Premature Deaths,Statistical Lives,and Years of Life Lost: Identification,Quantification, and Valuation of Mortality Risks

Mortality effects of exposure to air pollution and other environmental hazards are often described by the estimated number of “premature” or “attributable” deaths and the economic value of a reduction in exposure as the product of an estimate of “statistical lives saved” and a “value per statistical life.” These terms can be misleading because the number of deaths advanced by exposure cannot be determined from mortality data alone, whether from epidemiology or randomized trials (it is not statistically identified). The fraction of deaths “attributed” to exposure is conventionally derived as the hazard fraction (R – 1)/R, where R is the relative risk of mortality between high and low exposure levels. The fraction of deaths advanced by exposure (the “etiologic” fraction) can be substantially larger or smaller: it can be as large as one and as small as 1/e (≈0.37) times the hazard fraction (if the association is causal and zero otherwise). Recent literature reveals misunderstanding about these concepts. Total life years lost in a population due to exposure can be estimated but cannot be disaggregated by age or cause of death. Economic valuation of a change in exposure-related mortality risk to a population is not affected by inability to know the fraction of deaths that are etiologic. When individuals facing larger or smaller changes in mortality risk cannot be identified, the mean change in population hazard is sufficient for valuation; otherwise, the economic value can depend on the distribution of risk reductions.     

Approximations for Estimating Change in Life Expectancy Attributable to Air Pollution in Relation to Multiple Causes of Death Using a Cause Modified Life Table

There is considerable debate as to the most appropriate metric for characterizing the mortality impacts of air pollution. Life expectancy has been advocated as an informative measure. Although the life‐table calculus is relatively straightforward, it becomes increasingly cumbersome when repeated over large numbers of geographic areas and for multiple causes of death. Two simplifying assumptions were evaluated: linearity of the relation between excess rate ratio and change in life expectancy, and additivity of cause‐specific life‐table calculations. We employed excess rate ratios linking PM_2.5 and mortality from cerebrovascular disease, chronic obstructive pulmonary disease, ischemic heart disease, and lung cancer derived from a meta‐analysis of worldwide cohort studies. As a sensitivity analysis, we employed an integrated exposure response function based on the observed risk of PM_2.5 over a wide range of concentrations from ambient exposure, indoor exposure, second‐hand smoke, and personal smoking. Impacts were estimated in relation to a change in PM_2.5 from 19.5 μg/m³ estimated for Toronto to an estimated natural background concentration of 1.8 μg/m³. Estimated changes in life expectancy varied linearly with excess rate ratios, but at higher values the relationship was more accurately represented as a nonlinear function. Changes in life expectancy attributed to specific causes of death were additive with maximum error of 10%. Results were sensitive to assumptions about the air pollution concentration below which effects on mortality were not quantified. We have demonstrated valid approximations comprising expression of change in life expectancy as a function of excess mortality and summation across multiple causes of death.     

Life Years Lost at Hazardous Waste Sites: Remediation Worker Fatalities vs. Cancer Deaths to Nearby Residents

We present a hypothetical case study using the Years of Potential Life Lost (YPLL) metric to compare cancer risks incurred by residents living near a Superfund site to occupational fatality risks incurred by workers employed in that site's remediation. Since cancer occurs late in life, and because we assume its mortality rate is 60%, each case results in 8.8 YPLL. Each occupational fatality, which typically occurs earlier in life, results in 38.1 YPLL. In our case study, the residential population of 5000 incurred 1.3 YPLL, compared to 5.7 YPLL incurred by the 500 workers. Several uncertain assumptions may influence our calculations; moreover, occupational risks may be viewed as more "voluntary" than risks incurred by residents. However, because the magnitude of the YPLL incurred by workers and residents may be comparable, risk managers should consider occupational risks when evaluating remedial alternatives.     

Expert Elicitation of the Value per Statistical Life in an Air Pollution Context

The monetized value of avoided premature mortality typically dominates the calculated benefits of air pollution regulations; therefore, characterization of the uncertainty surrounding these estimates is key to good policymaking. Formal expert judgment elicitation methods are one means of characterizing this uncertainty. They have been applied to characterize uncertainty in the mortality concentration‐response function, but have yet to be used to characterize uncertainty in the economic values placed on avoided mortality. We report the findings of a pilot expert judgment study for Health Canada designed to elicit quantitative probabilistic judgments of uncertainties in Value‐per‐Statistical‐Life (VSL) estimates for use in an air pollution context. The two‐stage elicitation addressed uncertainties in both a base case VSL for a reduction in mortality risk from traumatic accidents and in benefits transfer‐related adjustments to the base case for an air quality application (e.g., adjustments for age, income, and health status). Results for each expert were integrated to develop example quantitative probabilistic uncertainty distributions for VSL that could be incorporated into air quality models.     

Miscommunicating Risk,Uncertainty, and Causation: Fine Particulate Air Pollution and Mortality Risk as an Example

A recent paper in this journal (Fann et al., 2012) estimated that “about 80,000 premature mortalities would be avoided by lowering PM_2.5 levels to 5 μg/m³ nationwide” and that 2005 levels of PM_2.5 cause about 130,000 premature mortalities per year among people over age 29, with a 95% confidence interval of 51,000 to 200,000 premature mortalities per year.⁽¹⁾ These conclusions depend entirely on misinterpreting statistical coefficients describing the association between PM_2.5 and mortality rates in selected studies and models as if they were known to be valid causal coefficients. But they are not, and both the expert opinions of EPA researchers and analysis of data suggest that a true value of zero for the PM_2.5 mortality causal coefficient is not excluded by available data. Presenting continuous confidence intervals that exclude the discrete possibility of zero misrepresents what is currently known (and not known) about the hypothesized causal relation between changes in PM_2.5 levels and changes in mortality rates, suggesting greater certainty about projected health benefits than is justified.     

Health Risks and Air Pollution — Error Analysis for a Cross-Sectional Mortality Study

An attempt is made to analyze in quantitative terms the uncertainties in multiple regression estimates of the effects of air pollution on death rates. A range of factors--statistical fluctuations in numbers of deaths, differences in local age distribution, differences in smoking habits, errors in estimated pollution levels, migration, and variability of the characterization of socioeconomic effects--are assessed as potential sources of error. Both the precision and the robustness of the regression calculation are shown to be poor. Examples and illustrative calculations are given based on a study of U. K. death rates around the 1971 Census.     

Estimating the Risks of Smoking, Air Pollution, and Passive Smoke on Acute Respiratory Conditions

Five years of the annual Health Interview Survey, conducted by the National Center for Health Statistics, are used to estimate the effects of air pollution, smoking, and environmental tobacco smoke on respiratory restrictions in activity for adults, and bed disability for children. After adjusting for several socioeconomic factors, the multiple regression estimates indicate that an independent and statistically significant association exists between these three forms of air pollution and respiratory morbidity. The comparative risks of these exposures are computed and the plausibility of the relative risks is examined by comparing the equivalent doses with actual measurements of exposure taken in the homes of smokers. The results indicate that: (1) smokers will have a 55-75% excess in days with respiratory conditions severe enough to cause reductions in normal activity; (2) a 1 microgram increase in fine particulate matter air pollution is associated with a 3% excess in acute respiratory disease; and (3) a pack-a-day smoker will increase respiratory restricted days for a nonsmoking spouse by 20% and increase the number of bed disability days for young children living in the household by 20%. The results also indicate that the estimates of the effects of secondhand smoking on children are improved when the mother's work status is known and incorporated into the exposure estimate.     

Caveats for Causal Interpretations of Linear Regression Coefficients for Fine Particulate (PM2.5) Air Pollution Health Effects

Recent linear regression analyses have concluded that decreasing levels of fine particulate matter (PM2.5) air pollution have increased life expectancy in the United States. These findings have left unresolved questions about the causal relation between reductions in PM2.5 levels and changes in cause‐specific (especially, cardiovascular disease, CVD) mortality risks. Their robustness (e.g., sensitivity to deletion of a single data point) has also been questioned. We investigate these issues in the National Mortality and Morbidity Air Pollution Study database. Comparing changes in PM2.5 levels and cause‐specific mortality rates for elderly people in 24 cities between two periods separated by a decade (1987–1989 and 1999–2000) shows that reductions in PM2.5 were significantly associated with increases in respiratory mortality rates and with decreases in CVD mortality rates. CVD and all‐cause mortality risks fell equally for all months of the year over this period, but average PM2.5 levels increased significantly for winter months. This casts doubts on the causal interpretation that declines in PM2.5 over the decade caused reduced short‐term mortality risks. Nonlinear regression suggests that reduced or negative marginal health benefits are associated with reductions of PM2.5 below 1999–2000 levels (about 15 μg/m³). Such nonlinear relations imply that risk communication statements that project a constant incremental reduction in mortality risks per unit reduction in PM2.5 do not adequately reflect the realistic possibility of nonlinear exposure‐response relations and diminishing returns to further exposure reductions.     

Risk Information Seeking and Processing About Particulate Air Pollution in South Korea: The Roles of Cultural Worldview

This study integrates cultural theory of risk into the risk information seeking and processing model in the context of particulate air pollution in South Korea. Specifically, it examines how cultural worldviews (hierarchy, individualism, egalitarianism, and fatalism) influence the way people interpret risk about an environmental risk, which may in turn promote or deter their information seeking and processing about the risk. An online survey (N = 645) showed that egalitarianism was positively associated with perceptions of societal and personal risks, affective responses toward the risk, and informational subjective norms. Perceived societal risk, in particular, mediated the effect of egalitarianism on information insufficiency. Moreover, cultural worldview was a significant moderator of the relationships between information insufficiency and risk information seeking and processing. The positive relationship between information insufficiency and information seeking grew stronger with increasing egalitarianism. In contrast, the negative relationship between information insufficiency and heuristic processing was strengthened with increasing hierarchy. This study extends prior theories and models in risk communication by addressing the roles of cultural worldview, an important individual difference factor in interpreting environmental risks.     

Public Perceptions of How Long Air Pollution and Carbon Dioxide Remain in the Atmosphere

The atmospheric residence time of carbon dioxide is hundreds of years, many orders of magnitude longer than that of common air pollution, which is typically hours to a few days. However, randomly selected respondents in a mail survey in Allegheny County, PA (N = 119) and in a national survey conducted with MTurk (N = 1,013) judged the two to be identical (in decades), considerably overestimating the residence time of air pollution and drastically underestimating that of carbon dioxide. Moreover, while many respondents believed that action is needed today to avoid climate change (regardless of cause), roughly a quarter held the view that if climate change is real and serious, we will be able to stop it in the future when it happens, just as we did with common air pollution. In addition to assessing respondents’ understanding of how long carbon dioxide and common air pollution stay in the atmosphere, we also explored the extent to which people correctly identified causes of climate change and how their beliefs affect support for action. With climate change at the forefront of politics and mainstream media, informing discussions of policy is increasingly important. Confusion about the causes and consequences of climate change, and especially about carbon dioxide's long atmospheric residence time, could have profound implications for sustained support of policies to achieve reductions in carbon dioxide emissions and other greenhouse gases.     

Empirical Bayes and Adjusted Estimates Approach to Estimating the Relation of Mortality to Exposure of PM10

Forward Links to Citing Articles Retraction . Risk Analysis 25: 6, 1683
In the framework of the APHEIS program (Air Pollution and Health: A European Information System), a health impact assessment of air pollution in 26 European cities was performed for particles of an aerodynamic diameter less than or equal to 10 μm (PM₁₀). For short-term effects, it was based on overall estimates from the APHEA-2 project (Air Pollution and Health: A European Approach). These city-specific risk assessments require city-specific concentration-response functions, raising the question of which concentration-response is most appropriate. Estimates from city-specific models are more specific, but have greater uncertainty than those provided from multicity analyses. We compared several estimates derived from the city-specific analyses in cities that were part of the APHEA-2 project, as well as in a city that was not included in APHEA-2 but was part of the APHEIS project. These estimates were: the estimates from a local regression model, the adjusted estimates based on two significant effect modifiers identified through meta-regression models, and the city-specific empirical Bayes (shrunken) estimates and their underlying distribution. The shrunken and adjusted estimates were used to improve the estimation of city-specific concentration-response function. From these different estimates, attributable numbers of deaths per year were calculated. The advantages and limits of the different approaches are discussed through real data and in a simulation study.     

Loss of Life Caused by the Flooding of New Orleans After Hurricane Katrina: Analysis of the Relationship Between Flood Characteristics and Mortality

In this article a preliminary analysis of the loss of life caused by Hurricane Katrina in the New Orleans metropolitan area is presented. The hurricane caused more than 1,100 fatalities in the state of Louisiana. A preliminary data set that gives information on the recovery locations and individual characteristics for 771 fatalities has been analyzed. One-third of the analyzed fatalities occurred outside the flooded areas or in hospitals and shelters in the flooded area. These fatalities were due to the adverse public health situation that developed after the floods. Two-thirds of the analyzed fatalities were most likely associated with the direct physical impacts of the flood and mostly caused by drowning. The majority of victims were elderly: nearly 60% of fatalities were over 65 years old. Similar to historical flood events, mortality rates were highest in areas near severe breaches and in areas with large water depths. An empirical relationship has been derived between the water depth and mortality and this has been compared with similar mortality functions proposed based on data for other flood events. The overall mortality among the exposed population for this event was approximately 1%, which is similar to findings for historical flood events. Despite the fact that the presented results are preliminary they give important insights into the determinants of loss of life and the relationship between mortality and flood characteristics.     

The Application of Genetic Information for Regulatory Standard Setting Under the Clean Air Act: A Decision-Analytic Approach

In 2002, the U.S. Environmental Protection Agency (EPA) released an “Interim Policy on Genomics,” stating a commitment to developing guidance on the inclusion of genetic information in regulatory decision making. This statement was followed in 2004 by a document exploring the potential implications. Genetic information can play a key role in understanding and quantifying human susceptibility, an essential step in many of the risk assessments used to shape policy. For example, the federal Clean Air Act (CAA) requires EPA to set National Ambient Air Quality Standards (NAAQS) for criteria pollutants at levels to protect even sensitive populations from adverse health effects with an adequate margin of safety. Asthmatics are generally regarded as a sensitive population, yet substantial research gaps in understanding genetic susceptibility and disease have hindered quantitative risk analysis. This case study assesses the potential role of genomic information regarding susceptible populations in the NAAQS process for fine particulate matter (PM_2.5) under the CAA. In this initial assessment, we model the contribution of a single polymorphism to asthma risk and mortality risk; however, multiple polymorphisms and interactions (gene‐gene and gene‐environment) are known to play key roles in the disease process. We show that the impact of new information about susceptibility on estimates of population risk or average risk derived from large epidemiological studies depends on the circumstances. We also suggest that analysis of a single polymorphism, or other risk factor such as health status, may or may not change estimates of individual risk enough to alter a particular regulatory decision, but this depends on specific characteristics of the decision and risk information. We also show how new information about susceptibility in the context of the NAAQS for PM_2.5 could have a large impact on the estimated distribution of individual risk. This would occur if a group were consequently identified (based on genetic and/or disease status), that accounted for a disproportionate share of observed effects. Our results highlight certain conditions under which genetic information is likely to have an impact on risk estimates and the balance of costs and benefits within groups, and highlight critical research needs. As future studies explore more fully the relationship between exposure, genetic makeup, and disease status, the opportunity for genetic information and disease status to play pivotal roles in regulation can only increase.     

Life Expectancy,Schooling, and Lifetime Labor Supply: Theory and Evidence Revisited

This paper presents a theoretical and empirical analysis of the role of life expectancy for optimal schooling and lifetime labor supply. The results of a simple prototype Ben‐Porath model with age‐specific survival rates show that an increase in lifetime labor supply is not a necessary, or a sufficient, condition for greater life expectancy to increase optimal schooling. The observed increase in survival rates during working ages that follows from the “rectangularization” of the survival function is crucial for schooling and labor supply. The empirical results suggest that the relative benefits of schooling have been increasing across cohorts of U.S. men born between 1840 and 1930. A simple quantitative analysis shows that a realistic shift in the survival function can lead to an increase in schooling and a reduction in lifetime labor hours.     

Value of a Life: What Difference Does It Make?1

A comparison of the costs and benefits of 57 lifesaving programs reveals striking disparities across agencies and programs in cost/life saved and even greater disparities in cost/life-year saved. Within a broad range the monetary value assigned to the benefits of averting a death usually does not alter the policy implications of the analyses. The findings suggest that despite the substantial disagreements and uncertainties in the theory and practice of valuing lives, careful quantitative analysis can be helpful in setting health, safety, and environmental priorities.     

The Value of a Statistical Life for Risk‐Averse and Risk‐Seeking Individuals

This article estimates the value of a statistical life (VSL) for Chile under the hedonic wage method while accounting for individual risk preferences. Two alternative measures of risk aversion are used. First, risk aversion is directly measured using survey measures of preferences over hypothetical gambles, and second, over observed individual behaviors that may proxy for risk preferences, such as smoking status, are used. I reconcile the results with a theoretical model of economic behavior that predicts how the wage‐risk tradeoff changes as risk aversion differs across individuals. The VSL estimates range between 0.61 and 8.68 million dollars. The results using smoking behavior as a proxy for risk attitudes are consistent with previous findings. However, directly measuring risk aversion corrects the wage‐risk tradeoff estimation bias in the opposite direction. The results are robust to other observed measures of risk aversion such as drinking behavior and stock investments. Results suggest that, consistent with the literature that connects smoking behavior with labor market outcomes, smoking status could be capturing poor health productivity effect in addition to purely risk preferences.     

大气污染府际间合作治理联盟的达成与稳定——基于演化博弈分析

地方政府的大气污染治理模式主要有属地治理和合作治理模式,合作治理逐渐成为当前大气污染治理的共识。从演化博弈的视角,分析地方政府在大气污染治理中的行为演化路径与稳定策略,探究地方政府间达成并巩固合作治理联盟的因素。比较有中央约束和无中央政府约束下地方政府属地治理和合作治理四种演化博弈结果表明：在属地治理背景下,无论中央政府是否对地方政府进行约束,地方政府均倾向于“搭便车”行为,而中央政府对地方政府的约束在属地治理中面临失灵;在合作治理场景中,地方政府的稳定策略均向达成合作治理或均不治理的方向演进,但在中央政府约束下,地方政府的稳定策略能快速有效得向合作治理的方向演进。为实现大气污染的有效治理,地方政府间必须形成有效的合作治理联盟,合作收益是达成大气污染合作治理联盟的必要条件,而合作成本与中央政府约束的程度决定了合作治理联盟的稳定性。     

控制权、现金流权与公司价值——基于企业生命周期的视角

本文以2005-2008年间我国752家上市公司为样本,借鉴现金流组合方法对上市公司所处生命周期进行界定,从企业生命周期的角度考察了不同性质的最终控制人控制权、现金流权及两权分离程度对公司价值的影响。研究发现,最终控制人控制权与公司价值负相关;而现金流权也与公司价值负相关,这与西方学者结论不同,主要是因为我国特殊的股权结构--第一大股东持有的股份多数为非流通股,导致了高现金流权并不能起到相应的激励作用;两权分离程度在成长期和成熟期越大会造成公司价值的降低,而在衰退期则有利于公司价值的提升;最终控制人为非国有性质的公司,相对于国有性质的公司在成长期和成熟期更有利于公司价值的提升,而衰退期则相反。     

Use of Quality-Adjusted Life Year Weights with Dose-Response Models for Public Health Decisions: A Case Study of the Risks and Benefits of Fish Consumption

Risks associated with toxicants in food are often controlled by exposure reduction. When exposure recommendations are developed for foods with both harmful and beneficial qualities, however, they must balance the associated risks and benefits to maximize public health. Although quantitative methods are commonly used to evaluate health risks, such methods have not been generally applied to evaluating the health benefits associated with environmental exposures. A quantitative method for risk-benefit analysis is presented that allows for consideration of diverse health endpoints that differ in their impact (i.e., duration and severity) using dose-response modeling weighted by quality-adjusted life years saved. To demonstrate the usefulness of this method, the risks and benefits of fish consumption are evaluated using a single health risk and health benefit endpoint. Benefits are defined as the decrease in myocardial infarction mortality resulting from fish consumption, and risks are defined as the increase in neurodevelopmental delay (i.e., talking) resulting from prenatal methylmercury exposure. Fish consumption rates are based on information from Washington State. Using the proposed framework, the net health impact of eating fish is estimated in either a whole population or a population consisting of women of childbearing age and their children. It is demonstrated that across a range of fish methylmercury concentrations (0-1 ppm) and intake levels (0-25 g/day), individuals would have to weight the neurodevelopmental effects 6 times more (in the whole population) or 250 times less (among women of child-bearing age and their children) than the myocardial infarction benefits in order to be ambivalent about whether or not to consume fish. These methods can be generalized to evaluate the merits of other public health and risk management programs that involve trade-offs between risks and benefits.