Quantile regression in environmental health: Early life lead exposure and end-of-grade exams

Conditional means regression, including ordinary least squares (OLS), provides an incomplete picture of exposure-response relationships particularly if the primary interest resides in the tail ends of the distribution of the outcome. Quantile regression (QR) offers an alternative methodological approach in which the influence of independent covariates on the outcome can be specified at any location along the distribution of the outcome. We implemented QR to examine heterogeneity in the influence of early childhood lead exposure on reading and math standardized fourth grade tests. In children from two urban school districts (n=1,076), lead exposure was associated with an 18.00 point decrease (95% CI: -48.72, -3.32) at the 10th quantile of reading scores, and a 7.50 point decrease (95% CI: -15.58, 2.07) at the 90th quantile. Wald tests indicated significant heterogeneity of the coefficients across the distribution of quantiles. Math scores did not show heterogeneity of coefficients, but there was a significant difference in the lead effect at the 10th (β=-17.00, 95% CI: -32.13, -3.27) versus 90th (β=-4.50, 95% CI: -10.55, 4.50) quantiles. Our results indicate that lead exposure has a greater effect for children in the lower tail of exam scores, a result that is masked by conditional means approaches.