Mark G. Vangel
Walter J. Rossiter and Mary E. McKnight
The design for this study is built on a single replicate of a full factorial on the following factors (levels): lead kits (8), lead concentration (10), kit operator (5), and lead type (2). The kits each make use of one of two active chemicals: sodium sulfide, which turns black in the presence of lead, or rhodizonate, which turns pink. Each kit was used according to the manufacturer's instructions, which varied substantially from kit to kit. Three of the five operators were lead-abatement professionals hired for this study and trained at NIST. The lead paint was prepared to have one of 10 concentrations, equally spaced over the nominal range of 0.0 to 3.5 , painted onto a substrate, and covered with an overlayer. Current HUD regulations mandate abatement for lead levels at or exceeding 1.0 . A relatively large number of lead levels was chosen so that we could estimate dose-response curves for various combinations of the other factors.
For each cell in the above full factorial design, a 23-1 design was used for the factors overlayer type (latex or oil), overlayer thickness (thin or thick), and substrate (nonreactive or reactive). Plaster was chosen as reactive for rhodizonate kits, and steel was used for this purpose for sodium sulfide kits. We hoped that either overlayer type or thickness would prove to be unimportant, but we expected substrate type to be important. If either of the overlayer factors proved to be insignificant, a full factorial would be available on the other factors. For kits with both overlayer factors insignificant, we would have two replicates of a full factorial in the rest of the factors.
Some results for one of the rhodizonate kits are displayed in the figure. The broken lines are curves (a modification of a logistic model) from the field study. For this kit, both overlayer factors are insignificant, and were omitted in all laboratory-data models. A single logistic regression was performed for the NIST data, with indicator variables for lead type, substrate, and operator.
The analysis of data from the full experiment has shown
that there are substantial differences in sensitivity of
the kits, including the fact that some kits are probably
inadequate. Large differences in sensitivity between
the two types of lead are also apparent. The kits
were compared by estimating a 95% lower confidence
limit on the concentration for which there is at least
a 95% probability of a positive response, for each
kit-lead-substrate combination, using Bayesian hierarchical
Figure 14: Plots of a logistic model for lead kit response for a typical rhodizonate lead-test kit, for reactive and nonreactive substrates, and white and yellow (less soluble) lead. Each curve corresponds to a different operator. Shaded areas indicate lead levels below the regulatory limit for abatement. Error bars are 95% binomial confidence intervals, which are omitted for cases where the observed proportions are zero or one. The broken curve is a modified logistic model taken from a published field study for the same lead-test kit.
Date created: 7/20/2001