Mixed model approaches

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. 

Mixed-model approach Similar and dissimilar Concentration response... 

Mixed model approach with Similar and dissimilar Mode of action information, recptor... 

In the fourth step of extrapolation, specific mixture extrapolation protocols are needed. Below, some details on the theories and the associated protocols are given for concentration addition, response addition, and mixed-model approaches, and for the species and assemblage levels separately (this section and, next section, respectively). 

Subsequently, the msPAF was introduced by Posthuma and Traas and coworkers (Traas et al. 2002 Posthuma et al. 2002a), and also applies the mixed-model approach, but in this case all compounds that share the same mode of action (not necessarily narcotic effects only) are grouped and addressed (within such groups) by concentration addition. Thereafter, response addition is used to aggregate over the numbers obtained. In this case, the PAF can be estimated not only from an SSD for all tested species but also for subgroups of species that are sensitive to a particular class of compounds (e.g., insects are sensitive for insecticides, and the SSD is constructed from insect data only see Posthuma et al. 2002a). 

FIGURE 5.2 Schematized presentation of the mixed-model approach for assemblage-level extrapolation. Note A similar approach is followed for species-level mixed-model extrapolation. The system can be simplified by assuming response addition for all extrapolations except the baseline toxicity assessment (approach of Hamers et al. [1996], yielding combi-PAF). The system can also be more complex when predictions for compound class effects are made for different species groups. 

The proposed mixed-model approach for assemblages, preceded by an exposure analysis, is in line with Ashford s ideas the ecological interactions need further attention. Whether Ashford s ideas can be fully worked out conceptually, tested experimentally, and applied in a validated predictive framework remains to be solved by mixture ecotoxicologists. 

A tiered system for mixture extrapolation is proposed. The lowest tier is based on extrapolation using toxicological point-estimate information such as EC50 values. This translates into the use of toxic units, toxic equivalencies, and similar techniques. The use of the entire concentration-response relationships of the separate compounds is recommended for Tier-2, in conjunction with the use of either concentration or response addition as a modeling approach. In Tier-3, a mixed-model approach can be considered, to more specifically address considerations on toxic modes of action. In the latter case, the approach may be extended to allow incorporation of the responses of different ecological receptors (Tier-4). Research needs have been clearly identified in community-level mixture assessments. 

Tier 3 involves the use of both CA and R A models together (mixed-model approaches). This approach differs from the previous tiers by using detailed information on the modes of action for the different mixture components as well as full-curve-based modeling approaches. Mixed models are used in human as well as ecological assessment. An example of mixed-model approaches in ecological risk assessments is the approach proposed for assemblages (De Zwart and Posthuma 2005) a similar approach has been proposed by Ra et al. (2006) see Chapter 4 and Figure 4.2. 

Vilchis et al. [81] presented a new idea to achieve better control of the particle size distribution by the synthesis in situ of a water-soluble copolymer of acrylic acid-styrene as suspension stabilizer without additional inorganic phosphate. Publications describe increasing the particle formation by using a physical (population balance, Maxwell fluid, power law viscosity, compartment mixing) modeling approach [22,60,98,105]. 

Although the simple two-component mixing model approach to stream hydrograph separation does not directly identify the actual runoff... 

From one point of view this illustrates the superiority of the mixed-models approach. However, in this particular instance the result is somewhat disturbing. It seems rather unnatural to add the value for the first and last visit together and subtract the value for the visit in the middle as a way of judging the efficacy of the treatment. It requires a lot of faith in the model being used. 

First, a number of simulations have shown how miserably last observation (carried forward) approaches perform compare with mixed-model approaches. However, in general one has to be very careful about assuming that simulations tell one what one thinks they do. For examples in other contexts where I have shown that they do not, the reader might be interested to consult Senn (1993, 1994, 1995, 1996, 2007). A key issue in comparing a simpler with a more sophisticated method is whether one has not implicitly assumed information that in practice one would not have. 

Guettel and Turek [56] compared four reactor types, namely, fixed bed, slurry bubble column, monolith loop, and microstructured. A one-dimensional (no axial mixing) modeling approach was used to make the comparisons. One of their conclusions was... 

To conclude, we acknowledge the main problem that arises from such a mixed-model approach to architecture verification how can we be sure that the different models are coherent when we integrate them in a final implementation ... 

Smith, A.B., Cullis, B.R., Thompson, R., 2005. The analysis of crop cultivar breeding and evaluation trials an overview of current mixed model approaches. J. Agric. Sci. 143, 449 62. 

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