Assessment of the Combined Effects of Substances: The Relationship between Concentration Addition and Independent Action

The assessment of the combined effects of substances is usually based on one of two different concepts: concentration addition or independent action. Both concepts are founded on different pharmacological assumptions about sites and modes of actions of substances, but in toxicology and ecotoxicology such knowledge is rare for most chemicals. In order to validate experimental results and to allow for precautious assessments, the quantitative relationships between concentration addition and independent action are therefore of interest. In this paper, we derive for the Weibull, the logistic, and the normal distribution functions the concentrations where the response probability due to concentration addition exceeds that due to independent action and vice versa. This is done (a) by analytically comparing both models for low and high mixture concentrations and (b) by numerically calculating the response probabilities when concentration addition and independent action agree. It is shown that the relationships between the models for joint action depend on the distribution functions, the corresponding slope parameters, and on the mixture concentrations administered.

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