Evaluating Sufficient Similarity for Drinking-Water Disinfection By-Product (DBP) Mixtures with Bootstrap Hypothesis Test Procedures

Abstract

In chemical mixtures risk assessment, the use of dose-response data developed for one mixture to estimate risk posed by a second mixture depends on whether the two mixtures are sufficiently similar. While evaluations of similarity may be made using qualitative judgments, this article uses nonparametric statistical methods based on the “bootstrap” resampling technique to address the question of similarity among mixtures of chemical disinfectant by-products (DBP) in drinking water. The bootstrap resampling technique is a general-purpose, computer-intensive approach to statistical inference that substitutes empirical sampling for theoretically based parametric mathematical modeling. Nonparametric, bootstrap-based inference involves fewer assumptions than parametric normal theory based inference. The bootstrap procedure is appropriate, at least in an asymptotic sense, whether or not the parametric, distributional assumptions hold, even approximately. The statistical analysis procedures in this article are initially illustrated with data from 5 water treatment plants (Schenck et al., 2009), and then extended using data developed from a study of 35 drinking-water utilities (U.S. EPA/AMWA, 1989), which permits inclusion of a greater number of water constituents and increased structure in the statistical models.

The views expressed in this article are those of the individual authors and do not necessarily reflect the views and policies of the U.S. Environmental Protection Agency (EPA). Those sections prepared by U.S. EPA scientists have been reviewed in accordance with U.S. EPA peer and administrative review policies and approved for presentation and publication. Mention of trade names or commercial products does not constitute endorsement or recommendations for use.

The authors acknowledge and appreciate the many helpful review comments and suggestions of Richard C. Hertzberg, Ph. (Emory University), and David Farrar, PhD (U.S. EPA/ORD/NCEA). These comments greatly improved this article.

Notes

¹The six haloacetic acids denoted as HAA6 are chloroacetic acid, bromoacetic acid, dichloroacetic acid, trichloroacetic acid, bromochloroacetic acid, and dibromoacetic acid.

²The reference citations refer to Morrison (1976), Multivariate Statistical Methods, second edition. There is now a fourth edition of this book available (2002); however, the second-edition citations were retained to maintain the page references.

³This relation between Pillai's Trace and the Hotelling–Lawley Trace is applicable in the special case when there is a single positive characteristic root.