Toxic responses to defined chemical mixtures: Mathematical models and experimental designs

The problem and relevance of assessing biological responses to chemical mixtures is presented with reference to the literature on this problem and its possible solutions. This review is intended for a general audience as an introduction to, and comment on, assessing the interactions of defined mixtures of xenobiotics. The focus is on experimental toxicology, however, the methods are also applicable to pharmacology. Much of the literature on this topic is quite specialized in statistics, theory, or specific applications. This may deter a significant portion of the growing number of investigators in this field from using this literature, and may partially account for the persistent use of methods which have been shown to permit precarious conclusions. References are given for some of the most comprehensive and recent work and reviews on the subject. The reader is given some familiarity with this topic's basic problems and ideas, and the controversy on terminology. One example is presented of a popular experimental design and data analysis method which while applicable in some situations, has been shown to lead to precarious and even erroneous conclusions. Eight other methods of data analysis are briefly presented and some of their advantages, disadvantages, assumptions, and limitations are discussed. These methods were selected to illustrate similarities and differences in the various approaches taken in addressing this problem. Three basic types of experimental design appropriate to these kinds of studies are outlined. General considerations, suggested guidelines, and possible pitfalls in experimental design, and data analysis of biological responses to chemical mixtures are discussed.