Department of Environmental and Radiological Health Sciences, Colorado State University, 1681 Campus Delivery, Fort Collins, CO 80523-1681, United States.
Department of Psychology, University of Wisconsin, 1202 West Johnson Street, Madison, WI 53706, United States.
Environ Res. 2015 Feb;137:108-19. doi: 10.1016/j.envres.2014.12.004. Epub 2014 Dec 19.
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.
条件均值回归，包括普通最小二乘法（OLS），尤其当主要关注点在结果分布的尾部时，提供了一种不完全的暴露-反应关系描述。分位数回归（QR）提供了一种替代的方法，在这种方法中，独立协变量对结果的影响可以在结果分布的任何位置上指定。我们实施 QR 来检验早期儿童铅暴露对阅读和数学标准化四年级测试的影响的异质性。在来自两个城市学区的儿童中（n=1,076），铅暴露与阅读成绩第 10 分位数降低 18.00 分（95%CI：-48.72，-3.32）相关，与第 90 分位数降低 7.50 分（95%CI：-15.58，2.07）相关。沃尔德检验表明，系数在分位数分布上存在显著的异质性。数学成绩的系数没有表现出异质性，但在第 10 分位数（β=-17.00，95%CI：-32.13，-3.27）与第 90 分位数（β=-4.50，95%CI：-10.55，4.50）之间，铅的效应存在显著差异。我们的结果表明，对于考试成绩处于较低尾部的儿童，铅暴露的影响更大，而这一结果被条件均值方法所掩盖。
