Nonlinear Statistical Models for the Joint Action of Toxins

A general approach using nonlinear regression models is presented for evaluating additivity, synergism, and antagonism of mixtures of toxins for proportions and ratio-scale response measures. This approach provides several advantages over the analysis methods typically used, which involve linear regression with logits or probits. A single model fit is performed, rather than a multistep procedure. Nonadditive alternative models can be easily constructed and tested against the appropriate additive models. The approach avoids the use of data "adjustments" for nonzero background response rates. The analyses are performed in the natural response metric, making interpretation straightforward. Also, the nonlinear regression model can be reparameterized to provide more meaningful primary parameters.