A Probabilistic Approach for Deriving Acceptable Human Intake Limits and Human Health Risks from Toxicological Studies: General Framework

The use of uncertainty factors in the standard method for deriving acceptable intake or exposure limits for humans, such as the Reference Dose (RfD), may be viewed as a conservative method of taking various uncertainties into account. As an obvious alternative, the use of uncertainty distributions instead of uncertainty factors is gaining attention. This paper presents a comprehensive discussion of a general framework that quantifies both the uncertainties in the no-adverse-effect level in the animal (using a benchmark-like approach) and the uncertainties in the various extrapolation steps involved (using uncertainty distributions). This approach results in an uncertainty distribution for the no-adverse-effect level in the sensitive human subpopulation, reflecting the overall scientific uncertainty associated with that level. A lower percentile of this distribution may be regarded as an acceptable exposure limit (e.g., RfD) that takes account of the various uncertainties in a nonconservative fashion. The same methodology may also be used as a tool to derive a distribution for possible human health effects at a given exposure level. We argue that in a probabilistic approach the uncertainty in the estimated no-adverse-effect-level in the animal should be explicitly taken into account. Not only is this source of uncertainty too large to be ignored, it also has repercussions for the quantification of the other uncertainty distributions.     

An Alternative Exact Solution of the Two-Stage Clonal Growth Model of Cancer

The approximate solution of the two-stage clonal expansion model of cancer may substantially deviate from the exact solution, and may therefore lead to erroneous conclusions in particular applications. However, for time-varying parameters the exact solution (method of characteristics) is not easy to implement, hampering the accessibility of the model to nonmathematicians. Based on intuitive reasoning, Clewell et al. (1995) proposed an improved approximate solution that is easy to implement whatever time-varying behavior the parameters may have. Here we provide the mathematical foundation for the approximation suggested by Clewell et al. (1995) and show that, after a slight modification, it is in fact an exact solution for the case of time-constant parameters. We were not able to prove that it is an exact solution for time-varying parameters as well. However, several computer simulations showed that the numerical results do not differ from the exact solution as proposed by Moolgavkar and Luebeck (1990). The advantage of this alternative solution is that the hazard rate of the first malignant cell can be evaluated by numerically integrating a single differential equation.     

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.     

Modeling Long-Term Exposure of the Whole Population to Chemicals in Food

This paper discusses a statistical exposure model (STEM) that can be used to estimate the percentage of the population exceeding ingestion intake criteria (e.g., ADI or TDI). In addition, STEM may be linked to toxicokinetic models to evaluate the interindividual variability in internal doses that results from variability in consumption habits. The assumptions of STEM are investigated by analyzing dioxin and cadmium intake data for the Dutch population.     

Integration of Probabilistic Exposure Assessment and Probabilistic Hazard Characterization

A method is proposed for integrated probabilistic risk assessment where exposure assessment and hazard characterization are both included in a probabilistic way. The aim is to specify the probability that a random individual from a defined (sub)population will have an exposure high enough to cause a particular health effect of a predefined magnitude, the critical effect size ( CES ). The exposure level that results in exactly that CES in a particular person is that person's individual critical effect dose ( ICED ). Individuals in a population typically show variation, both in their individual exposure ( IEXP ) and in their ICED . Both the variation in IEXP and the variation in ICED are quantified in the form of probability distributions. Assuming independence between both distributions, they are combined (by Monte Carlo) into a distribution of the individual margin of exposure ( IMoE ). The proportion of the IMoE distribution below unity is the probability of critical exposure ( PoCE ) in the particular (sub)population. Uncertainties involved in the overall risk assessment (i.e., both regarding exposure and effect assessment) are quantified using Monte Carlo and bootstrap methods. This results in an uncertainty distribution for any statistic of interest, such as the probability of critical exposure ( PoCE ). The method is illustrated based on data for the case of dietary exposure to the organophosphate acephate. We present plots that concisely summarize the probabilistic results, retaining the distinction between variability and uncertainty. We show how the relative contributions from the various sources of uncertainty involved may be quantified.     

A Comparison of Two Statistical Approaches to Estimate Long-Term Exposure Distributions from Short-Term Measurements

Two statistical approaches are briefly reviewed, both of which are suitable for estimating interindividual variation in long-term exposure: a recently published regression approach and the standard ANOVA approach. Simulation studies illustrate the performances of the two approaches in estimating the relevant parameters. Their relative advantages and applicability are discussed. It is concluded that when repeated exposure measurements from the same individuals are available, ANOVA is preferable. The regression approach however has its place because it can be applied to certain data types where ANOVA does not apply.     

Exploring the Uncertainties in Cancer Risk Assessment Using the Integrated Probabilistic Risk Assessment (IPRA) Approach

Current methods for cancer risk assessment result in single values, without any quantitative information on the uncertainties in these values. Therefore, single risk values could easily be overinterpreted. In this study, we discuss a full probabilistic cancer risk assessment approach in which all the generally recognized uncertainties in both exposure and hazard assessment are quantitatively characterized and probabilistically evaluated, resulting in a confidence interval for the final risk estimate. The methodology is applied to three example chemicals (aflatoxin, N‐nitrosodimethylamine, and methyleugenol). These examples illustrate that the uncertainty in a cancer risk estimate may be huge, making single value estimates of cancer risk meaningless. Further, a risk based on linear extrapolation tends to be lower than the upper 95% confidence limit of a probabilistic risk estimate, and in that sense it is not conservative. Our conceptual analysis showed that there are two possible basic approaches for cancer risk assessment, depending on the interpretation of the dose‐incidence data measured in animals. However, it remains unclear which of the two interpretations is the more adequate one, adding an additional uncertainty to the already huge confidence intervals for cancer risk estimates.     

Uncertainty Analysis in Multiplicative Models

Uncertainties are usually evaluated by Monte Carlo analysis. However, multiplicative models with lognormal uncertainties, which are ubiquitous in risk assessments, allow for a simple and quick analytical uncertainty analysis. The necessary formulae are given, which may be evaluated by a desk calculator. Two examples illustrate the method.