Using the Biological Two-Stage Model to Assess Risk from Short-Term Exposures

Two assumptions used in risk assessment are investigated: (1) the assumption of fraction of lifetime dose rate assumes that the risk from a fractional lifetime exposure at a given dose rate is equal to the risk from full lifetime exposure at that same fraction of the given dose rate; (2) the assumption of fraction of lifetime risk assumes that the risk from a fractional lifetime exposure at a given dose rate is equal to that same fraction of the risk from full lifetime exposure at the same dose rate. These two assumptions are equivalent when risk is a linear function of dose. Thus both can be thought of as generalizations of the assumption that cancer risk is proportional to the total accumulated lifetime dose (or average daily dose), which is often made to assess the risk from short-term exposures. In this paper, the age-specific cumulative hazard functions are derived using the two-stage model developed by Moolgavkar, Venzon, and Knudson for situations when the exposure occurs during a single period or a single instant. The two assumptions described above are examined for three types of carcinogens, initiator, completer, and promoter, in the context of the model. For initiator and completer, these two assumptions are equivalent in the low-dose region; for a promoter, using the fraction of lifetime risk assumption is generally more conservative than that of the fraction of lifetime dose rate assumption. Tables are constructed to show that the use of either the fraction of lifetime dose rate assumption or the fraction lifetime risk assumption can both underestimate and overestimate the true risk for the three types of carcinogens.     

Steady-State Solutions to PBPK Models and Their Applications to Risk Assessment I: Route-to-Route Extrapolation of Volatile Chemicals

Although analysis of in vivo pharmacokinetic data necessitates use of time-dependent physiologically-based pharmacokinetic (PBPK) models, risk assessment applications are often driven primarily by steady-state and/or integrated (e.g., AUC) dosimetry. To that end, we present an analysis of steady-state solutions to a PBPK model for a generic volatile chemical metabolized in the liver. We derive an equivalent model that is much simpler and contains many fewer parameters than the full PBPK model. The state of the system can be specified by two state variables-the rate of metabolism and the rate of clearance by exhalation. For a given oral dose rate or inhalation exposure concentration, the system state only depends on the blood-air partition coefficient, metabolic constants, and the rates of blood flow to the liver and of alveolar ventilation. At exposures where metabolism is close to linear, only the effective first-order metabolic rate is needed. Furthermore, in this case, the relationship between cumulative exposure and average internal dose (e.g., AUCs) remains the same for time-varying exposures. We apply our analysis to oral-inhalation route extrapolation, showing that for any dose metric, route equivalence only depends on the parameters that determine the system state. Even if the appropriate dose metric is unknown, bounds can be placed on the route-to-route equivalence with very limited data. We illustrate this analysis by showing that it reproduces exactly the PBPK-model-based route-to-route extrapolation in EPA's 2000 risk assessment for vinyl chloride. Overall, we find that in many cases, steady-state solutions exactly reproduce or closely approximate the solutions using the full PBPK model, while being substantially more transparent. Subsequent work will examine the utility of steady-state solutions for analyzing cross-species extrapolation and intraspecies variability.     

Uncertainty and Variation in Indirect Exposure Assessments: An Analysis of Exposure to Tetrachlorodibenzo-p-Dioxin from a Beef Consumption Pathway

Indirect exposures to 2,3,7,8-tetrachlorodibenzo- p -dioxin (TCDD) and other toxic materials released in incinerator emissions have been identified as a significant concern for human health. As a result, regulatory agencies and researchers have developed specific approaches for evaluating exposures from indirect pathways. This paper presents a quantitative assessment of the effect of uncertainty and variation in exposure parameters on the resulting estimates of TCDD dose rates received by individuals indirectly exposed to incinerator emissions through the consumption of home-grown beef. The assessment uses a nested Monte Carlo model that separately characterizes uncertainty and variation in dose rate estimates. Uncertainty resulting from limited data on the fate and transport of TCDD are evaluated, and variations in estimated dose rates in the exposed population that result from location-specific parameters and individuals'behaviors are characterized. The analysis indicates that lifetime average daily dose rates for individuals living within 10 km of a hypothetical incinerator range over three orders of magnitude. In contrast, the uncertainty in the dose rate distribution appears to vary by less than one order of magnitude, based on the sources of uncertainty included in this analysis. Current guidance for predicting exposures from indirect exposure pathways was found to overestimate the intakes for typical and high-end individuals.     

Cancer Risk Assessment with Intermittent Exposure

Applications of methods for carcinogenic risk assessment often focus on estimating lifetime cancer risk. With intermittent or time-dependent exposures, lifetime risk is often approximated on the basis of a lifetime average daily dose (LADD). In this article, we show that there exists a lifetime equivalent constant dose (LECD) which leads to the same lifetime risk as the actual time-dependent exposure pattern. The ratio C = LECD/LADD then provides a measure of accuracy of risk estimates based on the LADD, as well as a basis for correcting such estimates. Theoretical results derived under the classical multistage model and the two-stage birth-death-mutation model suggest that the maximum value of C, which represents the factor by which the LADD may lead to underestimates of risk, will often lie in the range of 2- to 5-fold. The practical application of these results is illustrated in the case of astronauts subjected to relatively short-term exposure to volatile organics in a closed space station environment, and in the case of the ingestion of pesticide residues in food where consumption patterns vary with age.     

Human Interindividual Variability–A Major Source of Uncertainty in Assessing Risks for Noncancer Health Effects

For noncancer effects, the degree of human interindividual variability plays a central role in determining the risk that can be expected at low exposures. This discussion reviews available data on observations of interindividual variability in (a) breathing rates, based on observations in British coal miners; (b) systemic pharmacokinetic parameters, based on studies of a number of drugs; (c) susceptibility to neurological effects from fetal exposure to methyl mercury, based on observations of the incidence of effects in relation to hair mercury levels; and (d) chronic lung function changes in relation to long-term exposure to cigarette smoke. The quantitative ranges of predictions that follow from uncertainties in estimates of interindividual variability in susceptibility are illustrated.     

Hormesis Without Cell Killing

Stochastic two-stage clonal expansion (TSCE) models of carcinogenesis offer the following clear theoretical explanation for U-shaped cancer dose-response relations. Low doses that kill initiated (premalignant) cells thereby create a protective effect. At higher doses, this effect is overwhelmed by an increase in the net number of initiated cells. The sum of these two effects, from cell killing and cell proliferation, gives a U-shaped or J-shaped dose-response relation. This article shows that exposures that do not kill, repair, or decrease cell populations, but that only hasten transitions that lead to cancer, can also generate U-shaped and J-shaped dose-response relations in a competing-risk (modified TSCE) framework where exposures disproportionately hasten transitions into carcinogenic pathways with relatively long times to tumor. Quantitative modeling of the competing effects of more transitions toward carcinogenesis (risk increasing) and a higher proportion of transitions into the slower pathway (risk reducing) shows that a J-shaped dose-response relation can occur even if exposure increases the number of initiated cells at every positive dose level. This suggests a possible new explanation for hormetic dose-response relations in response to carcinogenic exposures that do not have protective (cell-killing) effects. In addition, the examples presented emphasize the role of time in hormesis: exposures that monotonically increase risks at younger ages may nonetheless produce a U-shaped or J-shaped dose-response relation for lifetime risk of cancer.     

Expert Scientific Judgment and Cancer Risk Assessment: A Pilot Study of Pharmacokinetic Data

When high-dose tumor data are extrapolated to low doses, it is typically assumed that the dose of a carcinogen delivered to target cells is proportional to the dose administered to test animals, even at exposure levels below the experimental range. Since pharmacokinetic data are becoming available that in some cases question the validity of this assumption, risk assessors must decide whether to maintain the standard assumption. A pilot study of formaldehyde is reported that was undertaken to demonstrate how expert scientific judgment can help guide a controversial risk assessment where pharmacokinetic data are considered inconclusive. Eight experts on pharmacokinetic data were selected by a formal procedure, and each was interviewed personally using a structured interview protocol. The results suggest that expert scientific opinion is polarized in this case, a situation that risk assessors can respond to with a range of risk characterizations considered biologically plausible by the experts. Convergence of expert opinion is likely in this case of several specific research strategies ar executed in a competent fashion. Elicitation of expert scientific judgment is a promising vehicle for evaluating the quality of pharmacokinetic data, expressing uncertainty in risk assessment, and fashioning a research agenda that offers possible forging of scientific consensus.     

Uncertainties in the CIIT Model for Formaldehyde-Induced Carcinogenicity in the Rat: A Limited Sensitivity Analysis–I

Scientists at the CIIT Centers for Health Research (Conolly et al., 2000, 2003; Kimbell et al., 2001a, 2001b) developed a two-stage clonal expansion model of formaldehyde-induced nasal cancers in the F344 rat that made extensive use of mechanistic information. An inference of their modeling approach was that formaldehyde-induced tumorigenicity could be optimally explained without the role of formaldehyde's mutagenic action. In this article, we examine the strength of this result and modify select features to examine the sensitivity of the predicted dose response to select assumptions. We implement solutions to the two-stage cancer model that are valid for nonhomogeneous models (i.e., models with time-dependent parameters), thus accounting for time dependence in variables. In this reimplementation, we examine the sensitivity of model predictions to pooling historical and concurrent control data, and to lumping sacrificed animals in which tumors were discovered incidentally with those in which death was caused by the tumors. We found the CIIT model results were not significantly altered with the nonhomogeneous solutions. Dose-response predictions below the range of exposures where tumors occurred in the bioassays were highly sensitive to the choice of control data. In the range of exposures where tumors were observed, the model attributed up to 74% of the added tumor probability to formaldehyde's mutagenic action when our reanalysis restricted the use of the National Toxicology Program (NTP) historical control data to only those obtained from inhalation exposures. Model results were insensitive to hourly or daily temporal variations in DNA protein cross-link (DPX) concentration, a surrogate for the dose-metric linked to formaldehyde-induced mutations, prompting us to utilize weekly averages for this quantity. Various other biological and mathematical uncertainties in the model have been retained unmodified in this analysis. These include model specification of initiated cell division and death rates, and uncertainty and variability in the dose response for cell replication rates, issues that will be considered in a future paper.     

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.     

One-Hit Models of Carcinogenesis: Conservative or Not?

One-hit formulas are widely believed to be "conservative" when used to analyze carcinogenesis bioassays, in the sense that they will rarely underestimate risks of cancer at low exposures. Such formulas are generally applied to the lifetime incidence of cancer at a specific site, with risks estimated from animal data at zero dose (control), and two or more additional doses that are appreciable fractions of a maximum tolerated dose. No empirical study has demonstrated that the one-hit formula is conservative in the sense described. The Carcinogenesis Bioassay Database System contains data on 1212 separate bioassays of 308 chemical substances tested at exactly three evaluable doses. These provided sufficient data to examine 8432 specific combinations of cancer site with sex, species, and chemical. For each of these we fitted a one-hit formula to the zero and maximum dose data points, then examined the relation of the fitted curve to the incidence rate observed at the mid-dose, with and without adjustment for intercurrent mortality. Both underestimates and overestimates of risk at mid-dose occurred substantially more often than expected by chance. We cannot tell whether such underestimates would occur at lower doses, but offer six biological reasons why underestimates might be expected. In a high percentage of animal bioassays, the one-hit formula is not conservative when applied in the usual way to animal data. It remains possible that the one-hit formula may indeed be conservative at sufficiently low doses (below the observational range), but the usual procedure, applied to the usual dose range, can be nonconservative in estimating the slope of the formula at such low doses. Risk assessments for regulation of carcinogens should incorporate some measure of additional uncertainty.     

A Biologically-Based Dose—Response Model for Developmental Toxicology

The methods currently used to evaluate the risk of developmental defects in humans from exposure to potential toxic agents do not reflect biological processes in extrapolating estimated risks to low doses and from test species to humans. We develop a mathematical model to describe aspects of the dynamic process of organogenesis, based on branching process models of cell kinetics. The biological information that can be incorporated into the model includes timing and rates of dynamic cell processes such as differentiation, migration, growth, and replication. The dose-response models produced can explain patterns of malformation rates as a function of both dose and time of exposure, resulting in improvements in risk assessment and understanding of the underlying mechanistic processes. To illustrate the use of the model, we apply it to the prediction of the effects of methylmercury on brain development in rats.     

A Distributed Parameter Physiologically-Based Pharmacokinetic Model for Dermal and Inhalation Exposure to Volatile Organic Compounds

Estimates of dermal dose from exposures to toxic chemicals are typically derived using models that assume instantaneous establishment of steady-state dermal mass flux. However, dermal absorption theory indicates that this assumption is invalid for short-term exposures to volatile organic chemicals (VOCs). A generalized distributed parameter physiologically-based pharmacokinetic model (DP-PBPK), which describes unsteady state dermal mass flux via a partial differential equation (Fickian diffusion), has been developed for inhalation and dermal absorption of VOCs. In the present study, the DP-PBPK model has been parameterized for chloroform, and compared with two simpler PBPK models of chloroform. The latter are lumped parameter models, employing ordinary differential equations, that do not account for the dermal absorption time lag associated with the accumulation of permeant chemical in tissue represented by permeability coefficients. All three models were evaluated by comparing simulated post-exposure exhaled breath concentration profiles with measured concentrations following environmental chloroform exposures. The DP-PBPK model predicted a time-lag in the exhaled breath concentration profile, consistent with the experimental data. The DP-PBPK model also predicted significant volatilization of chloroform, for a simulated dermal exposure scenario. The end-exposure dermal dose predicted by the DP-PBPK model is similar to that predicted by the EPA recommended method for short-term exposures, and is significantly greater than the end-exposure dose predicted by the lumped parameter models. However, the net dermal dose predicted by the DP-PBPK model is substantially less than that predicted by the EPA method, due to the post-exposure volatilization predicted by the DP-PBPK model. Moreover, the net dermal dose of chloroform predicted by all three models was nearly the same, even though the lumped parameter models did not predict substantial volatilization.     

A Physiologically-Based Pharmacokinetic Model Assessment of Methyl t-Butyl Ether in Groundwater for a Bathing and Showering Determination

Methyl t -butyl ether (MTBE) is a gasoline additive that has appeared in private wells as a result of leaking underground storage tanks. Neurological symptoms (headache, dizziness) have been reported from household use of MTBE-affected water, consistent with animal studies showing acute CNS depression from MTBE exposure. The current research evaluates acute CNS effects during bathing/showering by application of physiologically-based pharmacokinetic (PBPK) techniques to compare internal doses in animal toxicity studies to human exposure scenarios. An additional reference point was the delivered dose associated with the acute Minimum Risk Level (MRL) for MTBE established by the Agency for Toxic Substances and Disease Registry. A PBPK model for MTBE and its principal metabolite, t -butyl alcohol (TBA) was developed and validated against published data in rats and humans. PBPK analysis of animal studies showed that acute CNS toxicity after MTBE exposure can be attributed principally to the parent compound since the metabolite (TBA) internal dose was below that needed for CNS effects. The PBPK model was combined with an exposure model for bathing and showering which integrates inhalation and dermal exposures. This modeling indicated that bathing or showering in water containing MTBE at 1 mg/L would produce brain concentrations ˜1000-fold below the animal effects level and twofold below brain concentrations associated with the acute MRL. These findings indicate that MTBE water concentrations of 1 mg/L or below are unlikely to trigger acute CNS effects during bathing and showering. However, MTBE's strong odor may be a secondary but deciding factor regarding the suitability of such water for domestic uses.     

Point Estimates of Cancer Risk at Low Doses

There has been considerable discussion regarding the conservativeness of low-dose cancer risk estimates based upon linear extrapolation from upper confidence limits. Various groups have expressed a need for best (point) estimates of cancer risk in order to improve risk/benefit decisions. Point estimates of carcinogenic potency obtained from maximum likelihood estimates of low-dose slope may be highly unstable, being sensitive both to the choice of the dose–response model and possibly to minimal perturbations of the data. For carcinogens that augment background carcinogenic processes and/or for mutagenic carcinogens, at low doses the tumor incidence versus target tissue dose is expected to be linear. Pharmacokinetic data may be needed to identify and adjust for exposure-dose nonlinearities. Based on the assumption that the dose response is linear over low doses, a stable point estimate for low-dose cancer risk is proposed. Since various models give similar estimates of risk down to levels of 1%, a stable estimate of the low-dose cancer slope is provided by ŝ = 0.01/ED01, where ED01 is the dose corresponding to an excess cancer risk of 1%. Thus, low-dose estimates of cancer risk are obtained by, risk = ŝ × dose. The proposed procedure is similar to one which has been utilized in the past by the Center for Food Safety and Applied Nutrition, Food and Drug Administration. The upper confidence limit, s , corresponding to this point estimate of low-dose slope is similar to the upper limit, q ₁ obtained from the generalized multistage model. The advantage of the proposed procedure is that ŝ provides stable estimates of low-dose carcinogenic potency, which are not unduly influenced by small perturbations of the tumor incidence rates, unlike ₁.     

Methodology for Determining the Appropriateness of a Linear Dose‐Response Function

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose‐response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose‐response functions are approximately linear when the dose is low. Nevertheless, what constitutes “low” is dependent on the parameters of the dose‐response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose‐response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose‐response approximation, for example, the expected value for exposure doses is two to three logs₁₀ smaller than the upper bound of the linear portion of the dose‐response function, then predicting the risk‐reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.     

Pricing of Full‐Service Repair Contracts with Learning,Optimized Maintenance,and Information Asymmetry

This article considers the optimal pricing of full‐service (FS) repair contracts by taking into account learning and maintenance efficiency effects, competition from service , and asymmetric information. We analyze on‐call service (OS) and FS contracts in a market where customers exhibit heterogeneous risk aversion. While the customers minimize their disutility over the equipment lifetime, the service provider maximizes expected profits arising from the portfolio of OS and FS contracts. We show that the optimal FS price depends inter alia on the customer's prior cost experience and on OS repair and maintenance costs. The optimal FS price is shown to increase as fewer OS customers are lost to competition, whereas improved repair learning enabled by FS reduces the optimal price. A numerical study based on data from a manufacturer of forklifts highlights the importance of learning in maintenance operations, which constitutes the key benefit of FS contracts; 81% of the customers select the FS option and are willing to pay an insurance premium of around 1.5% of total OS cost against volatility of repair costs.     

Bayesian Estimation of Pharmacokinetic and Pharmacodynamic Parameters in a Mode-of-Action-Based Cancer Risk Assessment for Chloroform

Chloroform is a carcinogen in rodents and its carcinogenicity is secondary to events associated with cytotoxicity and regenerative cell proliferation. In this study, a physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) model that links the processes of chloroform metabolism, reparable cell damage, cell death, and regenerative cellular proliferation was developed to support a new cancer dose-response assessment for chloroform. Model parameters were estimated using Markov Chain Monte Carlo (MCMC) analysis in a two-step approach: (1) metabolism parameters for male and female mice and rats were estimated against available closed chamber gas uptake data; and (2) PD parameters for each of the four rodent groups were estimated from hepatic and renal labeling index data following inhalation exposures. Subsequently, the resulting rodent PD parameters together with literature values for human age-dependent physiological and metabolism parameters were used to scale up the rodent model to a human model. The human model was used to predict exposure conditions under which chloroform-mediated cytolethality is expected to occur in liver and kidney of adults and children. Using the human model, inhalation Reference Concentrations (RfCs) and oral Reference Doses (RfDs) were derived using an uncertainty factor of 10. Based on liver and kidney dose metrics, the respective RfCs were 0.9 and 0.09 ppm; and the respective RfDs were 0.4 and 3 mg/kg/day.