On the Correlation Coefficient Between the TD50 and the MTD

The existence of correlation between the carcinogenic potency and the maximum tolerated dose has been the subject of many investigations in recent years. Several attempts have been made to quantify this correlation in different bioassay experiments. By using some distributional assumptions, Krewski et al .⁽¹⁾ derive an analytic expression for the coefficient of correlation between the carcinogenic potency TD₅₀ and the maximum tolerated dose. Here, we discuss the deviation that may result in using their analytical expression. By taking a more general approach we derive an expression for the correlation coefficient which includes the result of Krewski et al .⁽¹⁾ as a special case, and show that their expression may overestimate the correlation in some instances and yet underestimate the correlation in other instances. The proposed method is illustrated by application to a real dataset.     

An Overview of the Report: Correlation Between Carcinogenic Potency and the Maximum Tolerated Dose: Implications for Risk Assessment

Current practice in carcinogen bioassay calls for exposure of experimental animals at doses up to and including the maximum tolerated dose (MTD). Such studies have been used to compute measures of carcinogenic potency such as the TD₅₀ as well as unit risk factors such as q ₁ * for predicting low-dose risks. Recent studies have indicated that these measures of carcinogenic potency are highly correlated with the MTD. Carcinogenic potency has also been shown to be correlated with indicators of mutagenicity and toxicity. Correlation of the MTDs for rats and mice implies a corresponding correlation in TD₅₀ values for these two species. The implications of these results for cancer risk assessment are examined in light of the large variation in potency among chemicals known to induce tumors in rodents.     

On the Effect of Probability Distributions of Input Variables in Public Health Risk Assessment

A central part of probabilistic public health risk assessment is the selection of probability distributions for the uncertain input variables. In this paper, we apply the first-order reliability method (FORM)^(1–3) as a probabilistic tool to assess the effect of probability distributions of the input random variables on the probability that risk exceeds a threshold level (termed the probability of failure) and on the relevant probabilistic sensitivities. The analysis was applied to a case study given by Thompson et al. ⁽⁴⁾ on cancer risk caused by the ingestion of benzene contaminated soil. Normal, lognormal, and uniform distributions were used in the analysis. The results show that the selection of a probability distribution function for the uncertain variables in this case study had a moderate impact on the probability that values would fall above a given threshold risk when the threshold risk is at the 50th percentile of the original distribution given by Thompson et al. ⁽⁴⁾ The impact was much greater when the threshold risk level was at the 95th percentile. The impact on uncertainty sensitivity, however, showed a reversed trend, where the impact was more appreciable for the 50th percentile of the original distribution of risk given by Thompson et al. ⁴ than for the 95th percentile. Nevertheless, the choice of distribution shape did not alter the order of probabilistic sensitivity of the basic uncertain variables.     

Physiologically-Based Pharmacokinetic Model for Trichloroethylene Considering Enterohepatic Recirculation of Major Metabolites

Trichloroacetic acid (TCA) is major metabolite of trichloroethylene (TRI) thought to contribute to its hepatocarcinogenic effects in mice. Recent studies have shown that peak blood concentrations of TCA in rats do not occur until approximately 12 hours following an oral dose of TRI. However, blood concentrations of TRI reach maximum within an hour and are nondetectable after 2 hours.⁽¹⁾ The results of study which examined the enterohepatic recirculation (EHC) of the principle TRI metabolited⁽²⁾ was used to develop physiologically-based pharmacokinetic model for TRI, which includes enterohepatic recirculation of its metabolites. The model quantitatively predicts the uptake, distribution and elimination of TRI, trichloroethanol, trichloroethanol-glucuronide, and TCA and includes production of metabolites through the enterohepatic recirculation pathway. Physiologic parameters used in the model were obtained from the literature.^(3.4) Parameters for TRI metabolism were taken from Fisher et al.⁽⁵⁾ Other kinetic parameters were found in the literature or estimated from experimental data.⁽²⁾ The model was calibrated to data from experiments of an earlier study where TRI was orally administered⁽²⁾ Verification of the model was conducted using data on the enterohepatic recirculation of TCEOH and TCA⁽²⁾ chloral hydrate data (infusion doses) from Merdink,⁽¹⁾ and TRI data from Templin(l) and Larson and Bull.⁽¹⁾     

What Do We Know About Making Risk Comparisons?

The risks of unfamiliar technologies are often evaluated by comparing them with the risks of more familiar ones. Such risk comparisons have been criticized for neglecting critical dimensions of risky decisions. In a guide written for the Chemical Manufacturers Association, Covello et al. (¹) have summarized these critiques and developed a taxonomy that characterizes possible risk comparisons in terms of their acceptability (or objectionableness). We asked four diverse groups of subjects to judge the acceptability of 14 statements produced by Covello et al. as examples of their categories. We found no correlation between the judgments of acceptability produced by our subjects and those predicted by Covello et al. .     

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.     

The BSE Risk of Processing Meat and Bone Meal in Nonruminant Feed: A Quantitative Assessment for the Netherlands

The total ban on use of meat and bone meal (MBM) in livestock feed has been very successful in reducing bovine spongiform encephalopathy (BSE) spread, but also implies a waste of high-quality proteins resulting in economic and ecological loss. Now that the BSE epidemic is fading out, a partial lifting of the MBM ban might be considered. The objective of this study was to assess the BSE risk for the Netherlands if MBM derived from animals fit for human consumption, i.e., category 3 MBM, would be used in nonruminant feed. A stochastic simulation model was constructed that calculates (1) the probability that infectivity of undetected BSE-infected cows ends up with calves and (2) the quantity of infectivity ( Q_inf ) consumed by calves in case of such an incident. Three pathways were considered via which infectivity can reach cattle: (1) cross-contamination in the feed mill, (2) cross-contamination on the primary farm, and (3) pasture contamination. Model calculations indicate that the overall probability that infectivity ends up with calves is 3.2%. In most such incidents the Q_inf is extremely small (median = 6.5 × 10⁻¹² ID₅₀; mean = 1.8 × 10⁻⁴ ID₅₀), corresponding to an average probability of 1.3 × 10⁻⁴ that an incident results in ≥1 new BSE infections. Cross-contamination in the feed mill is the most risky pathway. Combining model results with Dutch BSE prevalence estimates for the coming years, it can be concluded that the BSE risk of using category 3 MBM derived from Dutch cattle in nonruminant feed is very low.     

The Possibility for "Natural" Generation of Chlorinated Organic Compounds

There is continuing concern for the exposure of persons to various chlorinated organics via the environment, for example, chlorinated disinfection byproducts in drinking water.⁽¹⁾ Some of these may be carcinogenic,⁽²⁾ although the evidence is far from strong.⁽³⁾ There is an accumulating body of evidence that one of the normal human immunological responses to foreign agents is the generation of hypochlorous acid. This evidence will be summarized. The possibility that this HOCl generated in vivo could result in the formation of organo-chlorine compounds does not appear to have been seriously considered. Based on best available information, the amount of such byproduct formation will be estimated.     

Reanalysis of Dose-Response Data from the Iraqi Methylmercury Poisoning Episode

Applying a hockey stick parametric dose-response model to data on late or retarded development in Iraqi children exposed in utero to methylmercury, with mercury (Hg) exposure characterized by the peak Hg concentration in mothers'hair during pregnancy, Cox et al. calculated the "best statistical estimate" of the threshold for health effects as 10 ppm Hg in hair with a 95% range of uncertainty of between 0 and 13.6 ppm.⁽¹⁾A new application of the hockey stick model to the Iraqi data shows, however, that the statistical upper limit of the threshold based on the hockey stick model could be as high as 255 ppm. Furthermore, the maximum likelihood estimate of the threshold using a different parametric model is virtually zero. These and other analyses demonstrate that threshold estimates based on parametric models exhibit high statistical variability and model dependency, and are highly sensitive to the precise definition of an abnormal response. Consequently, they are not a reliable basis for setting a reference dose (RfD) for methylmercury. Benchmark analyses and statistical analyses useful for deriving NOAELs are also presented. We believe these latter analyses—particularly the benchmark analyses—generally form a sounder basis for determining RfDs than the type of hockey stick analysis presented by Cox et al. However, the acute nature of the exposures, as well as other limitations in the Iraqi data suggest that other data may be more appropriate for determining acceptable human exposures to methylmercury.     

Cross-Cultural Differences in Risk Perception: A Model-Based Approach

The present study assessed cross-cultural differences in the perception of financial risks. Students at large universities in Hong Kong, Taiwan, the Netherlands, and the U.S., as well as a group of Taiwanese security analysts rated the riskiness of a set of monetary lotteries. Risk judgments differed with nationality, but not with occupation (students vs. security analysts) and were modeled by the Conjoint Expected Risk (CER) model.⁽¹⁾ Consistent with cultural differences in country uncertainty avoidance,⁽²⁾ CER model parameters of respondents from the two Western countries differed from those of respondents from the two countries with Chinese cultural roots: The risk judgments of respondents from Hong Kong and Taiwan were more sensitive to the magnitude of potential losses and less mitigated by the probability of positive outcomes.     

Characterizing Dose-Response I: Critical Assessment of the Benchmark Dose Concept

We present a critical assessment of the benchmark dose (BMD) method introduced by Crump⁽¹⁾ as an alternative method for setting a characteristic dose level for toxicant risk assessment. The no-observed-adverse-effect-level (NOAEL) method has been criticized because it does not use all of the data and because the characteristic dose level obtained depends on the dose levels and the statistical precision (sample sizes) of the study design. Defining the BMD in terms of a confidence bound on a point estimate results in a characteristic dose that also varies with the statistical precision and still depends on the study dose levels.⁽²⁾ Indiscriminate choice of benchmark response level may result in a BMD that reflects little about the dose-response behavior available from using all of the data. Another concern is that the definition of the BMD for the quantal response case is different for the continuous response case. Specifically, defining the BMD for continuous data using a ratio of increased effect divided by the background response results in an arbitrary dependence on the natural background for the endpoint being studied, making comparison among endpoints less meaningful and standards more arbitrary. We define a modified benchmark dose as a point estimate using the ratio of increased effect divided by the full adverse response range which enables consistent placement of the benchmark response level and provides a BMD with a more consistent relationship to the dose-response curve shape.     

Nonstop Flying Is Safer Than Driving

The relative safety of driving and flying is important in many situations that involve selecting a mode of transportation. The traditional view, that flying via scheduled airlines is safer than driving, has recently been challenged by Evans et al. ⁽¹⁾ They concluded that for a low-risk driver it is safer to drive on rural interstate highways (the safest roads) than to fly if the trip length is less than 602 miles. We reestimated the fatality probabilities for flying by taking into account that the risk of flying is dependent on the number of nonstop segments flown, but, for all practical purposes, is independent of the length of the trip. Our calculations indicate that, for average or high-risk drivers, it is always safer to fly than to drive. Furthermore, even for a low-risk driver, nonstop flying is safer than driving on rural interstate highways for a trip distance of more than 303 miles; the corresponding breakeven distances for flights that involve two and three segments are 606 and 909 miles, respectively.     

A Method for Computing the Fraction of Attributable Risk Related to Climate Damages

The recent decision of the U.S. Supreme Court on the regulation of CO₂ emissions from new motor vehicles^{( 1 )} shows the need for a robust methodology to evaluate the fraction of attributable risk from such emissions. The methodology must enable decisionmakers to reach practically relevant conclusions on the basis of expert assessments the decisionmakers see as an expression of research in progress, rather than as knowledge consolidated beyond any reasonable doubt.^{( 2,3,4 )} This article presents such a methodology and demonstrates its use for the Alpine heat wave of 2003. In a Bayesian setting, different expert assessments on temperature trends and volatility can be formalized as probability distributions, with initial weights (priors) attached to them. By Bayesian learning, these weights can be adjusted in the light of data. The fraction of heat wave risk attributable to anthropogenic climate change can then be computed from the posterior distribution. We show that very different priors consistently lead to the result that anthropogenic climate change has contributed more than 90% to the probability of the Alpine summer heat wave in 2003. The present method can be extended to a wide range of applications where conclusions must be drawn from divergent assessments under uncertainty.     

Source Attribution of Food-Borne Zoonoses in New Zealand: A Modified Hald Model

A Bayesian approach was developed by Hald et al .^{( 1 )} to estimate the contribution of different food sources to the burden of human salmonellosis in Denmark. This article describes the development of several modifications that can be used to adapt the model to different countries and pathogens. Our modified Hald model has several advantages over the original approach, which include the introduction of uncertainty in the estimates of source prevalence and an improved strategy for identifiability. We have applied our modified model to the two major food-borne zoonoses in New Zealand, namely, campylobacteriosis and salmonellosis. Major challenges were the data quality for salmonellosis and the inclusion of environmental sources of campylobacteriosis. We conclude that by modifying the Hald model we have improved its identifiability, made it more applicable to countries with less intensive surveillance, and feasible for other pathogens, in particular with respect to the inclusion of nonfood sources. The wider application and better understanding of this approach is of particular importance due to the value of the model for decision making and risk management.     

First-Order Reliability Analysis of Public Health Risk Assessment

This paper demonstrates a new methodology for probabilistic public health risk assessment using the first-order reliability method. The method provides the probability that incremental lifetime cancer risk exceeds a threshold level, and the probabilistic sensitivity quantifying the relative impact of considering the uncertainty of each random variable on the exceedance probability. The approach is applied to a case study given by Thompson et al. ⁽¹⁾ on cancer risk caused by ingestion of benzene-contaminated soil, and the results are compared to that of the Monte Carlo method. Parametric sensitivity analyses are conducted to assess the sensitivity of the probabilistic event with respect to the distribution parameters of the basic random variables, such as the mean and standard deviation. The technique is a novel approach to probabilistic risk assessment, and can be used in situations when Monte Carlo analysis is computationally expensive, such as when the simulated risk is at the tail of the risk probability distribution.     

Risk Assessment for Aflatoxin: An Evaluation Based on the Multistage Model

Lifetime cancer potency of alfatoxin was assessed based on the Yeh et al. study from China in which both aflatoxin exposure and hepatitis B prevalence were measured. This study provides the best available information for estimating the carcinogenic risk posed by aflatoxin to the U.S. population. Cancer potency of aflatoxin was estimated using a biologically motivated risk assessment model. The best estimate of aflatoxin potency was 9 (mg/kg/day)⁻¹ for individuals negative for hepatitis B and 230 (mg/kg/day)⁻¹ for individuals positive for hepatitis B.     

A Physiologically Based Model for Gastrointestinal Absorption and Excretion of Chemicals Carried by Lipids

Pharmacokinetic models which incorporate independently measured anatomical characteristics and physiological flows have been widely used to predict the pharmacokinetic behavior of drugs, anesthetics, and other chemicals. Models appearing in the literature have included as many as 18,⁽¹⁾ or as few as 5 tissue compartments.⁽²⁾ With the exception of the multiple-compartment delay trains used by Bischoff⁽³⁾ to model the delays inherent to the appearance of drug metabolites in bile and segments of the intestinal lumen, very little effort has been made to incorporate the available information on gastrointestinal anatomy and physiology into more accurate gastrointestinal absorption/enterohepatic recirculation submodels. Since several authors have shown that the lymphatic system is the most significant route of absorption for highly lipophilic chemicals, we have constructed a model of gastrointestinal absorption that emphasizes chylomicron production and transport as the most significant route of absorption for nonvolatile, lipophilic chemicals. The absorption and distribution of hexachlorobenzene after intravenous vs. oral dosing are used to demonstrate features of this model.     

Bounding Estimates for Critical Events When Directly Disposing Highly Enriched Spent Nuclear Fuel in Unsaturated Tuff

This paper examines the possibility of criticality in a nuclear waste repository. The estimated probabilities are rough bounds and do not entirely dismiss the possibility of a critical condition; however, they do point to the difficulty of creating conditions under which a critical mass could be assembled (i.e., corrosion of containers, separation of neutron absorbers from the fissile material, and collapse or precipitation of the fissile material). In addition, should a criticality occur in or near a container, the bounding consequence calculations showed that fissions from one critical event are quite small (<˜10²⁰ fissions, if similar to aqueous and metal accidents and experiments). Furthermore, a reasonable upper bound of total critical events of 10²⁸ fissions corresponds to only 0.1% of the number of fissions represented by the spent nuclear fuel inventory in a repository containing 70,000 metric tons of heavy metal (MTHM) (the expected size for the proposed repository at Yucca Mountain, Nevada).     

Calculation of Benchmark Doses from Continuous Data

A benchmark dose (BMD) is the dose of a substance that corresponds to a prescribed increase in the response (called the benchmark response or BMR) of a health effect. A statistical lower bound on the benchmark dose (BMDL) has been proposed as a replacement for the no-observed-adverse-effect-level (NOAEL) in setting acceptable human exposure levels. A method is developed in this paper for calculating BMDs and BMDLs from continuous data in a manner that is consistent with those calculated from quantal data. The method involves defining an abnormal response, either directly by specifying a cutoff x₀ that separates continuous responses into normal and abnormal categories, or indirectly by specifying the proportion P₀ of abnormal responses expected among unexposed subjects. The method does not involve actually dichotomizing individual continuous responses into quantal responses, and in certain cases can be applied to continuous data in summarized form (e.g., means and standard deviations of continuous responses among subjects in discrete dose groups). In addition to specifying the BMR and either x₀ or P₀ , the method requires specification of the distribution of continuous responses, including specification of the dose-response θ(d) for a measure of central tendency. A method is illustrated for selecting θ(d) to make the probability of an abnormal response any desired dose-response function. This enables the same dose-response model (Weibull, log-logistic, etc.) to be used for the probability of an abnormal response, regardless of whether the underlying data are continuous or quantal. Whenever the continuous responses are normally distributed with standard deviation σ (independent of dose), the method is equivalent to defining the BMD as the dose corresponding to a prescribed change in the mean response relative to σ.     

Comparing Toxicologic and Epidemiologic Studies: Methylene Chloride-A Case Study

Exposure to methylene chloride induces lung and liver cancers in mice. The mouse bioassay data have been used as the basis for several cancer risk assessments. ^(1,2) The results from epidemiologic studies of workers exposed to methylene chloride have been mixed with respect to demonstrating an increased cancer risk. The results from a negative epidemiologic study of Kodak workers have been used by two groups of investigators to test the predictions from the EPA risk assessment models.^(3,4) These two groups used very different approaches to this problem, which resulted in opposite conclusions regarding the consistency between the animal model predictions and the Kodak study results. The results from the Kodak study are used to test the predictions from OSHA's multistage models of liver and lung cancer risk. Confidence intervals for the standardized mortality ratios (SMRs) from the Kodak study are compared with the predicted confidence intervals derived from OSHA's risk assessment models. Adjustments for the "healthy worker effect," differences in length of follow-up, and dosimetry between animals and humans were incorporated into these comparisons. Based on these comparisons, we conclude that the negative results from the Kodak study are not inconsistent with the predictions from OSHA's risk assessment model.