Dose Response for Infectivity of Several Strains of Campylobacter jejuni in Chickens

Although some major risk studies have been done for Campylobacter jejuni, its dose response is not well characterized. Only a single human study is available, providing dose-response information for only a single isolate. As substantial heterogeneity in infectivity has been acknowledged for other pathogens, it remains unknown how well this single study represents the dose-response relation for this pathogen. As future human challenge studies with Campylobacter are unlikely, we have to find other means of studying its infectivity. Several dose-response studies have been done using chickens as host organisms. These studies may be used to obtain quantitative information on the variation in infectivity among different isolates of this pathogen. A hierarchical Bayesian model is well suited to describe heterogeneity, and we demonstrate how the beta-Poisson model of microbial infection may be adapted to allow for within- and between-isolate variation. Isolates tested in chickens can be categorized into two distinct groups: lab-adapted and fresh isolates, and we show how the hierarchical dose-response model can be used to quantitatively describe their differences. Fresh isolates show higher colonization potential and less within-isolate variation than lab isolates. The results indicate that Campylobacter jejuni is highly infectious in chickens. Different isolates show great variation in infectivity, especially between lab and fresh isolates, indicating that human clinical (volunteer) studies on infectivity must be interpreted cautiously.     

Significance of Exposure Assessment to Analysis of Cancer Risk from Inorganic Arsenic in Drinking Water in Taiwan

The primary source of evidence that inorganic arsenic in drinking water is associated with increased mortality from cancer at internal sites (bladder, liver, lung, and other organs) is a large ecologic study conducted in regions of Southwest Taiwan endemic to Blackfoot disease. The dose-response patterns for lung, liver, and bladder cancers display a nonlinear dose-response relationship with arsenic exposure. The data do not appear suitable, however, for the more refined task of dose-response assessment, particularly for inference of risk at the low arsenic concentrations found in some U.S. water supplies. The problem lies in variable arsenic concentrations between the wells within a village, largely due to a mix of shallow wells and deep artesian wells, and in having only one well test for 24 (40%) of the 60 villages. The current analysis identifies 14 villages where the exposure appears most questionable, based on criteria described in the text. The exposure values were then changed for seven of the villages, from the median well test being used as a default to some other point in the village's range of well tests that would contribute to smoothing the appearance of a dose-response curve. The remaining seven villages, six of which had only one well test, were deleted as outliers. The resultant dose-response patterns showed no evidence of excess risk below arsenic concentrations of 0.1 mg/l. Of course, that outcome is dependent on manipulation of the data, as described. Inclusion of the seven deleted villages would make estimates of risk much higher at low doses. In those seven villages, the cancer mortality rates are significantly high for their exposure levels, suggesting that their exposure values may be too low or that other etiological factors need to be taken into account.     

Optimal Designs for Estimating the Effective Dose in Developmental Toxicity Experiments

Recent advances in risk assessment have led to the development of joint dose-response models to describe prenatal death and fetal malformation rates in developmental toxicity experiments. These models can be used to estimate the effective dose corresponding to a 5% excess risk for both these toxicological endpoints, as well as for overall toxicity. In this article, we develop optimal experimental designs for the estimation of the effective dose for developmental toxicity using joint Weibull dose-response models for prenatal death and fetal malformation. Based on an extended series of developmental studies, near-optimal designs for prenatal death, malformation, and overall toxicity were found to involve three dose groups: an unexposed control group, a high dose equal to the maximum tolerated dose, and a low dose above or comparable to the effective dose. The effect on the optimal designs of changing the number of implants and the degree of intra-litter correlation is also investigated. Although the optimal design has only three dose groups in most cases, practical considerations involving model lack of fit and estimation of the shape of the dose-response curve suggest that, in practice, suboptimal designs with more than three doses will often be preferred.     

Dose-Response Models for Inhalation of Bacillus anthracis Spores: Interspecies Comparisons

Because experiments with Bacillus anthracis are costly and dangerous, the scientific, public health, and engineering communities are served by thorough collation and analysis of experiments reported in the open literature. This study identifies available dose-response data from the open literature for inhalation exposure to B. anthracis and, via dose-response modeling, characterizes the response of nonhuman animal models to challenges. Two studies involving four data sets amenable to dose-response modeling were found in the literature: two data sets of response of guinea pigs to intranasal dosing with the Vollum and ATCC-6605 strains, one set of responses of rhesus monkeys to aerosol exposure to the Vollum strain, and one data set of guinea pig response to aerosol exposure to the Vollum strain. None of the data sets exhibited overdispersion and all but one were best fit by an exponential dose-response model. The beta-Poisson dose-response model provided the best fit to the remaining data set. As indicated in prior studies, the response to aerosol challenges is a strong function of aerosol diameter. For guinea pigs, the LD₅₀ increases with aerosol size for aerosols at and above 4.5 μm. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD₅₀ when aerosol size is increased from 1 μm to 12 μm. Future experimental research and dose-response modeling should be performed to quantify differences in responses of subpopulations to B. anthracis and to generate data allowing development of interspecies correction factors.     

Applications of Multinomial Dose-Response Models in Developmental Toxicity Risk Assessment

Reproductive and developmental anomalies induced by toxic chemicals may be identified using laboratory experiments with small mammalian species such as rats, mice, and rabbits. In this paper, dose-response models for correlated multinomial data arising in studies of developmental toxicity are discussed. These models provide a joint characterization of dose-response relationships for both embryolethality and teratogenicity. Generalized estimating equations are used for model fitting, incorporating overdispersion relative to the multinomial variation due to correlation among littermates. The fitted dose-response models are used to estimate benchmark doses in a series of experiments conducted by the U.S. National Toxicology Program. Joint analysis of prenatal death and fetal malformation using an extended Dirichlet-trinomial covariance function to characterize overdispersion appears to have statistical and computational advantages over separate analysis of these two end points. Benchmark doses based on overall toxicity are below the minimum of those for prenatal death and fetal malformation and may, thus, be preferred for risk assessment purposes.     

A Parametric Model for Detecting Hormetic Effects in Developmental Toxicity Studies

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.     

Improving cancer dose-response characterization by using physiologically based pharmacokinetic modeling: an analysis of pooled data for acrylonitrile-induced brain tumors to assess cancer potency in the rat.

Historically, U.S. regulators have derived cancer slope factors by using applied dose and tumor response data from a single key bioassay or by averaging the cancer slope factors of several key bioassays. Recent changes in U.S. Environmental Protection Agency (EPA) guidelines for cancer risk assessment have acknowledged the value of better use of mechanistic data and better dose-response characterization. However, agency guidelines may benefit from additional considerations presented in this paper. An exploratory study was conducted by using rat brain tumor data for acrylonitrile (AN) to investigate the use of physiologically based pharmacokinetic (PBPK) modeling along with pooling of dose-response data across routes of exposure as a means for improving carcinogen risk assessment methods. In this study, two contrasting assessments were conducted for AN-induced brain tumors in the rat on the basis of (1) the EPA's approach, the dose-response relationship was characterized by using administered dose/concentration for each of the key studies assessed individually; and (2) an analysis of the pooled data, the dose-response relationship was characterized by using PBPK-derived internal dose measures for a combined database of ten bioassays. The cancer potencies predicted for AN by the contrasting assessments are remarkably different (i.e., risk-specific doses differ by as much as two to four orders of magnitude), with the pooled data assessments yielding lower values. This result suggests that current carcinogen risk assessment practices overestimate AN cancer potency. This methodology should be equally applicable to other data-rich chemicals in identifying (1) a useful dose measure, (2) an appropriate dose-response model, (3) an acceptable point of departure, and (4) an appropriate method of extrapolation from the range of observation to the range of prediction when a chemical's mode of action remains uncertain.     

Model Averaging in Microbial Risk Assessment Using Fractional Polynomials

The alleviation of food-borne diseases caused by microbial pathogen remains a great concern in order to ensure the well-being of the general public. The relation between the ingested dose of organisms and the associated infection risk can be studied using dose-response models. Traditionally, a model selected according to a goodness-of-fit criterion has been used for making inferences. In this article, we propose a modified set of fractional polynomials as competitive dose-response models in risk assessment. The article not only shows instances where it is not obvious to single out one best model but also illustrates that model averaging can best circumvent this dilemma. The set of candidate models is chosen based on biological plausibility and rationale and the risk at a dose common to all these models estimated using the selected models and by averaging over all models using Akaike's weights. In addition to including parameter estimation inaccuracy, like in the case of a single selected model, model averaging accounts for the uncertainty arising from other competitive models. This leads to a better and more honest estimation of standard errors and construction of confidence intervals for risk estimates. The approach is illustrated for risk estimation at low dose levels based on Salmonella typhi and Campylobacter jejuni data sets in humans. Simulation studies indicate that model averaging has reduced bias, better precision, and also attains coverage probabilities that are closer to the 95% nominal level compared to best-fitting models according to Akaike information criterion.     

Dose-Response Model for 13 Strains of Salmonella

Data from a human feeding trial with healthy men were used to develop a dose-response model for 13 strains of Salmonella and to determine the effects of strain variation on the shape of the dose-response curve. Dose-response data for individual strains were fit to a three-phase linear model to determine minimum, median, and maximum illness doses, which were used to define Pert distributions in a computer simulation model. Pert distributions for illness dose of individual strains were combined in an Excel spreadsheet using a discrete distribution to model strain prevalence. In addition, a discrete distribution was used to model dose groups and thus create a model that simulated human feeding trials. During simulation of the model with @Risk, an illness dose and a dose consumed were randomly assigned to each consumption event in the simulated feeding trial and if the illness dose was greater than the dose consumed then the model predicted no illness, otherwise the model predicted that an illness would occur. To verify the dose-response model predictions, the original feeding trial was simulated. The dose-response model predicted a median of 69 (range of 43-101) illnesses compared to 74 in the original trial. Thus, its predictions were in agreement with the data used to develop it. However, predictions of the model are only valid for eggnog, healthy men, and the strains and doses of Salmonella used to develop it. When multiple strains of Salmonella were simulated together, the predicted dose-response curves were irregular in shape. Thus, the sigmoid shape of dose-response curves in feeding trials with one strain of Salmonella may not accurately reflect dose response in naturally contaminated food where multiple strains may be present.     

Application of a Biologically-Based RFD Estimation Method to Tetrachlorodibenzo-P-Dioxin (TCDD) Mediated Immune Suppression and Enzyme Induction

The current methods for a reference dose (RfD) determination can be enhanced through the use of biologically-based dose-response analysis. Methods developed here utilizes information from tetrachlorodibenzo- p -dioxin (TCDD) to focus on noncancer endpoints, specifically TCDD mediated immune system alterations and enzyme induction. Dose-response analysis, using the Sigmoid-Emax (EMAX) function, is applied to multiple studies to determine consistency of response. Through the use of multiple studies and statistical comparison of parameter estimates, it was demonstrated that the slope estimates across studies were very consistent. This adds confidence to the subsequent effect dose estimates. This study also compares traditional methods of risk assessment such as the NOAEL/safety factor to a modified benchmark dose approach which is introduced here. Confidence in the estimation of an effect dose (ED₁₀) was improved through the use of multiple datasets. This is key to adding confidence to the benchmark dose estimates. In addition, the Sigmoid-Emax function when applied to dose-response data using nonlinear regression analysis provides a significantly improved fit to data increasing confidence in parameter estimates which subsequently improve effect dose estimates.     

Effects of the Mechanism of Receptor-Mediated Gene Expression on the Shape of the Dose-Response Curve

A mathematical model of receptor-mediated gene expression that includes receptor binding of natural and xenobiotic ligands, protein synthesis and degradation, and metabolism of the xenobiotic ligand was created to identify the determinants of the shape of the dose-response profile. Values of the model's parameters were varied to reflect alternative mechanisms of expression of the protein. These assumptions had dramatic effects on the computed response to a bolus dose of the xenobiotic ligand. If all processes in the model exhibit hyperbolic kinetics, the dose-response curves can appear sigmoidal but actually be linear with a positive slope at low doses. The slope of the curve only approached zero at low dose, indicative of a threshold for response, if binding of the xenobiotic ligand to the receptor exhibited positive cooperativity (ligand binding at one site increases the affinity for ligand at another binding site on the receptor). Positive cooperativity in the rate-limiting step of protein synthesis produced dose-response curves which were "U-shaped" at low doses, also indicative of a threshold. Positive cooperativity in the metabolism of the xenobiotic ligand produced dose-response curves that increased more rapidly than linearly with increasing dose. The model illustrates the fact that response cannot be predicted from qualitative mechanistic arguments alone; any assessment of risk to health from xenobiotic chemicals must be based on a detailed quantitative examination of the kinetic behavior of each chemical species individually.     

Use of Mechanistic Models to Estimate Low-Dose Cancer Risks

The utility of mechanistic models of cancer for predicting cancer risks at low doses is examined. Based upon a general approximation to the dose-response that is valid at low doses, it is shown that at low doses the dose-response predicted by a mechanistic model is a linear combination of the dose-responses for each of the physiological parameters in the model that are affected by exposure. This demonstrates that, unless the mechanistic model provides a theoretical basis for determining the dose-responses for these parameters, the extrapolation of risks to low doses using a mechanistic model is basically "curve fitting," just as is the case when extrapolating using statistical models. This suggests that experiments to generate data for use in mechanistic models should emphasize measuring the dose-response for dose-related parameters as accurately as possible and at the lowest feasible doses.     

What to Do at Low Doses: A Bounding Approach for Economic Analysis

To quantify the health benefits of environmental policies, economists generally require estimates of the reduced probability of illness or death. For policies that reduce exposure to carcinogenic substances, these estimates traditionally have been obtained through the linear extrapolation of experimental dose-response data to low-exposure scenarios as described in the U.S. Environmental Protection Agency's Guidelines for Carcinogen Risk Assessment (1986). In response to evolving scientific knowledge, EPA proposed revisions to the guidelines in 1996. Under the proposed revisions, dose-response relationships would not be estimated for carcinogens thought to exhibit nonlinear modes of action. Such a change in cancer-risk assessment methods and outputs will likely have serious consequences for how benefit-cost analyses of policies aimed at reducing cancer risks are conducted. Any tendency for reduced quantification of effects in environmental risk assessments, such as those contemplated in the revisions to EPA's cancer-risk assessment guidelines, impedes the ability of economic analysts to respond to increasing calls for benefit-cost analysis. This article examines the implications for benefit-cost analysis of carcinogenic exposures of the proposed changes to the 1986 Guidelines and proposes an approach for bounding dose-response relationships when no biologically based models are available. In spite of the more limited quantitative information provided in a carcinogen risk assessment under the proposed revisions to the guidelines, we argue that reasonable bounds on dose-response relationships can be estimated for low-level exposures to nonlinear carcinogens. This approach yields estimates of reduced illness for use in a benefit-cost analysis while incorporating evidence of nonlinearities in the dose-response relationship. As an illustration, the bounding approach is applied to the case of chloroform exposure.     

Time-Dose-Response Models for Microbial Risk Assessment

While microbial risk assessment (MRA) has been used for over 25 years, traditional dose-response analysis has only predicted the overall risk of adverse consequences from exposure to a given dose. An important issue for consequence assessment from bioterrorist and other microbiological exposure is the distribution of cases over time due to the initial exposure. In this study, the classical exponential and beta-Poisson dose-response models were modified to include exponential-power dependency of time post inoculation (TPI) or its simplified form, exponential-reciprocal dependency of TPI, to quantify the time of onset of an effect presumably associated with the kinetics of in vivo bacterial growth. Using the maximum likelihood estimation approach, the resulting time-dose-response models were found capable of providing statistically acceptable fits to all tested pooled animal survival dose-response data. These new models can consequently describe the development of animal infectious response over time and represent observed responses fairly accurately. This is the first study showing that a time-dose-response model can be developed for describing infections initiated by various pathogens. It provides an advanced approach for future MRA frameworks.     

Task Trade Between Similar Countries

We propose a theory of task trade between countries that have similar relative factor endowments and technological capabilities, but may differ in size. Firms produce differentiated goods by performing a continuum of tasks, each of which generates local spillovers. Tasks can be performed at home or abroad, but offshoring entails costs that vary by task. In equilibrium, the tasks with the highest offshoring costs may not be traded. Among the remainder, those with the relatively higher offshoring costs are performed in the country that has the higher wage and the higher aggregate output. We discuss the relationship between equilibrium wages, equilibrium outputs, and relative country size.     

A Comparison of Three Methods for Calculating Confidence Intervals for the Benchmark Dose

Various methods exist to calculate confidence intervals for the benchmark dose in risk analysis. This study compares the performance of three such methods in fitting nonlinear dose-response models: the delta method, the likelihood-ratio method, and the bootstrap method. A data set from a developmental toxicity test with continuous, ordinal, and quantal dose-response data is used for the comparison of these methods. Nonlinear dose-response models, with various shapes, were fitted to these data. The results indicate that a few thousand runs are generally needed to get stable confidence limits when using the bootstrap method. Further, the bootstrap and the likelihood-ratio method were found to give fairly similar results. The delta method, however, resulted in some cases in different (usually narrower) intervals, and appears unreliable for nonlinear dose-response models. Since the bootstrap method is more time consuming than the likelihood-ratio method, the latter is more attractive for routine dose-response analysis. In the context of a probabilistic risk assessment the bootstrap method has the advantage that it directly links to Monte Carlo analysis.     

A Method for Comparing the Impact on Carcinogenicity of Tobacco Products: A Case Study on Heated Tobacco Versus Cigarettes

Comparing the harmful health effects related to two different tobacco products by applying common risk assessment methods to each individual compound is problematic. We developed a method that circumvents some of these problems by focusing on the change in cumulative exposure (CCE) of the compounds emitted by the two products considered. The method consists of six steps. The first three steps encompass dose-response analysis of cancer data, resulting in relative potency factors with confidence intervals. The fourth step evaluates emission data, resulting in confidence intervals for the expected emission of each compound. The fifth step calculates the change in CCE, probabilistically, resulting in an uncertainty range for the CCE. The sixth step estimates the associated health impact by combining the CCE with relevant dose-response information. As an illustrative case study, we applied the method to eight carcinogens occurring both in the emissions of heated tobacco products (HTPs), a novel class of tobacco products, and tobacco smoke. The CCE was estimated to be 10- to 25-fold lower when using HTPs instead of cigarettes. Such a change indicates a substantially smaller reduction in expected life span, based on available dose-response information in smokers. However, this is a preliminary conclusion, as only eight carcinogens were considered so far. Furthermore, an unfavorable health impact related to HTPs remains as compared to complete abstinence. Our method results in useful information that may help policy makers in better understanding the potential health impact of new tobacco and related products. A similar approach can be used to compare the carcinogenicity of other mixtures.     

Model Averaging Using Fractional Polynomials to Estimate a Safe Level of Exposure

Quantitative risk assessment involves the determination of a safe level of exposure. Recent techniques use the estimated dose-response curve to estimate such a safe dose level. Although such methods have attractive features, a low-dose extrapolation is highly dependent on the model choice. Fractional polynomials, basically being a set of (generalized) linear models, are a nice extension of classical polynomials, providing the necessary flexibility to estimate the dose-response curve. Typically, one selects the best-fitting model in this set of polynomials and proceeds as if no model selection were carried out. We show that model averaging using a set of fractional polynomials reduces bias and has better precision in estimating a safe level of exposure (say, the benchmark dose), as compared to an estimator from the selected best model. To estimate a lower limit of this benchmark dose, an approximation of the variance of the model-averaged estimator, as proposed by Burnham and Anderson, can be used. However, this is a conservative method, often resulting in unrealistically low safe doses. Therefore, a bootstrap-based method to more accurately estimate the variance of the model averaged parameter is proposed.     

A Simple Data Transformation for Estimating Benchmark Doses in Developmental Toxicity Experiments

Developmental anomalies induced by toxic chemicals may be identified using laboratory experiments with rats, mice or rabbits. Multinomial responses of fetuses from the same mother are often positively correlated, resulting in overdispersion relative to multinomial variation. In this article, a simple data transformation based on the concept of generalized design effects due to Rao-Scott is proposed for dose-response modeling of developmental toxicity. After scaling the original multinomial data using the average design effect, standard methods for analysis of uncorrected multinomial data can be applied. Benchmark doses derived using this approach are comparable to those obtained using generalized estimating equations with an extended Dirichlet-trinomial covariance function to describe the dispersion of the original data. This empirical agreement, coupled with a large sample theoretical justification of the Rao-Scott transformation, confirms the applicability of the statistical methods proposed in this article for developmental toxicity risk assessment.     

Regulating Under Uncertainty: Newsboy for Exposure Limits

Setting action levels or limits for health protection is complicated by uncertainty in the dose-response relation across a range of hazards and exposures. To address this issue, we consider the classic newsboy problem. The principles used to manage uncertainty for that case are applied to two stylized exposure examples, one for high dose and high dose rate radiation and the other for ammonia. Both incorporate expert judgment on uncertainty quantification in the dose-response relationship. The mathematical technique of probabilistic inversion also plays a key role. We propose a coupled approach, whereby scientists quantify the dose-response uncertainty using techniques such as structured expert judgment with performance weights and probabilistic inversion, and stakeholders quantify associated loss rates.