A Study of the Specificaton of the Log-Log and Log-Additive Models for the Relationship between Blood Lead and Environmental Lead

Abstract

A Monte Carlo study was used to investigate the applicability of the log-log and log-additive models in predicting children's blood-lead levels (PbB). The data used in this study included information on the lead exposure history of over 700 children between birth and 5 years of age. The relationships between blood lead and the amount of lead on hands and the concentrations of lead in soil, paint, and dust were the major concern of this research. A simulation study was designed, based on the data collected under the auspices of the "Health Effects of Lead on Child Development" Program Project (LPP) and both models for PbB. Data were simulated in the study to follow either the log-log or logadditive model and were subsequently analyzed under situations of both correct and incorrect specification. This simulation explored whether and by what means a misspecified model may be detected. The distributions of the residuals from both models were tested for deviation from random error. As a test of the simulation results, three existing cohorts' data were analyzed-the Cincinnati LPP, the Cincinnati Soil Lead Abatement Demonstration Project data, and data collected by the Telluride, Colorado, Project. The log-log model was found to be the better model, except for post-abatement data. It was found that an incorrect population model specification can be detected more than 80% of the time using the criterion of a quadratic fit to the incorrect model's residuals.