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

Guidelines to restrict consumption of red meat to under 350 g/wk based on colorectal cancer risk are not consistent with health evidence

BACKGROUND

The Nordic Nutrition Recommendations of 2023 (NNR2023) incorporate sustainability, health, and nutrition in their food-based dietary guidelines (FBDGs). NNR2023 recommends a consumption of ≤350 g/wk of unprocessed red meat (RM) based on association with colorectal cancer (CRC). This recommendation is lower than other FBDGs such as the World Cancer Research Fund (WCRF) recommendation it is based on (350-500 g/wk).

OBJECTIVE

To evaluate the empirical evidence and models cited by the NNR2023 to support the RM guidance.

METHODS

We fitted least-assumption (LA) dose-response (DR) models to the studies included in two systematic reviews (SRs) selected by NNR2023 on the RM and CRC association. We compared them against six parametric models reported in the two SRs. We evaluated the statistical significance of modeled relative risks (RR) at different consumption levels.

RESULTS

Twenty-one studies (20,604,188 patient-years) were analyzed. We found no significant association (RR = 1.04, 0.99-1.09) between 350g/wk of RM and CRC using the LA models, in agreement with the least restrictive models reported by Lescinsky et al., 2022 (RR = 1.11[0.89-1.38]) and WCRF (RR= 1.01[0.96-1.07]). The association was significant at 350 g/wk only under restricting assumptions such as monotonicity RR=1.3[1.01-1.64], and linearity RR = 1.06 [1.00-1.12]. No significant empirical association is observed under 567 g/wk based on evidence used by NNR2023.

CONCLUSIONS

The sources cited by NNR2023 do not support a consumption restriction of ≤350 g/wk of RM due to CRC, and other studies omitted by NNR2023 do not support association between RM and CRC. We show that model assumptions rather than empirical evidence drive this recommendation. Model uncertainty should be explicitly incorporated in FBDGs.

A Bayesian benchmark concentration analysis for urinary fluoride and intelligence in adults in Guizhou, China

Environmental fluoride exposure has been linked to numerous cases of fluorosis worldwide. Previous studies have indicated that long-term exposure to fluoride can result in intellectual damage among children. However, a comprehensive health risk assessment of fluorosis-induced intellectual damage is still pending. In this research, we utilized the Bayesian Benchmark Dose Analysis System (BBMD) to investigate the dose-response relationship between urinary fluoride (U-F) concentration and Raven scores in adults from Nayong, Guizhou, China. Our research findings indecate a dose-response relationship between the concentration of U-F and intelligence scores in adults. As the benchmark response (BMR) increased, both the benchmark concentration (BMCs) and the lower bound of the credible interval (BMCLs) increased. Specifically, BMCs for the association between U-F and IQ score were determined to be 0.18 mg/L (BMCL1 = 0.08 mg/L), 0.91 mg/L (BMCL5 = 0.40 mg/L), 1.83 mg/L (BMCL10 = 0.83 mg/L) when using BMRs of 1 %, 5 %, and 10 %. These results indicate that U-F can serve as an effective biomarker for monitoring the loss of IQ in population. We propose three interim targets for public policy in preventing interllectual harm from fluoride exposure.

Advancing probabilistic risk assessment by integrating human biomonitoring, new approach methods, and Bayesian modeling: A case study with the mycotoxin deoxynivalenol

Deoxynivalenol (DON) is a mycotoxin frequently observed in cereals and cereal-based foods, with reported toxicological effects including reduced body weight, immunotoxicity and reproductive defects. The European Food Safety Authority used traditional risk assessment approaches to derive a deterministic Tolerable Daily Intake (TDI) of 1 μg/kg-day, however data from human biomarkers studies indicate widespread and variable exposure worldwide, necessitating more sophisticated and advanced methods to quantify population risk. The World Health Organization/International Programme on Chemical Safety (WHO/IPCS) has previously used DON as a case example in replacing the TDI with a probabilistic toxicity value, using default uncertainty and variability distributions to derive the Human Dose corresponding to an effect size M in the Ith percentile of the population (HDMI) for M = 5 % decrease in body weight and I = 1 %. In this study, we extend this case study by incorporating (1) Bayesian modeling approaches, (2) using both in vivo data and in vitro population new approach methods to replace default distributions for interspecies toxicokinetic (TK) differences and intraspecies TK and toxicodynamic (TD) variability, and (3) integrating biomonitoring data and probabilistic dose-response functions to characterize population risk distributions. We first derive an HDMI of 5.5 [1.4-24] μg/kg-day, also using TK modeling to converted the HDMI to Biomonitoring Equivalents, BEMI for comparison with biomonitoring data, with a blood BEMI of 0.53 [0.17-1.6] μg/L and a urinary excretion BEMI of 3.9 [1.0-16] μg/kg-day. We then illustrate how this integrative approach can advance quantitative risk characterization using two human biomonitoring datasets, estimating both the fraction of population with an effect size M ≥ 5 % as well as the distribution of effect sizes. Overall, we demonstrate that integration of Bayesian modeling, human biomonitoring data, and in vitro population-based TD data within the WHO/IPCS probabilistic framework yields more accurate, precise, and comprehensive risk characterization.

An investigation of non-informative priors for Bayesian dose-response modeling

Toxicology analyses are built around dose-response modeling, and increasingly these methodologies utilize Bayesian estimation techniques. Bayesian estimation is unique because it includes prior distributional information in the analysis, which may impact the dose-response estimate meaningfully. As such analyses are often used for human health risk assessment, the practitioner must understand the impact of adding prior information to the dose-response study. One proposal in the literature is the use of the flat uniform prior distribution, which places a uniform prior probability over the dose-response model's parameters for a chosen range of values. Though the motivation of such a prior distribution is laudable in that it is most like maximum likelihood estimation seeking unbiased estimates of the dose-response, one can show that such priors add information and may introduce unexpected biases into the analysis. This manuscript shows through numerous empirical examples why prior distributions that are non-informative across all endpoints of interest do not exist for dose-response models; that is, other quantities of interest will be informed by choosing one inferential quantity not informed.

Beyond the cancer slope factor: Broad application of Bayesian and probabilistic approaches for cancer dose-response assessment

Traditional cancer slope factors derived from linear low-dose extrapolation give little consideration to uncertainties in dose-response model choice, interspecies extrapolation, and human variability. As noted previously by the National Academies, probabilistic methods can address these limitations, but have only been demonstrated in a few case studies. Here, we applied probabilistic approaches for Bayesian Model Averaging (BMA), interspecies extrapolation, and human variability distributions to 255 animal cancer bioassay datasets previously used by governmental agencies. We then derived predictions for both population cancer incidence and individual cancer risk. For model uncertainty, we found that lower confidence limits from BMA and from U.S. Environmental Protection Agency (EPA)'s Benchmark Dose Software (BMDS) correlated highly, with 86% differing by <10-fold. Incorporating other uncertainties and human variability, the lower confidence limits of the probabilistic risk-specific dose (RSD) at 10-6 population incidence were typically 3- to 30-fold lower than traditional slope factors. However, in a small (<7%) number of cases of highly non-linear experimental dose-response, the probabilistic RSDs were >10-fold less stringent. Probabilistic RSDs were also protective of individual risks of 10-4 in >99% of the population. We conclude that implementing Bayesian and probabilistic methods provides a more scientifically rigorous basis for cancer dose-response assessment and thereby improves overall cancer risk characterization.

ToxicR: A computational platform in R for computational toxicology and dose-response analyses

The need to analyze the complex relationships observed in high-throughput toxicogenomic and other omic platforms has resulted in an explosion of methodological advances in computational toxicology. However, advancements in the literature often outpace the development of software researchers can implement in their pipelines, and existing software is frequently based on pre-specified workflows built from well-vetted assumptions that may not be optimal for novel research questions. Accordingly, there is a need for a stable platform and open-source codebase attached to a programming language that allows users to program new algorithms. To fill this gap, the Biostatistics and Computational Biology Branch of the National Institute of Environmental Health Sciences, in cooperation with the National Toxicology Program (NTP) and US Environmental Protection Agency (EPA), developed ToxicR, an open-source R programming package. The ToxicR platform implements many of the standard analyses used by the NTP and EPA, including dose-response analyses for continuous and dichotomous data that employ Bayesian, maximum likelihood, and model averaging methods, as well as many standard tests the NTP uses in rodent toxicology and carcinogenicity studies, such as the poly-K and Jonckheere trend tests. ToxicR is built on the same codebase as current versions of the EPA's Benchmark Dose software and NTP's BMDExpress software but has increased flexibility because it directly accesses this software. To demonstrate ToxicR, we developed a custom workflow to illustrate its capabilities for analyzing toxicogenomic data. The unique features of ToxicR will allow researchers in other fields to add modules, increasing its functionality in the future.

Benchmark dose in the presence of coexposure to melamine and diethylhexyl phthalate and urinary renal injury markers in pregnant women

Environmental exposures to mixtures of toxic chemicals have potential interaction effects that may lead to hazard index values exceeding one. However, current regulation levels, such as tolerable daily intake (TDI), are mostly based on experimental studies conducted with a single chemical compound. In this study, we assessed the relationships between melamine and di-(2-ethylhexyl) phthalate (DEHP) exposure and their coexposure with the early renal injury markers N-acetyl -D-glucosaminidase (NAG), albumin/creatinine ratio (ACR), and microalbuminuria in 1236 pregnant women. Various generalized linear models with interaction terms and Bayesian kernel machine regression models were used for the (co-)exposure response associations. We derived the benchmark dose (BMD) and the corresponding one-sided 95% confidence bound BMDL based on the estimated (covariate-adjusted) average daily intake of melamine and DEHP metabolites measured in spot urine of the women collected during the third trimester. Given a benchmark response of 0.1, the BMDL level of melamine (DEHP) exposure on NAG (ACR, microalbuminuria) was 2.67 (11.20, 4.45) μg/kg_bw/day, and it decreased to as low as 1.46 (3.83, 2.73) μg/kg_bw/day when considering coexposure to DEHP (melamine) up to the 90th percentile. Both the exposure threshold levels of melamine and DEHP for early renal injuries in pregnant women were several-fold to one order lower than the current recommended TDIs by the WHO and the US FDA and EPA and were even lower considering coexposure. Because of concurrent exposures in real-world environments, more stringent regulation levels are recommended in susceptible populations, such as pregnant women, due to potential synergistic mixture effects.

Continuous Model Averaging for Benchmark Dose Analysis: Averaging Over Distributional Forms

When estimating a benchmark dose (BMD) from chemical toxicity experiments, model averaging is recommended by the National Institute for Occupational Safety and Health, World Health Organization and European Food Safety Authority. Though numerous studies exist for Model Average BMD estimation using dichotomous responses, fewer studies investigate it for BMD estimation using continuous response. In this setting, model averaging a BMD poses additional problems as the assumed distribution is essential to many BMD definitions, and distributional uncertainty is underestimated when one error distribution is chosen a priori. As model averaging combines full models, there is no reason one cannot include multiple error distributions. Consequently, we define a continuous model averaging approach over distributional models and show that it is superior to single distribution model averaging. To show the superiority of the approach, we apply the method to simulated and experimental response data.

A computational system for Bayesian benchmark dose estimation of genomic data in BBMD

BACKGROUND

Existing studies have revealed that the benchmark dose (BMD) estimates from short-term in vivo transcriptomics studies can approximate those from long-term guideline toxicity assessments. Existing software applications follow this trend by analyzing omics data through the maximum likelihood estimation and choosing the "best" model for BMD estimates. However, this practice ignores the model uncertainty and may result in over-confident inferences and predictions, leading to an inadequate decision.

OBJECTIVE

By generally following the National Toxicology Program Approach to Genomic Dose-Response Modeling, we developed a web-based dose-response modeling and BMD estimation system, Bayesian BMD (BBMD), for genomic data to quantitatively address uncertainty from various sources. The performances of BBMD are compared with BMDExpress.

METHODS

The system is primarily based on the previously developed BBMD system and further developed in a genomic perspective. Bayesian model averaging method is applied to BMD estimation and pathways analyses. Generally, the system is unique regarding the flexibility in preparing/storing data and in characterizing uncertainties.

RESULTS

This system was tested and validated versus 24 previously published in-vivo microarray dose-response datasets (GSE45892) and 64 molecules data from the Open TG-Gates database. Short term transcriptional BMD values for the median pathway in BBMD are highly correlated with the long-term apical BMD values (R = 0.78-0.91). The BMD estimates obtained by BBMD were compared to those by BMDExpress. The results indicate that BBMD provides more adequate results in terms of less extreme values and no failure in BMD and BMDL calculations. Also, the pathway analysis in BBMD provides a conservative estimate because a broader confidence interval is established.

DISCUSSION

Overall, this study demonstrates that dose-response modeling using genomic data can play a substantial role in support of chemical risk assessment. BBMD represents a robust and user-friendly alternative for genomic dose-response data analysis with outstanding functionalities to quantify uncertainty from various sources.

Multi-model ensemble simulated non-point source pollution based on Bayesian model averaging method and model uncertainty analysis

Watershed models are cost-effective and powerful tools for evaluating and controlling non-point source pollution (NPSP), while the reliability of watershed models in a management context depends largely on inherent uncertainties in model predictions. The objective of this study is to present the use of multi-model ensemble applied to streamflow, total nitrogen (TN), and total phosphorus (TP) simulation and quantify the uncertainty resulting from model structure. In this study, three watershed models, which have different structures in simulating NPSP, were selected to conduct watershed monthly streamflow, TN load, and TP load ensemble simulation and 90% credible intervals based on Bayesian model averaging (BMA) method. The result using the observed data of the Yixunhe watershed revealed that the coefficient of determination and Nash-Sutcliffe coefficient of the BMA model simulate streamflow, TN load, and TP load were better than that of the single model. The higher the efficiency of a single model is, the greater the weight during the BMA ensemble simulation is. The 90% credible interval of BMA has a high coverage of measured values in this study. This indicates that the BMA method can not only provide simulation with better precision through ensemble simulation but also provide quantitative evaluation of the model structure through interval, which could offer rich information of the NPSP simulation and management.

An extended and unified modeling framework for benchmark dose estimation for both continuous and binary data

Protection and safety authorities recommend the use of model averaging to determine the benchmark dose approach as a scientifically more advanced method compared with the no-observed-adverse-effect-level approach for obtaining a reference point and deriving health-based guidance values. Model averaging however highly depends on the set of candidate dose-response models and such a set should be rich enough to ensure that a well-fitting model is included. The currently applied set of candidate models for continuous endpoints is typically limited to two models, the exponential and Hill model, and differs completely from the richer set of candidate models currently used for binary endpoints. The objective of this article is to propose a general and wide framework of dose response models, which can be applied both to continuous and binary endpoints and covers the current models for both type of endpoints. In combination with the bootstrap, this framework offers a unified approach to benchmark dose estimation. The methodology is illustrated using two data sets, one with a continuous and another with a binary endpoint.

Evaluation of pyrrolizidine alkaloid-induced genotoxicity using metabolically competent TK6 cell lines

Pyrrolizidine alkaloid (PA)-containing plants are among the most common poisonous plants affecting humans, livestock, and wildlife worldwide. A large number of PAs are known to induce genetic damage after metabolic activation. In the present study, using a battery of fourteen newly developed TK6 cell lines, each expressing a single human cytochrome P450 (CYP1A1, 1A2, 1B1, 2A6, 2B6, 2C8, 2C18, 2C9, 2C19, 2D6, 2E1, 3A4, 3A5, and 3A7), we identified specific CYPs responsible for bioactivating three PAs - lasiocarpine, riddelliine, and senkirkine. Among the fourteen cell lines, cells expressing CYP3A4 showed significant increases in PA-induced cytotoxicity, evidenced by decreased ATP production and cell viability, and increased caspase 3/7 activities. LC-MS/MS analysis revealed the formation of 1-hydroxymethyl-7-hydroxy-6,7-dihydropyrrolizine (DHP), the main reactive metabolite of PAs, in CYP3A4-expressing TK6 cells. DHP was also detected in CYP3A5- and 3A7-expressing cells after PA exposure, but to a much lesser extent. Subsequently, using a high-throughput micronucleus assay, we demonstrated that PAs induced concentration-dependent increases in micronuclei and G2/M phase cell cycle arrest in three CYP3A variant-expressing TK6 cell lines. Using Western blotting, we observed that PA-induced apoptosis, cell cycle changes, and DNA damage were primarily mediated by CYP3A4. Benchmark dose (BMD) modeling demonstrated that lasiocarpine, of the three PAs, was the most potent inducer of micronuclei, with a BMD₁₀₀ of 0.036 μM. These results indicate that our TK6 cell system holds promise for genotoxicity screening of compounds requiring metabolic activation, identifying specific CYPs involved in bioactivation, and discriminating the genotoxic compounds that have different chemical structures.

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.

Simulation-based assessment of model selection criteria during the application of benchmark dose method to quantal response data

Background

To employ the benchmark dose (BMD) method in toxicological risk assessment, it is critical to understand how the BMD lower bound for reference dose calculation is selected following statistical fitting procedures of multiple mathematical models. The purpose of this study was to compare the performances of various combinations of model exclusion and selection criteria for quantal response data.

Methods

Simulation-based evaluation of model exclusion and selection processes was conducted by comparing validity, reliability, and other model performance parameters. Three different empirical datasets for different chemical substances were analyzed for the assessment, each having different characteristics of the dose-response pattern (i.e. datasets with rich information in high or low response rates, or approximately linear dose-response patterns).

Results

The best performing criteria of model exclusion and selection were different across the different datasets. Model averaging over the three models with the lowest three AIC (Akaike information criteria) values (MA-3) did not produce the worst performance, and MA-3 without model exclusion produced the best results among the model averaging. Model exclusion including the use of the Kolmogorov-Smirnov test in advance of model selection did not necessarily improve the validity and reliability of the models.

Conclusions

If a uniform methodological suggestion for the guideline is required to choose the best performing model for exclusion and selection, our results indicate that using MA-3 is the recommended option whenever applicable.

A Web-Based System for Bayesian Benchmark Dose Estimation

BACKGROUND

Benchmark dose (BMD) modeling is an important step in human health risk assessment and is used as the default approach to identify the point of departure for risk assessment. A probabilistic framework for dose-response assessment has been proposed and advocated by various institutions and organizations; therefore, a reliable tool is needed to provide distributional estimates for BMD and other important quantities in dose-response assessment.

OBJECTIVES

We developed an online system for Bayesian BMD (BBMD) estimation and compared results from this software with U.S. Environmental Protection Agency's (EPA's) Benchmark Dose Software (BMDS).

METHODS

The system is built on a Bayesian framework featuring the application of Markov chain Monte Carlo (MCMC) sampling for model parameter estimation and BMD calculation, which makes the BBMD system fundamentally different from the currently prevailing BMD software packages. In addition to estimating the traditional BMDs for dichotomous and continuous data, the developed system is also capable of computing model-averaged BMD estimates.

RESULTS

A total of 518 dichotomous and 108 continuous data sets extracted from the U.S. EPA's Integrated Risk Information System (IRIS) database (and similar databases) were used as testing data to compare the estimates from the BBMD and BMDS programs. The results suggest that the BBMD system may outperform the BMDS program in a number of aspects, including fewer failed BMD and BMDL calculations and estimates.

CONCLUSIONS

The BBMD system is a useful alternative tool for estimating BMD with additional functionalities for BMD analysis based on most recent research. Most importantly, the BBMD has the potential to incorporate prior information to make dose-response modeling more reliable and can provide distributional estimates for important quantities in dose-response assessment, which greatly facilitates the current trend for probabilistic risk assessment. https://doi.org/10.1289/EHP1289.

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.

Estimating the Probability of Rare Events Occurring Using a Local Model Averaging

In statistical applications, logistic regression is a popular method for analyzing binary data accompanied by explanatory variables. But when one of the two outcomes is rare, the estimation of model parameters has been shown to be severely biased and hence estimating the probability of rare events occurring based on a logistic regression model would be inaccurate. In this article, we focus on estimating the probability of rare events occurring based on logistic regression models. Instead of selecting a best model, we propose a local model averaging procedure based on a data perturbation technique applied to different information criteria to obtain different probability estimates of rare events occurring. Then an approximately unbiased estimator of Kullback-Leibler loss is used to choose the best one among them. We design complete simulations to show the effectiveness of our approach. For illustration, a necrotizing enterocolitis (NEC) data set is analyzed.

A Unified Probabilistic Framework for Dose-Response Assessment of Human Health Effects

BACKGROUND

When chemical health hazards have been identified, probabilistic dose-response assessment ("hazard characterization") quantifies uncertainty and/or variability in toxicity as a function of human exposure. Existing probabilistic approaches differ for different types of endpoints or modes-of-action, lacking a unifying framework.

OBJECTIVES

We developed a unified framework for probabilistic dose-response assessment.

METHODS

We established a framework based on four principles: a) individual and population dose responses are distinct; b) dose-response relationships for all (including quantal) endpoints can be recast as relating to an underlying continuous measure of response at the individual level; c) for effects relevant to humans, "effect metrics" can be specified to define "toxicologically equivalent" sizes for this underlying individual response; and d) dose-response assessment requires making adjustments and accounting for uncertainty and variability. We then derived a step-by-step probabilistic approach for dose-response assessment of animal toxicology data similar to how nonprobabilistic reference doses are derived, illustrating the approach with example non-cancer and cancer datasets.

RESULTS

Probabilistically derived exposure limits are based on estimating a "target human dose" (HDMI), which requires risk management-informed choices for the magnitude (M) of individual effect being protected against, the remaining incidence (I) of individuals with effects ≥ M in the population, and the percent confidence. In the example datasets, probabilistically derived 90% confidence intervals for HDMI values span a 40- to 60-fold range, where I = 1% of the population experiences ≥ M = 1%-10% effect sizes.

CONCLUSIONS

Although some implementation challenges remain, this unified probabilistic framework can provide substantially more complete and transparent characterization of chemical hazards and support better-informed risk management decisions.

Bayesian model-averaged benchmark dose analysis via reparameterized quantal-response models

An important objective in biomedical and environmental risk assessment is estimation of minimum exposure levels that induce a pre-specified adverse response in a target population. The exposure points in such settings are typically referred to as benchmark doses (BMDs). Parametric Bayesian estimation for finding BMDs has grown in popularity, and a large variety of candidate dose-response models is available for applying these methods. Each model can possess potentially different parametric interpretation(s), however. We present reparameterized dose-response models that allow for explicit use of prior information on the target parameter of interest, the BMD. We also enhance our Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce point estimates and (lower) credible bounds, overcoming associated questions of model adequacy when multimodel uncertainty is present. An example from carcinogenicity testing illustrates the calculations.

Historical Context and Recent Advances in Exposure-Response Estimation for Deriving Occupational Exposure Limits

Virtually no occupational exposure standards specify the level of risk for the prescribed exposure, and most occupational exposure limits are not based on quantitative risk assessment (QRA) at all. Wider use of QRA could improve understanding of occupational risks while increasing focus on identifying exposure concentrations conferring acceptably low levels of risk to workers. Exposure-response modeling between a defined hazard and the biological response of interest is necessary to provide a quantitative foundation for risk-based occupational exposure limits; and there has been considerable work devoted to establishing reliable methods quantifying the exposure-response relationship including methods of extrapolation below the observed responses. We review several exposure-response modeling methods available for QRA, and demonstrate their utility with simulated data sets.

Simultaneous inference for model averaging of derived parameters

Model averaging is a useful approach for capturing uncertainty due to model selection. Currently, this uncertainty is often quantified by means of approximations that do not easily extend to simultaneous inference. Moreover, in practice there is a need for both model averaging and simultaneous inference for derived parameters calculated in an after-fitting step. We propose a method for obtaining asymptotically correct standard errors for one or several model-averaged estimates of derived parameters and for obtaining simultaneous confidence intervals that asymptotically control the family-wise Type I error rate. The performance of the method in terms of coverage is evaluated using a simulation study and the applicability of the method is demonstrated by means of three concrete examples.

Benchmark dose calculation for ordered categorical responses

The use of benchmark dose (BMD) calculations for dichotomous or continuous responses is well established in the risk assessment of cancer and noncancer endpoints. In some cases, responses to exposure are categorized in terms of ordinal severity effects such as none, mild, adverse, and severe. Such responses can be assessed using categorical regression (CATREG) analysis. However, while CATREG has been employed to compare the benchmark approach and the no-adverse-effect-level (NOAEL) approach in determining a reference dose, the utility of CATREG for risk assessment remains unclear. This study proposes a CATREG model to extend the BMD approach to ordered categorical responses by modeling severity levels as censored interval limits of a standard normal distribution. The BMD is calculated as a weighted average of the BMDs obtained at dichotomous cutoffs for each adverse severity level above the critical effect, with the weights being proportional to the reciprocal of the expected loss at the cutoff under the normal probability model. This approach provides a link between the current BMD procedures for dichotomous and continuous data. We estimate the CATREG parameters using a Markov chain Monte Carlo simulation procedure. The proposed method is demonstrated using examples of aldicarb and urethane, each with several categories of severity levels. Simulation studies comparing the BMD and BMDL (lower confidence bound on the BMD) using the proposed method to the correspondent estimates using the existing methods for dichotomous and continuous data are quite compatible; the difference is mainly dependent on the choice of cutoffs for the severity levels.