Assessment of the Dose–Response Relationship Between Folate Exposure and Cognitive Impairment: Synthesizing Data from Documented Studies

The dose–response relationship between folate levels and cognitive impairment among individuals with vitamin B12 deficiency is an essential component of a risk-benefit analysis approach to regulatory and policy recommendations regarding folic acid fortification. Epidemiological studies provide data that are potentially useful for addressing this research question, but the lack of analysis and reporting of data in a manner suitable for dose–response purposes hinders the application of the traditional evidence synthesis process. This study aimed to estimate a quantitative dose–response relationship between folate exposure and the risk of cognitive impairment among older adults with vitamin B12 deficiency using “probabilistic meta-analysis,” a novel approach for synthesizing data from observational studies. Second-order multistage regression was identified as the best-fit model for the association between the probability of cognitive impairment and serum folate levels based on data generated by randomly sampling probabilistic distributions with parameters estimated based on summarized information reported in relevant publications. The findings indicate a “J-shape” effect of serum folate levels on the occurrence of cognitive impairment. In particular, an excessive level of folate exposure is predicted to be associated with a higher risk of cognitive impairment, albeit with greater uncertainty than the association between low folate exposure and cognitive impairment. This study directly contributes to the development of a practical solution to synthesize observational evidence for dose–response assessment purposes, which will help strengthen future nutritional risk assessments for the purpose of informing decisions on nutrient fortification in food.     

Estimating Benchmark Concentrations and Other Noncancer Endpoints in Epidemiology Studies

Methods for evaluating the hazards associated with noncancer responses with epidemiologic data are considered. The methods for noncancer risk assessment have largely been developed for experimental data, and are not always suitable for the more complex structure of epidemiologic data. In epidemiology, the measurement of the response and the exposure is often either continuous or dichotomous. For a continuous noncancer response modeled with multiple regression, a variety of endpoints may be examined: (1) the concentration associated with absolute or relative decrements in response; (2) a threshold concentration associated with no change in response; and (3) the concentration associated with a particular added risk of impairment. For a dichotomous noncancer response modeled with logistic regression, concentrations associated with specified added/extra risk or with a threshold responses may be estimated. No-observed-effect concentrations may also be estimated for categorizations of exposures for both continuous and dichotomous responses but these may depend on the arbitrary categories chosen. Respiratory function in miners exposed to coal dust is used to illustrate these methods.     

Model-Averaged Benchmark Concentration Estimates for Continuous Response Data Arising from Epidemiological Studies

Worker populations often provide data on adverse responses associated with exposure to potential hazards. The relationship between hazard exposure levels and adverse response can be modeled and then inverted to estimate the exposure associated with some specified response level. One concern is that this endpoint may be sensitive to the concentration metric and other variables included in the model. Further, it may be that the models yielding different risk endpoints are all providing relatively similar fits. We focus on evaluating the impact of exposure on a continuous response by constructing a model-averaged benchmark concentration from a weighted average of model-specific benchmark concentrations. A method for combining the estimates based on different models is applied to lung function in a cohort of miners exposed to coal dust. In this analysis, we see that a small number of the thousands of models considered survive a filtering criterion for use in averaging. Even after filtering, the models considered yield benchmark concentrations that differ by a factor of 2 to 9 depending on the concentration metric and covariates. The model-average BMC captures this uncertainty, and provides a useful strategy for addressing model uncertainty.     

Heterogeneity: A Major Factor Influencing Microbial Exposure and Risk Assessment

Microbial risk assessment is dependent on several biological and environmental factors that affect both the exposure characteristics to the biological agents and the mechanisms of pathogenicity involved in the pathogen‐host relationship. Many exposure assessment studies still focus on the location parameters of the probability distribution representing the concentration of the pathogens and/or toxin. However, the mean or median by themselves are insufficient to evaluate the adverse effects that are associated with a given level of exposure. Therefore, the effects on the risk of disease of a number of factors, including the shape parameters characterizing the distribution patterns of the pathogen in their environment, were investigated. The statistical models, which were developed to provide a better understanding of the factors influencing the risk, highlight the role of heterogeneity and its consequences on the commonly used risk assessment paradigm. Indeed, the heterogeneity characterizing the spatial and temporal distribution of the pathogen and/or the toxin contained in the water or food consumed is shown to be a major factor that may influence the magnitude of the risk dramatically. In general, the risk diminishes with higher levels of heterogeneity. This scheme is totally inverted in the presence of a threshold in the dose‐response relationship, since heterogeneity will then have a tremendous impact, namely, by magnifying the risk when the mean concentration of pathogens is below the threshold. Moreover, the approach of this article may be useful for risk ranking analysis, regarding different exposure conditions, and may also lead to improved water and food quality guidelines.     

Correlation of Noncancer Benchmark Doses in Short‐ and Long‐Term Rodent Bioassays

This study investigated whether, in the absence of chronic noncancer toxicity data, short‐term noncancer toxicity data can be used to predict chronic toxicity effect levels by focusing on the dose–response relationship instead of a critical effect. Data from National Toxicology Program (NTP) technical reports have been extracted and modeled using the Environmental Protection Agency's Benchmark Dose Software. Best‐fit, minimum benchmark dose (BMD), and benchmark dose lower limits (BMDLs) have been modeled for all NTP pathologist identified significant nonneoplastic lesions, final mean body weight, and mean organ weight of 41 chemicals tested by NTP between 2000 and 2012. Models were then developed at the chemical level using orthogonal regression techniques to predict chronic (two years) noncancer health effect levels using the results of the short‐term (three months) toxicity data. The findings indicate that short‐term animal studies may reasonably provide a quantitative estimate of a chronic BMD or BMDL. This can allow for faster development of human health toxicity values for risk assessment for chemicals that lack chronic toxicity data.     

Modeling for Risk Assessment of Neurotoxic Effects

The regulation of noncancer toxicants, including neurotoxicants, has usually been based upon a reference dose (allowable daily intake). A reference dose is obtained by dividing a no-observed-effect level by uncertainty (safety) factors to account for intraspecies and interspecies sensitivities to a chemical. It is assumed that the risk at the reference dose is negligible, but no attempt generally is made to estimate the risk at the reference dose. A procedure is outlined that provides estimates of risk as a function of dose. The first step is to establish a mathematical relationship between a biological effect and the dose of a chemical. Knowledge of biological mechanisms and/or pharmacokinetics can assist in the choice of plausible mathematical models. The mathematical model provides estimates of average responses as a function of dose. Secondly, estimates of risk require selection of a distribution of individual responses about the average response given by the mathematical model. In the case of a normal or lognormal distribution, only an estimate of the standard deviation is needed. The third step is to define an adverse level for a response so that the probability (risk) of exceeding that level can be estimated as a function of dose. Because a firm response level often cannot be established at which adverse biological effects occur, it may be necessary to at least establish an abnormal response level that only a small proportion of individuals would exceed in an unexposed group. That is, if a normal range of responses can be established, then the probability (risk) of abnormal responses can be estimated. In order to illustrate this process, measures of the neurotransmitter serotonin and its metabolite 5-hydroxyindoleacetic acid in specific areas of the brain of rats and monkeys are analyzed after exposure to the neurotoxicant methylene-dioxymethamphetamine. These risk estimates are compared with risk estimates from the quantal approach in which animals are classified as either abnormal or not depending upon abnormal serotonin levels.     

Methodology for Determining the Appropriateness of a Linear Dose‐Response Function

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose‐response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose‐response functions are approximately linear when the dose is low. Nevertheless, what constitutes “low” is dependent on the parameters of the dose‐response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose‐response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose‐response approximation, for example, the expected value for exposure doses is two to three logs₁₀ smaller than the upper bound of the linear portion of the dose‐response function, then predicting the risk‐reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.     

Development and application of a dose–response model for Elizabethkingia spp

Elizabethkingia spp. are common environmental pathogens responsible for infections in more vulnerable populations. Although the exposure routes of concern are not well understood, some hospital-associated outbreaks have indicated possible waterborne transmission. In order to facilitate quantitative microbial risk assessment (QMRA) for Elizabethkingia spp., this study fit dose–response models to frog and mice datasets that evaluated intramuscular and intraperitoneal exposure to Elizabethkingia spp. The frog datasets could be pooled, and the exact beta-Poisson model was the best fitting model with optimized parameters α  = 0.52 and β = 86,351. Using the exact beta-Poisson model, the dose of Elizabethkingia miricola resulting in a 50% morbidity response (LD₅₀) was estimated to be approximately 237,000 CFU. The model developed herein was used to estimate the probability of infection for a hospital patient under a modeled exposure scenario involving a contaminated medical device and reported Elizabethkingia spp. concentrations isolated from hospital sinks after an outbreak. The median exposure dose was approximately 3 CFU/insertion event, and the corresponding median risk of infection was 3.4E-05. The median risk estimated in this case study was lower than the 3% attack rate observed in a previous outbreak, however, there are noted gaps pertaining to the possible concentrations of Elizabethkingia spp. in tap water and the most likely exposure routes. This is the first dose–response model developed for Elizabethkingia spp. thus enabling future risk assessments to help determine levels of risk and potential effective risk management strategies.     

Estimating Preventable Fractions of Disease Caused by a Specified Biological Mechanism: PAHs in Smoking Lung Cancers as an Example

Epidemiology textbooks often interpret population attributable fractions based on 2 x 2 tables or logistic regression models of exposure-response associations as preventable fractions, i.e., as fractions of illnesses in a population that would be prevented if exposure were removed. In general, this causal interpretation is not correct, since statistical association need not indicate causation; moreover, it does not identify how much risk would be prevented by removing specific constituents of complex exposures. This article introduces and illustrates an approach to calculating useful bounds on preventable fractions, having valid causal interpretations, from the types of partial but useful molecular epidemiological and biological information often available in practice. The method applies probabilistic risk assessment concepts from systems reliability analysis, together with bounding constraints for the relationship between event probabilities and causation (such as that the probability that exposure X causes response Y cannot exceed the probability that exposure X precedes response Y, or the probability that both X and Y occur) to bound the contribution to causation from specific causal pathways. We illustrate the approach by estimating an upper bound on the contribution to lung cancer risk made by a specific, much-discussed causal pathway that links smoking to a polycyclic aromatic hydrocarbon (PAH) (specifically, benzo(a)pyrene diol epoxide-DNA) adducts at hot spot codons at p53 in lung cells. The result is a surprisingly small preventable fraction (of perhaps 7% or less) for this pathway, suggesting that it will be important to consider other mechanisms and non-PAH constituents of tobacco smoke in designing less risky tobacco-based products.     

Risk Assessment of Nongenotoxic Carcinogens Based upon Cell Proliferation/Death Rates in Rodents

Increased cell proliferation increases the opportunity for transformations of normal cells to malignant cells via intermediate cells. Nongenotoxic cytotoxic carcinogens that increase cell proliferation rates to replace necrotic cells are likely to have a threshold dose for cytotoxicity below which necrosis and hence, carcinogenesis do not occur. Thus, low dose cancer risk estimates based upon nonthreshold, linear extrapolation are inappropriate for this situation. However, a threshold dose is questionable if a nongenotoxic carcinogen acts via a cell receptor. Also, a nongenotoxic carcinogen that increases the cell proliferation rate, via the cell division rate and/or cell removal rate by apoptosis, by augmenting an existing endogenous mechanism is not likely to have a threshold dose. Whether or not a threshold dose exists for nongenotoxic carcinogens, it is of interest to study the relationship between lifetime tumor incidence and the cell proliferation rate. The Moolgavkar–Venzon–Knudson biologically based stochastic two-stage clonal expansion model is used to describe a carcinogenic process. Because the variability in cell proliferation rates among animals often makes it impossible to detect changes of less than 20% in the rate, it is shown that small changes in the cell proliferation rate, that may be obscured by the background noise in rates, can produce large changes in the lifetime tumor incidence as calculated from the Moolgavkar–Venzon–Knudson model. That is, dose response curves for cell proliferation and tumor incidence do not necessarily mimic each other. This makes the use of no observed effect levels (NOELs) for cell proliferation rates often inadmissible for establishing acceptable daily intakes (ADIs) of nongenotoxic carcinogens. In those cases where low dose linearity is not likely, a potential alternative to a NOEL is a benchmark dose corresponding to a small increase in the cell proliferation rate, e. g., 1%, to which appropriate safety (uncertainty) factors can be applied to arrive at an ADI.     

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.     

An Integrated Model of Infection Risk in a Health-Care Environment

Certain respiratory tract infections can be transmitted by hand-to-mucous-membrane contact, inhalation, and/or direct respiratory droplet spray. In a room occupied by a patient with such a transmissible infection, pathogens present on textile and nontextile surfaces, and pathogens present in the air, provide sources of exposure for an attending health-care worker (HCW); in addition, close contact with the patient when the latter coughs allows for droplet spray exposure. We present an integrated model of pertinent source-environment-receptor pathways, and represent physical elements in these pathways as "states" in a discrete-time Markov chain model. We estimate the rates of transfer at various steps in the pathways, and their relationship to the probability that a pathogen in one state has moved to another state by the end of a specified time interval. Given initial pathogen loads on textile and nontextile surfaces and in room air, we use the model to estimate the expected pathogen dose to a HCW's mucous membranes and respiratory tract. In turn, using a nonthreshold infectious dose model, we relate the expected dose to infection risk. The system is illustrated with a hypothetical but plausible scenario involving a viral pathogen emitted via coughing. We also use the model to show that a biocidal finish on textile surfaces has the potential to substantially reduce infection risk via the hand-to-mucous-membrane exposure pathway.     

Comparison of the EU T25 Single Point Estimate Method with Benchmark Dose Response Modeling for Estimating Potency of Carcinogens

The T25 single-point estimate method of evaluating the carcinogenic potency of a chemical, which is currently used by the European Union (EU) and is denoted the EU approach, is based on the selection of a single dose in a chronic bioassay with an incidence rate that is significantly higher than the background rate. The T25 is determined from that single point by a linear extrapolation or interpolation to the chronic dose (in mg/kg/day), at which a 25% increase in the incidence of the specified tumor type is expected, corrected for the background rate. Another method used to obtain a carcinogenic potency value based on a 25% increase in incidence above the background rate is the estimation of a T25 derived from a benchmark dose (BMD) response model fit to the chronic bioassay data for the specified tumor type. A comparison was made between these two methods using 276 chronic bioassays conducted by the National Toxicology Program. In each of the 2-year bioassays, a tumor type was selected based on statistical and biological significance, and both EU T25 and BMD T25 estimates were determined for that end point. In addition, simulations were done using underlying cumulative probability distributions to examine the effect of dose spacing, the number of animals per dose group, the possibility of a dose threshold, and variation in the background incidence rates on the EU T25 and BMD estimates. The simulations showed that in the majority of cases the EU T25 method underestimated the true T25 dose and overestimated the carcinogenic potency. The BMD estimate is generally less biased and has less variation about the true T25 value than the EU estimate.     

A Health Risk Benchmark for the Neurologic Effects of Styrene: Comparison with NOAEL/LOAEL Approach

Benchmark dose (BMD) analysis was used to estimate an inhalation benchmark concentration for styrene neurotoxicity. Quantal data on neuropsychologic test results from styrene-exposed workers [Mutti et al. (1984). American Journal of Industrial Medicine, 5, 275-286] were used to quantify neurotoxicity, defined as the percent of tested workers who responded abnormally to > or = 1, > or = 2, or > or = 3 out of a battery of eight tests. Exposure was based on previously published results on mean urinary mandelic- and phenylglyoxylic acid levels in the workers, converted to air styrene levels (15, 44, 74, or 115 ppm). Nonstyrene-exposed workers from the same region served as a control group. Maximum-likelihood estimates (MLEs) and BMDs at 5 and 10% response levels of the exposed population were obtained from log-normal analysis of the quantal data. The highest MLE was 9 ppm (BMD = 4 ppm) styrene and represents abnormal responses to > or = 3 tests by 10% of the exposed population. The most health-protective MLE was 2 ppm styrene (BMD = 0.3 ppm) and represents abnormal responses to > or = 1 test by 5% of the exposed population. A no observed adverse effect level/lowest observed adverse effect level (NOAEL/LOAEL) analysis of the same quantal data showed workers in all styrene exposure groups responded abnormally to > or = 1, > or = 2, or > or = 3 tests, compared to controls, and the LOAEL was 15 ppm. A comparison of the BMD and NOAEL/LOAEL analyses suggests that at air styrene levels below the LOAEL, a segment of the worker population may be adversely affected. The benchmark approach will be useful for styrene noncancer risk assessment purposes by providing a more accurate estimate of potential risk that should, in turn, help to reduce the uncertainty that is a common problem in setting exposure levels.     

Estimation of Benchmark Dose as the Threshold Amount of Alcohol Consumption for Blood Pressure in Japanese Workers

In order to determine the threshold amount of alcohol consumption for blood pressure, we calculated the benchmark dose (BMD) of alcohol consumption and its 95% lower confidence interval (BMDL) in Japanese workers. The subjects consisted of 4,383 males and 387 females in a Japanese steel company. The target variables were systolic, diastolic, and mean arterial pressures. The effects of other potential covariates such as age and body mass index were adjusted by including these covariates in the multiple linear regression models. In male workers, BMD/BMDL for alcohol consumption (g/week) at which the probability of an adverse response was estimated to increase by 5% relative to no alcohol consumption, were 396/315 (systolic blood pressure), 321/265 (diastolic blood pressure), and 326/269 (mean arterial pressures). These values were based on significant regression coefficients of alcohol consumption. In female workers, BMD/BMDL for alcohol consumption based on insignificant regression coefficients were 693/134 (systolic blood pressure), 199/90 (diastolic blood pressure), and 267/77 (mean arterial pressure). Therefore, BMDs/BMDLs in males were more informative than those in females as there was no significant relationship between alcohol and blood pressure in females. The threshold amount of alcohol consumption determined in this study provides valuable information for preventing alcohol-induced hypertension.     

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.     

On Summarizing Group Exposures in Risk Assessment: Is an Arithmetic Mean or a Geometric Mean More Appropriate?

Since substantial bias can result from assigning some type of mean exposure to a group, risk assessments based on epidemiological data should avoid the grouping of data whenever possible. However, ungrouped data are frequently unavailable, and the question arises as to whether an arithmetic or geometric mean is the most appropriate summary measure of exposure. It is argued in this paper that one should use the type of mean for which the total risk that would result if every member of the population was exposed to the mean level is as close as possible to the actual total population risk. Using this criterion an arithmetic mean is always preferred over a geometric mean whenever the dose response is convex. In each of several data sets examined in this paper for which the dose response was not convex, an arithmetic mean was still preferred based on this criterion.     

Estimation of a Benchmark Dose in the Presence or Absence of Hormesis Using Posterior Averaging

U.S. Environment Protection Agency benchmark doses for dichotomous cancer responses are often estimated using a multistage model based on a monotonic dose‐response assumption. To account for model uncertainty in the estimation process, several model averaging methods have been proposed for risk assessment. In this article, we extend the usual parameter space in the multistage model for monotonicity to allow for the possibility of a hormetic dose‐response relationship. Bayesian model averaging is used to estimate the benchmark dose and to provide posterior probabilities for monotonicity versus hormesis. Simulation studies show that the newly proposed method provides robust point and interval estimation of a benchmark dose in the presence or absence of hormesis. We also apply the method to two data sets on carcinogenic response of rats to 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin.     

Bayesian Development of a Dose‐Response Model for Aspergillus fumigatus and Invasive Aspergillosis

Invasive aspergillosis (IA) is a major cause of mortality in immunocompromized hosts, most often consecutive to the inhalation of spores of Aspergillus. However, the relationship between Aspergillus concentration in the air and probability of IA is not quantitatively known. In this study, this relationship was examined in a murine model of IA. Immunosuppressed Balb/c mice were exposed for 60 minutes at day 0 to an aerosol of A. fumigatus spores (Af293 strain). At day 10, IA was assessed in mice by quantitative culture of the lungs and galactomannan dosage. Fifteen separate nebulizations with varying spore concentrations were performed. Rates of IA ranged from 0% to 100% according to spore concentrations. The dose‐response relationship between probability of infection and spore exposure was approximated using the exponential model and the more flexible beta‐Poisson model. Prior distributions of the parameters of the models were proposed then updated with data in a Bayesian framework. Both models yielded close median dose‐responses of the posterior distributions for the main parameter of the model, but with different dispersions, either when the exposure dose was the concentration in the nebulized suspension or was the estimated quantity of spores inhaled by a mouse during the experiment. The median quantity of inhaled spores that infected 50% of mice was estimated at 1.8 × 10⁴ and 3.2 × 10⁴ viable spores in the exponential and beta‐Poisson models, respectively. This study provides dose‐response parameters for quantitative assessment of the relationship between airborne exposure to the reference A. fumigatus strain and probability of IA in immunocompromized hosts.     

Characterizing Dose-Response I: Critical Assessment of the Benchmark Dose Concept

We present a critical assessment of the benchmark dose (BMD) method introduced by Crump⁽¹⁾ as an alternative method for setting a characteristic dose level for toxicant risk assessment. The no-observed-adverse-effect-level (NOAEL) method has been criticized because it does not use all of the data and because the characteristic dose level obtained depends on the dose levels and the statistical precision (sample sizes) of the study design. Defining the BMD in terms of a confidence bound on a point estimate results in a characteristic dose that also varies with the statistical precision and still depends on the study dose levels.⁽²⁾ Indiscriminate choice of benchmark response level may result in a BMD that reflects little about the dose-response behavior available from using all of the data. Another concern is that the definition of the BMD for the quantal response case is different for the continuous response case. Specifically, defining the BMD for continuous data using a ratio of increased effect divided by the background response results in an arbitrary dependence on the natural background for the endpoint being studied, making comparison among endpoints less meaningful and standards more arbitrary. We define a modified benchmark dose as a point estimate using the ratio of increased effect divided by the full adverse response range which enables consistent placement of the benchmark response level and provides a BMD with a more consistent relationship to the dose-response curve shape.