Log-Additive versus Log-Linear Analysis of Lead-Contaminated House Dust and Children's Blood-Lead Levels

Abstract

The Environmental Protection Agency has been mandated to develop a health-based standard for lead in residential dwellings in the United States. Prior estimates of the relationship between residential dust-lead levels and children's blood-lead concentrations have usually been obtained by using a log-linear regression of blood-lead concentration on levels of lead-contaminated house dust. It remains unknown, however, whether the log-linear model or a frequently cited alternative, the log-additive model, is the preferable regression method for analyzing these data. Secondary analysis of the Lead-in-Dust Study data was undertaken to compare log-additive with log-linear regression analysis for the purpose of developing a health-based dust lead standard. Specifically, we were interested in comparing the log-additive and log-linear analyses in their ability to characterize adequately the relationship of dust-lead loading on various surfaces with blood-lead concentrations among urban children and to develop a predictive model to estimate the risk that a child will develop an elevated blood-lead level on the basis of a known level of dust lead. We used two dust sampling methods, the Baltimore Repair and Maintenance (BRM) vacuum method and the wipe method, to compare the log-linear and log-additive models. The log-linear model was consistently superior to the log-additive model in its ability to explain the variability in the observed blood-lead concentrations of the studied children, for both the wipe sampler and the BRM sampler. In addition, the log-additive model often predicted only a limited increase in the probability of blood-lead concentrations exceeding 10 μg/dl as a result of doubling the dust-lead loading exposure, whereas the log-linear model consistently demonstrated a significant increase in the probability of blood-lead concentrations exceeding 10 μg/dl. BRM lead loading explained additional variability in blood lead above and beyond that explained by wipe loading for both carpeted and uncarpeted floors. In contrast, wipe-lead loading explained significant additional variability after adjustment for BRM loading for both uncarpeted floors and interior window sills. Although BRM loading better predicted children's blood-lead concentrations than did wipe loading, these differences were not statistically significant. We conclude that the log-linear model explained a greater percentage of the variability in blood-lead concentrations than did the log-additive model, indicating that the log-linear model should be the default model of choice for developing a dust-lead standard.