Statistical Models for the Evaluation of Portable Lead Measurement Technologies, Part I: Chemical Test Kits

Chemical test kits, used to test for lead in paint, were evaluated in a study sponsored by the U.S. Environmental Protection Agency and the U.S. Department of Housing and Urban Development. A pool of nonprofessional testers applied five commercially available test kits to a variety of painted building components encountered in public housing units. A sixth test kit that was not commercially available was applied by professional testers. Operating characteristic (OC) curves were estimated under an enhanced logistic regression model in order to describe test kit performance. This article discusses estimation of the OC curves from numerical and stochastic points of view. The use of nonparametric estimates in graphical and quantitative analyses is also discussed. Attention is given to the fact that the true lead levels were themselves estimated by a process that was affected by paint collection and laboratory analysis procedures.

Key Words
Bootstrap; Isotonic regression; Lead-based paint testing; Logistic regression; Mixture model; Nonstandard asymptotics.

Robert A. Koyak is Assistant Professor, Department of Operations Research, Naval Postgraduate School, Monterey, CA 93943. R. L. Schmehl is Senior Statistican, D. C. Cox is President, and F. G. Dewalt is Senior Scientist, QuanTech, 1911 N. Fort Myer Drive, Suite 1000, Arlington, VA 22009-1607. M. M. Haugen is Software Developer, Special Systems, Inc., 12817 Shadow Oak Lane, Fairfax, VA 22033. J. G. Schwemberger, Jr., is Statistician, and J. V. Scalera is Chemist, Technical Branch, National Program Chemicals Division, Office of Pollution Prevention and Toxics, Office of Prevention, Pesticides and Toxic Substances, U.S. Environmental Protection Agency, 401 M Street, S.W., Mail Code 7404 Washington, D.C. 20460.