Statistical models for low dose exposure

Leukemia risk assessment of exposure to low-levels of benzene based on the linearized multistage model

Objectives

To assess leukemia risk in occupational populations exposed to low levels of benzene.

Methods

Leukemia incidence data from the Chinese Benzene Cohort Study were fitted using the Linearized multistage (LMS) model. Individual benzene exposure levels, urinary S-phenylmercapturic acid (S-PMA) and trans, trans-muconic acid (t, t-MA) were measured among 98 benzene-exposed workers from factories in China. Subjects were categorized into four groups by rounding the quartiles of cumulative benzene concentrations (< 3, 3-5, 5-12, ≥12 mg/m3·year, respectively). The risk of benzene-induced leukemia was assessed using the LMS model, and the results were validated using the EPA model and the Singapore semi-quantitative risk assessment model.

Results

The leukemia risks showed a positive correlation with increasing cumulative concentration in the four exposure groups (excess leukemia risks were 4.34, 4.37, 4.44 and 5.52 × 10-4, respectively; Ptrend < 0.0001) indicated by the LMS model. We also found that the estimated leukemia risk using urinary t, t-MA in the LMS model was more similar to those estimated by airborne benzene compared to S-PMA. The leukemia risk estimated by the LMS model was consistent with both the Singapore semi-quantitative risk assessment model at all concentrations and the EPA model at high concentrations (5-12, ≥12 mg/m3·year), while exceeding the EPA model at low concentrations (< 3 and 3-5 mg/m3·year). However, in all four benzene-exposed groups, the leukemia risks estimated by these three models exceeded the lowest acceptable limit for carcinogenic risk set by the EPA at 1 × 10-6.

Conclusion

This study demonstrates the utility of the LMS model derived from the Chinese benzene cohort in assessing leukemia risk associated with low-level benzene exposure, and suggests that leukemia risk may occur at cumulative concentrations below 3 mg/m3·year.

Molecular signaling network motifs provide a mechanistic basis for cellular threshold responses

BACKGROUND

Increasingly, there is a move toward using in vitro toxicity testing to assess human health risk due to chemical exposure. As with in vivo toxicity testing, an important question for in vitro results is whether there are thresholds for adverse cellular responses. Empirical evaluations may show consistency with thresholds, but the main evidence has to come from mechanistic considerations.

OBJECTIVES

Cellular response behaviors depend on the molecular pathway and circuitry in the cell and the manner in which chemicals perturb these circuits. Understanding circuit structures that are inherently capable of resisting small perturbations and producing threshold responses is an important step towards mechanistically interpreting in vitro testing data.

METHODS

Here we have examined dose-response characteristics for several biochemical network motifs. These network motifs are basic building blocks of molecular circuits underpinning a variety of cellular functions, including adaptation, homeostasis, proliferation, differentiation, and apoptosis. For each motif, we present biological examples and models to illustrate how thresholds arise from specific network structures.

DISCUSSION AND CONCLUSION

Integral feedback, feedforward, and transcritical bifurcation motifs can generate thresholds. Other motifs (e.g., proportional feedback and ultrasensitivity)produce responses where the slope in the low-dose region is small and stays close to the baseline. Feedforward control may lead to nonmonotonic or hormetic responses. We conclude that network motifs provide a basis for understanding thresholds for cellular responses. Computational pathway modeling of these motifs and their combinations occurring in molecular signaling networks will be a key element in new risk assessment approaches based on in vitro cellular assays.

Toward a unified approach to dose-response modeling in ecotoxicology

This study reviews dose-response models that are used in ecotoxicology. The focus lies on clarification of differences and similarities between models, and as a side effect, their different guises in ecotoxicology are unravelled. A look at frequently used dose-response models reveals major discrepancies, among other things in naming conventions. Therefore, there is a need for a unified view on dose-response modeling in order to improve the understanding of it and to facilitate communication and comparison of findings across studies, thus realizing its full potential. This study attempts to establish a general framework that encompasses most dose-response models that are of interest to ecotoxicologists in practice. The framework includes commonly used models such as the log-logistic and Weibull models, but also features entire suites of models as found in various guidance documents. An outline on how the proposed framework can be implemented in statistical software systems is also provided.

Statistical model to estimate a threshold dose and its confidence limits for the analysis of sublinear dose-response relationships, exemplified for mutagenicity data

Strongly sublinear dose-response relationships (slope increasing with dose) raise the question about a putative threshold dose below which no biologically relevant effect would be expected. A mathematical threshold with a break in the curve at the threshold dose is generally rejected for consequences of genotoxicity such as mutation, because proportionality between low dose and the rate of DNA-adduct formation is a reasonable hypothesis. In view of an increasing database for distinct deviation from linearity for mutagenicity, we offer a statistical model to analyze continuous response data and estimate a threshold dose together with its confidence limits, thereby taking data quality and degree of sublinearity into account. The simplest mathematical threshold model is a hockey stick defined by a low-dose part with slope zero at background level a to a theoretical break point at threshold dose td, followed by a linear increase above td with slope b. The function is y (dose d)=a+bx(d-td)x1([d>td]). Using the free statistics software package "R", we make a procedure available to estimate the parameters a, b, and td. Confidence intervals are calculated for all parameters at a significance level that can be defined by the user. If the lower limit of the confidence interval for td is >0, linearity is rejected. The procedure is illustrated by two examples. A small data set with three replicates per dose group, indicating a threshold for the induction of thymidine kinase mutants in L5178Y tk(+/-) mouse lymphoma cells treated with methyl methanesulfonate, did not achieve significance. On the other hand, the large data set reported in this issue (Gocke et al.) on lacZ mutants in bone marrow cells of transgenic mice treated with ethyl methanesulfonate strongly favoured the hockey stick model. The question of a theoretically expected linear dose-related increase below the threshold dose is addressed by linear regression of the data below the break point and estimation of an upper limit of the slope. The question of biological relevance of the resulting slope is discussed against the normal variation of background measures in the control group.

Simultaneous Confidence Bands for Abbott-Adjusted Quantal Response Models

We study use of a Scheffé-style simultaneous confidence band as applied to low-dose risk estimation with quantal response data. We consider two formulations for the dose-response risk function, an Abbott-adjusted Weibull model and an Abbott-adjusted log-logistic model. Using the simultaneous construction, we derive methods for estimating upper confidence limits on predicted extra risk and, by inverting the upper bands on risk, lower bounds on the benchmark dose, or BMD, at which a specific level of 'benchmark risk' is attained. Monte Carlo evaluations explore the operating characteristics of the simultaneous limits.

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.

SIMULTANEOUS CONFIDENCE BOUNDS FOR LOW-DOSE RISK ASSESSMENT WITH NONQUANTAL DATA

We study the use of simultaneous confidence bounds for making low-dose inferences in quantitative risk analysis. Confidence limits are constructed for outcomes measured on a continuous scale, assuming a simple linear model for the observed response. From the simultaneous confidence bounds, simultaneous lower limits on the benchmark dose associated with a particular risk are also constructed.

Practical threshold for micronucleated reticulocyte induction observed for low doses of mitomycin C, Ara-C and colchicine

Micronucleus induction was studied for the DNA target clastogens mitomycin C (MMC) and 1-beta-D-arabinofuranosylcytosine (Ara-C), and also the non-DNA target aneugen colchicine (COL) in order to evaluate the dose-response relationship at very low dose levels. The acridine orange (AO) supravital staining method was used for microscopy and the anti-CD71-FITC based method was used for flow cytometric analysis. In the AO method, 2000 reticulocytes were analysed as commonly advised, but in the flow cytometric method, 2000, 20,000, 200,000 and 1,000,000 reticulocytes were analysed for each sample to increase the detecting power (i.e. sensitivity) of the assay. The present data show that increasing the number of cells scored increases the statistical power of the assay when the cell was considered as a statistical unit. Even so, statistically significant differences from respective vehicle controls were not observed at the lowest dose level for MMC and Ara-C, or the lower four dose levels for COL, even after one million cells were analysed. When the animal was considered as a statistical unit, only the top dose group for each chemical showed significant increase of micronucleated reticulocytes frequency. As non-linear dose-response curves were obtained for each of the three chemicals studied, these observations provide evidence for the existence of a practical threshold for the DNA target clastogens as well as the non-DNA target aneugen studied.

The role of the benchmark dose in a regulatory context

The use of no observed adverse effect levels (NOAELs) as a way of interpreting toxicology studies carries a number of problems, and the benchmark dose (BMD), or its lower confidence limit have been proposed as potential replacements. In practice, the theoretical advantages of the BMD approach are often outweighed by the practical disadvantages posed in a regulatory context. Attempts to seek consensus for the routine use of BMD methodology tend to involve diluting its potential advantages as much as they address the disadvantages, resulting in a relatively complex interpolation tool that delivers little more than the NOAEL. It is time to recognise that the BMD will never entirely replace the NOAEL. The two methods can have complementary roles. The NOAEL is well suited as a routine simple summary of effects in toxicology studies, whilst the BMD can be a higher tier approach for the interpretation of the most critical studies in a regulatory data package.

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

The benchmark dose (BMD) method was evaluated using the USEPA BMD software. Dose-response data on cleft palate and hydronephrosis for a number of related polyhalogenated aromatic compounds were obtained from the literature. According to chi(2) test statistics, each dichotomous USEPA model failed to adequately describe only 1 of 12 cleft palate data sets. For hydronephrosis, the models were discriminated to a higher extent according to global goodness-of-fit. NOAELs for cleft palate corresponded to BMDLs (the approximate lower confidence limit on the BMD) for extra risks in the range of 5% or below. Model dependence of the BMDL estimate was more pronounced at lower levels of benchmark response (BMR). A BMR of 5% (extra risk) is recommended for cleft palate since model differences at this level were limited for all data. In addition, at BMRs of 5-10% the BMDL for all models was little affected by the specified confidence limit size (in the 90-99% range). For BMDL determination a conservative model selection approach was applied. At the suggested level of BMR (5%) this procedure resulted in use of the same model (multistage model) for the cleft palate endpoint in general. Akaike's information criterion (AIC) was considered for comparison between models. Determination of appropriateness of use of such methods in dose-response applications requires further analysis.

Dose-response and threshold-mediated mechanisms in mutagenesis: statistical models and study design

The objective of this paper is to review the use, in mutagenesis, of various mathematical models to describe the dose-response relationship and to try to identify thresholds. It is often taken as axiomatic that genotoxic carcinogens could damage DNA at any level of exposure, leading to a mutation, and that this could ultimately result in tumour development. This has led to the assumption that for genotoxic chemicals, there is no discernible threshold. This assumption is increasingly being challenged in the case of aneugens. The distinction between 'absolute' and 'pragmatic' thresholds is made and the difficulties in determining 'absolute' thresholds using hypothesis testing approaches are described. The potential of approaches, based upon estimation rather than statistical significance for the characterization of dose-response relationships, is stressed. The achievement of a good fit of a mathematical model to experimental data is not proof that the mechanism supposedly underlying this model is operating. It has been argued, in the case of genotoxic chemicals, that any effects produced by a genotoxic chemical which augments that producing a background incidence in unexposed individuals will lead to a dose-response relationship that is non-thresholded and is linear at low doses. The assumptions underlying this presumption are explored in the context of the increasing knowledge of the mechanistic basis of mutagenicity and carcinogenicity. The possibility that exposure to low levels of genotoxic chemicals may induce and enhance defence and repair mechanisms is not easily incorporated into many of the existing mathematical models and should be an objective in the development of the next generation of biologically based dose-response (BB-DR) models. Studies aimed at detecting or characterizing non-linearities in the dose-response relationship need appropriate experimental designs with careful attention to the choice of biomarker, number and selection of dose levels, optimum allocation of experimental units and appropriate levels of replication within and repetition of experiments. The characterization of dose-response relationships with appropriate measures of uncertainty can help to identify 'pragmatic' thresholds based upon biologically relevant criteria which can help in the regulatory process.