Modeling for Risk Assessment of Neurotoxic Effects

The regulation of noncancer toxicants, including neurotoxicants, has usually been based upon a reference dose (allowable daily intake). A reference dose is obtained by dividing a no-observed-effect level by uncertainty (safety) factors to account for intraspecies and interspecies sensitivities to a chemical. It is assumed that the risk at the reference dose is negligible, but no attempt generally is made to estimate the risk at the reference dose. A procedure is outlined that provides estimates of risk as a function of dose. The first step is to establish a mathematical relationship between a biological effect and the dose of a chemical. Knowledge of biological mechanisms and/or pharmacokinetics can assist in the choice of plausible mathematical models. The mathematical model provides estimates of average responses as a function of dose. Secondly, estimates of risk require selection of a distribution of individual responses about the average response given by the mathematical model. In the case of a normal or lognormal distribution, only an estimate of the standard deviation is needed. The third step is to define an adverse level for a response so that the probability (risk) of exceeding that level can be estimated as a function of dose. Because a firm response level often cannot be established at which adverse biological effects occur, it may be necessary to at least establish an abnormal response level that only a small proportion of individuals would exceed in an unexposed group. That is, if a normal range of responses can be established, then the probability (risk) of abnormal responses can be estimated. In order to illustrate this process, measures of the neurotransmitter serotonin and its metabolite 5-hydroxyindoleacetic acid in specific areas of the brain of rats and monkeys are analyzed after exposure to the neurotoxicant methylene-dioxymethamphetamine. These risk estimates are compared with risk estimates from the quantal approach in which animals are classified as either abnormal or not depending upon abnormal serotonin levels.     

Influence of Distribution of Animals between Dose Groups on Estimated Benchmark Dose and Animal Welfare for Continuous Effects

The benchmark dose (BMD) approach is increasingly used as a preferred approach for dose–effect analysis, but standard experimental designs are generally not optimized for BMD analysis. The aim of this study was to evaluate how the use of unequally sized dose groups affects the quality of BMD estimates in toxicity testing, with special consideration of the total burden of animal distress. We generated continuous dose–effect data by Monte Carlo simulation using two dose–effect curves based on endpoints with different shape parameters. Eighty‐five designs, each with four dose groups of unequal size, were examined in scenarios ranging from low‐ to high‐dose placements and with a total number of animals set to 40, 80, or 200. For each simulation, a BMD value was estimated and compared with the “true” BMD. In general, redistribution of animals from higher to lower dose groups resulted in an improved precision of the calculated BMD value as long as dose placements were high enough to detect a significant trend in the dose–effect data with sufficient power. The improved BMD precision and the associated reduction of the number of animals exposed to the highest dose, where chemically induced distress is most likely to occur, are favorable for the reduction and refinement principles. The result thereby strengthen BMD‐aligned design of experiments as a means for more accurate hazard characterization along with animal welfare improvements.     

Optimal Designs for Estimating the Effective Dose in Developmental Toxicity Experiments

Recent advances in risk assessment have led to the development of joint dose-response models to describe prenatal death and fetal malformation rates in developmental toxicity experiments. These models can be used to estimate the effective dose corresponding to a 5% excess risk for both these toxicological endpoints, as well as for overall toxicity. In this article, we develop optimal experimental designs for the estimation of the effective dose for developmental toxicity using joint Weibull dose-response models for prenatal death and fetal malformation. Based on an extended series of developmental studies, near-optimal designs for prenatal death, malformation, and overall toxicity were found to involve three dose groups: an unexposed control group, a high dose equal to the maximum tolerated dose, and a low dose above or comparable to the effective dose. The effect on the optimal designs of changing the number of implants and the degree of intra-litter correlation is also investigated. Although the optimal design has only three dose groups in most cases, practical considerations involving model lack of fit and estimation of the shape of the dose-response curve suggest that, in practice, suboptimal designs with more than three doses will often be preferred.     

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.     

Impact of Acquired Immunity and Dose‐Dependent Probability of Illness on Quantitative Microbial Risk Assessment

Dose‐response models in microbial risk assessment consider two steps in the process ultimately leading to illness: from exposure to (asymptomatic) infection, and from infection to (symptomatic) illness. Most data and theoretical approaches are available for the exposure‐infection step; the infection‐illness step has received less attention. Furthermore, current microbial risk assessment models do not account for acquired immunity. These limitations may lead to biased risk estimates. We consider effects of both dose dependency of the conditional probability of illness given infection, and acquired immunity to risk estimates, and demonstrate their effects in a case study on exposure to Campylobacter jejuni. To account for acquired immunity in risk estimates, an inflation factor is proposed. The inflation factor depends on the relative rates of loss of protection over exposure. The conditional probability of illness given infection is based on a previously published model, accounting for the within‐host dynamics of illness. We find that at low (average) doses, the infection‐illness model has the greatest impact on risk estimates, whereas at higher (average) doses and/or increased exposure frequencies, the acquired immunity model has the greatest impact. The proposed models are strongly nonlinear, and reducing exposure is not expected to lead to a proportional decrease in risk and, under certain conditions, may even lead to an increase in risk. The impact of different dose‐response models on risk estimates is particularly pronounced when introducing heterogeneity in the population exposure distribution.     

Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data

The benchmark dose (BMD) approach has gained acceptance as a valuable risk assessment tool, but risk assessors still face significant challenges associated with selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose‐response models. Current approaches do not explicitly address model uncertainty, and there is an existing need to more fully inform health risk assessors in this regard. In this study, a Bayesian model averaging (BMA) BMD estimation method taking model uncertainty into account is proposed as an alternative to current BMD estimation approaches for continuous data. Using the “hybrid” method proposed by Crump, two strategies of BMA, including both “maximum likelihood estimation based” and “Markov Chain Monte Carlo based” methods, are first applied as a demonstration to calculate model averaged BMD estimates from real continuous dose‐response data. The outcomes from the example data sets examined suggest that the BMA BMD estimates have higher reliability than the estimates from the individual models with highest posterior weight in terms of higher BMDL and smaller 90th percentile intervals. In addition, a simulation study is performed to evaluate the accuracy of the BMA BMD estimator. The results from the simulation study recommend that the BMA BMD estimates have smaller bias than the BMDs selected using other criteria. To further validate the BMA method, some technical issues, including the selection of models and the use of bootstrap methods for BMDL derivation, need further investigation over a more extensive, representative set of dose‐response data.     

Potential Uncertainty Reduction in Model‐Averaged Benchmark Dose Estimates Informed by an Additional Dose Study

A methodology is presented for assessing the information value of an additional dosage experiment in existing bioassay studies. The analysis demonstrates the potential reduction in the uncertainty of toxicity metrics derived from expanded studies, providing insights for future studies. Bayesian methods are used to fit alternative dose‐response models using Markov chain Monte Carlo (MCMC) simulation for parameter estimation and Bayesian model averaging (BMA) is used to compare and combine the alternative models. BMA predictions for benchmark dose (BMD) are developed, with uncertainty in these predictions used to derive the lower bound BMDL. The MCMC and BMA results provide a basis for a subsequent Monte Carlo analysis that backcasts the dosage where an additional test group would have been most beneficial in reducing the uncertainty in the BMD prediction, along with the magnitude of the expected uncertainty reduction. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values and increases in BMDL values that occur as a result of this reduced uncertainty. The methodology is illustrated using two existing data sets for TCDD carcinogenicity, fitted with two alternative dose‐response models (logistic and quantal‐linear). The example shows that an additional dose at a relatively high value would have been most effective for reducing the uncertainty in BMA BMD estimates, with predicted reductions in the widths of uncertainty intervals of approximately 30%, and expected increases in BMDL values of 5–10%. The results demonstrate that dose selection for studies that subsequently inform dose‐response models can benefit from consideration of how these models will be fit, combined, and interpreted.     

Quantal Risk Assessment Database: A Database for Exploring Patterns in Quantal Dose‐Response Data in Risk Assessment and its Application to Develop Priors for Bayesian Dose‐Response Analysis

Quantitative risk assessments for physical, chemical, biological, occupational, or environmental agents rely on scientific studies to support their conclusions. These studies often include relatively few observations, and, as a result, models used to characterize the risk may include large amounts of uncertainty. The motivation, development, and assessment of new methods for risk assessment is facilitated by the availability of a set of experimental studies that span a range of dose‐response patterns that are observed in practice. We describe construction of such a historical database focusing on quantal data in chemical risk assessment, and we employ this database to develop priors in Bayesian analyses. The database is assembled from a variety of existing toxicological data sources and contains 733 separate quantal dose‐response data sets. As an illustration of the database's use, prior distributions for individual model parameters in Bayesian dose‐response analysis are constructed. Results indicate that including prior information based on curated historical data in quantitative risk assessments may help stabilize eventual point estimates, producing dose‐response functions that are more stable and precisely estimated. These in turn produce potency estimates that share the same benefit. We are confident that quantitative risk analysts will find many other applications and issues to explore using this database.     

Influence of Distribution of Animals between Dose Groups on Estimated Benchmark Dose and Animal Distress for Quantal Responses

Increasingly, dose‐response data are being evaluated with the benchmark dose (BMD) approach rather than by the less precise no‐observed‐adverse‐effect‐level (NOAEL) approach. However, the basis for designing animal experiments, using equally sized dose groups, is still primed for the NOAEL approach. The major objective here was to assess the impact of using dose groups of unequal size on both the quality of the BMD and overall animal distress. We examined study designs with a total number of 200 animals distributed in four dose groups employing quantal data generated by Monte Carlo simulations. Placing more animals at doses close to the targeted BMD provided an estimate of BMD that was slightly better than the standard design with equally sized dose groups. In situations involving a clear dose‐response, this translates into fewer animals receiving high doses and thus less overall animal distress. Accordingly, in connection with risk and safety assessment, animal distress can potentially be reduced by distributing the animals appropriately between dose groups without decreasing the quality of the information obtained.     

Modeling Rabbit Responses to Single and Multiple Aerosol Exposures of Bacillus anthracis Spores

Survival models are developed to predict response and time‐to‐response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple‐dose data set to predict the probability of death through specifying functions of dose response and the time between exposure and the time‐to‐death (TTD). Among the models developed, the best‐fitting survival model (baseline model) is an exponential dose–response model with a Weibull TTD distribution. Alternative models assessed use different underlying dose–response functions and use the assumption that, in a multiple‐dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this article. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high‐dose rabbit data sets. More accurate survival models depend upon future development of dose–response data sets specifically designed to assess potential multiple‐dose effects on response and time‐to‐response. The process used in this article to develop the best‐fitting survival model for exposure of rabbits to multiple aerosol doses of B. anthracis spores should have broad applicability to other host–pathogen systems and dosing schedules because the empirical modeling approach is based upon pathogen‐specific empirically‐derived parameters.     

Evaluation of Inhaled Versus Deposited Dose Using the Exponential Dose‐Response Model for Inhalational Anthrax in Nonhuman Primate,Rabbit, and Guinea Pig

The application of the exponential model is extended by the inclusion of new nonhuman primate (NHP), rabbit, and guinea pig dose‐lethality data for inhalation anthrax. Because deposition is a critical step in the initiation of inhalation anthrax, inhaled doses may not provide the most accurate cross‐species comparison. For this reason, species‐specific deposition factors were derived to translate inhaled dose to deposited dose. Four NHP, three rabbit, and two guinea pig data sets were utilized. Results from species‐specific pooling analysis suggested all four NHP data sets could be pooled into a single NHP data set, which was also true for the rabbit and guinea pig data sets. The three species‐specific pooled data sets could not be combined into a single generic mammalian data set. For inhaled dose, NHPs were the most sensitive (relative lowest LD₅₀) species and rabbits the least. Improved inhaled LD₅₀s proposed for use in risk assessment are 50,600, 102,600, and 70,800 inhaled spores for NHP, rabbit, and guinea pig, respectively. Lung deposition factors were estimated for each species using published deposition data from Bacillus spore exposures, particle deposition studies, and computer modeling. Deposition was estimated at 22%, 9%, and 30% of the inhaled dose for NHP, rabbit, and guinea pig, respectively. When the inhaled dose was adjusted to reflect deposited dose, the rabbit animal model appears the most sensitive with the guinea pig the least sensitive species.     

Comparing Experimental Designs for Benchmark Dose Calculations for Continuous Endpoints

The BMD (benchmark dose) method that is used in risk assessment of chemical compounds was introduced by Crump (1984) and is based on dose-response modeling. To take uncertainty in the data and model fitting into account, the lower confidence bound of the BMD estimate (BMDL) is suggested to be used as a point of departure in health risk assessments. In this article, we study how to design optimum experiments for applying the BMD method for continuous data. We exemplify our approach by considering the class of Hill models. The main aim is to study whether an increased number of dose groups and at the same time a decreased number of animals in each dose group improves conditions for estimating the benchmark dose. Since Hill models are nonlinear, the optimum design depends on the values of the unknown parameters. That is why we consider Bayesian designs and assume that the parameter vector has a prior distribution. A natural design criterion is to minimize the expected variance of the BMD estimator. We present an example where we calculate the value of the design criterion for several designs and try to find out how the number of dose groups, the number of animals in the dose groups, and the choice of doses affects this value for different Hill curves. It follows from our calculations that to avoid the risk of unfavorable dose placements, it is good to use designs with more than four dose groups. We can also conclude that any additional information about the expected dose-response curve, e.g., information obtained from studies made in the past, should be taken into account when planning a study because it can improve the design.     

Application of a Biologically-Based RFD Estimation Method to Tetrachlorodibenzo-P-Dioxin (TCDD) Mediated Immune Suppression and Enzyme Induction

The current methods for a reference dose (RfD) determination can be enhanced through the use of biologically-based dose-response analysis. Methods developed here utilizes information from tetrachlorodibenzo- p -dioxin (TCDD) to focus on noncancer endpoints, specifically TCDD mediated immune system alterations and enzyme induction. Dose-response analysis, using the Sigmoid-Emax (EMAX) function, is applied to multiple studies to determine consistency of response. Through the use of multiple studies and statistical comparison of parameter estimates, it was demonstrated that the slope estimates across studies were very consistent. This adds confidence to the subsequent effect dose estimates. This study also compares traditional methods of risk assessment such as the NOAEL/safety factor to a modified benchmark dose approach which is introduced here. Confidence in the estimation of an effect dose (ED₁₀) was improved through the use of multiple datasets. This is key to adding confidence to the benchmark dose estimates. In addition, the Sigmoid-Emax function when applied to dose-response data using nonlinear regression analysis provides a significantly improved fit to data increasing confidence in parameter estimates which subsequently improve effect dose estimates.     

Monotonic Bayesian Semiparametric Benchmark Dose Analysis

Quantitative risk assessment proceeds by first estimating a dose‐response model and then inverting this model to estimate the dose that corresponds to some prespecified level of response. The parametric form of the dose‐response model often plays a large role in determining this dose. Consequently, the choice of the proper model is a major source of uncertainty when estimating such endpoints. While methods exist that attempt to incorporate the uncertainty by forming an estimate based upon all models considered, such methods may fail when the true model is on the edge of the space of models considered and cannot be formed from a weighted sum of constituent models. We propose a semiparametric model for dose‐response data as well as deriving a dose estimate associated with a particular response. In this model formulation, the only restriction on the model form is that it is monotonic. We use this model to estimate the dose‐response curve from a long‐term cancer bioassay, as well as compare this to methods currently used to account for model uncertainty. A small simulation study is conducted showing that the method is superior to model averaging when estimating exposure that arises from a quantal‐linear dose‐response mechanism, and is similar to these methods when investigating nonlinear dose‐response patterns.     

Dose‐Response Modeling for Inhalational Anthrax in Rabbits Following Single or Multiple Exposures

There is a need to advance our ability to characterize the risk of inhalational anthrax following a low‐dose exposure. The exposure scenario most often considered is a single exposure that occurs during an attack. However, long‐term daily low‐dose exposures also represent a realistic exposure scenario, such as what may be encountered by people occupying areas for longer periods. Given this, the objective of the current work was to model two rabbit inhalational anthrax dose‐response data sets. One data set was from single exposures to aerosolized Bacillus anthracis Ames spores. The second data set exposed rabbits repeatedly to aerosols of B. anthracis Ames spores. For the multiple exposure data the cumulative dose (i.e., the sum of the individual daily doses) was used for the model. Lethality was the response for both. Modeling was performed using Benchmark Dose Software evaluating six models: logprobit, loglogistic, Weibull, exponential, gamma, and dichotomous‐Hill. All models produced acceptable fits to either data set. The exponential model was identified as the best fitting model for both data sets. Statistical tests suggested there was no significant difference between the single exposure exponential model results and the multiple exposure exponential model results, which suggests the risk of disease is similar between the two data sets. The dose expected to cause 10% lethality was 15,600 inhaled spores and 18,200 inhaled spores for the single exposure and multiple exposure exponential dose‐response model, respectively, and the 95% lower confidence intervals were 9,800 inhaled spores and 9,200 inhaled spores, respectively.     

An Approach for Modeling Noncancer Dose Responses with an Emphasis on Uncertainty

This paper presents an approach for characterizing the probability of adverse effects occurring in a population exposed to dose rates in excess of the Reference Dose (RfD). The approach uses a linear threshold (hockey stick) model of response and is based on the current system of uncertainty factors used in setting RfDs. The approach requires generally available toxicological estimates such as No-Observed-Adverse-Effect Levels (NOAELs) or Benchmark Doses and doses at which adverse effects are observed in 50% of the test animals (ED₅₀s). In this approach, Monte Carlo analysis is used to characterize the uncertainty in the dose response slope based on the range and magnitude of the key sources of uncertainty in setting protective doses. The method does not require information on the shape of the dose response curve for specific chemicals, but is amenable to the inclusion of such data. The approach is applied to four compounds to produce estimates of response rates for dose rates greater than the RfD     

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.     

Regression Models and Risk Estimation for Mixed Discrete and Continuous Outcomes in Developmental Toxicology

Multivariate dose-response models have recently been proposed for developmental toxicity data to simultaneously model malformation incidence (a binary outcome), and reductions in fetal weight (a continuous outcome). In this and other applications, the binary outcome often represents a dichotomization of another outcome or a composite of outcomes, which facilitates analysis. For example, in Segment II developmental toxicology studies, multiple malformation types (i.e., external, visceral, skeletal) are evaluated on each fetus; malformation status may also be ordinally measured (e.g., normal, signs of variation, full malformation). A model is proposed is for fetal weight and multiple malformation variables measured on an ordinal scale, where the correlations between the outcomes and between the offspring within a litter are taken into account. Fully specifying the joint distribution of outcomes within a litter is avoided by specifying only the distribution of the multivariate outcome for each fetus and using generalized estimating equation methodology to account for correlations due to litter clustering. The correlations between the outcomes are required to characterize joint risk to the fetus, and are therefore a focus of inference. Dose-response models and their application to quantitative risk assessment are illustrated using data from a recent developmental toxicology experiment of ethylene oxide in mice.     

A Simulation Study of Quantitative Risk Assessment for Bivariate Continuous Outcomes

The neurotoxic effects of chemical agents are often investigated in controlled studies on rodents, with binary and continuous multiple endpoints routinely collected. One goal is to conduct quantitative risk assessment to determine safe dose levels. Yu and Catalano (2005) describe a method for quantitative risk assessment for bivariate continuous outcomes by extending a univariate method of percentile regression. The model is likelihood based and allows for separate dose‐response models for each outcome while accounting for the bivariate correlation. The approach to benchmark dose (BMD) estimation is analogous to that for quantal data without having to specify arbitrary cutoff values. In this article, we evaluate the behavior of the BMD relative to background rates, sample size, level of bivariate correlation, dose‐response trend, and distributional assumptions. Using simulations, we explore the effects of these factors on the resulting BMD and BMDL distributions. In addition, we illustrate our method with data from a neurotoxicity study of parathion exposure in rats.