A novel flexible approach for evaluating fixed ratio mixtures of full and partial agonists

Assessing for interactions among chemicals in a mixture involves the comparison of actual mixture responses to those predicted under the assumption of zero interaction (additivity), based on individual chemical dose-response data. However, current statistical methods do not adequately account for differences in the shapes of the dose-response curves of the individual mixture components, as occurs with mixtures of full and partial receptor agonists. We present here a novel extension of current methods, which overcomes some of these limitations. Flexible single chemical concentration-effect curves combined with a common background parameter are used to describe an additivity surface along each axis. The predicted mixture response under the assumption of additivity is based on the constraint of Berenbaum's definition of additivity. Iterative algorithms are used to estimate mean responses at observed mixture combinations using only single chemical parameters. A full model allowing for different maximum response levels, different thresholds, and different slope parameters for each mixture component is compared to a reduced model under the assumption of additivity. A likelihood-ratio test is used to test the hypothesis of additivity by utilizing the full and reduced model predictions. This approach is useful for mixtures of chemicals with threshold regions and whose component chemicals exhibit differing response maxima (e.g., mixtures of full and partial agonists). The methods are illustrated with a combination of six chemicals in an estrogen receptor-alpha (ER-α) reporter gene assay.