Using data on the uncertainty of LOAELs to model the probability of observing adverse effects in low-dose studies of the toxicity of chemical mixtures

Studies of chemical mixtures toxicity are often designed to differentiate mixtures that follow dose-addition from those that follow response-addition. One design used for this purpose doses animals at levels below the levels that separately have been shown to cause a detectable occurence of a common effect. Under response addition, no effects are expected to be observed since no chemical would independently cause an observable response at the administered doses. Effects, however, could be observed if some or all of the chemicals follow dose addition. Thus, any observation of response can be taken as evidence of dose addition. A recent publication estimated interstudy variation in chemicals' LOAELs. These estimates are here used to predict the probability of observing an effect in mixtures that follow response- or dose-addition models. Two case studies are presented. One is on a set of hypothetical mixtures containing from 2 to 20 chemicals. The second is on mixtures of anti-androgenic chemicals. In these studies, LOAEL uncertainty blurred the difference between dose and response models, and for many mixtures, it is not possible to determine whether response or dose additivity occurred. These findings suggest that caution should be taken when using these studies as evidence for dose addition.