Evaluation of the benchmark dose method for dichotomous data: model dependence and model selection

Endocrine, metabolic and apical effects of in utero and lactational exposure to non-dioxin-like 2,2',3,4,4',5,5'-heptachlorobiphenyl (PCB 180): A postnatal follow-up study in rats

PCB 180 is a persistent and abundant non-dioxin-like PCB (NDL-PCB). We determined the developmental toxicity profile of ultrapure PCB 180 in developing offspring following in utero and lactational exposure with the focus on endocrine, metabolic and retinoid system alterations. Pregnant rats were given total doses of 0, 10, 30, 100, 300 or 1000 mg PCB 180/kg bw on gestational days 7-10 by oral gavage, and the offspring were sampled on postnatal days (PND) 7, 35 and 84. Decreased serum testosterone and triiodothyronine concentrations on PND 84, altered liver retinoid levels, increased liver weights and induced 7-pentoxyresorufin O-dealkylase (PROD) activity were the sensitive effects used for margin of exposure (MoE) calculations. Liver weights were increased together with induction of the metabolizing enzymes cytochrome P450 (CYP) 2B1, CYP3A1, and CYP1A1. Less sensitive effects included decreased serum estradiol and increased luteinizing hormone levels in females, decreased prostate and seminal vesicle weight and increased pituitary weight in males, increased cortical bone area and thickness of tibial diaphysis in females and decreased cortical bone mineral density in males. Developmental toxicity profiles were partly different in male and female offspring, males being more sensitive to increased liver weight, PROD induction and decreased thyroxine concentrations. MoE assessment indicated that the 95^th percentile of current maternal PCB 180 concentrations do not exceed the estimated tolerable human lipid-based PCB 180 concentration. Although PCB 180 is much less potent than dioxin-like compounds, it shares several toxicological targets suggesting a potential for interactions.

Using benchmark dose modeling for the quantitative risk assessment: Carbon nanotubes, asbestos, glyphosate

Benchmark dose method is one of the most famous quantitative approaches available for toxicological risks prediction. However, it is not fully clear how occupational health professionals can use it for specific workplace scenarios requiring carcinogen risk assessment. The paper explores the hypothesis that benchmark dose method allows to effectively approximate dose-response data on carcinogenic response, providing reasonable estimations of risks in the situations when a choice between more complex models is not warranted for practical purposes. Three case studies were analyzed for the agents with different levels of scientific confidence in human carcinogenicity: carbon nanotubes, amosite asbestos, and glyphosate. For each agent, a critical study was determined, and a dose-response slope factor was quantified, based on the weighted average lower bound benchmark dose. The linear slope factors of 0.111 lifetime excess cases of lung carcinoma per mg/m³ of MWCNT-7 (in rats exposure equivalent), 0.009 cases of mesothelioma per f/cc-years of cumulative exposure to amosite asbestos, and 0.000094 cases of malignant lymphoma per mg/kg/day of glyphosate (in mice equivalent) were determined. The correlations between the proposed linear predictive models and observed data points were R = 0.96 (R² = 0.92) for carbon nanotubes, R = 0.97 (R² = 0.95) for amosite asbestos, and R = 0.89 (R² = 0.79) for glyphosate. In all three cases, the linear extrapolation yielded comparable level of risk estimations with the "best fit" nonlinear model; for nanoparticles and amosite asbestos, linear estimations were more conservative. By performing a simulation study, it was demonstrated that a weighted average benchmark dose expressed the highest correlation with multistage and quantal-linear models.

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.

Phthalate Exposure and Long-Term Epigenomic Consequences: A Review

Phthalates are esters of phthalic acid which are used in cosmetics and other daily personal care products. They are also used in polyvinyl chloride (PVC) plastics to increase durability and plasticity. Phthalates are not present in plastics by covalent bonds and thus can easily leach into the environment and enter the human body by dermal absorption, ingestion, or inhalation. Several in vitro and in vivo studies suggest that phthalates can act as endocrine disruptors and cause moderate reproductive and developmental toxicities. Furthermore, phthalates can pass through the placental barrier and affect the developing fetus. Thus, phthalates have ubiquitous presence in food and environment with potential adverse health effects in humans. This review focusses on studies conducted in the field of toxicogenomics of phthalates and discusses possible transgenerational and multigenerational effects caused by phthalate exposure during any point of the life-cycle.

Time-to-Event Modeling of Left- or Right-Censored Toxicity Data in Nonclinical Drug Toxicology

A time-to-event (TTE) model has been developed to characterize a histopathology toxicity that can only be detected at the time of animal sacrifice. The model of choice was a hazard model with a Weibull distribution and dose was a significant covariate. The diagnostic plots showed a satisfactory fit of the data, despite the high degree of left and right censoring. Comparison to a probabilistic logit model shows similar performance in describing the data with a slight underestimation of survival by the Logit model. However, the TTE model was found to be more predictive in extrapolating toxicity risk beyond the observation range of a truncated dataset. The diagnostic and comparison outcomes would suggest using the TTE approach as a first choice for characterizing short and long-term risk from nonclinical toxicity studies. However, further investigations are needed to explore the domain of application of this kind of approach in drug safety assessment.

Neuromuscular anomalies following oral exposure to 3-nitro-1,2,4-triazol-5-one (NTO) in a one-generation study with Japanese quail (Coturnix japonica)

Substances used as explosives in munitions by the military often result in environmental releases through manufacturing, testing, training, and combat activities. The toxicity of 3-nitro-1,2,4-triazol-5-one (nitrotriazolone or NTO) was evaluated following oral exposure in Japanese quail (Coturnix japonica) to determine if environmental releases result in unacceptable risks to avian populations. In an acute test at the limit dose (2000 mg/kg), one female was ataxic, exhibited tremors, and showed signs of neurological toxicity approximately 24 h after dosing. In a subsequent one-generation study, parental generation (F0) birds were exposed orally to 1000, 500, 100, or 20mg/kg-day NTO suspended in corn oil. After 5 consecutive days of dosing, 2-week-old birds receiving 1000 mg/kg-day displayed ataxia, convulsions, backward arching of the neck (opisthotonos), and alternated between prostrate inactivity and ataxic wing activity. Birds in the 500 mg/kg-day group exhibited neuromuscular anomalies after 17 days exposure. Ultimately, all of the 1000 mg/kg-day birds and all but one of the 500 mg/kg-day birds met euthanasia criteria and were humanely euthanized prior to behavioral and reproductive evaluation. As such, first-generation (F1) birds were exposed to 100 or 20 mg/kg-day NTO. Mild neuromuscular anomalies occurred in 10% of F1 birds from the 100 mg/kg-day group, but not in birds from 20 mg/kg-day or controls in either generation. Vacuolization of cerebellum and/or the brainstem was observed on histopathologic examination in a dose-dependent manner. Therefore, brain vacuoles and neuromuscular anomalies were identified as critical endpoints in this study. A mean Benchmark Dose (BMD) for brain vacuoles of 62 mg/kg-day was derived for male and female F0-generation quail, which corresponded to a Benchmark Dose Low (BMDL₁₀) of 35 mg/kg-day.

Model Selection and Estimation with Quantal-Response Data in Benchmark Risk Assessment

This article describes several approaches for estimating the benchmark dose (BMD) in a risk assessment study with quantal dose-response data and when there are competing model classes for the dose-response function. Strategies involving a two-step approach, a model-averaging approach, a focused-inference approach, and a nonparametric approach based on a PAVA-based estimator of the dose-response function are described and compared. Attention is raised to the perils involved in data "double-dipping" and the need to adjust for the model-selection stage in the estimation procedure. Simulation results are presented comparing the performance of five model selectors and eight BMD estimators. An illustration using a real quantal-response data set from a carcinogenecity study is provided.

Update: use of the benchmark dose approach in risk assessment

The Scientific Committee (SC) reconfirms that the benchmark dose (BMD) approach is a scientifically more advanced method compared to the NOAEL approach for deriving a Reference Point (RP). Most of the modifications made to the SC guidance of 2009 concern the section providing guidance on how to apply the BMD approach. Model averaging is recommended as the preferred method for calculating the BMD confidence interval, while acknowledging that the respective tools are still under development and may not be easily accessible to all. Therefore, selecting or rejecting models is still considered as a suboptimal alternative. The set of default models to be used for BMD analysis has been reviewed, and the Akaike information criterion (AIC) has been introduced instead of the log-likelihood to characterise the goodness of fit of different mathematical models to a dose-response data set. A flowchart has also been inserted in this update to guide the reader step-by-step when performing a BMD analysis, as well as a chapter on the distributional part of dose-response models and a template for reporting a BMD analysis in a complete and transparent manner. Finally, it is recommended to always report the BMD confidence interval rather than the value of the BMD. The lower bound (BMDL) is needed as a potential RP, and the upper bound (BMDU) is needed for establishing the BMDU/BMDL per ratio reflecting the uncertainty in the BMD estimate. This updated guidance does not call for a general re-evaluation of previous assessments where the NOAEL approach or the BMD approach as described in the 2009 SC guidance was used, in particular when the exposure is clearly smaller (e.g. more than one order of magnitude) than the health-based guidance value. Finally, the SC firmly reiterates to reconsider test guidelines given the expected wide application of the BMD approach.

Comparing probabilistic and descriptive analyses of time-dose-toxicity relationship for determining no-observed-adverse-effect level in drug development

The no-observed-adverse-effect level (NOAEL) of a drug defined from animal studies is important for inferring a maximal safe dose in human. However, several issues are associated with its concept, determination and application. It is confined to the actual doses used in the study; becomes lower with increasing sample size or dose levels; and reflects the risk level seen in the experiment rather than what may be relevant for human. We explored a pharmacometric approach in an attempt to address these issues. We first used simulation to examine the behaviour of the NOAEL values as determined by current common practice; and then fitted the probability of toxicity as a function of treatment duration and dose to data collected from all applicable toxicology studies of a test compound. Our investigation was in the context of an irreversible toxicity that is detected at the end of the study. Simulations illustrated NOAEL's dependency on experimental factors such as dose and sample size, as well as the underlying uncertainty. Modelling the probability as a continuous function of treatment duration and dose simultaneously to data from multiple studies allowed the estimation of the dose, along with its confidence interval, for a maximal risk level that might be deemed as acceptable for human. The model-based data integration also reconciled between-study inconsistency and explicitly provided maximised estimation confidence. Such alternative NOAEL determination method should be explored for its more efficient data use, more quantifiable insight to toxic doses, and the potential for more relevant animal-to-human translation.

Benchmark dose and the three Rs. Part I. Getting more information from the same number of animals

Evaluating dose-response data using the Benchmark dose (BMD) approach rather than by the no observed adverse effect (NOAEL) approach implies a considerable step forward from the perspective of the Reduction, Replacement, and Refinement, three Rs, in particular the R of reduction: more information is obtained from the same number of animals, or, vice versa, similar information may be obtained from fewer animals. The first part of this twin paper focusses on the former, the second on the latter aspect. Regarding the former, the BMD approach provides more information from any given dose-response dataset in various ways. First, the BMDL (= BMD lower confidence bound) provides more information by its more explicit definition. Further, as compared to the NOAEL approach the BMD approach results in more statistical precision in the value of the point of departure (PoD), for deriving exposure limits. While part of the animals in the study do not directly contribute to the numerical value of a NOAEL, all animals are effectively used and do contribute to a BMDL. In addition, the BMD approach allows for combining similar datasets for the same chemical (e.g., both sexes) in a single analysis, which further increases precision. By combining a dose-response dataset with similar historical data for other chemicals, the precision can even be substantially increased. Further, the BMD approach results in more precise estimates for relative potency factors (RPFs, or TEFs). And finally, the BMD approach is not only more precise, it also allows for quantification of the precision in the BMD estimate, which is not possible in the NOAEL approach.

The Impact of Model Uncertainty on Benchmark Dose Estimation

We study the popular benchmark dose (BMD) approach for estimation of low exposure levels in toxicological risk assessment, focusing on dose-response experiments with quantal data. In such settings, representations of the risk are traditionally based on a specified, parametric, dose-response model. It is a well-known concern, however, that uncertainty can exist in specification and selection of the model. If the chosen parametric form is in fact misspecified, this can lead to inaccurate, and possibly unsafe, lowdose inferences. We study the effects of model selection and possible misspecification on the BMD, on its corresponding lower confidence limit (BMDL), and on the associated extra risks achieved at these values, via large-scale Monte Carlo simulation. It is seen that an uncomfortably high percentage of instances can occur where the true extra risk at the BMDL under a misspecified or incorrectly selected model can surpass the target BMR, exposing potential dangers of traditional strategies for model selection when calculating BMDs and BMDLs.

Determination of the di-(2-ethylhexyl) phthalate NOAEL for reproductive development in the rat: importance of the retention of extra animals to adulthood

Deriving No Observed Adverse Effect Level (NOAEL) or benchmark dose is important for risk assessment and can be influenced by study design considerations. In order to define the di-(2-ethylhexyl) phthalate (DEHP) dose-response curve for reproductive malformations, we retained more offspring to adulthood to improve detection of these malformations in the reproductive assessment by continuous breeding study design. Sprague-Dawley rats were given a dietary administration of 1.5 (control), 10, 30, 100, 300, 1000, 7500, and 10,000 ppm DEHP. Male pups were evaluated for gross reproductive tract malformations (RTMs) associated with the "phthalate syndrome." DEHP treatment had minimal effects on P0 males. There was a statistically significant increase in F1 and F2 total RTMs (testis, epididymides, seminal vesicle, and prostate) in the 7500-ppm dose group and F1 10,000-ppm dose group. The 10,000-ppm exposed F1 males did not produce an F2 generation. The NOAEL for F1 and F2 RTM combined data, because in utero exposures were similar, were 100 ppm (4.8 mg/kg/day), which was close to the 5% response benchmark dose lower confidence limit of 142 ppm. The utility of evaluating more pups per litter was examined by generating power curves from a Monte Carlo simulation. These curves indicate a substantial increase in detection rate when three males are evaluated per litter rather than one. A 10% effect across male pups would be detected 5% of the time if one pup per litter was evaluated, but these effects would be detected 66% of the time if three pups per litter were evaluated. Taken together, this study provides a well-defined dose response of DEHP-induced RTMs and demonstrates that retention of more adult F1 and F2 males per litter, animals that were already produced, increases the ability to detect RTMs and presumably other low-incidence phenomena.

Translational benchmark risk analysis

Translational development - in the sense of translating a mature methodology from one area of application to another, evolving area - is discussed for the use of benchmark doses in quantitative risk assessment. Illustrations are presented with traditional applications of the benchmark paradigm in biology and toxicology, and also with risk endpoints that differ from traditional toxicological archetypes. It is seen that the benchmark approach can apply to a diverse spectrum of risk management settings. This suggests a promising future for this important risk-analytic tool. Extensions of the method to a wider variety of applications represent a significant opportunity for enhancing environmental, biomedical, industrial, and socio-economic risk assessments.

Confidence limits on one-stage model parameters in benchmark risk assessment

In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.

Statistical power considerations show the endocrine disruptor low-dose issue in a new light

BACKGROUND

The endocrine disruptor field has been vexed by difficulties in reproducing various claims of effects at unusually low doses. In previous analyses, variations in control responses from experiment to experiment and problems with observing effects in positive controls have been identified as possible explanations of the resulting impasse.

OBJECTIVE

In this article, we argue that both of these viewpoints fail to take sufficient account of the problems that exist in estimating low effects and low-effect doses. We have carried out post hoc power analyses on selected published data to illustrate that claims of low-dose effects (or their absence) are often compromised by insufficient statistical power of the chosen experimental design.

CONCLUSIONS

We demonstrate that low-dose estimates such as the no observed adverse effect levels derived from statistical hypothesis-testing procedures are dependent on the specific experimental conditions used for testing. Thus, below the statistical detection limit of the experiment, the presence of effects can neither be proven nor ruled out. Common practice is to attempt to establish "doses without effect." However, low-dose estimations in the endocrine-disruptor field could be improved if decisions regarding the toxicologic effect size of relevance formed the starting point of testing procedures. Statistical power considerations could then reveal the resources necessary to demonstrate effect magnitudes of concern.

Benchmark analysis for quantifying urban vulnerability to terrorist incidents

We describe a quantitative methodology to characterize the vulnerability of U.S. urban centers to terrorist attack, using a place-based vulnerability index and a database of terrorist incidents and related human casualties. Via generalized linear statistical models, we study the relationships between vulnerability and terrorist events, and find that our place-based vulnerability metric significantly describes both terrorist incidence and occurrence of human casualties from terrorist events in these urban centers. We also introduce benchmark analytic technologies from applications in toxicological risk assessment to this social risk/vulnerability paradigm, and use these to distinguish levels of high and low urban vulnerability to terrorism. It is seen that the benchmark approach translates quite flexibly from its biological roots to this social scientific archetype.

Assessment factors--applications in health risk assessment of chemicals

We review the scientific basis for default assessment factors used in risk assessment of nongenotoxic chemicals including the use of chemical- and pathways specific assessment factors, and extrapolation approaches relevant to species differences, age and gender. One main conclusion is that the conventionally used default factor of 100 does not cover all inter-species and inter-individual differences. We suggest that a species-specific default factor based on allometric scaling should be used for inter-species extrapolation (basal metabolic rate). Regarding toxicodynamic and remaining toxicokinetic differences we suggest that a percentile from a probabilistic distribution is chosen to derive the assessment factor. Based on the scarce information concerning the human-to-human variability it is more difficult to suggest a specific assessment factor. However, extra emphasis should be put on sensitive populations such as neonates and genetically sensitive subgroups, and also fetuses and children which may be particularly vulnerable during development and maturation. Factors that also need to be allowed for are possible gender differences in sensitivity, deficiencies in the databases, nature of the effect, duration of exposure, and route-to-route extrapolation. Since assessment factors are used to compensate for lack of knowledge we feel that it is prudent to adopt a "conservative" approach, erring on the side of protectiveness.

Copper and human health: biochemistry, genetics, and strategies for modeling dose-response relationships

Copper (Cu) and its alloys are used extensively in domestic and industrial applications. Cu is also an essential element in mammalian nutrition. Since both copper deficiency and copper excess produce adverse health effects, the dose-response curve is U-shaped, although the precise form has not yet been well characterized. Many animal and human studies were conducted on copper to provide a rich database from which data suitable for modeling the dose-response relationship for copper may be extracted. Possible dose-response modeling strategies are considered in this review, including those based on the benchmark dose and categorical regression. The usefulness of biologically based dose-response modeling techniques in understanding copper toxicity was difficult to assess at this time since the mechanisms underlying copper-induced toxicity have yet to be fully elucidated. A dose-response modeling strategy for copper toxicity was proposed associated with both deficiency and excess. This modeling strategy was applied to multiple studies of copper-induced toxicity, standardized with respect to severity of adverse health outcomes and selected on the basis of criteria reflecting the quality and relevance of individual studies. The use of a comprehensive database on copper-induced toxicity is essential for dose-response modeling since there is insufficient information in any single study to adequately characterize copper dose-response relationships. The dose-response modeling strategy envisioned here is designed to determine whether the existing toxicity data for copper excess or deficiency may be effectively utilized in defining the limits of the homeostatic range in humans and other species. By considering alternative techniques for determining a point of departure and low-dose extrapolation (including categorical regression, the benchmark dose, and identification of observed no-effect levels) this strategy will identify which techniques are most suitable for this purpose. This analysis also serves to identify areas in which additional data are needed to better define the characteristics of dose-response relationships for copper-induced toxicity in relation to excess or deficiency.

On use of the multistage dose-response model for assessing laboratory animal carcinogenicity

We explore how well a statistical multistage model describes dose-response patterns in laboratory animal carcinogenicity experiments from a large database of quantal response data. The data are collected from the US EPA's publicly available IRIS data warehouse and examined statistically to determine how often higher-order values in the multistage predictor yield significant improvements in explanatory power over lower-order values. Our results suggest that the addition of a second-order parameter to the model only improves the fit about 20% of the time, while adding even higher-order terms apparently does not contribute to the fit at all, at least with the study designs we captured in the IRIS database. Also included is an examination of statistical tests for assessing significance of higher-order terms in a multistage dose-response model. It is noted that bootstrap testing methodology appears to offer greater stability for performing the hypothesis tests than a more-common, but possibly unstable, "Wald" test.

A benchmark dose analysis for sodium monofluoroacetate (1080) using dichotomous toxicity data

The use of a benchmark dose (BMD) as an alternative to a no-observed-adverse-effect-level (NOAEL) approach was investigated as a means to improve current risk assessment values of sodium monofluoroacetate (1080). The feasibility of implementing the two approaches was investigated for three critical toxicological end points, namely cardiomyopathy, testicular toxicity and teratogenic effects identified from the few available critical studies. The BMD provides better representation of the dose-response relationship, offering an advantage over the current NOAEL approach. The calculated BMDs and lower-bound confidence limits (BMDLs) for the three end points were estimated using the Weibull, probit and quantal linear models for each end point. All models passed the chi2 test statistics (p > or = 0.1) for all three toxicity endpoints tested. A benchmark response (BMR) of 10% (extra risk) was chosen and the Akaike's information criterion (AIC) was used in selecting the appropriate model. The BMDL estimates derived were found to be generally slightly higher but comparable to the NOAEL for those same endpoints. The BMD(10) and BMDL(10) for cardiomyopathy and testicular effects were 0.21 mgkg(-1) bw and 0.10 mgkg(-1) bw, respectively. These values are proposed for use in the eventual determination of the tolerable daily intake (TDI) for 1080.

Identification of a Critical Dose Level for Risk Assessment: Developments in Benchmark Dose Analysis of Continuous Endpoints

The benchmark dose (BMD) method has been recommended to replace the no-observed-adverse-effect-level (NOAEL) approach in health risk assessment of chemical substances. In the present article, developments in BMD analysis from continuous experimental data are proposed. The suggested approach defines the BMD as the dose at which the slope of the S-shaped dose-response relationship changes the most in the low-dose region. This dose resides in a region where the sensitivity to chemical exposure may start to change noticeably. It is shown that the response (defined as a percent change relative to the magnitude, or size, of response) corresponding to the dose where the slope changes the most depends on the geometrical shape of the dose-response curve; the response becomes lower as the curve becomes more asymmetrical and threshold-like in the low-dose region. Given a symmetrical case, described by the Hill function, the response associated with the critical dose level becomes 21% (defined as a percent change relative to the magnitude, or size, of response). According to a limiting case of asymmetry and threshold-like characteristics, reflected by a Gompertz curve, the response corresponding to the dose of interest becomes as low as 7.3% (defined as a percent change relative to the magnitude, or size, of response). Use of a response in the range of 5-10% when estimating the BMD conservatively accounts for uncertainties associated with the proposed strategy, and may be appropriate in a risk assessment point of view. The present investigation also indicated that a BMD defined according to the suggested procedure may be estimated more precisely relative to BMDs defined under other approaches for continuous data.

Benchmark calculations in risk assessment using continuous dose-response information: the influence of variance and the determination of a cut-off value

A benchmark dose (BMD) is the dose of a chemical that corresponds to a predetermined increase in the response (the benchmark response, BMR) of a health effect. In this article, a method (the hybrid approach) for benchmark calculations from continuous dose-response information is investigated. In the formulation of the methodology, a cut-off value for an adverse health effect has to be determined. It is shown that the influence of variance on the hybrid model depends on the choice of determination of the cut-off point. If the cut-off value is determined as corresponding to a specified tail proportion of the control distribution, P(0), the BMD becomes biased upward when the variance is biased upward. On the contrary, if the cut-off value is directly determined to some level of the continuous response variable, the BMD becomes biased upward when the variance is biased downward. A simulation study was also performed in which the accuracy and precision of the BMD was compared for the two ways of determining the cut-off value. In general, considering BMRs of 1, 5, and 10% (additional risk) the precision of the BMD became higher when the cut-off value was estimated by specifying P(0), relative to the case with a direct determination. Use of the square-root of the maximum-likelihood estimator of the variance in BMD estimation may provide a bias that is reflected by the cut-off formulation (downward bias if specifying P(0), and upward bias if specifying the cut-off, c, directly). This feature may be reduced if an unbiased estimator of the standard deviation is used in the calculations.

Comparison of available benchmark dose softwares and models using trichloroethylene as a model substance

By using trichloroethylene as a model substance the U.S. EPA benchmark dose software was compared to the software by Crump and the software by Kalliomaa. Dose-response and dose-effect data on the liver, kidneys, central nervous system (CNS), and tumours were selected for the evaluation. Based on the present study the U.S. EPA software is preferable to the other softwares for dichotomous data. A wider range in benchmark doses was often observed for dichotomous data when the numbers of dose levels were limited. The log-logistic model in most cases gave the best fit when ranking the dichotomous models. In addition, the log-logistic model often implied a more conservative benchmark dose. For continuous data it was more difficult to find a model describing the data. The softwares by Kalliomaa and by the U.S. EPA offered the best opportunities for benchmark dose modelling of continuous data. Flexible models, like the Hill- and the Mult model, are needed for S-shaped continuous data but these models demand more dose levels in order to describe the data. Since the number of dose levels are important for model selection study design is important and should be further evaluated.