Abstract
In the kinetic evaluation of chemical degradation data, degradation models are fitted to the data by varying degradation model parameters to obtain the best possible fit. Today, constant variance of the deviations of the observed data from the model is frequently assumed (error model “constant variance”). Allowing for a different variance for each observed variable (“variance by variable”) has been shown to be a useful refinement. On the other hand, experience gained in analytical chemistry shows that the absolute magnitude of the analytical error often increases with the magnitude of the observed value, which can be explained by an error component which is proportional to the true value. Therefore, kinetic evaluations of chemical degradation data using a two-component error model with a constant component (absolute error) and a component increasing with the observed values (relative error) are newly proposed here as a third possibility. In order to check which of the three error models is most adequate, they have been used in the evaluation of datasets obtained from pesticide evaluation dossiers published by the European Food Safety Authority (EFSA). For quantitative comparisons of the fits, the Akaike information criterion (AIC) was used, as the commonly used error level defined by the FOrum for the Coordination of pesticide fate models and their USe(FOCUS) is based on the assumption of constant variance. A set of fitting routines was developed within the mkin software package that allow for robust fitting of all three error models. Comparisons using parent only degradation datasets, as well as datasets with the formation and decline of transformation products showed that in many cases, the two-component error model proposed here provides the most adequate description of the error structure. While it was confirmed that the variance by variable error model often provides an improved representation of the error structure in kinetic fits with metabolites, it could be shown that in many cases, the two-component error model leads to a further improvement. In addition, it can be applied to parent only fits, potentially improving the accuracy of the fit towards the end of the decline curve, where concentration levels are lower.
Highlights
In recent discussions, the realism and adequacy of current environmental risk assessment methods for pesticides [1], and in particular of their exposure assessment part, e.g., for surface water [2,3,4], have been questioned
While it was confirmed that the variance by variable error model often provides an improved representation of the error structure in kinetic fits with metabolites, it could be shown that in many cases, the two-component error model leads to a further improvement
The optimum solution sometimes was not even found, but only a local minimum. The reason for this is to be seen in the fact that in the case of constant variance, the degradation model parameters and the single error model parameter σ are independent
Summary
The realism and adequacy of current environmental risk assessment methods for pesticides [1], and in particular of their exposure assessment part, e.g., for surface water [2,3,4], have been questioned. The error models generally used for the concentration data in such evaluations either assume constant variance (ordinary least squares (OLS)) across all concentrations for all observed compounds and compartments (error model “constant variance”) or alternatively allow for a different variance for each observed variable [6] For the latter error model, fitting by the iteratively reweighted least squares (IRLS) method is widely used in regulatory risk assessments due to its availability in the kinetic evaluation software packages KinGUII [10] and CAKE [11]. In the field of analytical chemistry, as well as in the bioassay literature referenced therein, it has been observed that the specification of the error model often has a negligible influence on the parameters derived [13] When it comes to the calculation of confidence intervals or other measures of confidence in the measured values like limits of detection, the introduction of a more appropriate error model can have a large effect on the results [14,15]. It is discussed why methods for the direct or stepwise minimization of the complete negative log-likelihood function have been implemented for fitting the two-component error model instead of using an IRLS algorithm
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