• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1295-1309
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• 2016

This paper is to reproduce the result of Kim et al. (2014) by deriving a benchmark dose lower bound (BMDL) of lead based on the 2005 cohort data set of Children's Health and Environmental Research (CHEER) data set. The ADHD rating scales in the 2005 cohort were not consistent along the three follow-ups since two different ADHD rating scales were used in the cohort. We first unified the ADHD rating scales in the 2005 cohort by deriving a conversion formula using a penalized linear spline. We then constructed two linear mixed models for the 2005 cohort which reflected the longitudinal characteristics of the data set. The first model introduced the random intercept and the random slope terms and the second model assumed the first order autoregressive structure of the error term. Using these two models, we derived the BMDLs of lead and reconfirmed the "regression to the mean" nature of the ADHD score discovered by Kim et al. (2014). We also noticed that there was a definite difference between the sampling distributions of the two cohorts. As a result, taking this difference into account, we were able to obtain the consistent result with Kim et al. (2014).