Variance Estimators for Three "Probabilities of Causation"

This article introduces the definitions of three "probabilities of causation" suggested by Pearl (1999), which are used to evaluate the causal effect of an exposure on a disease in epidemiological studies. Pearl (1999) and Tian and Pearl (2000a, 2000b) provided identification formulas for three "probabilities of causation" from statistical data under some assumptions. In order to examine the estimation accuracy problem, this article derives variance estimators for three "probabilities of causation" correspondent to each case in Pearl (1999) and at the same time clarify their properties. In addition, we conduct simulation experiments and show that the proposed method can approximate sufficiently to the variance of "probabilities of causation." The results of this article provide a complete framework for using "probabilities of causation" effectively in order to analyze responsibility and susceptibility in epidemiological studies.     

Artifactual Uncertainty in Risk Analysis

The field of comparative risk analysis of electrical energy alternatives has traditionally been plagued by highly uncertain estimates of risk rates, and consequently by conflicting judgements of relative risk. To the extent that this uncertainty arises from traditional sources–imperfect observations or actual variance in the data–it can be brought within a Bayesian statistical framework which allows policy conclusions to be formulted and tested at different levels of confidence. It is shown that there are important methodological or "artifactual" sources of uncertainty, however, that cannot be treated by statistical means; these require conceptual advances for their resolution. By identifying these sources of uncertainty in simple thought experiments and examples, it is shown in what ways the concept of attributable risk, which is the policy-maker's chief concern, must be sharpened and refined to have unambiguous meaning. The conventional "multilinear" formula for calculating risk indices is challenged as a measure of attributable risk, and directions for further research to improve the methodological foundations of comparative risk analysis are identified.     

Probability of Causation and the Attributable Proportion Risk

A uranium miner who smokes develops lung cancer: what is the probability that radiation, rather than tobacco, caused it? This paper briefly explains the principles and limits of probability models for which this question makes sense, and then shows how principles of risk accounting can be applied to obtain a solution to the general problem of attributing risk in the presence of joint, possibly interacting, causes. A procedure for calculating each factor's “share” in a jointly caused risk is proposed, and shown to be a generalization of the “probability of causation” concept. Problems of implementation and interpretation for the proposed attribution procedure are discussed, and illustrative error bounds are derived for a simple decision rule, in which probability of causation or attributable risk share calculations are made using aggregate data as a proxy for unknown individual data.     

Expert Judgment in Risk Analysis and Management: Process, Context, and Pitfalls

The regulation and management of hazardous industrial activities increasingly rely on formal expert judgment processes to provide wisdom in areas of science and technology where traditional "good science" is, in practice, unable to supply unambiguous "facts." Expert judgment has always played a significant, if often unrecognized, role in analysis; however, recent trends are to make it formal, explicit, and documented so it can be identified and reviewed by others. We propose four categories of expert judgment and present three case studies which illustrate some of the pitfalls commonly encountered in its use. We conclude that there will be an expanding policy role for formal expert judgment and that the openness, transparency, and documentation that it requires have implications for enhanced public involvement in scientific and technical affairs.     

Dangerous Climate Change: The Role for Risk Research

The notion of "dangerous climate change" constitutes an important development of the 1992 United Nations Framework Convention on Climate Change. It persists, however, as an ambiguous expression, sustained by multiple definitions of danger. It also implicitly contains the question of how to respond to the complex and multi-disciplinary risk issues that climate change poses. The invaluable role of the climate science community, which relies on risk assessments to characterize system uncertainties and to identify limits beyond which changes may become dangerous, is acknowledged. But this alone will not suffice to develop long-term policy. Decisions need to include other considerations, such as value judgments about potential risks, and societal and individual perceptions of "danger," which are often contested. This article explores links and cross-overs between the climate science and risk communication and perception approaches to defining danger. Drawing upon nine articles in this Special Issue of Risk Analysis, we examine a set of themes: limits of current scientific understanding; differentiated public perceptions of danger from climate change; social and cultural processes amplifying and attenuating perceptions of, and responses to, climate change; risk communication design; and new approaches to climate change decision making. The article reflects upon some of the difficulties inherent in responding to the issue in a coherent, interdisciplinary fashion, concluding nevertheless that action should be taken, while acknowledging the context-specificity of "danger." The need for new policy tools is emphasised, while research on nested solutions should be aimed at overcoming the disjunctures apparent in interpretations of climate change risks.     

Clarifying Types of Uncertainty: When Are Models Accurate,and Uncertainties Small?

Professor Aven has recently noted the importance of clarifying the meaning of terms such as "scientific uncertainty" for use in risk management and policy decisions, such as when to trigger application of the precautionary principle. This comment examines some fundamental conceptual challenges for efforts to define "accurate" models and "small" input uncertainties by showing that increasing uncertainty in model inputs may reduce uncertainty in model outputs; that even correct models with "small" input uncertainties need not yield accurate or useful predictions for quantities of interest in risk management (such as the duration of an epidemic); and that accurate predictive models need not be accurate causal models.     

Uncertainties in Biologically-Based Modeling of Formaldehyde-Induced Respiratory Cancer Risk: Identification of Key Issues

In a series of articles and a health-risk assessment report, scientists at the CIIT Hamner Institutes developed a model (CIIT model) for estimating respiratory cancer risk due to inhaled formaldehyde within a conceptual framework incorporating extensive mechanistic information and advanced computational methods at the toxicokinetic and toxicodynamic levels. Several regulatory bodies have utilized predictions from this model; on the other hand, upon detailed evaluation the California EPA has decided against doing so. In this article, we study the CIIT model to identify key biological and statistical uncertainties that need careful evaluation if such two-stage clonal expansion models are to be used for extrapolation of cancer risk from animal bioassays to human exposure. Broadly, these issues pertain to the use and interpretation of experimental labeling index and tumor data, the evaluation and biological interpretation of estimated parameters, and uncertainties in model specification, in particular that of initiated cells. We also identify key uncertainties in the scale-up of the CIIT model to humans, focusing on assumptions underlying model parameters for cell replication rates and formaldehyde-induced mutation. We discuss uncertainties in identifying parameter values in the model used to estimate and extrapolate DNA protein cross-link levels. The authors of the CIIT modeling endeavor characterized their human risk estimates as "conservative in the face of modeling uncertainties." The uncertainties discussed in this article indicate that such a claim is premature.     

The Theory of Risk Homeostasis: Implications for Safety and Health

No strategy for countermeasure design or future directions of research in the areas of human behavior which leads to traffic accidents or lifestyle-related diseases can be rationally developed without an acceptable working theory of human behavior in these domains. For this purpose, an attempt has been made to conceptually integrate the available evidence with respect to the role of human behavior in the causation of road accidents. From this integrative effort it would seem that the accident rate is ultimately dependent on one factor only, the target level of risk in the population concerned which acts as the reference variable in a homeostatic process relating accident rate to human motivation. Various policy tactics for the purpose of modifying this target level of risk have been pointed out and the theory of risk homeostasis has been speculatively extended to the areas of lifestyle-dependent morbidity and mortality.     

Combining Experts' Risk Judgments on Technology Performance of Phytoremediation: Self-Confidence Ratings, Averaging Procedures, and Formative Consensus Building

Expert panels and averaging procedures are common means for coping with the uncertainty of effects of technology application in complex environments. We investigate the connection between confidence and the validity of expert judgment. Moreover, a formative consensus building procedure (FCB) is introduced that generates probability statements on the performance of technologies, and we compare different algorithms for the statistical aggregation of individual judgments. The case study refers to an expert panel of 10 environmental scientists assessing the performance of a soil cleanup technology that uses the capability of certain plants to accumulate heavy metals from the soil in the plant body (phytoremediation). The panel members first provided individual statements on the effectiveness of a phytoremediation. Such statements can support policymakers, answering the questions concerning the expected performance of the new technology in contaminated areas. The present study reviews (1) the steps of the FCB, (2) the constraints of technology application (contaminants, soil structure, etc.), (3) the measurement of expert knowledge, (4) the statistical averaging and the discursive agreement procedures, and (5) the boundaries of application for the FCB method. The quantitative statement oriented part of FCB generates terms such as: "The probability that the concentration of soil contamination will be reduced by at least 50% is 0.8." The data suggest that taking the median of the individual expert estimates provides the most accurate aggregated estimate. The discursive agreement procedure of FCB appears suitable for deriving politically relevant singular statements rather than for obtaining comprehensive information about uncertainties as represented by probability distributions.     

An Integrated Methodology for Assessment and Selection of the Project Risk Response Actions

In a systematic process of project risk management, after risk assessment is implemented, the risk analysts encounter the phase of assessment and selection of the project risk response actions (RA). As indicated by many researchers, there are less systematic and well-developed solutions in the area of risk response assessment and selection. The present article introduces a methodology including a modeling approach with the objective of selecting a set of RA that minimizes the undesirable deviation from achieving the project scope. The developed objective function comprises the three key success criteria of a project, namely, time, quality, and cost. Our model integrates overall project management into the project risk response planning (P2RP). Furthermore, the proposed model stresses on an equivalent importance for both "risk" and "response." We believe that applying the proposed model helps the project risk analyst in most effective and efficient manner dealing with his or her complicated RA selection problems. The application of the proposed model was implemented in projects in the construction industry in which it showed tremendous time, cost, and quality improvements.     

VMI供应链下考虑补货策略的的契约设计

结合(r,Q)和(s,S)两种库存补货策略,提出了货权属供应商的VMI供应链的契约设计问题。采用风险分担的思想,给出了两种可行的风险分担的契约形式。在离散需求下,通过参数试验的形式,分别研究了两种契约形式对供应链效率的影响。研究结果表明,两种契约能够使得供应链的效率达到满意,同时对于影响效率的参数有一定的鲁棒性,并且在一定情况下能协调供应链。相比收益分享契约,引入风险分享的契约形式能够使得供应链协作的效率更高。研究结论对VMI契约设计有参考意义。     

Estimating Noncancer Uncertainty Factors: Are Ratios NOAELs Informative?

The prominent role of animal bioassay evidence in environmental regulatory decisions compels a careful characterization of extrapolation uncertainties. In noncancer risk assessment, uncertainty factors are incorporated to account for each of several extrapolations required to convert a bioassay outcome into a putative subthreshold dose for humans. Measures of relative toxicity taken between different dosing regimens, different endpoints, or different species serve as a reference for establishing the uncertainty factors. Ratios of no observed adverse effect levels (NOAELs) have been used for this purpose; statistical summaries of such ratios across sets of chemicals are widely used to guide the setting of uncertainty factors. Given the poor statistical properties of NOAELs, the informativeness of these summary statistics is open to question. To evaluate this, we develop an approach to calibrate the ability of NOAEL ratios to reveal true properties of a specified distribution for relative toxicity. A priority of this analysis is to account for dependencies of NOAEL ratios on experimental design and other exogenous factors. Our analysis of NOAEL ratio summary statistics finds (1) that such dependencies are complex and produce pronounced systematic errors and (2) that sampling error associated with typical sample sizes (50 chemicals) is non-negligible. These uncertainties strongly suggest that NOAEL ratio summary statistics cannot be taken at face value; conclusions based on such ratios reported in well over a dozen published papers should be reconsidered.     

Competitive strategies: a cognitive choice model

A theory of competition between firms in heterogeneous markets is formulated using a psychological model of choice, the heteroscedastic form of the Thurstone random strength model. Market shares are defined in terms of random variables which portray individual variation in perceived utility. The analysis focuses on the relationship between market shares and utility variances. Besides the general theory of competition two special cases are analyzed, each of which can be identified without precise knowledge of the utility parameters. The conclusions tend to support conventional marketing wisdom but emphasize that the degree of dominance of the market leader is a significant factor in its competitive strategy. Short and long-run analyses of the model are presented, and it is shown that the best policy for a particular firm in the short run remains optimal in the presence of competitors' reactions, but it may no longer be effective. The paper concludes with some comments on statistical implementation.     

Air Pollution and Human Health: Perspectives for the '90s and Beyond

This paper considers the health effects of air pollution from three perspectives: historical, statistical, and public policy, and also as depicted by the recent epidemiology, primarily mortality studies. The historical perspectives establish the reality of population-based health effects, and they provide data with which to evaluate more recent evidence. Statistical perspectives imply that, while there is strong evidence that associations between air quality and health persist, many details of these relationships remain obscure, especially as to the existence of concentration thresholds that might define safe exposure levels. Additional major questions include the effects of uncertainties in actual pollution exposures, the degree of prematurity of "excess" deaths, and whether the development of new cases of chronic disease is associated with air pollution. Public policy issues center around interpreting the new epidemiological studies in the light of these uncertainties and the analysis and management of the concomitant health risks.     

The European Commission''s White Paper "Strategy for a Future Chemicals Policy": A Review

The European Commission has proposed a radical new policy for the regulation of chemicals in the EU in the form of a White Paper. The current system has separate regulatory provisions for "new" chemicals (introduced to the market since September 18, 1981) and "existing" chemicals (on the market before September 18,1981). The proposed future policy will have a single unified regulatory system for all chemicals, which should result in better regulation of chemicals in the EU single market. It will be better because risk assessments will be targeted at the chemicals of greatest concern. Furthermore, the system will be streamlined, making regulatory decisions faster, and thus reducing the so-called burden of the past (the large number of chemicals that have never been assessed for their risks to human health or the environment). The new system incorporates the precautionary principle, which will be applied where there is an early indication of unacceptable risk or where there is undue delay in the regulatory process. Moreover, the new strategy is intended to promote greater transparency for all stakeholders.     

Probabilistic Risk Analysis for a High-Level Radioactive Waste Repository

A probabilistic risk analysis (PRA) for a high-level radioactive waste repository is very important since it gives an estimate of its health impacts, allowing comparisons to be made with the health impacts of competing technologies. However, it is extremely difficult to develop a credible PRA for a specific repository site because of large uncertainties in future climate, hydrology, geological processes, etc. At best, such a PRA would not be understandable to the public. An alternative proposed here is to develop a PRA for an average U.S. site, taking all properties of the site to be the U.S. average. The results are equivalent to the average results for numerous randomly selected sites. Such a PRA is presented here; it is easy to understand, and it is not susceptible to substantial uncertainty. Applying the results to a specific repository site then requires only a simple, intuitively acceptable "leap of faith" in assuming that with large expenditures of effort and money, experts can select a site that would be at least as secure as a randomly selected site.     

Assigned Shares in Compensation for Radiation-Related Cancers

At the request of Congress, a Working Group of the National Institutes of Health prepared radioepidemiologic tables which estimate the likelihood that cancer victims previously exposed to a dose of radiation developed their cancer as a result of this exposure. The ultimate purpose of the tables is to provide a scientific basis for determining compensation for such victims, and their use would represent a marked departure from the current tort system for deciding compensation. The preparation of radioepidemiologic tables requires extensive mathematical modeling because matters such as sex, size of dose, age at exposure, type of cancer, and age at diagnosis must be taken into account. The limited data require many assumptions about the quantitative relationship between radiation dose and the age-specific incidence rate of cancer. After partitioning a population into reference sets based on age at exposure, size of dose, type of cancer, etc., an assigned share is computed for each reference set and then assigned to all of its members. The assigned share represents the fraction of the cancer cases in the reference set that are attributed to the radiation dose. Because the population can be partitioned in many ways, each individual's assigned share depends on the partition used and will change with different partitions. Options for modeling and limitations in epidemiologic data lead to considerable uncertainties in estimates of assigned shares that have been scientifically evaluated for the Working Group's tables. In contrast, the uncertainties associated with the current approach for determining the likelihood that a claimant's cancer was caused by radiation have not been appraised, but are likely to be even greater than those associated with the Working Group's tables. One issue is how to use such tables to compensate victims. Some among many possibilities are: to use them together with a compensation formula to determine the fraction of a standard award to be given; to use them as a starting value for the fraction, to be modified by an authority on the basis of additional information supplied by the claimant and defendant; and to use them as input to the present compensation system.     

Assessing the Multidimensionality of Coastal Erosion Risks: Public Participation and Multicriteria Analysis in a Mediterranean Coastal System

The complex and multidimensional nature of coastal erosion risks makes it necessary to move away from single-perspective assessment and management methods that have conventionally predominated in coastal management. This article explores the suitability of participatory multicriteria analysis (MCA) for improving the integration of diverse expertises and values and enhancing the social-ecological robustness of the processes that lead to the definition of relevant policy options to deal with those risks. We test this approach in the Mediterranean coastal locality of Lido de Sète in France. Results show that the more adaptive alternatives such as "retreating the shoreline" were preferred by our selected stakeholders to those corresponding to "protecting the shoreline" and the business as usual proposals traditionally put forward by experts and policymakers on these matters. Participative MCA contributed to represent coastal multidimensionality, elicit and integrate different views and preferences, facilitated knowledge exchange, and allowed highlighting existing uncertainties.