A lognormal model for evaluating maximum residue levels of pesticides in crops.

To evaluate pesticide regulatory standards in agricultural crops, we introduced a regulatory modeling framework that can flexibly evaluate a population's aggregate exposure risk via maximum residue levels (MRLs) under good agricultural practice (GAP). Based on the structure of the aggregate exposure model and the nature of variable distributions, we optimized the framework to achieve a simplified mathematical expression based on lognormal variables including the lognormal sum approximation and lognormal product theorem. The proposed model was validated using Monte Carlo simulation, which demonstrates a good match for both head and tail ends of the distribution (e.g., the maximum error = 2.01% at the 99th percentile). In comparison with the point estimate approach (i.e., theoretical maximum daily intake, TMDI), the proposed model produced higher simulated daily intake (SDI) values based on empirical and precautionary assumptions. For example, the values at the 75th percentile of the SDI distributions simulated from the European Union (EU) MRLs of 13 common pesticides in 12 common crops were equal to the estimated TMDI values, and the SDI values at the 99th percentile were over 1.6-times the corresponding TMDI values. Furthermore, the model was refined by incorporating the lognormal distributions of biometric variables (i.e., food intake rate, processing factor, and body weight) and varying the unit-to-unit variability factor (VF) of the pesticide residues in crops. This ensures that our proposed model is flexible across a broad spectrum of pesticide residues. Overall, our results show that the SDI is significantly reduced, which may better reflect reality. In addition, using a point estimate or lognormal PF distribution is effective as risk assessments typically focus on the upper end of the distribution.