Utilizing concentration-response data from individual components to detect statistically significant departures from additivity in chemical mixtures

The classical approach for detecting interactions in a combination of drugs or chemicals is that of the isobologram, quantified and generalized by Berenbaum (1981, Advances in Cancer Research 35, 269-335). In this formulation it is assumed that contours of constant response of the dose- response surface planar if the compounds do not interact. Building upon this approach, this paper develops methodology for detecting and characterizing departures from additivity. Reflecting the local rather than global nature of departure from additivity, this methodology only requires dose response data for the individual components and the specific combination(s) of interest. This is in contrast to the larger experiments required to estimate the multidimensional dose-response surface for the combination. Procedures for incorporating data from multiple control groups are developed for a fixed effects model, a random-effects model, and through use of a generalized estimating equations approach. An example is given that illustrates the application of these techniques to the analysis of a mixture of polycyclic aromatic hydrocarbons found in kerosene soot.