Sample size and power determination for detecting interactions in mixtures of chemicals

In the analysis of mixtures of drugs/chemicals it is often of interest to test for the presence of interaction. If the hypothesis of no interaction (additivity) is not rejected, then the analyst may reasonably claim additivity if and only if the study is powered to a desired (e.g., biologically meaningful) level. The objective of this article is to address the sample size and power issues related to testing the hypothesis of additivity at specified mixture points. The study of disinfectant by-products (DBPs) found in drinking water, described in earlier literature, is used to illustrate the procedures for estimating power and sample sizes for detecting interactions at specified mixtures. The four trihalomethanes used in the study are bromodichloromethane (BDCM), chlorodibromomethane (CDBM), chloroform (CHCl3), and bromoform (CHBr3).