Quantitative Risk Assessment: Developing a Bayesian Approach to Dichotomous Dose-Response Uncertainty.

Model averaging for dichotomous dose-response estimation is preferred to estimate the benchmark dose (BMD) from a single model, but challenges remain regarding implementing these methods for general analyses before model averaging is feasible to use in many risk assessment applications, and there is little work on Bayesian methods that include informative prior information for both the models and the parameters of the constituent models. This article introduces a novel approach that addresses many of the challenges seen while providing a fully Bayesian framework. Furthermore, in contrast to methods that use Monte Carlo Markov Chain, we approximate the posterior density using maximum a posteriori estimation. The approximation allows for an accurate and reproducible estimate while maintaining the speed of maximum likelihood, which is crucial in many applications such as processing massive high throughput data sets. We assess this method by applying it to empirical laboratory dose-response data and measuring the coverage of confidence limits for the BMD. We compare the coverage of this method to that of other approaches using the same set of models. Through the simulation study, the method is shown to be markedly superior to the traditional approach of selecting a single preferred model (e.g., from the U.S. EPA BMD software) for the analysis of dichotomous data and is comparable or superior to the other approaches.

A model of functional thyroid disease status over the lifetime.

Mathematical models of the natural history of disease can predict incidence rates based on prevalence data and support simulations of populations where thyroid function affects other aspects of physiology. We developed a Markov chain model of functional thyroid disease status over the lifetime. Subjects were in one of seven thyroid disease states at any given point in their lives [normal, subclinical hypothyroidism, overt hypothyroidism, treated thyroid disease (ever), subclinical hyperthyroidism, overt hyperthyroidism, and reverted to normal thyroid status]. We used a Bayesian approach to fitting model parameters. A priori probabilities of changing from each disease state to another per unit time were based on published data and summarized using meta-analysis, when possible. The probabilities of changing state were fitted to observed prevalence data based on the National Health and Nutrition Examination Survey 2007-2012. The fitted model provided a satisfactory fit to the observed prevalence data for each disease state, by sex and decade of age. For example, for males 50-59 years old, the observed prevalence of ever having treated thyroid disease was 4.4% and the predicted value was 4.6%. Comparing the incidence rates of treated disease predicted from our model with published values revealed that 82% were within a 4-fold difference. The differences seemed to be systematic and were consistent with expectation based on national iodine intakes. The model provided new and comprehensive estimates of functional thyroid disease incidence rates for the U.S. Because the model provides a reasonable fit to national prevalence data and predicts thyroid disease status over the lifetime, it is suitable for simulating populations, thereby making possible quantitative bias analyses of selected epidemiologic data reporting an association of thyroid disease with serum concentrations of environmental contaminants.

Bayesian Hierarchical Structure for Quantifying Population Variability to Inform Probabilistic Health Risk Assessments.

Human variability is a very important factor considered in human health risk assessment for protecting sensitive populations from chemical exposure. Traditionally, to account for this variability, an interhuman uncertainty factor is applied to lower the exposure limit. However, using a fixed uncertainty factor rather than probabilistically accounting for human variability can hardly support probabilistic risk assessment advocated by a number of researchers; new methods are needed to probabilistically quantify human population variability. We propose a Bayesian hierarchical model to quantify variability among different populations. This approach jointly characterizes the distribution of risk at background exposure and the sensitivity of response to exposure, which are commonly represented by model parameters. We demonstrate, through both an application to real data and a simulation study, that using the proposed hierarchical structure adequately characterizes variability across different populations.

Temporal concordance between apical and transcriptional points of departure for chemical risk assessment.

The number of legacy chemicals without toxicity reference values combined with the rate of new chemical development is overwhelming the capacity of the traditional risk assessment paradigm. More efficient approaches are needed to quantitatively estimate chemical risks. In this study, rats were dosed orally with multiple doses of six chemicals for 5 days and 2, 4, and 13 weeks. Target organs were analyzed for traditional histological and organ weight changes and transcriptional changes using microarrays. Histological and organ weight changes in this study and the tumor incidences in the original cancer bioassays were analyzed using benchmark dose (BMD) methods to identify noncancer and cancer points of departure. The dose-response changes in gene expression were also analyzed using BMD methods and the responses grouped based on signaling pathways. A comparison of transcriptional BMD values for the most sensitive pathway with BMD values for the noncancer and cancer apical endpoints showed a high degree of correlation at all time points. When the analysis included data from an earlier study with eight additional chemicals, transcriptional BMD values for the most sensitive pathway were significantly correlated with noncancer (r = 0.827, p = 0.0031) and cancer-related (r = 0.940, p = 0.0002) BMD values at 13 weeks. The average ratio of apical-to-transcriptional BMD values was less than two, suggesting that for the current chemicals, transcriptional perturbation did not occur at significantly lower doses than apical responses. Based on our results, we propose a practical framework for application of transcriptomic data to chemical risk assessment.

Integrating pathway-based transcriptomic data into quantitative chemical risk assessment: a five chemical case study.

The traditional approach for performing a chemical risk assessment is time and resource intensive leading to a limited number of published assessments on which to base human health decisions. In comparison, most contaminated sites contain chemicals without published reference values or cancer slope factors that are not considered quantitatively in the overall hazard index calculation. The integration of transcriptomic technology into the risk assessment process may provide an efficient means to evaluate quantitatively the health risks associated with data poor chemicals. In a previous study, female B6C3F1 mice were exposed to multiple concentrations of five chemicals that were positive for lung and/or liver tumor formation in a two-year rodent cancer bioassay. The mice were exposed for a period of 13 weeks and the target tissues were analyzed for traditional histological and organ weight changes and transcriptional changes using microarrays. In this study, the dose-response changes in gene expression were analyzed using a benchmark dose (BMD) approach and the responses grouped based on pathways. A comparison of the transcriptional BMD values with those for the traditional non-cancer and cancer apical endpoints showed a high degree of correlation for specific pathways. Many of the correlated pathways have been implicated in non-cancer and cancer disease pathogenesis. The results demonstrate that transcriptomic changes in pathways can be used to estimate non-cancer and cancer points-of-departure for use in quantitative risk assessments and have identified potential toxicity pathways involved in chemically induced mouse lung and liver responses.

Application of transcriptional benchmark dose values in quantitative cancer and noncancer risk assessment.

The traditional approach for estimating noncancer and cancer reference values in quantitative chemical risk assessment is time and resource intensive. The extent and nature of the studies required under the traditional approach has limited the number of chemicals with published risk assessments. In this study, female mice were exposed for 13 weeks to multiple concentrations of five chemicals that were positive in a 2-year cancer bioassay. Traditional histological and organ weight changes were evaluated, and gene expression microarray analysis was performed on the target tissues. The histological, organ weight changes, and the original tumor incidences in the original cancer bioassay were analyzed using standard benchmark dose (BMD) methods to identify noncancer and cancer points of departure, respectively. The dose-related changes in gene expression were also analyzed using a BMD approach and the responses grouped based on cellular biological processes. A comparison of the transcriptional BMD values with those for the traditional noncancer and cancer apical endpoints showed a high degree of correlation for specific cellular biological processes. For chemicals with human exposure data, the transcriptional BMD values were also used to calculate a margin of exposure. The margins of exposure ranged from 1900 to 54,000. Both the correlation between the BMD values for the transcriptional and apical endpoints and the margin of exposure analysis suggest that transcriptional BMD values may be used as potential points of departure for noncancer and cancer risk assessment.

Dose response assessment for effects of acute exposure to methyl isothiocyanate (MITC).

The preplant fumigants, metam-sodium, metam-potassium, and dazomet undergo decomposition to the biocide methyl isothiocyanate (MITC) in moist soils. Since MITC vapor can migrate from its site of application, we developed an estimate of health protective concentrations for airborne exposures to MITC that prevents effects among bystanders near treated agricultural fields. Our findings show that, at concentrations of environmental relevance, MITC most likely acts via stimulation of the trigeminal nerve, which mediates sensory irritation in the eyes and nose. Several lines of evidence support the conclusion that sensory irritation of the eyes is the most sensitive effect relevant for health risk assessment arising from short-term MITC exposures. The outcome of a clinical study that included sensitive individuals and measured multiple ocular responses to irritation (e.g., perceived irritation, tearing, and blinking of the eyes) is consistent with this proposed mode of action, as are experimental animal data. Databases and studies by the California Department of Pesticide Regulation (CDPR) show that, in accidental exposures, human eye irritation is consistently the most sensitive endpoint at low-modeled acute exposure and is often the most sensitive endpoint from acute exposures of unknown, but likely higher, concentrations. Based upon benchmark concentration lower limits from the clinical study and consideration of uncertainties, health protective concentrations of MITC were estimated as 0.2 ppm for 4h of exposure and 0.8 ppm for 14-min of exposure.

Bayesian analysis of a rat formaldehyde DNA-protein cross-link model.

As the initial effort in a multi-step uncertainty analysis of a biologically based cancer model for formaldehyde, a Markov chain Monte Carlo (MCMC) analysis was performed for a compartmental model that predicts DNA-protein cross-links (DPX) produced by formaldehyde exposure. The Bayesian approach represented by the MCMC analysis integrates existing knowledge of the model parameters with observed, formaldehyde-DPX-specific data, providing a statistically sound basis for estimating model output uncertainty. Uncertainty and variability were evaluated through a hierarchical structure, where interindividual variability was considered for all model parameters and that variability was assumed to be uncertain on population levels. The uncertainty of the population mean and that of the population variance were significantly reduced through the MCMC analysis. Our investigation highlights several issues that must be dealt with in many real-world analyses (e.g., issues of parameters' nonidentifiability due to limited data) while demonstrating the feasibility of conducting a comprehensive quantitative uncertainty evaluation. The current analysis can be viewed as a case study, for a relatively simple model, illustrating some of the constraints that analysts will face when applying Bayesian approaches to biologically or physiologically based models of increasing complexity.

Analysis of in vivo mutation data can inform cancer risk assessment.

Under the new U.S. Environmental Protection Agency (EPA) Cancer Risk Assessment Guidelines [U.S. EPA, 2005. Guidelines for Carcinogen Risk Assessment. EPA/630/P-03/001B, March 2005], the quantitative model chosen for cancer risk assessment is based on the mode-of-action (MOA) of the chemical under consideration. In particular, the risk assessment model depends on whether or not the chemical causes tumors through a direct DNA-reactive mechanism. It is assumed that direct DNA-reactive carcinogens initiate carcinogenesis by inducing mutations and have low-dose linear dose-response curves, whereas carcinogens that operate through a nonmutagenic MOA may have nonlinear dose-responses. We are currently evaluating whether the analysis of in vivo gene mutation data can inform the risk assessment process by better defining the MOA for cancer and thus influencing the choice of the low-dose extrapolation model. This assessment includes both a temporal analysis of mutation induction and a dose-response concordance analysis of mutation with tumor incidence. Our analysis of published data on riddelliine in rats and dichloroacetic acid in mice indicates that our approach has merit. We propose an experimental design and graphical analysis that allow for assessing time-to-mutation and dose-response concordance, thereby optimizing the potential for in vivo mutation data to inform the choice of the quantitative model used in cancer risk assessment.

Use of Markov Chain Monte Carlo analysis with a physiologically-based pharmacokinetic model of methylmercury to estimate exposures in US women of childbearing age.

A Bayesian approach, implemented using Markov Chain Monte Carlo (MCMC) analysis, was applied with a physiologically-based pharmacokinetic (PBPK) model of methylmercury (MeHg) to evaluate the variability of MeHg exposure in women of childbearing age in the U.S. population. The analysis made use of the newly available National Health and Nutrition Survey (NHANES) blood and hair mercury concentration data for women of age 16-49 years (sample size, 1,582). Bayesian analysis was performed to estimate the population variability in MeHg exposure (daily ingestion rate) implied by the variation in blood and hair concentrations of mercury in the NHANES database. The measured variability in the NHANES blood and hair data represents the result of a process that includes interindividual variation in exposure to MeHg and interindividual variation in the pharmacokinetics (distribution, clearance) of MeHg. The PBPK model includes a number of pharmacokinetic parameters (e.g., tissue volumes, partition coefficients, rate constants for metabolism and elimination) that can vary from individual to individual within the subpopulation of interest. Using MCMC analysis, it was possible to combine prior distributions of the PBPK model parameters with the NHANES blood and hair data, as well as with kinetic data from controlled human exposures to MeHg, to derive posterior distributions that refine the estimates of both the population exposure distribution and the pharmacokinetic parameters. In general, based on the populations surveyed by NHANES, the results of the MCMC analysis indicate that a small fraction, less than 1%, of the U.S. population of women of childbearing age may have mercury exposures greater than the EPA RfD for MeHg of 0.1 microg/kg/day, and that there are few, if any, exposures greater than the ATSDR MRL of 0.3 microg/kg/day. The analysis also indicates that typical exposures may be greater than previously estimated from food consumption surveys, but that the variability in exposure within the population of U.S. women of childbearing age may be less than previously assumed.