On the Treatment of Uncertainty and Variability in Making Decisions About Risk

Much attention has been paid to the treatment of dependence and to the characterization of uncertainty and variability (including the issue of dependence among inputs) in performing risk assessments to avoid misleading results. However, with relatively little progress in communicating about the effects and implications of dependence, the effort involved in performing relatively sophisticated risk analyses (e.g., two‐dimensional Monte Carlo analyses that separate variability from uncertainty) may be largely wasted, if the implications of those analyses are not clearly understood by decisionmakers. This article emphasizes that epistemic uncertainty can introduce dependence among related risks (e.g., risks to different individuals, or at different facilities), and illustrates the potential importance of such dependence in the context of two important types of decisions—evaluations of risk acceptability for a single technology, and comparisons of the risks for two or more technologies. We also present some preliminary ideas on how to communicate the effects of dependence to decisionmakers in a clear and easily comprehensible manner, and suggest future research directions in this area.     

Further Notes on Public Response to Uncertainty in Risks and Science

Given the prevalence of uncertainty and variability in estimates of environmental health risks, it is important to know how citizens interpret information representing uncertainty in risk estimates. Ranges of risk estimates from a hypothetical industry source elicited divergent evaluations of risk assessors' honesty and competence among New Jersey residents within one mile of one or more factories. A plurality saw ranges of risk estimates as both honest and competent, but with most judging such ranges as deficient on one or both dimensions. They wanted definitive conclusions about safety, tended to believe the high end of the range was more likely to be an accurate estimate of the risk, and believed that institutions only discuss risks when they are "high." Acknowledgment of scientific, as opposed to self-interested, reasons for uncertainty and disputes among experts was low. Attitude toward local industry seemed associated with, if not a cause of, attitudes about ranges of risk estimates. These reactions by industry neighbors appear to replicate the findings of Johnson and Slovic (1995, 1998), despite the hypothetical producer of risk estimates being industry instead of government. Respondents were older and less educated on average than were the earlier samples, but more diverse. Regression analyses suggested attitude toward industry was a major factor in these reactions, although other explanations (e.g., level of scientific understanding independent of general education) were not tested in this study.     

Integrating Uncertainty and Interindividual Variability in Environmental Risk Assessment

An integrated, quantitative approach to incorporating both uncertainty and interindividual variability into risk prediction models is described. Individual risk R is treated as a variable distributed in both an uncertainty dimension and a variability dimension, whereas population risk I (the number of additional cases caused by R) is purely uncertain. I is shown to follow a compound Poisson-binomial distribution, which in low-level risk contexts can often be approximated well by a corresponding compound Poisson distribution. The proposed analytic framework is illustrated with an application to cancer risk assessment for a California population exposed to 1,2-dibromo-3-chloropropane from ground water.     

Importance of Uncertainty and Variability to Predicted Risks from Trophic Transfer of PCBs in Dredged Sediments

Biomagnification of organochlorine and other persistent organic contaminants by higher trophic level organisms represents one of the most significant sources of uncertainty and variability in evaluating potential risks associated with disposal of dredged materials. While it is important to distinguish between population variability (e.g., true population heterogeneity in fish weight, and lipid content) and uncertainty (e.g., measurement error), they can be operationally difficult to define separately in probabilistic estimates of human health and ecological risk. We propose a disaggregation of uncertain and variable parameters based on: (1) availability of supporting data; (2) the specific management and regulatory context (in this case, of the U.S. Army Corps of Engineers/U.S. Environmental Protection Agency tiered approach to dredged material management); and (3) professional judgment and experience in conducting probabilistic risk assessments. We describe and quantitatively evaluate several sources of uncertainty and variability in estimating risk to human health from trophic transfer of polychlorinated biphenyls (PCBs) using a case study of sediments obtained from the New York-New Jersey Harbor and being evaluated for disposal at an open water off-shore disposal site within the northeast region. The estimates of PCB concentrations in fish and dietary doses of PCBs to humans ingesting fish are expressed as distributions of values, of which the arithmetic mean or mode represents a particular fractile. The distribution of risk values is obtained using a food chain biomagnification model developed by Gobas by specifying distributions for input parameters disaggregated to represent either uncertainty or variability. Only those sources of uncertainty that could be quantified were included in the analysis. Results for several different two-dimensional Latin Hypercube analyses are provided to evaluate the influence of the uncertain versus variable disaggregation of model parameters. The analysis suggests that variability in human exposure parameters is greater than the uncertainty bounds on any particular fractile, given the described assumptions.     

A Method for Estimating Lifetime Cancer Risks from Limited Epidemiologic Data

Partly because of the poor quality of exposure information on humans, most lifetime carcinogenic risk assessments have been based on animal data. There are, however, surrogate measures for exposure that have not been fully utilized. One of these is duration of exposure where data on mean exposure levels are available. A method is presented for the use of such data, and the method is illustrated by developing a risk assessment from the available epidemiologic literature on gasoline and kidney cancer. This risk assessment is fairly consistent across studies and close to a risk assessment based upon an experiment with rats. While there needs to be much improvement in the quality of environmental data available to epidemiologists, it is possible that a number of risk assessments can be made from existing epidemiologic data and efforts directed away from extrapolation from animal data.     

Chronic Health Risks from Aggregate Exposures to Ionizing Radiation and Chemicals: Scientific Basis for an Assessment Framework

Very little quantitative analysis is currently available on the cumulative effects of exposure to multiple hazardous agents that have either similar or different mechanisms of action. Over the past several years, efforts have been made to develop the methodologies for risk assessment of chemical mixtures, but mixed exposures to two or more dissimilar agents such as radiation and one or more chemical agents have not yet been addressed in any substantive way. This article reviews the current understanding of the health risks arising from mixed exposures to ionizing radiation and specific chemicals. Specifically discussed is how mixed radiation/chemical exposures, when evaluated in aggregation, were linked to chronic health endpoints such as cancer and intermediate health outcomes such as chromosomal aberrations. Also considered is the extent to which the current practices are consistent with the scientific understanding of the health risks associated with mixed-agent exposures. From this the discussion moves to the research needs for assessing the cumulative health risks from aggregate exposures to ionizing radiation and chemicals. The evaluation indicates that essentially no guidance has been provided for conducting risk assessment for two agents with different mechanisms of action (i.e., energy deposition from ionizing radiation versus DNA interactions with chemicals) but similar biological endpoints (i.e., chromosomal aberrations, mutations, and cancer). The literature review also reveals the problems caused by the absence of both the basic science and an appropriate evaluation framework for the combined effects of mixed-agent exposures. This makes it difficult to determine whether there is truly no interaction or somehow the interaction is masked by the scale of effect observation or inappropriate dose-response assumptions.     

A Framework for Assessing Uncertainty Associated with Human Health Risks from MSW Landfill Leachate Contamination

Landfilling is a cost‐effective method, which makes it a widely used practice around the world, especially in developing countries. However, because of the improper management of landfills, high leachate leakage can have adverse impacts on soils, plants, groundwater, aquatic organisms, and, subsequently, human health. A comprehensive survey of the literature finds that the probabilistic quantification of uncertainty based on estimations of the human health risks due to landfill leachate contamination has rarely been reported. Hence, in the present study, the uncertainty about the human health risks from municipal solid waste landfill leachate contamination to children and adults was quantified to investigate its long‐term risks by using a Monte Carlo simulation framework for selected heavy metals. The Turbhe sanitary landfill of Navi Mumbai, India, which was commissioned in the recent past, was selected to understand the fate and transport of heavy metals in leachate. A large residential area is located near the site, which makes the risk assessment problem both crucial and challenging. In this article, an integral approach in the form of a framework has been proposed to quantify the uncertainty that is intrinsic to human health risk estimation. A set of nonparametric cubic splines was fitted to identify the nonlinear seasonal trend in leachate quality parameters. LandSim 2.5, a landfill simulator, was used to simulate the landfill activities for various time slices, and further uncertainty in noncarcinogenic human health risk was estimated using a Monte Carlo simulation followed by univariate and multivariate sensitivity analyses.     

A Model for Partial Product Complementarity and Strategic Production Decisions under Demand Uncertainty

This paper considers a general industrial setting where multiple manufacturers each produce a different product and sell it to the markets. These products are partially complementary in the sense that there is a common demand stream that requests all these products as complementary sets and there are streams of individual demands each requesting only one of the products. All demands are uncertain and may follow any general, joint distributions. Facing demand uncertainties, the manufacturers each choose a production quantity for its product with an objective to maximize its own expected profit. We formulate the problem as a non‐cooperative game to study the strategic interactions of such firms and their implications to supply chain performance. We show that such a game may have numerous equilibria. Among all the possible equilibria, however, we prove that there always exists a unique one that maximizes each and every manufacturer's profit, and we derive an explicit solution for this Pareto‐optimal equilibrium point. We further study the optimal solution for a centralized system and compare it with the decentralized solution. Managerial insights are drawn as to how system parameters and control mechanisms affect firms' decisions and performance.     

Uncertainty and Variability in Health-Related Damages from Coal-Fired Power Plants in the United States

The health‐related damages associated with emissions from coal‐fired power plants can vary greatly across facilities as a function of plant, site, and population characteristics, but the degree of variability and the contributing factors have not been formally evaluated. In this study, we modeled the monetized damages associated with 407 coal‐fired power plants in the United States, focusing on premature mortality from fine particulate matter (PM_2.5). We applied a reduced‐form chemistry‐transport model accounting for primary PM_2.5 emissions and the influence of sulfur dioxide (SO₂) and nitrogen oxide (NO_x) emissions on secondary particulate formation. Outputs were linked with a concentration‐response function for PM_2.5‐related mortality that incorporated nonlinearities and model uncertainty. We valued mortality with a value of statistical life approach, characterizing and propagating uncertainties in all model elements. At the median of the plant‐specific uncertainty distributions, damages across plants ranged from $30,000 to $500,000 per ton of PM_2.5, $6,000 to $50,000 per ton of SO₂, $500 to $15,000 per ton of NO_x, and $0.02 to $1.57 per kilowatt‐hour of electricity generated. Variability in damages per ton of emissions was almost entirely explained by population exposure per unit emissions (intake fraction), which itself was related to atmospheric conditions and the population size at various distances from the power plant. Variability in damages per kilowatt‐hour was highly correlated with SO₂ emissions, related to fuel and control technology characteristics, but was also correlated with atmospheric conditions and population size at various distances. Our findings emphasize that control strategies that consider variability in damages across facilities would yield more efficient outcomes.     

规避农副产品原材料产出不确定风险的商业保险策略

为了保证产品质量、降低生产成本,许多农副产品制造商选择自己种植原材料以满足农副产品的加工生产。然而,农作物的产出易受不利事件（如各种自然灾害）的影响而具有不确定性。这种不确定性可能导致最终产品产出不足,严重时甚至引发财务危机。为了应对潜在风险,农副产品制造商可向金融机构购买商业保险。本文建立了单周期农副产品制造商的计划产量决策模型,通过研究制造商购买商业保险的边界条件及最优商业保险策略,分析商业保险策略在制造商规避原材料产出不确定风险时所具有的价值。研究结果表明：（1）只有保费的安全因子低于外部融资的单位惩罚成本时,制造商才会购买商业保险;（2）最优商业保险策略与计划产量无关;（3）最终产品单位净收益越低,商业保险的价值反而越高。     

Estimating the Predicted Environmental Concentration of the Residues of Veterinary Medicines: Should Uncertainty and Variability Be Ignored?

European directives require that all veterinary medicines be assessed to determine the harmful effects that their use may have on the environment. Fundamental to this assessment is the calculation of the predicted environmental concentration (PEC), which is dependent on the type of drug, its associated treatment characteristics, and the route by which residues enter the environment. Deterministic models for the calculation of the PEC have previously been presented. In this article, the inclusion of variability and uncertainty within such models is introduced. In particular, models for the calculation of the PEC for residues excreted directly onto pasture by grazing animals are considered and comparison of deterministic and stochastic results suggest that uncertainty and variability cannot be ignored.     

Variability and Uncertainty in Swedish Exposure Factors for Use in Quantitative Exposure Assessments

Information of exposure factors used in quantitative risk assessments has previously been compiled and reported for U.S. and European populations. However, due to the advancement of science and knowledge, these reports are in continuous need of updating with new data. Equally important is the change over time of many exposure factors related to both physiological characteristics and human behavior. Body weight, skin surface, time use, and dietary habits are some of the most obvious examples covered here. A wealth of data is available from literature not primarily gathered for the purpose of risk assessment. Here we review a number of key exposure factors and compare these factors between northern Europe—here represented by Sweden—and the United States. Many previous compilations of exposure factor data focus on interindividual variability and variability between sexes and age groups, while uncertainty is mainly dealt with in a qualitative way. In this article variability is assessed along with uncertainty. As estimates of central tendency and interindividual variability, mean, standard deviation, skewness, kurtosis, and multiple percentiles were calculated, while uncertainty was characterized using 95% confidence intervals for these parameters. The presented statistics are appropriate for use in deterministic analyses using point estimates for each input parameter as well as in probabilistic assessments.     

Methods for Characterizing Variability and Uncertainty: Comparison of Bootstrap Simulation and Likelihood-Based Approaches

Variability arises due to differences in the value of a quantity among different members of a population. Uncertainty arises due to lack of knowledge regarding the true value of a quantity for a given member of a population. We describe and evaluate two methods for quantifying both variability and uncertainty. These methods, bootstrap simulation and a likelihood-based method, are applied to three datasets. The datasets include a synthetic sample of 19 values from a Lognormal distribution, a sample of nine values obtained from measurements of the PCB concentration in leafy produce, and a sample of five values for the partitioning of chromium in the flue gas desulfurization system of coal-fired power plants. For each of these datasets, we employ the two methods to characterize uncertainty in the arithmetic mean and standard deviation, cumulative distribution functions based upon fitted parametric distributions, the 95th percentile of variability, and the 63rd percentile of uncertainty for the 81st percentile of variability. The latter is intended to show that it is possible to describe any point within the uncertain frequency distribution by specifying an uncertainty percentile and a variability percentile. Using the bootstrap method, we compare results based upon use of the method of matching moments and the method of maximum likelihood for fitting distributions to data. Our results indicate that with only 5–19 data points as in the datasets we have evaluated, there is substantial uncertainty based upon random sampling error. Both the boostrap and likelihood-based approaches yield comparable uncertainty estimates in most cases.     

Bounds in Competing Risks Models and the War on Cancer

In 1971, President Nixon declared war on cancer. Thirty years later, many declared this war a failure: the age‐adjusted mortality rate from cancer in 2000 was essentially the same as in the early 1970s. Meanwhile the age‐adjusted mortality rate from cardiovascular disease fell dramatically. Since the causes that underlie cancer and cardiovascular disease are likely dependent, the decline in mortality rates from cardiovascular disease may partially explain the lack of progress in cancer mortality. Because competing risks models (used to model mortality from multiple causes) are fundamentally unidentified, it is difficult to estimate cancer trends. We derive bounds for aspects of the underlying distributions without assuming that the underlying risks are independent. We then estimate changes in cancer and cardiovascular mortality since 1970. The bounds for the change in duration until death for either cause are fairly tight and suggest much larger improvements in cancer than previously estimated.     

Perceived Risk and Uncertainty of Nuclear Waste: Differences Among Science,Business, and Environmental Group Members1

This paper presents survey results on perceived risk regarding the management of nuclear waste. Using data taken from random mail surveys of members of scientific, business, and environmental groups in Colorado and New Mexico in the summer of 1990, we examine differences between the groups in their expressed perceptions of risk and also their assessments of the certainty of their beliefs. We consider whether (a) greater uncertainty is associated with greater perceived risks and (b) whether there is greater responsiveness to new information for those whose beliefs are least certain. We find that there are connections between perceived risk and uncertainty, and there is a greater tendency to update risk assessements from a position of greater initial uncertainty. There are, however, differences between the groups as well as asymmetries in their responses to new information. The latter suggests that perceived risks will ratchet upward over time even when information is not biased toward more or less risk.