Environmental Tobacco Smoke Revisited: The Reliability of the Data Used for Risk Assessment

Several epidemiological studies have found a weak, but consistent association between lung cancer in nonsmokers and exposure to environmental tobacco smoke (ETS). In addition, a purported link between such exposure and coronary heart disease (CHD) has been of major concern. Although it is biologically plausible that ETS has a contributory role in the induction of lung cancer in nonsmoking individuals, dose-response extrapolation-supported by the more solid database for active smokers-gives an additional risk for lung cancer risk that is more than one order of magnitude lower than that indicated by major positive epidemiological studies. The discrepancy between available epidemiological data and dosimetric estimates seems, to a major part, to reflect certain systematic biases in the former that are difficult to control by statistical analysis when dealing with risks of such low magnitudes. These include, most importantly, misclassification of smoking status, followed by inappropriate selection of controls, as well as certain confounding factors mainly related to lifestyle, and possibly also hereditary disposition. A significant part of an association between lung cancer and exposure to ETS would disappear, if, on the average, 1 patient out of 20 nonsmoking cases had failed to tell the interviewer that he had, in fact, recently stopped smoking. In the large International Agency for Research on Cancer (IARC) multicenter study even lower misclassification rates would abolish the weak, statistically nonsignificant associations that were found. In the former study an apparent significant protective effect from exposure to ETS in childhood with respect to lung cancer later in life was reported, a most surprising finding. The fact that the mutation spectrum of the p53 tumor suppressor gene in lung tumors of ETS-exposed nonsmokers generally differs from that found in tumors of active smokers lends additional support to the notion that the majority of tumors found in ETS-exposed nonsmokers have nothing to do with tobacco smoke. The one-sided preoccupation with ETS as a causative factor of lung cancer in nonsmokers may seriously hinder the elucidation of the multifactorial etiology of these tumors. Due to the high prevalence of cardiovascular disease in the population, even a modest causal association with ETS would, if valid, constitute a serious public health problem. By pooling data from 20 published studies on ETS and heart disease, some of which reported higher risks than is known to be caused by active smoking, a statistically significant association with spousal smoking is obtained. However, in most of these studies, many of the most common confounding risk factors were ignored and there appears to be insufficient evidence to support an association between exposure to ETS and CHD. Further, it seems highly improbable that exposure to a concentration of tobacco smoke at a level that is generally much less than 1% of that inhaled by a smoker could result in an excess risk for CHD that-as has been claimed-is some 30% to 50% of that found in active smokers. There are certainly valid reasons to limit exposure to ETS as well as to other air pollutants in places such as offices and homes in order to improve indoor air quality. This goal can be achieved, however, without the introduction of an extremist legislation based on a negligible risk of lung cancer as well as an unsupported and highly hypothetical risk for CHD.     

An Enforceable Indoor Air Quality Standard for Environmental Tobacco Smoke in the Workplace1

Environmental tobacco smoke (ETS)has recently been determined by U.S. environmental and occupational health authorities to be a human carcinogen. We develop a model which permits using atmospheric nicotine measurements to estimate nonsmokers’ETS lung cancer risks in individual workplaces for the first time. We estimate that during the 1980s, the U.S. nonsmoking adult population's median nicotine lung exposure (homes and workplaces combined)was 143 micrograms (μg)of nicotine daily, and that most-exposed adult nonsmokers inhaled 1430 μg/day. These exposure estimates are validated by pharmacokinetic modeling which yields the corresponding steady-state dose of the nicotine metabolite, cotinine. For U.S. adult nonsmokers of working age, we estimate median cotinine values of about 1.0 nanogram per milliliter (ng/ml)in plasma, and 6.2 ng/ml in urine; for most-exposed nonsmokers, we estimate cotinine concentrations of about 10 ng/ml in plasma and 62 ng/ml in urine. These values are consistent to within 15% of the cotinine values observed in contemporaneous clinical epidemiological studies. Corresponding median risk from ETS exposure in U.S. nonsmokers during the 1980s is estimated at about two lung cancer deaths (LCDs)per 1000 at risk, and for most-exposed nonsmokers, about two LCDs per 100. Risks abroad appear similar. Modeling of the lung cancer mortality risk from passive smoking suggests that de minimis [i.e., “acceptable” (10^-6)], risk occurs at an 8-hr time-weighted-average exposure concentration of 7.5 nanograms of ETS nicotine per cubic meter of workplace air for a working lifetime of 40 years. This model is based upon a linear exposure-response relationship validated by physical, clinical, and epidemiological data. From available data, it appears that workplaces without effective smoking policies considerably exceed this de minimis risk standard. For a substantial fraction of the 59 million nonsmoking workers in the U.S., current workplace exposure to ETS also appears to pose risks exceeding the de manifestos risk level above which carcinogens are strictly regulated by the federal government.     

A Parametric Model for Detecting Hormetic Effects in Developmental Toxicity Studies

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.     

Improving cancer dose-response characterization by using physiologically based pharmacokinetic modeling: an analysis of pooled data for acrylonitrile-induced brain tumors to assess cancer potency in the rat.

Historically, U.S. regulators have derived cancer slope factors by using applied dose and tumor response data from a single key bioassay or by averaging the cancer slope factors of several key bioassays. Recent changes in U.S. Environmental Protection Agency (EPA) guidelines for cancer risk assessment have acknowledged the value of better use of mechanistic data and better dose-response characterization. However, agency guidelines may benefit from additional considerations presented in this paper. An exploratory study was conducted by using rat brain tumor data for acrylonitrile (AN) to investigate the use of physiologically based pharmacokinetic (PBPK) modeling along with pooling of dose-response data across routes of exposure as a means for improving carcinogen risk assessment methods. In this study, two contrasting assessments were conducted for AN-induced brain tumors in the rat on the basis of (1) the EPA's approach, the dose-response relationship was characterized by using administered dose/concentration for each of the key studies assessed individually; and (2) an analysis of the pooled data, the dose-response relationship was characterized by using PBPK-derived internal dose measures for a combined database of ten bioassays. The cancer potencies predicted for AN by the contrasting assessments are remarkably different (i.e., risk-specific doses differ by as much as two to four orders of magnitude), with the pooled data assessments yielding lower values. This result suggests that current carcinogen risk assessment practices overestimate AN cancer potency. This methodology should be equally applicable to other data-rich chemicals in identifying (1) a useful dose measure, (2) an appropriate dose-response model, (3) an acceptable point of departure, and (4) an appropriate method of extrapolation from the range of observation to the range of prediction when a chemical's mode of action remains uncertain.     

An Exploratory Study of Variations in Exposure to Environmental Tobacco Smoke in the United States

There is considerable interest in assessing exposure to environmental tobacco smoke (ETS) and in understanding the factors that affect exposure at various venues. The impact of these complex factors can be researched only if monitoring studies are carefully designed. Prior work by Jenkins et al. gathered personal monitor and diary data from 1,564 nonsmokers in 16 metropolitan areas of the United States and compared workplace exposures to ETS with exposures away from work. In this study, these data were probed further to examine (1) the correspondence between work and away-from-work exposure concentrations of ETS; (2) the variability in exposure concentration levels across cities; and (3) the association of ETS exposure concentrations with select socioeconomic, occupation, and lifestyle variables. The results indicate (1) at the population level, there was a positive association between ETS concentrations at the work and away-from-work environments; (2) exposure concentration levels across the 16 cities under consideration were highly variable; and (3) exposure concentration levels were significantly associated with occupation, education, household income, age, and dietary factors. Workplace smoking restrictions were associated with low ETS concentration levels at work as well as away from work. Generally, the same cities that exhibited either lower or higher away-from-work exposure concentration levels also showed lower or higher work exposure concentration levels. The observations suggest that similar avoidance characteristics as well as socioeconomic and other lifestyle factors that affect exposure to ETS may have been in operation in both away-from-work and work settings.     

Quantitative Cancer Risk Estimation for Formaldehyde

Of primary concern are irreversible effects, such as cancer induction, that formaldehyde exposure could have on human health. Dose-response data from human exposure situations would provide the most solid foundation for risk assessment, avoiding problematic extrapolations from the health effects seen in nonhuman species. However, epidemiologic studies of human formaldehyde exposure have provided little definitive information regarding dose-response. Reliance must consequently be placed on laboratory animal evidence. An impressive array of data points to significantly nonlinear relationships between rodent tumor incidence and administered dose, and between target tissue dose and administered dose (the latter for both rodents and Rhesus monkeys) following exposure to formaldehyde by inhalation. Disproportionately less formaldehyde binds covalently to the DNA of nasal respiratory epithelium at low than at high airborne concentrations. Use of this internal measure of delivered dose in analyses of rodent bioassay nasal tumor response yields multistage model estimates of low-dose risk, both point and upper bound, that are lower than equivalent estimates based upon airborne formaldehyde concentration. In addition, risk estimates obtained for Rhesus monkeys appear at least 10-fold lower than corresponding estimates for identically exposed Fischer-344 rats.     

Dose-Response and Risk Assessment of Airborne Hexavalent Chromium and Lung Cancer Mortality

This study evaluates the dose-response relationship for inhalation exposure to hexavalent chromium [Cr(VI)] and lung cancer mortality for workers of a chromate production facility, and provides estimates of the carcinogenic potency. The data were analyzed using relative risk and additive risk dose-response models implemented with both Poisson and Cox regression. Potential confounding by birth cohort and smoking prevalence were also assessed. Lifetime cumulative exposure and highest monthly exposure were the dose metrics evaluated. The estimated lifetime additional risk of lung cancer mortality associated with 45 years of occupational exposure to 1 microg/m3 Cr(VI) (occupational exposure unit risk) was 0.00205 (90%CI: 0.00134, 0.00291) for the relative risk model and 0.00216 (90%CI: 0.00143, 0.00302) for the additive risk model assuming a linear dose response for cumulative exposure with a five-year lag. Extrapolating these findings to a continuous (e.g., environmental) exposure scenario yielded an environmental unit risk of 0.00978 (90%CI: 0.00640, 0.0138) for the relative risk model [e.g., a cancer slope factor of 34 (mg/kg-day)-1] and 0.0125 (90%CI: 0.00833, 0.0175) for the additive risk model. The relative risk model is preferred because it is more consistent with the expected trend for lung cancer risk with age. Based on statistical tests for exposure-related trend, there was no statistically significant increased lung cancer risk below lifetime cumulative occupational exposures of 1.0 mg-yr/m3, and no excess risk for workers whose highest average monthly exposure did not exceed the current Permissible Exposure Limit (52 microg/m3). It is acknowledged that this study had limited power to detect increases at these low exposure levels. These cancer potency estimates are comparable to those developed by U.S. regulatory agencies and should be useful for assessing the potential cancer hazard associated with inhaled Cr(VI).     

Distribution of Exposure Concentrations and Doses for Constituents of Environmental Tobacco Smoke

The ultimate goal of the research reported in this series of three articles is to derive distributions of doses of selected environmental tobacco smoke (ETS)-related chemicals for nonsmoking workers. This analysis uses data from the 16-City Study collected with personal monitors over the course of one workday in workplaces where smoking occurred. In this article, we describe distributions of ETS chemical concentrations and the characteristics of those distributions (e.g., whether the distribution was log normal for a given constituent) for the workplace exposure. Next, we present population parameters relevant for estimating dose distributions and the methods used for estimating those dose distributions. Finally, we derive distributions of doses of selected ETS-related constituents obtained in the workplace for people in smoking work environments. Estimating dose distributions provided information beyond the usual point estimate of dose and showed that the preponderance of individuals exposed to ETS in the workplace were exposed at the low end of the dose distribution curve. The results of this analysis include estimations of hourly maxima and time-weighted average (TWA) doses of nicotine from workplace exposures to ETS (extrapolated from 1 day to 1 week) and doses derived from modeled lung burdens of ultraviolet-absorbing particulate matter (UVPM) and solanesol resulting from workplace exposures to ETS (extrapolated from 1 day to 1 year).     

Model Averaging Using the Kullback Information Criterion in Estimating Effective Doses for Microbial Infection and Illness

Since the National Food Safety Initiative of 1997, risk assessment has been an important issue in food safety areas. Microbial risk assessment is a systematic process for describing and quantifying a potential to cause adverse health effects associated with exposure to microorganisms. Various dose-response models for estimating microbial risks have been investigated. We have considered four two-parameter models and four three-parameter models in order to evaluate variability among the models for microbial risk assessment using infectivity and illness data from studies with human volunteers exposed to a variety of microbial pathogens. Model variability is measured in terms of estimated ED01s and ED10s, with the view that these effective dose levels correspond to the lower and upper limits of the 1% to 10% risk range generally recommended for establishing benchmark doses in risk assessment. Parameters of the statistical models are estimated using the maximum likelihood method. In this article a weighted average of effective dose estimates from eight two- and three-parameter dose-response models, with weights determined by the Kullback information criterion, is proposed to address model uncertainties in microbial risk assessment. The proposed procedures for incorporating model uncertainties and making inferences are illustrated with human infection/illness dose-response data sets.     

Significance of Exposure Assessment to Analysis of Cancer Risk from Inorganic Arsenic in Drinking Water in Taiwan

The primary source of evidence that inorganic arsenic in drinking water is associated with increased mortality from cancer at internal sites (bladder, liver, lung, and other organs) is a large ecologic study conducted in regions of Southwest Taiwan endemic to Blackfoot disease. The dose-response patterns for lung, liver, and bladder cancers display a nonlinear dose-response relationship with arsenic exposure. The data do not appear suitable, however, for the more refined task of dose-response assessment, particularly for inference of risk at the low arsenic concentrations found in some U.S. water supplies. The problem lies in variable arsenic concentrations between the wells within a village, largely due to a mix of shallow wells and deep artesian wells, and in having only one well test for 24 (40%) of the 60 villages. The current analysis identifies 14 villages where the exposure appears most questionable, based on criteria described in the text. The exposure values were then changed for seven of the villages, from the median well test being used as a default to some other point in the village's range of well tests that would contribute to smoothing the appearance of a dose-response curve. The remaining seven villages, six of which had only one well test, were deleted as outliers. The resultant dose-response patterns showed no evidence of excess risk below arsenic concentrations of 0.1 mg/l. Of course, that outcome is dependent on manipulation of the data, as described. Inclusion of the seven deleted villages would make estimates of risk much higher at low doses. In those seven villages, the cancer mortality rates are significantly high for their exposure levels, suggesting that their exposure values may be too low or that other etiological factors need to be taken into account.     

Modeling the Modification of the Risk of Radon-Induced Lung Cancer by Environmental Tobacco Smoke

The presence of environmental tobacco smoke (ETS) in homes has been implicated in the causation of lung cancer. While of interest in its own right, ETS also influences the risk imposed by radon and its decay products. The interaction between radon progeny and ETS alters the exposure, intake, uptake, biokinetics, dosimetry, and radiobiology of those progeny. The present paper details model predictions of the various influences of ETS on these factors in the U.S. population and provides estimates of the resulting change in the risk from average levels of radon progeny. It is predicted that the presence of ETS produces a very small (perhaps unmeasurable) increase in the risk of radiation-induced tracheobronchial cancer in homes with initially very high particle concentrations for both active and never-smokers, but significantly lowers the risk in homes with initially lower particle concentrations for both groups when generation 4 of the lung is considered the target site. For generation 16, the presence of ETS generally increases the radon-induced risk of lung cancer, although the increase should be unmeasurable at high initial particle concentrations. The net effect of ETS on human health is suggested to be a complicated function of the initial housing conditions, the concentration of particles introduced by smoking, the target generation considered, and the smoking status of exposed populations. This situation precludes any simple statements concerning the role of ETS in governing the incidence of lung cancer in a population.     

Dose-response assessment for influenza A virus based on data sets of infection with its live attenuated reassortants

Reported data sets on infection of volunteers challenged with wild-type influenza A virus at graded doses are few. Alternatively, we aimed at developing a dose-response assessment for this virus based on the data sets for its live attenuated reassortants. Eleven data sets for live attenuated reassortants that were fit to beta-Poisson and exponential dose-response models. Dose-response relationships for those reassortants were characterized by pooling analysis of the data sets with respect to virus subtype (H1N1 or H3N2), attenuation method (cold-adapted or avian-human gene reassortment), and human age (adults or children). Furthermore, by comparing the above data sets to a limited number of reported data sets for wild-type virus, we quantified the degree of attenuation of wild-type virus with gene reassortment and estimated its infectivity. As a result, dose-response relationships of all reassortants were best described by a beta-Poisson model. Virus subtype and human age were significant factors determining the dose-response relationship, whereas attenuation method affected only the relationship of H1N1 virus infection to adults. The data sets for H3N2 wild-type virus could be pooled with those for its reassortants on the assumption that the gene reassortment attenuates wild-type virus by at least 63 times and most likely 1,070 times. Considering this most likely degree of attenuation, 10% infectious dose of H3N2 wild-type virus for adults was estimated at 18 TCID50 (95% CI = 8.8-35 TCID50). The infectivity of wild-type H1N1 virus remains unknown as the data set pooling was unsuccessful.     

Risk assessment methodologies for passive smoking-induced lung cancer

Risk assessment methodologies have been successfully applied to control societal risk from outdoor air pollutants. They are now being applied to indoor air pollutants such as environmental tobacco smoke (ETS) and radon. Nonsmokers' exposures to ETS have been assessed based on dosimetry of nicotine, its metabolite, continine, and on exposure to the particulate phase of ETS. Lung cancer responses have been based on both the epidemiology of active and of passive smoking. Nine risk assessments of nonsmokers' lung cancer risk from exposure to ETS have been performed. Some have estimated risks for lifelong nonsmokers only; others have included ex-smokers; still others have estimated total deaths from all causes. To facilitate interstudy comparison, in some cases lung cancers had to be interpolated from a total, or the authors' original estimate had to be adjusted to include ex-smokers. Further, all estimates were adjusted to 1988. Excluding one study whose estimate differs from the mean of the others by two orders of magnitude, the remaining risk assessments are in remarkable agreement. The mean estimate is approximately 5000 +/- 2400 nonsmokers' lung cancer deaths (LCDSs) per year. This is a 25% greater risk to nonsmokers than is indoor radon, and is about 57 times greater than the combined estimated cancer risk from all the hazardous outdoor air pollutants currently regulated by the Environmental Protection Agency: airborne radionuclides, asbestos, arsenic, benzene, coke oven emissions, and vinyl chloride.     

Diesel Engine Exhaust and Lung Cancer Mortality: Time‐Related Factors in Exposure and Risk

To develop a quantitative exposure‐response relationship between concentrations and durations of inhaled diesel engine exhaust (DEE) and increases in lung cancer risks, we examined the role of temporal factors in modifying the estimated effects of exposure to DEE on lung cancer mortality and characterized risk by mine type in the Diesel Exhaust in Miners Study (DEMS) cohort, which followed 12,315 workers through December 1997. We analyzed the data using parametric functions based on concepts of multistage carcinogenesis to directly estimate the hazard functions associated with estimated exposure to a surrogate marker of DEE, respirable elemental carbon (REC). The REC‐associated risk of lung cancer mortality in DEMS is driven by increased risk in only one of four mine types (limestone), with statistically significant heterogeneity by mine type and no significant exposure‐response relationship after removal of the limestone mine workers. Temporal factors, such as duration of exposure, play an important role in determining the risk of lung cancer mortality following exposure to REC, and the relative risk declines after exposure to REC stops. There is evidence of effect modification of risk by attained age. The modifying impact of temporal factors and effect modification by age should be addressed in any quantitative risk assessment (QRA) of DEE. Until there is a better understanding of why the risk appears to be confined to a single mine type, data from DEMS cannot reliably be used for QRA.     

Regulating Under Uncertainty: Newsboy for Exposure Limits

Setting action levels or limits for health protection is complicated by uncertainty in the dose-response relation across a range of hazards and exposures. To address this issue, we consider the classic newsboy problem. The principles used to manage uncertainty for that case are applied to two stylized exposure examples, one for high dose and high dose rate radiation and the other for ammonia. Both incorporate expert judgment on uncertainty quantification in the dose-response relationship. The mathematical technique of probabilistic inversion also plays a key role. We propose a coupled approach, whereby scientists quantify the dose-response uncertainty using techniques such as structured expert judgment with performance weights and probabilistic inversion, and stakeholders quantify associated loss rates.     

A Method for Estimating Lifetime Cancer Risks from Limited Epidemiologic Data

Partly because of the poor quality of exposure information on humans, most lifetime carcinogenic risk assessments have been based on animal data. There are, however, surrogate measures for exposure that have not been fully utilized. One of these is duration of exposure where data on mean exposure levels are available. A method is presented for the use of such data, and the method is illustrated by developing a risk assessment from the available epidemiologic literature on gasoline and kidney cancer. This risk assessment is fairly consistent across studies and close to a risk assessment based upon an experiment with rats. While there needs to be much improvement in the quality of environmental data available to epidemiologists, it is possible that a number of risk assessments can be made from existing epidemiologic data and efforts directed away from extrapolation from animal data.     

Assessing Cancer Risks from Short-Term Exposures in Children

For the vast majority of chemicals that have cancer potency estimates on IRIS, the underlying database is deficient with respect to early-life exposures. This data gap has prevented derivation of cancer potency factors that are relevant to this time period, and so assessments may not fully address children's risks. This article provides a review of juvenile animal bioassay data in comparison to adult animal data for a broad array of carcinogens. This comparison indicates that short-term exposures in early life are likely to yield a greater tumor response than short-term exposures in adults, but similar tumor response when compared to long-term exposures in adults. This evidence is brought into a risk assessment context by proposing an approach that: (1) does not prorate children's exposures over the entire life span or mix them with exposures that occur at other ages; (2) applies the cancer slope factor from adult animal or human epidemiology studies to the children's exposure dose to calculate the cancer risk associated with the early-life period; and (3) adds the cancer risk for young children to that for older children/adults to yield a total lifetime cancer risk. The proposed approach allows for the unique exposure and pharmacokinetic factors associated with young children to be fully weighted in the cancer risk assessment. It is very similar to the approach currently used by U.S. EPA for vinyl chloride. The current analysis finds that the database of early life and adult cancer bioassays supports extension of this approach from vinyl chloride to other carcinogens of diverse mode of action. This approach should be enhanced by early-life data specific to the particular carcinogen under analysis whenever possible.     

Dose-Response Models for Inhalation of Bacillus anthracis Spores: Interspecies Comparisons

Because experiments with Bacillus anthracis are costly and dangerous, the scientific, public health, and engineering communities are served by thorough collation and analysis of experiments reported in the open literature. This study identifies available dose-response data from the open literature for inhalation exposure to B. anthracis and, via dose-response modeling, characterizes the response of nonhuman animal models to challenges. Two studies involving four data sets amenable to dose-response modeling were found in the literature: two data sets of response of guinea pigs to intranasal dosing with the Vollum and ATCC-6605 strains, one set of responses of rhesus monkeys to aerosol exposure to the Vollum strain, and one data set of guinea pig response to aerosol exposure to the Vollum strain. None of the data sets exhibited overdispersion and all but one were best fit by an exponential dose-response model. The beta-Poisson dose-response model provided the best fit to the remaining data set. As indicated in prior studies, the response to aerosol challenges is a strong function of aerosol diameter. For guinea pigs, the LD₅₀ increases with aerosol size for aerosols at and above 4.5 μm. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD₅₀ when aerosol size is increased from 1 μm to 12 μm. Future experimental research and dose-response modeling should be performed to quantify differences in responses of subpopulations to B. anthracis and to generate data allowing development of interspecies correction factors.     

A Malformation Incidence Dose-Response Model Incorporating Fetal Weight and/or Litter Size as Covariates

A dose-response model is often fit to bioassay data to provide a mathematical relationship between the incidence of a developmental malformation and dose of a toxicant. To utilize the interrelations among the fetal weight, incidence of malformation and number of the live fetuses, a conditional Gaussian regression chain model is proposed to model the dose-response function for developmental malformation incidence using the litter size and/or the fetal weight as covariates. The litter size is modeled as a function of dose, the fetal weight is modeled as a function of dose conditional on the litter size, and the malformation incidence is modeled as a function of dose conditional on both the litter size and the fetal weight, which itself is also conditional on the litter size. Data from a developmental experiment conducted at the National Center for Toxicological Research to investigate the growth stunting and increased incidence of cleft palate induced by Dexamethasone (DEX) exposure in rats was used as an illustration.     

Properties of Model-Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation

Model averaging (MA) has been proposed as a method of accounting for model uncertainty in benchmark dose (BMD) estimation. The technique has been used to average BMD dose estimates derived from dichotomous dose-response experiments, microbial dose-response experiments, as well as observational epidemiological studies. While MA is a promising tool for the risk assessor, a previous study suggested that the simple strategy of averaging individual models' BMD lower limits did not yield interval estimators that met nominal coverage levels in certain situations, and this performance was very sensitive to the underlying model space chosen. We present a different, more computationally intensive, approach in which the BMD is estimated using the average dose-response model and the corresponding benchmark dose lower bound (BMDL) is computed by bootstrapping. This method is illustrated with TiO(2) dose-response rat lung cancer data, and then systematically studied through an extensive Monte Carlo simulation. The results of this study suggest that the MA-BMD, estimated using this technique, performs better, in terms of bias and coverage, than the previous MA methodology. Further, the MA-BMDL achieves nominal coverage in most cases, and is superior to picking the "best fitting model" when estimating the benchmark dose. Although these results show utility of MA for benchmark dose risk estimation, they continue to highlight the importance of choosing an adequate model space as well as proper model fit diagnostics.