Dose-Response Modeling

Abstract

For any definition of additivity, evaluating whether an organism’s response to a mixture is additive depends on the dose-response relationships for each of the mixture’s component chemicals. Consequently, the statistical analysis of dose-response relationships is fundamental to mixture toxicology – as well as to other areas of toxicology. This chapter offers a broad overview of dose-response modeling and an introduction to some statistical issues that arise in the use of dose-response models – with an eye to evaluating additivity. It does not, however, attempt to be a handbook or guide to the use of any specific models; instead, it tries to make readers aware of issues that need attention to achieve efficient and valid inference. The chapter mentions features of study design and describes how they can influence both aspects of model fitting and the quality of results. It considers the choice of functional form used to describe how the mean response changes as dose increases as well as the evaluation of how well the chosen form fits the data at hand. The chapter also points out that proper modeling of the variability inherent in the structure of the data is crucial to efficient statistical inference. Finally, because many dose-response models require iterative numerical methods, it offers a few pointers to help overcome problems when these methods fail to converge. Dose-response modeling is an essential tool in mixture toxicology but one that demands careful application to achieve the best results.