Plausible Upper Bounds: Are Their Sums Plausible?1

Quantitative cancer risk assessments are typically expressed as plausible upper bounds rather than estimates of central tendency. In analyses involving several carcinogens, these upper bounds are often summed to estimate overall risk. This begs the question of whether a sum of upper bounds is itself a plausible estimate of overall risk. This question can be asked in two ways: whether the sum yields an improbable estimate of overall risk (that is, is it only remotely possible for the true sum of risks to match the sum of upper bounds), or whether the sum gives a misleading estimate (that is, is the true sum of risks likely to be very different from the sum of upper bounds). Analysis of four case studies shows that as the number of risk estimates increases, their sum becomes increasingly improbable, but not misleading. Though the overall risk depends on the independence, additivity, and number of risk estimates, as well as the shapes of the underlying risk distributions, sums of upper bounds provide useful information about the overall risk and can be adjusted downward to give a more plausible [perhaps probable] upper bound, or even a central estimate of overall risk.     

Threshold Evaluation of Emergency Risk Communication for Health Risks Related to Hazardous Ambient Temperature

Emergency risk communication (ERC) programs that activate when the ambient temperature is expected to cross certain extreme thresholds are widely used to manage relevant public health risks. In practice, however, the effectiveness of these thresholds has rarely been examined. The goal of this study is to test if the activation criteria based on extreme temperature thresholds, both cold and heat, capture elevated health risks for all‐cause and cause‐specific mortality and morbidity in the Minneapolis‐St. Paul Metropolitan Area. A distributed lag nonlinear model (DLNM) combined with a quasi‐Poisson generalized linear model is used to derive the exposure–response functions between daily maximum heat index and mortality (1998–2014) and morbidity (emergency department visits; 2007–2014). Specific causes considered include cardiovascular, respiratory, renal diseases, and diabetes. Six extreme temperature thresholds, corresponding to 1st–3rd and 97th–99th percentiles of local exposure history, are examined. All six extreme temperature thresholds capture significantly increased relative risks for all‐cause mortality and morbidity. However, the cause‐specific analyses reveal heterogeneity. Extreme cold thresholds capture increased mortality and morbidity risks for cardiovascular and respiratory diseases and extreme heat thresholds for renal disease. Percentile‐based extreme temperature thresholds are appropriate for initiating ERC targeting the general population. Tailoring ERC by specific causes may protect some but not all individuals with health conditions exacerbated by hazardous ambient temperature exposure.     

Quantifying Cancer Risk from Radiation

Complex statistical models fitted to data from studies of atomic bomb survivors are used to estimate the human health effects of ionizing radiation exposures. We describe and illustrate an approach to estimate population risks from ionizing radiation exposure that relaxes many assumptions about radiation‐related mortality. The approach draws on developments in methods for causal inference. The results offer a different way to quantify radiation's effects and show that conventional estimates of the population burden of excess cancer at high radiation doses are driven strongly by projecting outside the range of current data. Summary results obtained using the proposed approach are similar in magnitude to those obtained using conventional methods, although estimates of radiation‐related excess cancers differ for many age, sex, and dose groups. At low doses relevant to typical exposures, the strength of evidence in data is surprisingly weak. Statements regarding human health effects at low doses rely strongly on the use of modeling assumptions.     

Diesel Engine Exhaust and Lung Cancer Mortality: Time‐Related Factors in Exposure and Risk

To develop a quantitative exposure‐response relationship between concentrations and durations of inhaled diesel engine exhaust (DEE) and increases in lung cancer risks, we examined the role of temporal factors in modifying the estimated effects of exposure to DEE on lung cancer mortality and characterized risk by mine type in the Diesel Exhaust in Miners Study (DEMS) cohort, which followed 12,315 workers through December 1997. We analyzed the data using parametric functions based on concepts of multistage carcinogenesis to directly estimate the hazard functions associated with estimated exposure to a surrogate marker of DEE, respirable elemental carbon (REC). The REC‐associated risk of lung cancer mortality in DEMS is driven by increased risk in only one of four mine types (limestone), with statistically significant heterogeneity by mine type and no significant exposure‐response relationship after removal of the limestone mine workers. Temporal factors, such as duration of exposure, play an important role in determining the risk of lung cancer mortality following exposure to REC, and the relative risk declines after exposure to REC stops. There is evidence of effect modification of risk by attained age. The modifying impact of temporal factors and effect modification by age should be addressed in any quantitative risk assessment (QRA) of DEE. Until there is a better understanding of why the risk appears to be confined to a single mine type, data from DEMS cannot reliably be used for QRA.     

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.     

A Risk Assessment for Occupational Acrylonitrile Exposure Using Epidemiology Data

The extensive data from the Blair et al.((1)) epidemiology study of occupational acrylonitrile exposure among 25460 workers in eight plants in the United States provide an excellent opportunity to update quantitative risk assessments for this widely used commodity chemical. We employ the semiparametric Cox relative risk (RR) regression model with a cumulative exposure metric to model cause-specific mortality from lung cancer and all other causes. The separately estimated cause-specific cumulative hazards are then combined to provide an overall estimate of age-specific mortality risk. Age-specific estimates of the additional risk of lung cancer mortality associated with several plausible occupational exposure scenarios are obtained. For age 70, these estimates are all markedly lower than those generated with the cancer potency estimate provided in the USEPA acrylonitrile risk assessment.((2)) This result is consistent with the failure of recent occupational studies to confirm elevated lung cancer mortality among acrylonitrile-exposed workers as was originally reported by O'Berg,((3)) and it calls attention to the importance of using high-quality epidemiology data in the risk assessment process.     

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.     

Modeling Lung Carcinogenesis in Radon‐Exposed Miner Cohorts: Accounting for Missing Information on Smoking

Epidemiological miner cohort data used to estimate lung cancer risks related to occupational radon exposure often lack cohort‐wide information on exposure to tobacco smoke, a potential confounder and important effect modifier. We have developed a method to project data on smoking habits from a case‐control study onto an entire cohort by means of a Monte Carlo resampling technique. As a proof of principle, this method is tested on a subcohort of 35,084 former uranium miners employed at the WISMUT company (Germany), with 461 lung cancer deaths in the follow‐up period 1955–1998. After applying the proposed imputation technique, a biologically‐based carcinogenesis model is employed to analyze the cohort's lung cancer mortality data. A sensitivity analysis based on a set of 200 independent projections with subsequent model analyses yields narrow distributions of the free model parameters, indicating that parameter values are relatively stable and independent of individual projections. This technique thus offers a possibility to account for unknown smoking habits, enabling us to unravel risks related to radon, to smoking, and to the combination of both.     

TCDD Exposure-Response Analysis and Risk Assessment

We examined the relation between cancer mortality and time-dependent cumulative exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) estimated from a concentration- and age-dependent kinetic model of elimination, and we estimated incremental cancer risks at age 75. Data from the National Institute for Occupational Safety and Health study of 3,538 workers with occupational exposure to TCDD were analyzed using standardized mortality ratios and Cox regression procedures. Analyses adjusted for potential confounding by age, year of birth, and race and considered exposure lag periods of 0, 10, or 15 years. Other potential confounders including smoking and other occupational exposures were evaluated indirectly. To explore the influence of extreme values of cumulative TCDD ppt-years, we restricted the analysis to observations with exposure below the 95th percentile or used logarithmic (ln) transformed exposure values. We applied penalized smoothing splines to examine variation in the exposure-response relation across the exposure range. TCDD was not statistically significantly associated with cancer mortality using the full data set, regardless of the lag period. When we restricted the analysis to observations with exposure below the 95th percentile, TCDD was associated positively with cancer mortality, particularly when a 15-year lag was applied (untransformed exposure data: regression coefficient , standard error (s.e.) = 1.4 x 10(-6), p < 0.05; ln-transformed exposure data: , s.e. = 2.9 x 10(-2), p < 0.05). The estimated incremental lifetime risk of mortality at age 75 from all cancers was about 6 to more than 10 times lower than previous estimates derived from this cohort using exposure models that did not consider the age and concentration dependence of TCDD elimination.     

All The Same? On a Certain Pattern in Cross-National Death Risk

This article considers whether a nation that fares relatively well (or badly) on a particular dimension of mortality risk tends also to do so on others. Working with 2016 data from the Global Burden of Disease (GBD) Study, we focus on six causes of premature death: transport accidents, other accidents, homicide, early-childhood diseases, and both communicable and noncommunicable diseases beyond early childhood. We consider data from all 26 nations that had populations of at least 50 million in 2016, as well as 15 clusters of smaller nations that are similar in longevity (e.g., Scandinavia). We use an analytic method that facilitates useful comparisons across nations, for it recognizes that some potential death risks can be underestimated because citizens die sooner from other causes. We estimate reductions in lifespan from each of the six causes relative to natural lifespan as defined by GBD. It emerges that, for all 15 pairings among the six causes, these reductions are positively correlated. We introduce metrics to summarize a nation's overall “safety status,” and find that losses of longevity because of premature deaths are nearly three decades fewer in the safest countries than in the least safe ones. Turning to possible explanations for the cross-national differences, we find a strong association between a nation's safety status and both its economic wherewithal as indicated by the 2016 GDP per capita (adjusted for purchasing power parity) and its income inequality as reflected by its Gini coefficient.     

Preventing and Diagnosing Colorectal Cancer with a Limited Colonoscopy Resource

This paper explores how the capacity of colonoscopy services should be allocated for screening and diagnosis of colorectal cancer to improve health outcomes. Both of these services are important since screening prevents cancer by removing polyps, while diagnosis is required to start treatment for cancer. This paper first presents a basic compartmental model to illustrate the trade‐off between these two analytically. Further, a more realistic population dynamics model with resource constraints is introduced for colorectal cancer screening and analyzed numerically. The best resource allocation decisions are investigated with the objectives of minimizing mortality or incidence rates. We provide a sensitivity analysis with respect to policy and disease‐related parameters. We conclude that to minimize mortality, the capacity should be rationed to ensure that the wait for diagnosis is at reasonable levels. When the relevant performance measure is the incidence rate, screening is allocated more capacity compared to the case with mortality rate measure. We also show that benefits from increasing compliance to screening programs can only be realized if there is sufficient service capacity.     

Risk assessment methodologies for passive smoking-induced lung cancer

Risk assessment methodologies have been successfully applied to control societal risk from outdoor air pollutants. They are now being applied to indoor air pollutants such as environmental tobacco smoke (ETS) and radon. Nonsmokers' exposures to ETS have been assessed based on dosimetry of nicotine, its metabolite, continine, and on exposure to the particulate phase of ETS. Lung cancer responses have been based on both the epidemiology of active and of passive smoking. Nine risk assessments of nonsmokers' lung cancer risk from exposure to ETS have been performed. Some have estimated risks for lifelong nonsmokers only; others have included ex-smokers; still others have estimated total deaths from all causes. To facilitate interstudy comparison, in some cases lung cancers had to be interpolated from a total, or the authors' original estimate had to be adjusted to include ex-smokers. Further, all estimates were adjusted to 1988. Excluding one study whose estimate differs from the mean of the others by two orders of magnitude, the remaining risk assessments are in remarkable agreement. The mean estimate is approximately 5000 +/- 2400 nonsmokers' lung cancer deaths (LCDSs) per year. This is a 25% greater risk to nonsmokers than is indoor radon, and is about 57 times greater than the combined estimated cancer risk from all the hazardous outdoor air pollutants currently regulated by the Environmental Protection Agency: airborne radionuclides, asbestos, arsenic, benzene, coke oven emissions, and vinyl chloride.     

An Empirical Model of Perceived Mortality Risks for Selected U.S. Arsenic Hot Spots

Researchers have long recognized that subjective perceptions of risk are better predictors of choices over risky outcomes than science‐based or experts’ assessments of risk. More recent work suggests that uncertainty about risks also plays a role in predicting choices and behavior. In this article, we develop and estimate a formal model for an individual's perceived health risks associated with arsenic contamination of his or her drinking water. The modeling approach treats risk as a random variable, with an estimable probability distribution whose variance reflects uncertainty. The model we estimate uses data collected from a survey given to a sample of people living in arsenic‐prone areas in the United States. The findings from this article support the fact that scientific information is essential to explaining the mortality rate perceived by the individuals, but uncertainty about the probability remains significant.     

Diminishing Willingness to Pay per Quality‐Adjusted Life Year: Valuing Acute Foodborne Illness

We design and conduct a stated‐preference survey to estimate willingness to pay (WTP) to reduce foodborne risk of acute illness and to test whether WTP is proportional to the corresponding gain in expected quality‐adjusted life years (QALYs). If QALYs measure utility for health, then economic theory requires WTP to be nearly proportional to changes in both health quality and duration of illness and WTP could be estimated by multiplying the expected change in QALYs by an appropriate monetary value. WTP is elicited using double‐bounded, dichotomous‐choice questions in which respondents (randomly selected from the U.S. general adult population, n = 2,858) decide whether to purchase a more expensive food to reduce the risk of foodborne illness. Health risks vary by baseline probability of illness, reduction in probability, duration and severity of illness, and conditional probability of mortality. The expected gain in QALYs is calculated using respondent‐assessed decrements in health‐related quality of life if ill combined with the duration of illness and reduction in probability specified in the survey. We find sharply diminishing marginal WTP for severity and duration of illness prevented. Our results suggest that individuals do not have a constant rate of WTP per QALY, which implies that WTP cannot be accurately estimated by multiplying the change in QALYs by an appropriate monetary value.     

Bounding Analysis of Drinking Water Health Risks from a Spill of Hydraulic Fracturing Flowback Water

A bounding risk assessment is presented that evaluates possible human health risk from a hypothetical scenario involving a 10,000‐gallon release of flowback water from horizontal fracturing of Marcellus Shale. The water is assumed to be spilled on the ground, infiltrates into groundwater that is a source of drinking water, and an adult and child located downgradient drink the groundwater. Key uncertainties in estimating risk are given explicit quantitative treatment using Monte Carlo analysis. Chemicals that contribute significantly to estimated health risks are identified, as are key uncertainties and variables to which risk estimates are sensitive. The results show that hypothetical exposure via drinking water impacted by chemicals in Marcellus Shale flowback water, assumed to be spilled onto the ground surface, results in predicted bounds between 10⁻¹⁰ and 10⁻⁶ (for both adult and child receptors) for excess lifetime cancer risk. Cumulative hazard indices (HI_CUMULATIVE) resulting from these hypothetical exposures have predicted bounds (5th to 95th percentile) between 0.02 and 35 for assumed adult receptors and 0.1 and 146 for assumed child receptors. Predicted health risks are dominated by noncancer endpoints related to ingestion of barium and lithium in impacted groundwater. Hazard indices above unity are largely related to exposure to lithium. Salinity taste thresholds are likely to be exceeded before drinking water exposures result in adverse health effects. The findings provide focus for policy discussions concerning flowback water risk management. They also indicate ways to improve the ability to estimate health risks from drinking water impacted by a flowback water spill (i.e., reducing uncertainty).     

Air Nicotine and Saliva Cotinine as Indicators of Workplace Passive Smoking Exposure and Risk1

We model nicotine from environmental tobacco smoke (ETS) in office air and salivary cotinine in nonsmoking U.S. workers. We estimate that: an average salivary cotinine level of 0.4 ng/ml corresponds to an increased lifetime mortality risk of 1/1000 for lung cancer, and 1/100 for heart disease; >95% of ETS-exposed office workers exceed OSHA's significant risk level for heart disease mortality, and 60% exceed significant risk for lung cancer mortality; 4000 heart disease deaths and 400 lung cancer deaths occur annually among office workers from passive smoking in the workplace, at the current 28% prevalence of unrestricted smoking in the office workplace.     

Potency Factors for Risk Assessment at Libby,Montana

We reanalyzed the Libby vermiculite miners’ cohort assembled by Sullivan to estimate potency factors for lung cancer, mesothelioma, nonmalignant respiratory disease (NMRD), and all‐cause mortality associated with exposure to Libby fibers. Our principal statistical tool for analyses of lung cancer, NMRD, and total mortality in the cohort was the time‐dependent proportional hazards model. For mesothelioma, we used an extension of the Peto formula. For a cumulative exposure to Libby fiber of 100 f/mL‐yr, our estimates of relative risk (RR) are as follows: lung cancer, RR = 1.12, 95% confidence interval (CI) =[1.06, 1.17]; NMRD, RR = 1.14, 95% CI =[1.09, 1.18]; total mortality, RR = 1.06, 95% CI =[1.04, 1.08]. These estimates were virtually identical when analyses were restricted to the subcohort of workers who were employed for at least one year. For mesothelioma, our estimate of potency is K_M = 0.5 × 10^?8, 95% CI =[0.3 × 10^?8, 0.8 × 10^?8]. Finally, we estimated the mortality ratios standardized against the U.S. population for lung cancer, NMRD, and total mortality and obtained estimates that were in good agreement with those reported by Sullivan. The estimated potency factors form the basis for a quantitative risk assessment at Libby.     

QALYs versus WTP.

Quality adjusted life years (QALYs) and willingness to pay (WTP) are alternative measures of the value of reductions in health risk that are often used in evaluating environmental, health, and safety practices. Although both methods are based on individual preferences, the underlying assumptions differ. The different bases yield systematically different conclusions about the relative value of reducing health and mortality risks to individuals that differ in age, preexisting health conditions, income, and other factors. The choice of which method to use depends on judgments about what constraints should be placed on individual preferences and what factors should be considered in aggregating preferences across people.     

Hexavalent Chromium and Lung Cancer in the Chromate Industry: A Quantitative Risk Assessment

The purpose of this investigation was to estimate excess lifetime risk of lung cancer death resulting from occupational exposure to hexavalent-chromium-containing dusts and mists. The mortality experience in a previously studied cohort of 2,357 chromate chemical production workers with 122 lung cancer deaths was analyzed with Poisson regression methods. Extensive records of air samples evaluated for water-soluble total hexavalent chromium were available for the entire employment history of this cohort. Six different models of exposure-response for hexavalent chromium were evaluated by comparing deviances and inspection of cubic splines. Smoking (pack-years) imputed from cigarette use at hire was included in the model. Lifetime risks of lung cancer death from exposure to hexavalent chromium (assuming up to 45 years of exposure) were estimated using an actuarial calculation that accounts for competing causes of death. A linear relative rate model gave a good and readily interpretable fit to the data. The estimated rate ratio for 1 mg/m3-yr of cumulative exposure to hexavalent chromium (as CrO3), with a lag of five years, was RR=2.44 (95% CI=1.54-3.83). The excess lifetime risk of lung cancer death from exposure to hexavalent chromium at the current OSHA permissible exposure limit (PEL) (0.10 mg/m3) was estimated to be 255 per 1,000 (95% CI: 109-416). This estimate is comparable to previous estimates by U.S. EPA, California EPA, and OSHA using different occupational data. Our analysis predicts that current occupational standards for hexavalent chromium permit a lifetime excess risk of dying of lung cancer that exceeds 1 in 10, which is consistent with previous risk assessments.     

A probabilistic transmission and population dynamic model to assess tuberculosis infection risk

The purpose of this study was to examine tuberculosis (TB) population dynamics and to assess potential infection risk in Taiwan. A well‐established mathematical model of TB transmission built on previous models was adopted to study the potential impact of TB transmission. A probabilistic risk model was also developed to estimate site‐specific risks of developing disease soon after recent primary infection, exogenous reinfection, or through endogenous reactivation (latently infected TB) among Taiwan regions. Here, we showed that the proportion of endogenous reactivation (53–67%) was larger than that of exogenous reinfection (32–47%). Our simulations showed that as epidemic reaches a steady state, age distribution of cases would finally shift toward older age groups dominated by latently infected TB cases as a result of endogenous reactivation. A comparison of age‐weighted TB incidence data with our model simulation output with 95% credible intervals revealed that the predictions were in an apparent agreement with observed data. The median value of overall basic reproduction number (R₀) in eastern Taiwan ranged from 1.65 to 1.72, whereas northern Taiwan had the lowest R₀ estimate of 1.50. We found that total TB incidences in eastern Taiwan had 25–27% probabilities of total proportion of infected population exceeding 90%, whereas there were 36–66% probabilities having exceeded 20% of total proportion of infected population attributed to latently infected TB. We suggested that our Taiwan‐based analysis can be extended to the context of developing countries, where TB remains a substantial cause of elderly morbidity and mortality.