Mixture extrapolation

Scheme 15 could be a reaction pathway parallel to the classical reaction (equation 1), and it was postulated to explain the third order in amine observed in the reactions of FDNB and aromatic amines in benzene and in chloroform184. The K values were calculated from the absorbances of the reaction mixture extrapolated to zero reaction time, in a wavelength range in which the starting materials do not show an appreciable absorbance value. Good agreement was observed between the values of K for the FDNB/aniline complex in chloroform by U.V. and 111-NMR spectroscopy, as well as for the K obtained kinetically (based on Scheme 15) and spectroscopically. 

Third Step Mixture Extrapolation in Tiered Risk Assessments.149... 

Fifth Step Executing and Interpreting Mixture Extrapolation.151... 

Predicting the combined effects of a mixture from knowledge of the effects of its components requires a reference model of what to expect for a mixture. Reference models used in mixture extrapolation practice are typically based on pharmacodynamic assumptions on the type of interaction between a chemical and a biological system. 

Many studies offer extrapolation approaches when addressing the issue of mixtures. However, when evaluating mixture papers for their support for mixture extrapolation procedures, study quality is a critical consideration. A set of criteria applies to evaluate the quality of the data (Altenburger et al. 1990), and these criteria can be applied to estimate whether and to what extent the data support the chosen extrapolation option. 

To address the quality limitations for extrapolation, the available experimental data on observed mixture effects were evaluated with care, and a pragmatic approach for mixture extrapolation was followed. Although mechanistic understanding was often not the purpose of the experiments, the extrapolation approach is based upon mechanistic principles, that is, regarding the choice between mixture toxicity models. Conceptual considerations on biases and mathematical characteristics of the models were included (see Section 5.3.3). 

Given the reviewed data, the first issue relevant for mixture extrapolation is whether extrapolation can be justified at all over no mixture extrapolation, in which separate responses only are assumed. In our opinion, the single-species test data are sufficiently clear to suggest that mixture extrapolation is preferred over no extrapolation. Although some exceptions exist (e.g., low effect range and specific compound mixtures), the majority of studies (aquatic and terrestrial) generally concluded that concentration addition is a reasonable conservative approximation of mixture responses. Indeed, the species-level experimental data we have reviewed clearly... 

In light of the large number of interaction levels that may influence the mixture toxicity response at the sites of toxic action, especially in terrestrial systems, it may come as a surprise that we are able to draw the conclusion that mixture extrapolations appear to be justified by the data. Although the interactions may all be relevant and may all require extrapolations according to the methods explained in the other chapters of this book, the net effect is apparently, and often relatively well, predicted by concentration addition. 

In our opinion, the data are sufficiently clear to suggest that when it is not feasible to test the mixture in question, mixture extrapolation is the preferred option compared to no extrapolation. Indeed, all literature observations suggest that applying mixture extrapolation is to be preferred over not applying mixture extrapolation. Technical options for extrapolation are concentration addition, response addition, and the mixed-model approach, of which concentration addition is most often applied. Exceptions may apply in cases that are more specific. For example, when it is clear that 2 compounds precipitate (a situation of no exposure due to chemical interactions in the environment), one should acknowledge this prior to assessing mixture risks by mixture extrapolation approaches. When the data of a study allow, refined conclusions are possible. For example, when the study design is appropriate and the mathematical models are appropriate, researchers are able to discriminate between concentration addition and response addition, and (with sufficient experiment efforts) between these models and the mixed-model approach. 

Mixture extrapolation can be complex due to the variety of model approaches, the optional tiers, and the different extrapolation targets. Therefore, apart from the technical mixture extrapolation protocols sensu stricto, a general stepwise protocol should be followed. Here, we propose a protocol of 5 steps. 

The first step in mixture extrapolation for mixtures of known composition is the definition of the assessment problem. What exactly is the context of the mixture assessment To address this problem, answers should be given to the following questions ... 

Because there are various options to account for possible combined effects, including concentration addition alone, response addition alone, or concentration addition and response addition in concert, and motives from study quality, assessment endpoint, mechanistic features, and statistical characteristics and biases, there should be a way to logically choose amongst methods for mixture extrapolation. The logical and pragmatic way to choose amongst alternative approaches is to design and follow a tiered approach (see Chapter 1). 

Tiering is often applied in risk assessment in order to reduce expenditures in time, money, and labor when the assessment requires only simple and possibly conservative output. Table 5.3 provides a suggested tiered approach in mixture extrapolation and is further described in the bulleted list below. The tiering is based on the way that mixture mechanisms are addressed in the approach. It is assumed that issues such as matrix and media extrapolation have been addressed according to the methods described in the pertinent chapters. 

The following tiered approach is suggested for mixture extrapolation ... 

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