Evaluating sufficient similarity for disinfection by-product (DBP) mixtures: multivariate statistical procedures

For evaluation of the adverse health effects associated with exposures to complex chemical mixtures in the environment, the U.S. Environmental Protection Agency (EPA) (2000) states, "if no data are available on the mixture of concern, but health effects data are available on a similar mixture ... a decision must be made whether the mixture on which health effects are available is 'sufficiently' similar to the mixture of concern to permit a risk assessment." This article provides a detailed discussion of statistical considerations for evaluation of the similarity of mixtures. Multivariate statistical procedures are suggested to determine whether individual samples of drinking-water disinfection by-products (DBPs) vary significantly from a group of samples that are considered to be similar. The application of principal components analysis to (1) reduce the dimensionality of the vectors of water samples and (2) permit visualization and statistical comparisons in lower dimensional space is suggested. Formal analysis of variance tests of homogeneity are illustrated. These multivariate statistical procedures are applied to a data set describing samples from multiple water treatment plants. Essential data required for carrying out sensitive analyses include (1) identification and measurement of toxicologically sensitive process input and output characteristics, and (2) estimates of variability within the data to construct statistically efficient estimates and tests.