Detection of Departures from Additivity in Mixtures of Many Chemicals with a Threshold Model

The evaluation of risk associated with mixtures of chemicals is often needed when the number of chemicals in the mixture is large and when the concentration of individual chemicals is low. A useful approach for detecting chemical interactions is to compare the observed response of a particular mixture to that predicted from an additivity model. This is economical because the additivity model only requires support for the concentration-response curves of the individual components in the mixture. Further, for noncancer health effects it may be reasonable to describe additivity under the assumption of the existence of a threshold. Such a model assumes that exposure to the mixture below the threshold surface results in a response equivalent to background. A fixed-effects model and a random-effects model are developed. Use of a threshold additivity model is illustrated with an example.