Analysis of an interaction threshold in a mixture of drugs and/or chemicals

Abstract

Increasingly, humans are exposed to drug/chemical mixtures. These exposures can result from therapeutic interventions or environmental sources. Of interest is the interaction that may occur among the components of these mixtures. Since interaction can be dose-dependent, it is important to determine exposure levels to either exploit the benefits of the interaction in a therapeutic application or to avoid the effect of the interaction in the case of an environmental risk assessment. We propose generalized linear models that permit the estimation of interaction threshold boundaries. The methods developed are applied to the combination of ethanol and chloral hydrate.

Modeling toxicity of binary metal mixtures (Cu2+–Ag+, Cu2+–Zn2+) to lettuce, Lactuca sativa, with the biotic ligand model

“…The present study shows a strong dependence of mixture toxicity on the composition and proportion of the metal mixture, that is, the TEQ of the mixture and the specific amount of Cu 2þ in the mixture. This observation was previously reported by Sharma et al [21] and Hamm et al [22]. This dependence is potentially attributed to physiological processes that are highly specific, depending on the exposure level.…”

A Random Effects Model for Binary Mixture Toxicity Experiments

“…Such generalizations of the set-up are certainly possible, but we hesitate to do so with mixture data where only a few mixture ratios have been tested (like ours) since results from complex models are rarely reproducible for this type of data (Cedergreen et al 2007a). In other words, there is a severe risk of "overfitting" unless results from many mixture ratios are available as in the study from Gessner and Cabana (1970) and Hamm, Carter, and Gennings (2005). The interaction analysis is carried out at a predefined effect level of particular interest, and does not provide estimates (or a test) of synergism/antagonism across all effect levels.…”

“…On the other hand, if only a few species are used and there is reason to believe that they behave differently towards mixtures of chemicals, then it is not reasonable to join them for an interaction analysis. Hamm, Carter, and Gennings (2005) studied models with interaction thresholds allowing for regions with CA and regions with synergism/antagonism. In order to achieve a similar pattern in our set-up the isobole model (3.2) should be replaced by a more complex model.…”

“…The Hewlett model (3.2) is just one possible interaction model and may not be flexible enough with only one parameter describing the deviation from CA. For example, it does not allow for asymmetric isoboles, extreme antagonism (Streibig, Kudsk, and Jensen 1998;Cedergreen et al 2007b;Belz, Cedergreen, and Sørensen 2008) and interaction thresholds (Hamm, Carter, and Gennings 2005). The model can be replaced by more flexible models, for example that of Vølund (1992) which was used successfully by Streibig, Kudsk, and Jensen (1998), Cedergreen et al (2007b), Belz, Cedergreen, and Sørensen (2008).…”

“…It is certainly possible that the interaction properties differ between mixture ratios, with regions of CA and regions of synergism/antagonism (Hamm, Carter, and Gennings 2005), and such a structure could be accomplished with a more complicated isobole model. However, Cedergreen et al (2007a) showed that results from complex models are rarely reproducible for this type of experiments.…”