Lead Human Exposure and Health Risk Assessments for Selected ...

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 • Log-linear function with low-exposure linearization (concurrent metric): - beta (slope): -2.70 - linear slope to be applied below 1.0 µg/dL: -2.70 • Log-linear function with low-exposure linearization (lifetime average metric): - beta (slope): -3.04 - linear slope to be applied below 1.47 µg/dL: -2.1 4.1.1.3 Two-piece Linear Function This category of concentration-response function was developed by fitting a two-piece linear model to the log-linear IQ-loss function obtained from the pooled analysis (Lanphear et al., 2005). Inclusion of this function in the risk assessment is intended to address the practical problem of the shape associated with application of the log-linear model at the low end of the blood Pb value range. In this case, we consider an alternate functional form that allows ready prediction of IQ loss across the full range of modeled Pb exposure. The procedure involved first generating blood Pb values for each of the two blood Pb metrics, concurrent and lifetime average, for a set of N = 1,333 simulated children representative of those included in the pooled analysis (Lanphear et al., 2005). This was accomplished by sampling from a blood Pb distribution constructed from the median and 95th percentile of the concurrent and lifetime average blood Pb indices, respectively, reported in Lanphear et al. (2005). IQ values for each of the 1,333 simulated children were then estimated using the reported log-linear models that relate blood Pb to absolute IQ (Lanphear, et al., 2005). Nonlinear regression techniques were then used to fit two piece linear models to these two sets of simulated children with their matched pairs of blood Pb and IQ values. The regressions provided parameter estimates (slopes and "hinge" point) of the best fitting two piece linear segment function for each blood Pb metric, concurrent and lifetime average. As discussed in Section 4.3.1, that the use of a constructed dataset introduces uncertainty related to fitting of a model to a model. Parameterization for the two two-piece linear functions is presented below, with the mathematical form of the function: • Form of function: - For blood Pb level > hinge: IQ loss = beta 2 * concurrent blood Pb - For blood Pb level < hinge: IQ loss = beta 1 * concurrent blood Pb • Two-piece linear function (concurrent metric): - "hinge" linking two segments: 10.82 µg/dL - beta 1 (slope at 10.82 µg/dL: -0.1130 July 2007 4-4 Draft – Do Not Quote or Cite
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 • Two-piece linear function (lifetime average metric): - "hinge" linking two segments: 13.39 µg/dL - beta 1 (slope at 13.39 µg/dL: -0.1187 4.1.2 Projection of Population Risk Risk characterization completed for this assessment involved converting the populationlevel blood Pb distributions generated for the three case studies into population-level distributions of IQ loss using the three types of concentration-response functions described in the last section. This procedure is described below for each of the functions. • Log-linear function with cutpoint: Each modeled blood Pb level is compared against the cutpoint. If the blood Pb level is lower than the cutpoint, then no IQ loss is estimated because the simulated individual’s blood Pb level is below the level for predicting IQ loss with this function. If the blood Pb level is greater than the cutpoint, then the log-linear function is used to predict IQ loss for the portion of the estimated blood Pb level extending above the cutpoint. • Log-linear function with low-exposure linearization: Each modeled blood Pb level is compared against the point of linearization. If the blood Pb level is below the point where the function becomes linear, than the linear slope is used to predict IQ loss. If the modeled Pb level is above the point where the function becomes linear, than IQ loss is calculated as the sum of IQ loss across the linear portion of the curve plus the additional contribution from the log-linear portion of the function extending up to the total blood Pb level. • Two-piece linear function: Similar to the last function, the modeled blood Pb level is compared against the blood Pb level of the “hinge”. If the blood Pb level falls below the hinge, as is the case for most simulated individuals at the three case studies, then the steeper, low-exposure slope is used to estimate IQ loss. If the simulated blood Pb level falls above the hinge, then IQ loss associated with the low-exposure (steeper slope) piece of the function (for the portion of the blood Pb level up to the hinge) is combined with IQ loss estimated using the shallower and higher exposure slope, for that portion of the blood Pb level extending above the hinge. The IQ loss estimates generated using this approach are pooled to form a population-level distribution of IQ loss for a given study area. Each of these IQ loss estimates are pathway apportioned based on pathway contribution to the underlying blood Pb levels. That is, IQ loss estimates are apportioned among policy-relevant background pathways, recent air-related July 2007 4-5 Draft – Do Not Quote or Cite
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Lead Human Exposure and Health Risk
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DISCLAIMER This document has been r
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comment. A final version of this do
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2.4 ANALYTICAL APPROACH ...........
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List of Figures Figure 1-1. Princip
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