Derivation of a Target Level of Lead in Soil at Residential Sites Corresponding to a De Minimis Contribution to Blood Lead Concentration1

Inability to define either a clear toxicologic threshold or a stochastic all-or-nothing (cancer-type) response model for the noncarcinogenic effects of lead (Pb) in young children has posed difficulties for derivation of risk-based target levels of Pb in residential soil. Approaches based on empirical relationships between Pb levels in blood (PbB) and Pb in soil suffer from inability to specify the numerous variables which mediate between these two quantities. Approaches based on achieving a toxicologically de minimis target PbB level (e.g., 10 μg/dl) are subject to large uncertainty in estimating the distribution of existing PbB levels in a specific exposed population and in estimating the relative contribution from nonsoil sources of Pb. The multisource contribution to the distribution of PbB makes this approach unsuited for determination of a target Pb level in a single medium. An alternative approach is presented based on achieving a de minimis contribution to PbB (ΔPbB) from soil. Contributions to Pb exposure from outdoor soil and indoor soil-derived dust (ISDD) are modeled and appropriate values are suggested for input parameters. This analysis predicts that chronic exposure of young children to 200 μg Pb/g (ppm) in residential soil will result in a ΔPbB of 2 μg Pb/dl blood. This concentration of Pb in soil may provide an appropriate target level for residential soil when other significant sources of Pb exposure are present. In other cases, this approach can be used to predict a soil concentration of Pb corresponding to an appropriate non-de minimisΔPbB.     

Dietary and Inhalation Intake of Lead and Estimation of Blood Lead Levels in Adults and Children in Kanpur, India

This research was initiated to study lead levels in various food items in the city of Kanpur, India, to assess the dietary intake of lead and to estimate blood lead (PbB) levels, a biomarker of lead toxicity. For this purpose, sampling of food products, laboratory analysis, and computational exercises were undertaken. Specifically, six food groups (leafy vegetables, nonleafy vegetables, fruits, pulses, cereals, and milk), drinking water, and lead air concentration were considered for estimating lead intake. Results indicated highest lead content in leafy vegetables followed by pulses. Fruits showed low lead content and drinking water lead levels were always within tolerable limits. It was estimated that average daily lead intake through diet was about 114 microg/day for adults and 50 microg/day in children; tolerable limit is 250 microg/day for adults and 90 microg/day for children. The estimated lead intakes were translated into the resultant PbB concentrations for children and adults using a physiologically-based pharmacokinetic (PBPK) model. Monte Carlo simulation of PbB level variations for adults showed that probability of exceeding the tolerable limit of PbB (i.e.,10 microg/dL) was 0.062 for the pre-unleaded and 0.000328 for the post-unleaded gasoline period. The probability of exceeding tolerable limits in PbB level was reduced by a factor of 189 in the post-unleaded scenario. The study also suggested that in spite of the introduction of unleaded gasoline, children continue to be at a high risk (probability of exceeding 10 microg/dL = 0.39) because of a high intake of lead per unit body weight.     

Issues Related to Time Averaging of Exposure in Modeling Risks Associated with Intermittent Exposures to Lead

Typical exposures to lead often involve a mix of long-term exposures to relatively constant exposure levels (e.g., residential yard soil and indoor dust) and highly intermittent exposures at other locations (e.g., seasonal recreational visits to a park). These types of exposures can be expected to result in blood lead concentrations that vary on a temporal scale with the intermittent exposure pattern. Prediction of short-term (or seasonal) blood lead concentrations arising from highly variable intermittent exposures requires a model that can reliably simulate lead exposures and biokinetics on a temporal scale that matches that of the exposure events of interest. If exposure model averaging times (EMATs) of the model exceed the shortest exposure duration that characterizes the intermittent exposure, uncertainties will be introduced into risk estimates because the exposure concentration used as input to the model must be time averaged to account for the intermittent nature of the exposure. We have used simulation as a means of determining the potential magnitude of these uncertainties. Simulations using models having various EMATs have allowed exploration of the strengths and weaknesses of various approaches to time averaging of exposures and impact on risk estimates associated with intermittent exposures to lead in soil. The International Commission of Radiological Protection (ICRP) model of lead pharmacokinetics in humans simulates lead intakes that can vary in intensity over time spans as small as one day, allowing for the simulation of intermittent exposures to lead as a series of discrete daily exposure events. The ICRP model was used to compare the outcomes (blood lead concentration) of various time-averaging adjustments for approximating the time-averaged intake of lead associated with various intermittent exposure patterns. Results of these analyses suggest that standard approaches to time averaging (e.g., U.S. EPA) that estimate the long-term daily exposure concentration can, in some cases, result in substantial underprediction of short-term variations in blood lead concentrations when used in models that operate with EMATs exceeding the shortest exposure duration that characterizes the intermittent exposure. Alternative time-averaging approaches recommended for use in lead risk assessment more reliably predict short-term periodic (e.g., seasonal) elevations in blood lead concentration that might result from intermittent exposures. In general, risk estimates will be improved by simulation on shorter time scales that more closely approximate the actual temporal dynamics of the exposure.     

Benchmark Dose of Lead Inducing Anemia at the Workplace

To estimate the critical dose of lead inducing anemia in humans, the effects of lead on hemoglobin (Hb) and hematocrit (Hct) levels and red blood cell (RBC) count were examined in 388 male lead-exposed workers with blood lead (BPb) levels of 0.05-5.5 (mean 1.3) micromol/L by using the benchmark dose (BMD) approach. The BPb level was significantly related to Hb (regression coefficient beta=-0.276), RBC (beta=-11.35), and Hct (beta=-0.563) among the workers (p < 0.001) when controlling for age and working status. The average BPb levels were significantly higher in the workers with anemia (1.85 micromol/L), based on the WHO criteria, than in those without anemia (1.26 micromol/L). The benchmark dose levels of BPb (i.e., lower 95% confidence limits of BMD), calculated from the K-power model set at an abnormal probability of 5% in unexposed workers and an excess risk of 5% in exposed workers were estimated to be 0.94 micromol/L (19.5 microg/dl) for Hb, 0.94 micromol/L (19.4 microg/dl) for RBC, and 1.43 micromol/L (29.6 microg/dl) for Hct. These findings suggest that reduction in hematopoietic indicators may be initiated at BPbs below the level currently considered without effect.     

The Bioaccessibility of Lead (Pb) from Vacuumed House Dust on Carpets in Urban Residences

Risk assessments for toxicants in environmental media via oral exposure often rely on measurements of total concentration in a collected sample. However, the human digestive system cannot dissolute all of a toxicant present in the binding matrix, and cannot absorb it with nearly 100% efficiency. In vitro bioaccessibility has been developed as a method to estimate oral bioavailability of a toxicant using a physiologically-based extraction procedure. Bioaccessibility measurements are more physiologically relevant than strong acid leaching measurements of concentration. A method for measuring bioaccessible lead in house dust was derived from the bioaccessibility method currently used for heavy metals in contaminated soils. House dust was collected from carpets in typical urban residences. Bioaccessible lead was measured in house dust (<75 microm) from the homes of 15 participants. The bioaccessibility ranged from 52.4% to 77.2% in gastric fluid, and 4.9% to 32.1% in intestinal fluid. House dust samples from five homes were analyzed to assess the relationship among lead bioaccessibility of three particle size fractions (<75, 75-150, and 150-250 microm). Changes in lead bioaccessibility as a function of particle size fraction were not significant for gastric fluid (p= 0.7019); however they were significant for intestinal fluid (p= 0.0067). This decrease of bioaccessibility may result from the readsorption of dissolved lead onto the dust particles or precipitation of lead with phosphates in a high-pH environment. The bioaccessibility data obtained for two biofluids were applied to the IEUBK model, and results for intestinal bioaccessibility of lead provide support for the model default value of 30% lead bioavailability of dust as a reasonable population indicator for dose, but the higher values for gastric bioaccessibility of lead appeared to provide an upper bound that approached actual blood lead levels in the children living in the studied homes. This upper bound seemed to overcome some of the limitations of the model when it lacks child-specific activity data and characterization of all exposure routes.     

An International Pooled Analysis for Obtaining a Benchmark Dose for Environmental Lead Exposure in Children

Lead is a recognized neurotoxicant, but estimating effects at the lowest measurable levels is difficult. An international pooled analysis of data from seven cohort studies reported an inverse and supra‐linear relationship between blood lead concentrations and IQ scores in children. The lack of a clear threshold presents a challenge to the identification of an acceptable level of exposure. The benchmark dose (BMD) is defined as the dose that leads to a specific known loss. As an alternative to elusive thresholds, the BMD is being used increasingly by regulatory authorities. Using the pooled data, this article presents BMD results and applies different statistical techniques in the analysis of multistudy data. The calculations showed only a limited variation between studies in the steepness of the dose‐response functions. BMD results were quite robust to modeling assumptions with the best fitting models yielding lower confidence limits (BMDLs) of about 0.1–1.0 μ g/dL for the dose leading to a loss of one IQ point. We conclude that current allowable blood lead concentrations need to be lowered and further prevention efforts are needed to protect children from lead toxicity.     

The Effect of Lead Time Uncertainty on Safety Stocks

The pressure to reduce inventory investments in supply chains has increased as competition expands and product variety grows. Managers are looking for areas they can improve to reduce inventories without hurting the level of service provided. Two areas that managers focus on are the reduction of the replenishment lead time from suppliers and the variability of this lead time. The normal approximation of lead time demand distribution indicates that both actions reduce inventories for cycle service levels above 50%. The normal approximation also indicates that reducing lead time variability tends to have a greater impact than reducing lead times, especially when lead time variability is large. We build on the work of Eppen and Martin (1988) to show that the conclusions from the normal approximation are flawed, especially in the range of service levels where most companies operate. We show the existence of a service‐level threshold greater than 50% below which reorder points increase with a decrease in lead time variability. Thus, for a firm operating just below this threshold, reducing lead times decreases reorder points, whereas reducing lead time variability increases reorder points. For firms operating at these service levels, decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability.     

A Risk Assessment for Consumers of Mourning Doves

Recreational and subsistence hunters and anglers consume a wide range of species, including birds, mammals, fish and shellfish, some of which represent significant exposure pathways for environmental toxic agents. This study focuses on the Department of Energy's (DOE'S) Savannah River Site (SRS), a former nuclear weapons production facility in South Carolina. The potential risk of contaminant intake from consuming mourning doves ( Zenaida macroura ), the most popular United States game bird, was examined under various risk scenarios. For all of these scenarios we used the mean tissue concentration of six metals (lead, mercury, cadmium, selenium, chromium, manganese) and radiocesium, in doves collected on and near SRS. We also estimated risk to a child consuming doves that had the maximum contaminant level. We used the cancer slope factor for radiocesium, the Environmental Protection Agencies UptakeBiokinetic model for lead, and published reference doses for the other metals. As a result of our risk assessments we recommend management of water levels in contaminated reservoirs so that lake bed sediments are not exposed to use by gamebirds and other terrestrial wildlife. Particularly, measures should be taken to insure that the hunting public does not have access to such a site. Our data also indicate that doves on popular hunting areas are exposed to excess lead, suggesting that banning lead shot for doves, as has been done for waterfowl, is desirable.     

Linking Indoor Air and Pharmacokinetic Models to Assess Tetrachloroethylene Risk

Physiologically based pharmacokinetic (PBPK) models describing the uptake, metabolism, and excretion of xenobiotic compounds are now proposed for use in regulatory health-risk assessments. In this study we investigate the extent of PCE metabolism arising from domestic respiratory exposure to tetrachloroethylene (PCE) from ground water, as predicted using a PBPK model. Indoor exposure patterns we use as input to the PBPK model are realistic ones generated from a three-compartment model describing volatilization of PCE from domestic water into household air. Values we use for the metabolic parameters of the PBPK model are estimated from data on urinary metabolites in workers exposed to PCE. It is shown that for respiratory PCE exposure due to typical levels of PCE in ground water, use of time-weighted average air concentrations with a steady-state PBPK model yields estimates of total metabolized PCE similar to those obtained using completely dynamic modeling, despite considerable uncertainty in key exposure- and metabolic-model parameters. These findings suggest that, for PCE, risk estimation taking pharmacokinetics into account may be accomplished using a simple analytic approach.     

Combined workplace stressors and their relationship with mood, physiology, and performance

The majority of working individuals are exposed to low levels of a large number of potential stressors. Although each is unlikely to be particularly detrimental in itself, such stressors may be harmful cumulatively. The aim of this study was to investigate whether exposures to combinations of stressors were associated with harmful levels on some measures of mood, physiology, and performance. The study was conducted with 84 participants, all employed, mostly “white-collar” workers. A questionnaire was administered and physiological outcome measures were taken on four occasions: before and after work on the first and last days of one working week (repeated measures, within-subjects factor). Workers were categorized as exposed to either: (1) no stressors, (2) temporal stressors only, (3) physical stressors only, or (4) both temporal and physical stressors (between-subjects factor). Data were analysed using mixed design ANOVAs. Key significant between-subjects effects were found for blood pressure and salivary cortisol; participants exposed to a combination of stressors had significantly elevated levels of both. The identified physiological differences are tentatively supported by the literature and can be explained by increased subjective stress levels. Significant differences in performance were not found. This may be explained by methodological issues, or participants' increased effort expended to perform on the tasks. It is concluded that the consideration of combined (low level) stressors and cumulative exposure is important in assessing the health risk associated with the work environment.     

Development of a Screening Approach to Interpret Human Biomonitoring Data on Volatile Organic Compounds: Reverse Dosimetry on Biomonitoring Data for Trichloroethylene

A screening approach is developed for volatile organic compounds (VOCs) to estimate exposures that correspond to levels measured in fluids and/or tissues in human biomonitoring studies. The approach makes use of a generic physiologically-based pharmacokinetic (PBPK) model coupled with exposure pattern characterization, Monte Carlo analysis, and quantitative structure property relationships (QSPRs). QSPRs are used for VOCs with minimal data to develop chemical-specific parameters needed for the PBPK model. The PBPK model is capable of simulating VOC kinetics following multiple routes of exposure, such as oral exposure via water ingestion and inhalation exposure during shower events. Using published human biomonitoring data of trichloroethylene (TCE), the generic model is evaluated to determine how well it estimates TCE concentrations in blood based on the known drinking water concentrations. In addition, Monte Carlo analysis is conducted to characterize the impact of the following factors: (1) uncertainties in the QSPR-estimated chemical-specific parameters; (2) variability in physiological parameters; and (3) variability in exposure patterns. The results indicate that uncertainty in chemical-specific parameters makes only a minor contribution to the overall variability and uncertainty in the predicted TCE concentrations in blood. The model is used in a reverse dosimetry approach to derive estimates of TCE concentrations in drinking water based on given measurements of TCE in blood, for comparison to the U.S. EPA's Maximum Contaminant Level in drinking water. This example demonstrates how a reverse dosimetry approach can be used to facilitate interpretation of human biomonitoring data in a health risk context by deriving external exposures that are consistent with a biomonitoring data set, thereby permitting comparison with health-based exposure guidelines.     

Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability

In quantitative uncertainty analysis, it is essential to define rigorously the endpoint or target of the assessment. Two distinctly different approaches using Monte Carlo methods are discussed: (1) the end point is a fixed but unknown value (e.g., the maximally exposed individual, the average individual, or a specific individual) or (2) the end point is an unknown distribution of values (e.g., the variability of exposures among unspecified individuals in the population). In the first case, values are sampled at random from distributions representing various "degrees of belief" about the unknown "fixed" values of the parameters to produce a distribution of model results. The distribution of model results represents a subjective confidence statement about the true but unknown assessment end point. The important input parameters are those that contribute most to the spread in the distribution of the model results. In the second case, Monte Carlo calculations are performed in two dimensions producing numerous alternative representations of the true but unknown distribution. These alternative distributions permit subject confidence statements to be made from two perspectives: (1) for the individual exposure occurring at a specified fractile of the distribution or (2) for the fractile of the distribution associated with a specified level of individual exposure. The relative importance of input parameters will depend on the fractile or exposure level of interest. The quantification of uncertainty for the simulation of a true but unknown distribution of values represents the state-of-the-art in assessment modeling.     

Risk Assessment for Aflatoxin: III. Modeling the Relative Risk of Hepatocellular Carcinoma

Estimates have been made of the cancer potency of aflatoxin exposure among the U.S. population. Risk modeling is used to assess the dose-response relationship between aflatoxin exposure and primary liver cancer, controlling for hepatitis B virus (HBV), based on data provided by the Yeh et al. study in China. A relative risk model is proposed as a more appropriate alternative to the additive ("absolute" risk) model for transportation of risk coefficients between populations with different baseline rates. Several general relative risk models were examined; the exponential model provided the best fit. The Poisson regression method was used to fit the relative risk model to the grouped data. The effects of exposure to aflatoxin (AFB1) and hepatitis B infection were both found to be statistically significant. The risk of death from liver cancer for those exposed to AFB1 relative to the unexposed population, increases by 0.05% per ng/kg/day exposure of AFB1 (p less than 0.001). The results also indicated a 25-fold increase in the risk of death from liver cancer among those infected with hepatitis B virus, relative to noncarriers (p less than 0.0001). With a hepatitis prevalence rate of 1%, the aflatoxin intake level associated with liver cancer lifetime excess risk of 1 x 10(-5) for the U.S. population was estimated as 253 ng/day, based on a liver cancer baseline rate of 3.4/100,000/yr.     

Development of a Single-Meal Fish Consumption Advisory for Methyl Mercury

Methyl mercury (meHg) contamination of fish is the leading cause of fish consumption advisories in the United States. These advisories have focused upon repeated or chronic exposure, whereas risks during pregnancy may also exist from a single-meal exposure if the fish tissue concentration is high enough. In this study, acute exposure to meHg from a single fish meal was analyzed by using the one-compartment meHg biokinetic model to predict maternal hair concentrations. These concentrations were evaluated against the mercury hair concentration corresponding to the U.S. Environmental Protection Agency's reference dose (RfD), which is intended to protect against neurodevelopmental effects. The one-compartment model was validated against blood concentrations from three datasets in which human subjects ingested meHg in fish, either as a single meal or multiple meals. Model simulations of the single-meal scenario at different fish meHg concentrations found that concentrations of 2.0 ppm or higher can be associated with maternal hair concentrations elevated above the RfD level for days to weeks during gestation. A single-meal fish concentration cutoff of > or = 2.0 ppm is an important consideration, especially because this single high exposure event might be in addition to a baseline meHg body burden from other types of fish consumption. This type of single-meal advisory requires that fish sampling programs provide data for individual rather than composited fish, and take into account seasonal differences that may exist in fish concentrations.     

Assessment of the Dose–Response Relationship Between Folate Exposure and Cognitive Impairment: Synthesizing Data from Documented Studies

The dose–response relationship between folate levels and cognitive impairment among individuals with vitamin B12 deficiency is an essential component of a risk-benefit analysis approach to regulatory and policy recommendations regarding folic acid fortification. Epidemiological studies provide data that are potentially useful for addressing this research question, but the lack of analysis and reporting of data in a manner suitable for dose–response purposes hinders the application of the traditional evidence synthesis process. This study aimed to estimate a quantitative dose–response relationship between folate exposure and the risk of cognitive impairment among older adults with vitamin B12 deficiency using “probabilistic meta-analysis,” a novel approach for synthesizing data from observational studies. Second-order multistage regression was identified as the best-fit model for the association between the probability of cognitive impairment and serum folate levels based on data generated by randomly sampling probabilistic distributions with parameters estimated based on summarized information reported in relevant publications. The findings indicate a “J-shape” effect of serum folate levels on the occurrence of cognitive impairment. In particular, an excessive level of folate exposure is predicted to be associated with a higher risk of cognitive impairment, albeit with greater uncertainty than the association between low folate exposure and cognitive impairment. This study directly contributes to the development of a practical solution to synthesize observational evidence for dose–response assessment purposes, which will help strengthen future nutritional risk assessments for the purpose of informing decisions on nutrient fortification in food.     

A Pharmacokinetic Study of Occupational and Environmental Benzene Exposure with Regard to Gender

Using physiologically-based pharmacokinetic (PBPK) modeling, occupational, personal, and environmental benzene exposure scenarios are simulated for adult men and women. This research identifies differences in internal exposure due to physiological and biochemical gender differences. Physiological and chemical-specific model parameters were obtained from other studies reported in the literature and medical texts for the subjects of interest. Women were found to have a higher blood/air partition coefficient and maximum velocity of metabolism for benzene than men (the two most sensitive parameters affecting gender-specific differences). Additionally, women generally have a higher body fat percentage than men. These factors influence the internal exposure incurred by the subjects and should be considered when conducting a risk assessment. Results demonstrated that physicochemical gender differences result in women metabolizing 23–26% more benzene than men when subject to the same exposure scenario even though benzene blood concentration levels are generally higher in men. These results suggest that women may be at significantly higher risk for certain effects of benzene exposure. Thus, exposure standards based on data from male subjects may not be protective for the female population.     

Predicted Infant Exposure to Tetrachloroethene in Human Breastmilk

Based on a variety of maternal occupational and residential inhalation exposure scenarios, estimates of infant exposure to the dry-cleaning solvent tetrachlorothylene (perchloroethylene, PCE) in breastmilk were made. Physiologically based pharmacokinetic (PBPK) modeling indicates that infants may be exposed to elevated levels of PCE in breastmilk due to their mothers' inhalation of PCE. The PBPK-predicted breastmilk PCE concentrations agree very well with measured concentrations, where available. Based on this analysis, infants may be exposed to this workplace chemical via breastmilk at doses corresponding to rather high levels of risk. Predicted breastmilk doses provide the infant with little margin of exposure to doses associated with adverse health effects. In addition, the estimated increased cancer risks associated with these infant exposures are large under certain exposure scenarios. The actual concentrations of PCE in breastmilk of exposed mothers can only be known with certainty if monitoring is conducted. Due to the widespread exposure potential, monitoring studies should be undertaken so that the appropriate risk management alternatives can be better evaluated.     

A Spatio‐Temporal Exposure‐Hazard Model for Assessing Biological Risk and Impact

We developed a simulation model for quantifying the spatio‐temporal distribution of contaminants (e.g., xenobiotics) and assessing the risk of exposed populations at the landscape level. The model is a spatio‐temporal exposure‐hazard model based on (i) tools of stochastic geometry (marked polygon and point processes) for structuring the landscape and describing the exposed individuals, (ii) a dispersal kernel describing the dissemination of contaminants from polygon sources, and (iii) an (eco)toxicological equation describing the toxicokinetics and dynamics of contaminants in affected individuals. The model was implemented in the briskaR package (b iological risk a ssessment with R ) of the R software. This article presents the model background, the use of the package in an illustrative example, namely, the effect of genetically modified maize pollen on nontarget Lepidoptera, and typical comparisons of landscape configurations that can be carried out with our model (different configurations lead to different mortality rates in the treated example). In real case studies, parameters and parametric functions encountered in the model will have to be precisely specified to obtain realistic measures of risk and impact and accurate comparisons of landscape configurations. Our modeling framework could be applied to study other risks related to agriculture, for instance, pathogen spread in crops or livestock, and could be adapted to cope with other hazards such as toxic emissions from industrial areas having health effects on surrounding populations. Moreover, the R package has the potential to help risk managers in running quantitative risk assessments and testing management strategies.     

Demand and Production Management with Uniform Guaranteed Lead Time

Recently, innovation‐oriented firms have been competing along dimensions other than price, lead time being one such dimension. Increasingly, customers are favoring lead time guarantees as a means to hedge supply chain risks. For a make‐to‐order environment, we explicitly model the impact of a lead time guarantee on customer demands and production planning. We study how a firm can integrate demand and production decisions to optimize expected profits by quoting a uniform guaranteed maximum lead time to all customers. Our analysis highlights the increasing importance of lead time for customers, as well as the tradeoffs in achieving a proper balance between revenue and cost drivers associated with lead‐time guarantees. We show that the optimal lead time has a closed‐form solution with a newsvendor‐like structure. We prove comparative statics results for the change in optimal lead time with changes in capacity and cost parameters and illustrate the insights using numerical experimentation.     

Model-Averaged Benchmark Concentration Estimates for Continuous Response Data Arising from Epidemiological Studies

Worker populations often provide data on adverse responses associated with exposure to potential hazards. The relationship between hazard exposure levels and adverse response can be modeled and then inverted to estimate the exposure associated with some specified response level. One concern is that this endpoint may be sensitive to the concentration metric and other variables included in the model. Further, it may be that the models yielding different risk endpoints are all providing relatively similar fits. We focus on evaluating the impact of exposure on a continuous response by constructing a model-averaged benchmark concentration from a weighted average of model-specific benchmark concentrations. A method for combining the estimates based on different models is applied to lung function in a cohort of miners exposed to coal dust. In this analysis, we see that a small number of the thousands of models considered survive a filtering criterion for use in averaging. Even after filtering, the models considered yield benchmark concentrations that differ by a factor of 2 to 9 depending on the concentration metric and covariates. The model-average BMC captures this uncertainty, and provides a useful strategy for addressing model uncertainty.