the lognormal distribution and to examine more realistic alternatives. Possibilities include:
1. Bayesian non-parametric analysis of pooled data to form a generic empirical distribution and rescaling this for individual assessments,
2. Using extreme value theory to model the upper tails of distributions (requires moderate to large samples),
3. Investigate ways to model just the tails, seeking a single form which fits all datasets (this combines elements of approaches 1 and 2, and may be better able to cope with mixed distributions),
4. Consider working on scales other than the logarithm of concentration,
5. An optimisation approach which iteratively searches for a non-parametric distribution consistent with the pooled sample data.
This one year project will investigate the theoretical and practical applicability of these and other options and compare them with existing approaches using selected example datasets. The results will be used to evaluate the feasibility, reliability and practical usefulness of the improved approaches, and in particular whether they provide rigorous and worthwhile reductions of uncertainty in dietary exposure assessments. If the conclusions are positive, the project may be extended to refine the most effective solutions and develop practical tools and guidance for their use in regulatory risk assessment.
The methods developed in this project could, if successful, be applied with additional work to a wide range of other problems involving distributions needed in risk assessment. For example, they could be applied to variation in toxicity between species, which is one of the most important sources of uncertainty in ecological risk assessments for pesticides.