The impact of exposure to a mixture of eighteen polyhalogenated aromatic hydrocarbons on thyroid function: Estimation of an interaction threshold

When an interaction has been detected among the chemicals in a mixture, it may be of interest to predict the interaction threshold. A method is presented for estimation of an interaction threshold along a mixture ray which allows differences in the shapes of the dose-response curves of the individual components (e.g., mixtures of full and partial agonists with differing response maxima). A point estimate and confidence interval for the interaction threshold may be estimated. The methods are illustrated with data from a study of a mixture of 18 polyhalogenated aromatic hydrocarbons (PHAHs) in rats exposed by oral gavage for four consecutive days. Serum total thyroxine (T4) was the response variable. Previous analysis of these data demonstrated a dose-dependent interaction among the 18 chemicals in the mixture, with additivity suggested in the lower portion of the dose-response curve and synergy (greater than additive response) in the higher portion of the dose-response curve. The present work builds on this analysis by construction of an interaction threshold model along the mixture ray. This interaction threshold model has two components: an implicit additivity region and an explicit region that describes the departure from additivity; the interaction threshold is the boundary between the two regions. Estimation of the interaction threshold within the observed experimental region suggested evidence of additivity in the low dose region. Total doses of the mixture that exceed the upper limit of the confidence interval on the interaction threshold were associated with a greater-than-additive interaction.