Quantitative risk assessment for multivariate continuous outcomes with application to neurotoxicology: the bivariate case

The neurotoxic effects of chemical agents are often investigated in controlled studies on rodents, with multiple binary and continuous endpoints routinely collected. One goal is to conduct quantitative risk assessment to determine safe dose levels. Such studies face two major challenges for continuous outcomes. First, characterizing risk and defining a benchmark dose are difficult. Usually associated with an adverse binary event, risk is clearly definable in quantal settings as presence or absence of an event; finding a similar probability scale for continuous outcomes is less clear. Often, an adverse event is defined for continuous outcomes as any value below a specified cutoff level in a distribution assumed normal or log normal. Second, while continuous outcomes are traditionally analyzed separately for such studies, recent literature advocates also using multiple outcomes to assess risk. We propose a method for modeling and quantitative risk assessment for bivariate continuous outcomes that address both difficulties by extending existing percentile regression methods. The model is likelihood based; it allows separate dose-response models for each outcome while accounting for the bivariate correlation and overall characterization of risk. The approach to estimation of a benchmark dose is analogous to that for quantal data without the need to specify arbitrary cutoff values. We illustrate our methods with data from a neurotoxicity study of triethyl tin exposure in rats.     

Issues in Exposure and Dose Assessment for Epidemiology and Risk Assessment

Epidemiologic studies have been effective in identifying human environmental and occupational hazards. However, most epidemiologic data has been difficult to use in quantitative risk assessments because of the vague specification of exposure and dose. Toxicologic animal studies have used applied doses (quantities administered, or exposures with fixed duration) and well characterized end points to determine effects. However, direct use of animal data in human risk assessment has been limited by uncertainties in the extrapolation. The applied dose paradigm of toxicology is not suited for cross species extrapolation, nor for use in epidemiology as a dose metric because of the complexity of human exposures. Physiologically based pharmacokinetic (PBPK) modeling can estimate the time course of tissue concentrations in humans, given an exposure-time profile, and it has been used for extrapolating findings from animals to humans. It is proposed that human PBPK modeling can be used in appropriately designed epidemiologic studies to estimate tissue concentrations. Secondly, tissue time courses can be used to form dose metrics based on the type and time course of adverse effects. These dose metrics will strengthen the determination of epidemiologic dose-response relationships by reducing misclassification. Findings from this approach can be readily integrated into quantitative risk assessment.     

Statistical models for low dose exposure

Extrapolation of health risks from high to low doses has received a considerable amount of attention in carcinogenic risk assessment over decades. Fitting statistical dose-response models to experimental data collected at high doses and use of the fitted model for estimating effects at low doses lead to quite different risk predictions. Dissatisfaction with this procedure was formulated both by toxicologists who saw a deficit of biological knowledge in the models as well as by risk modelers who saw the need of mechanistically-based stochastic modeling. This contribution summarizes the present status of low dose modeling and the determination of the shape of dose-response curves. We will address the controversial issues of the appropriateness of threshold models, the estimation of no observed adverse effect levels (NOAEL), and their relevance for low dose modeling. We will distinguish between quantal dose-response models for tumor incidence and models of the more informative age/time dependent tumor incidence. The multistage model and the two-stage model of clonal expansion are considered as dose-response models accounting for biological mechanisms. Problems of the identifiability of mechanisms are addressed, the relation between administered dose and effective target dose is illustrated by examples, and the recently proposed Benchmark Dose concept for risk assessment is presented with its consequences for mechanistic modeling and statistical estimation.     

Benchmark dose profiles for joint‐action continuous data in quantitative risk assessment

Benchmark analysis is a widely used tool in biomedical and environmental risk assessment. Therein, estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a prespecified benchmark response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This paper demonstrates how the benchmark modeling paradigm can be expanded from the single‐agent setting to joint‐action, two‐agent studies. Focus is on continuous response outcomes. Extending the single‐exposure setting, representations of risk are based on a joint‐action dose–response model involving both agents. Based on such a model, the concept of a benchmark profile—a two‐dimensional analog of the single‐dose BMD at which both agents achieve the specified BMR—is defined for use in quantitative risk characterization and assessment.     

Improving Risk Assessment: Research Opportunities in Dose Response Modeling to Improve Risk Assessment

Substantial improvements in dose response modeling for risk assessment may result from recent and continuing advances in biological research, biochemical techniques, biostatistical/mathematical methods and computational power. This report provides a ranked set of recommendations for proposed research to advance the state of the art in dose response modeling. The report is the result of a meeting of invited workgroup participants charged with identifying five areas of research in dose response modeling that could be incorporated in a national agenda to improve risk assessment methods. Leading topics of emphasis are interindividual variability, injury risk assessment modeling, and procedures to incorporate distributional methods and mechanistic considerations into now-standard methods of deriving a reference dose (RfD), reference concentration (RfC), minimum risk level (MRL) or similar dose-response parameter estimates.     

Combining multiple comparisons and modeling techniques in dose-response studies

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.     

Improving the Development and Use of Biologically Based Dose Response Models (BBDR) in Risk Assessment

Biologically based dose-response (BBDR) models predict health outcomes (response) resulting from the presence of a toxicant at a biological target (dose). The benefits of BBDR models are many, and research programs are increasingly focusing on mechanistic research to support model development; however, progress has been slow. Impediments to progress include the complexity of dose response modeling, the need for a multidisciplinary team and consistent funding support, and difficulty in identifying and extracting the needed data. Of immediate concern is the lack of transparency of published models to the supporting data and literature, difficulty in accessing model code and simulation conditions sufficient to allow independent replication of results, and absence of well-defined quality criteria. Suggestions are presented to improve the development and use of BBDR models in risk assessment and to address the above limitations. Examples from BBDR models for methylmercury neurotoxicity and 5-fluorouracil embryotoxicity are presented to illustrate the suggestions including what kinds of databases are needed to support model development and transparency, quality assurance for modeling, and how the internet can advance database development and collaboration within the biological modeling community.     

Benchmark Dose Profiles for Joint‐Action Quantal Data in Quantitative Risk Assessment

Summary Benchmark analysis is a widely used tool in public health risk analysis. Therein, estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a prespecified Benchmark Response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This article demonstrates how the benchmark modeling paradigm can be expanded from the single‐dose setting to joint‐action, two‐agent studies. Focus is on response outcomes expressed as proportions. Extending the single‐exposure setting, representations of risk are based on a joint‐action dose–response model involving both agents. Based on such a model, the concept of a benchmark profile (BMP) – a two‐dimensional analog of the single‐dose BMD at which both agents achieve the specified BMR – is defined for use in quantitative risk characterization and assessment. The resulting, joint, low‐dose guidelines can improve public health planning and risk regulation when dealing with low‐level exposures to combinations of hazardous agents.     

Improving Risk Assessment: Priorities for Epidemiologic Research

The Epidemiology Work Group at the Workshop on Future Research for Improving Risk Assessment Methods, Of Mice, Men, and Models, held August 16 to 18, 2000, at Snowmass Village, Aspen, Colorado, concluded that in order to improve the utility of epidemiologic studies for risk assessment, methodologic research is needed in the following areas: (1) aspects of epidemiologic study designs that affect doseresponse estimation; (2) alternative methods for estimating dose in human studies; and (3) refined methods for dose-response modeling for epidemiologic data. Needed research in aspects of epidemiologic study design includes recognition and control of study biases, identification of susceptible subpopulations, choice of exposure metrics, and choice of epidemiologic risk parameters. Much of this research can be done with existing data. Research needed to improve determinants of dose in human studies includes additional individual-level data (e.g., diet, co-morbidity), development of more extensive human data for physiologically based pharmacokinetic (PBPK) dose modeling, tissue registries to increase the availability of tissue for studies of exposure/dose and susceptibility biomarkers, and biomarker data to assess exposures in humans and animals. Research needed on dose-response modeling of human studies includes more widespread application of flexible statistical methods (e.g., general additive models), development of methods to compensate for epidemiologic bias in dose-response models, improved biological models using human data, and evaluation of the benchmark dose using human data. There was consensus among the Work Group that, whereas most prior risk assessments have focused on cancer, there is a growing need for applications to other health outcomes. Developmental and reproductive effects, injuries, respiratory disease, and cardiovascular disease were identified as especially high priorities for research. It was also a consensus view that epidemiologists, industrial hygienists, and other scientists focusing on human data need to play a stronger role throughout the risk assessment process. Finally, the group agreed that there was a need to improve risk communication, particularly on uncertainty inherent in risk assessments that use epidemiologic data.     

Univariate Dose-Response Models in Case-Control Studies

For modelling dose-response relationships in case-control studies the multiplicative logistic regression model, assuming the relative risk to be an exponential function of the dose, is widely known. If the relative risk is assumed to be a linear function of the dose, several authors (see e.g. BERRY (1980)) have proposed an additive (linear) model. This model has a better fit with the data if such a linear relation holds. Confidence limits for the relative risk derived from the information matrix, however, appear to be rather inaccurate. Therefore, use of the ‘standard’ logistic model in two different ways was studied: extension with a quadratic term or a logarithmic transformation of the dose. By applying the methods both to an empirical data set and in a simulation experiment, it is shown that appropriate transformation (often logarithmic) of the dosage and then applying the ‘standard’ logistic model is an useful approach if a linear dose-response relationship holds.     

Effects of increasing doses of glucagon-like peptide-1 on insulin-releasing phases during intravenous glucose administration in mice

The increase in insulin secretion caused by glucagon-like peptide-1 (GLP-1) and GLP-1 mimetics observed during an intravenous glucose test (IVGTT) has been reported in both normal and disease animal models, as well as in humans. In this study, a hierarchical population modeling approach is used, together with a previously reported model relating glucose to insulin appearance, to determine quantitative in vivo dose-response relationships between GLP-1 dose level and both first- and second-phase insulin release. Parameters of the insulin kinetic model were estimated from the complete set of glucose and insulin data collected in 219 anesthetized nonfasted NMR-imaged mice after intravenous injection of glucose (1 g/kg) alone or with GLP-1 (0.03-100 nmol/kg). The resulting dose-response curves indicate a difference in GLP-1 effect on the two release phases, as is also evident from the different ED(50) parameter values (0.107 vs. 6.65 nmol/kg for phase 1 vs. phase 2 insulin release parameters). The first phase of insulin release is gradually augmented with increasing GLP-1 dose, reaching saturation at a dose of ~1 nmol/kg, while the second-phase release changes more abruptly at GLP-1 doses between 3 and 10 nmol/kg and shows a more pronounced 100-fold increase between control and the high GLP-1 dose of 100 nmol/kg Moreover, separate disposition indices calculated for phase 1 and 2 insulin release, show a different pattern of increase with increasing GLP-1 dose.     

A Simulation-Assessment Modeling Approach for Analyzing Environmental Risks of Groundwater Contamination at Waste Landfill Sites

An integrated simulation-assessment modeling approach for analyzing environmental risks of groundwater contamination is proposed in this paper. It incorporates an analytical groundwater solute transport model, an exposure dose model, and a fuzzy risk assessment model within a general framework. The transport model is used for predicting contaminant concentrations in subsurface, and the exposure dose model is used for calculating contaminant ingestion during the exposure period under given exposure pathways. Both models are solved through the Monte Carlo simulation technique to reflect the associated uncertainties. Based on consideration of fuzzy relationships between exposure doses and cancer risks, risk levels of different exposure doses for each contaminant can be calculated to form a fuzzy relation matrix. The overall risks can then be quantified through further fuzzy synthesizing operations. Thus, probabilistic quantification of different risk levels (possibilities) can be realized. Results of the case study indicate that environmental risks at the waste landfill site can be effectively analyzed through the developed methodology. They are useful for supporting the related risk-management and remediation decisions.     

Estimation of the benchmark dose by structural equation models

While epidemiological data typically contain a multivariate response and often also multiple exposure parameters, current methods for safe dose calculations, including the widely used benchmark approach, rely on standard regression techniques. In practice, dose-response modeling and calculation of the exposure limit are often based on the seemingly most sensitive outcome. However, this procedure ignores other available data, is inefficient, and fails to account for multiple testing. Instead, risk assessment could be based on structural equation models, which can accommodate both a multivariate exposure and a multivariate response function. Furthermore, such models will allow for measurement error in the observed variables, which is a requirement for unbiased estimation of the benchmark dose. This methodology is illustrated with the data on neurobehavioral effects in children prenatally exposed to methylmercury, where results based on standard regression models cause an underestimation of the true risk.     

Defining EMS and ENU dose-response relationships using the Pig-a mutation assay in rats

In recent years, experimental evidence has accumulated that supports the existence of sublinear dose-response relationships at low doses of DNA reactive mutagens. However, creating the in vivo data necessary to allow for a more detailed dose-response modeling with the currently available tools might not always be practical. The purpose of the current work was to evaluate the utility of the Pig-a gene mutation assay to rapidly identify dose-response relationships for direct acting genotoxicants. The induction of mutations in the peripheral blood of rats was evaluated following 28 days of exposure down to low doses of the direct acting alkylating agents ethyl methane sulfonate (EMS) and ethylnitrosourea (ENU). Using statistical modeling based on the 28-day studies, a threshold for mutation induction for EMS was estimated to be 21.9mg/kg, whereas for the more potent ENU, the threshold was estimated to be 0.88mg/kg. Comparing mutation frequencies from acute and sub-chronic dosing indicated less than additive dose-response relationships, further confirming the possibility of a threshold dose-response relationship for both compounds. In conclusion, the work presented provides evidence that the Pig-a assay might be a practical alternative to other in vivo mutation assays when assessing dose-response relationships for direct acting mutagens and that an experimental approach using fractionated dosing could be used to substantiate a biological mechanism responsible for the observation of a sublinear dose-response relationship.     

Use of Preclinical Dog Studies and Absorption Modeling to Facilitate Late Stage Formulation Bridging for a BCS II Drug Candidate

Formulation changes are common during drug development either due to clinical or manufacturing considerations. These changes especially at later stages of drug development oftentimes raise questions on the potential impact of a new formulation on bioavailability. In this work, the preclinical assessment of formulation bridging risk for a Biopharmaceutics Classification System II development compound is presented. Early clinical studies were conducted using a liquid-filled capsule (LFC). To assess the feasibility of a conventional solid dosage form, an initial analysis was conducted using absorption modeling which indicated conventional formulation of micronized active pharmaceutical ingredient (API) could be a viable option. Subsequently, test formulations were prepared and tested in vivo in dogs. The solid formulations were able to match exposures of the LFC capsule in the dog model; in addition, a sensitivity to API PSD was observed in line with the modeling predictions. When tested in the clinic, the conventional solid formulation resulted in exposures of approximately 25% lower compared to the LFC on an equivalent dose basis; however, bridging with a small dose adjustment would be feasible. The outcome of the clinical study was better predicted by the modeling approach while the dog model appeared to somewhat overestimate absorption. Through the use of preclinical tools and modeling and simulation, a risk assessment around formulation bridging can be conducted and inform formulation decisions or subsequent clinical study designs.     

PBPK models in risk assessment--A focus on chloroprene

Mathematical models are increasingly being used to simulate events in the exposure-response continuum, and to support quantitative predictions of risks to human health. Physiologically based pharmacokinetic (PBPK) models address that portion of the continuum from an external chemical exposure to an internal dose at a target site. Essential data needed to develop a PBPK model include values of key physiological parameters (e.g., tissue volumes, blood flow rates) and chemical specific parameters (rate of chemical absorption, distribution, metabolism, and elimination) for the species of interest. PBPK models are commonly used to: (1) predict concentrations of an internal dose over time at a target site following external exposure via different routes and/or durations; (2) predict human internal concentration at a target site based on animal data by accounting for toxicokinetic and physiological differences; and (3) estimate variability in the internal dose within a human population resulting from differences in individual pharmacokinetics. Himmelstein et al. [M.W. Himmelstein, S.C. Carpenter, P.M. Hinderliter, Kinetic modeling of beta-chloroprene metabolism. I. In vitro rates in liver and lung tissue fractions from mice, rats, hamsters, and humans, Toxicol. Sci. 79 (1) (2004) 18-27; M.W. Himmelstein, S.C. Carpenter, M.V. Evans, P.M. Hinderliter, E.M. Kenyon, Kinetic modeling of beta-chloroprene metabolism. II. The application of physiologically based modeling for cancer dose response analysis, Toxicol. Sci. 79 (1) (2004) 28-37] developed a PBPK model for chloroprene (2-chloro-1,3-butadiene; CD) that simulates chloroprene disposition in rats, mice, hamsters, or humans following an inhalation exposure. Values for the CD-PBPK model metabolic parameters were obtained from in vitro studies, and model simulations compared to data from in vivo gas uptake studies in rats, hamsters, and mice. The model estimate for total amount of metabolite in lung correlated better with rodent tumor incidence than did the external dose. Based on this PBPK model analytical approach, Himmelstein et al. [M.W. Himmelstein, S.C. Carpenter, M.V. Evans, P.M. Hinderliter, E.M. Kenyon, Kinetic modeling of beta-chloroprene metabolism. II. The application of physiologically based modeling for cancer dose response analysis, Toxicol. Sci. 79 (1) (2004) 28-37; M.W. Himmelstein, R. Leonard, R. Valentine, Kinetic modeling of beta-chloroprene metabolism: default and physiologically-based modeling approaches for cancer dose response, in: IISRP Symposium on Evaluation of Butadiene & Chloroprene Health Effects, September 21, 2005, TBD--reference in this proceedings issue of Chemical-Biological Interactions] propose that observed species differences in the lung tumor dose-response result from differences in CD metabolic rates. The CD-PBPK model has not yet been submitted to EPA for use in developing the IRIS assessment for chloroprene, but is sufficiently developed to be considered. The process that EPA uses to evaluate PBPK models is discussed, as well as potential applications for the CD-PBPK model in an IRIS assessment.