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.     

Dose-Response and Risk Assessment of Airborne Hexavalent Chromium and Lung Cancer Mortality

This study evaluates the dose-response relationship for inhalation exposure to hexavalent chromium [Cr(VI)] and lung cancer mortality for workers of a chromate production facility, and provides estimates of the carcinogenic potency. The data were analyzed using relative risk and additive risk dose-response models implemented with both Poisson and Cox regression. Potential confounding by birth cohort and smoking prevalence were also assessed. Lifetime cumulative exposure and highest monthly exposure were the dose metrics evaluated. The estimated lifetime additional risk of lung cancer mortality associated with 45 years of occupational exposure to 1 microg/m3 Cr(VI) (occupational exposure unit risk) was 0.00205 (90%CI: 0.00134, 0.00291) for the relative risk model and 0.00216 (90%CI: 0.00143, 0.00302) for the additive risk model assuming a linear dose response for cumulative exposure with a five-year lag. Extrapolating these findings to a continuous (e.g., environmental) exposure scenario yielded an environmental unit risk of 0.00978 (90%CI: 0.00640, 0.0138) for the relative risk model [e.g., a cancer slope factor of 34 (mg/kg-day)-1] and 0.0125 (90%CI: 0.00833, 0.0175) for the additive risk model. The relative risk model is preferred because it is more consistent with the expected trend for lung cancer risk with age. Based on statistical tests for exposure-related trend, there was no statistically significant increased lung cancer risk below lifetime cumulative occupational exposures of 1.0 mg-yr/m3, and no excess risk for workers whose highest average monthly exposure did not exceed the current Permissible Exposure Limit (52 microg/m3). It is acknowledged that this study had limited power to detect increases at these low exposure levels. These cancer potency estimates are comparable to those developed by U.S. regulatory agencies and should be useful for assessing the potential cancer hazard associated with inhaled Cr(VI).     

Estimation of Unit Risk for Coke Oven Emissions

In 1984, based on epidemiological data on cohorts of coke oven workers, USEPA estimated a unit risk for lung cancer associated with continuous exposure from birth to 1 pg/m3 of coke oven emissions, of 6.2 × This risk assessment was based on information on the cohorts available through 1966. Follow-up of these cohorts has now been extended to 1982 and, moreover, individual job histories, which were not available in 1984, have been constructed. In this study, lung cancer mortality in these cohorts of coke oven workers with extended follow-up was analyzed using standard techniques of survival analysis and a new approach based on the two stage clonal expansion model of carcinogenesis. The latter approach allows the explicit consideration of detailed patterns of exposure of each individual in the cohort. The analyses used the extended follow-up data through 1982 and the detailed job histories now available. Based on these analyses, the best estimate of unit risk is 1.5 × with 95% confidence interval = 1.2 × 10-"1.8 X     

Estimation of Potential Health Effects from Acute Exposure to Hydrogen Fluoride Using a "Benchmark Dose" Approach

Communities across the United States are examining the manufacture, use, transport, and storage of hydrogen fluoride (HF) near residential areas as a consequence of a major release of HF in Texas in 1987. Reference exposure levels for routine and accidental HF emissions are calculated using existing animal and human data. The approach employs a logprobit extrapolation of concentration-response data to the 95% lower confidence limit on the toxic concentration producing a "benchmark dose" of 1% response (TC01), called a practical threshold. Species-specific and chemical-specific adjustment factors are applied to develop exposure levels applicable to the general public. Using this method, the 1-hr reference exposure level to protect the public against any irritation from a routine emission (REL-1) is 0.7 ppm and the level to protect against severe irritation from a once-in-a-lifetime (REL-2) release is 2 ppm. This approach is compared to a modified "uncertainty factor" approach.     

Exposure Misclassification and Threshold Concentrations in Time Series Analyses of Air Pollution Health Effects

Linear, no-threshold relationships are typically reported for time series studies of air pollution and mortality. Since regulatory standards and economic valuations typically assume some threshold level, we evaluated the fundamental question of the impact of exposure misclassification on the persistence of underlying personal-level thresholds when personal data are aggregated to the population level in the assessment of exposure-response relationships. As an example, we measured personal exposures to two particle metrics, PM2.5 and sulfate (SO4(2-)), for a sample of lung disease patients and compared these with exposures estimated from ambient measurements Previous work has shown that ambient:personal correlations for PM2.5 are much lower than for SO4(2-), suggesting that ambient PM2.5 measurements misclassify exposures to PM2.5. We then developed a method by which the measured:estimated exposure relationships for these patients were used to simulate personal exposures for a larger population and then to estimate individual-level mortality risks under different threshold assumptions. These individual risks were combined to obtain the population risk of death, thereby exhibiting the prominence (and the value) of the threshold in the relationship between risk and estimated exposure. Our results indicated that for poorly classified exposures (PM2.5 in this example) population-level thresholds were apparent at lower ambient concentrations than specified common personal thresholds, while for well-classified exposures (e.g., SO4(2-)), the apparent thresholds were similar to these underlying personal thresholds. These results demonstrate that surrogate metrics that are not highly correlated with personal exposures obscure the presence of thresholds in epidemiological studies of larger populations, while exposure indicators that are highly correlated with personal exposures can accurately reflect underlying personal thresholds.     

Parameters of a Dose‐Response Model Are on the Boundary: What Happens with BMDL?

It is well known that, under appropriate regularity conditions, the asymptotic distribution for the likelihood ratio statistic is χ². This result is used in EPA's benchmark dose software to obtain a lower confidence bound (BMDL) for the benchmark dose (BMD) by the profile likelihood method. Recently, based on work by Self and Liang, it has been demonstrated that the asymptotic distribution of the likelihood ratio remains the same if some of the regularity conditions are violated, that is, when true values of some nuisance parameters are on the boundary. That is often the situation for BMD analysis of cancer bioassay data. In this article, we study by simulation the coverage of one- and two-sided confidence intervals for BMD when some of the model parameters have true values on the boundary of a parameter space. Fortunately, because two-sided confidence intervals (size 1–2α) have coverage close to the nominal level when there are 50 animals in each group, the coverage of nominal 1−α one-sided intervals is bounded between roughly 1–2α and 1. In many of the simulation scenarios with a nominal one-sided confidence level of 95%, that is, α= 0.05, coverage of the BMDL was close to 1, but for some scenarios coverage was close to 90%, both for a group size of 50 animals and asymptotically (group size 100,000). Another important observation is that when the true parameter is below the boundary, as with the shape parameter of a log-logistic model, the coverage of BMDL in a constrained model (a case of model misspecification not uncommon in BMDS analyses) may be very small and even approach 0 asymptotically. We also discuss that whenever profile likelihood is used for one-sided tests, the Self and Liang methodology is needed to derive the correct asymptotic distribution.     

Estimating Risk Assessment Exposure Point Concentrations when the Data Are Not Normal or Lognormal

The U.S. Environmental Protection Agency (EPA) recommends the use of the one-sided 95% upper confidence limit of the arithmetic mean based on either a normal or lognormal distribution for the contaminant (or exposure point) concentration term in the Superfund risk assessment process. When the data are not normal or lognormal this recommended approach may overestimate the exposure point concentration (EPC) and may lead to unecessary cleanup at a hazardous waste site. The EPA concentration term only seems to perform like alternative EPC methods when the data are well fit by a lognormal distribution. Several alternative methods for calculating the EPC are investigated and compared using soil data collected from three hazardous waste sites in Montana, Utah, and Colorado. For data sets that are well fit by a lognormal distribution, values for the Chebychev inequality or the EPA concentration term may be appropriate EPCs. For data sets where the soil concentration data are well fit by gamma distributions, Wong's method may be used for calculating EPCs. The studentized bootstrap-t and Hall's bootstrap-t transformation are recommended for EPC calculation when all distribution fits are poor. If a data set is well fit by a distribution, parametric bootstrap may provide a suitable EPC.     

Dose‐Response Modeling for Inhalational Anthrax in Rabbits Following Single or Multiple Exposures

There is a need to advance our ability to characterize the risk of inhalational anthrax following a low‐dose exposure. The exposure scenario most often considered is a single exposure that occurs during an attack. However, long‐term daily low‐dose exposures also represent a realistic exposure scenario, such as what may be encountered by people occupying areas for longer periods. Given this, the objective of the current work was to model two rabbit inhalational anthrax dose‐response data sets. One data set was from single exposures to aerosolized Bacillus anthracis Ames spores. The second data set exposed rabbits repeatedly to aerosols of B. anthracis Ames spores. For the multiple exposure data the cumulative dose (i.e., the sum of the individual daily doses) was used for the model. Lethality was the response for both. Modeling was performed using Benchmark Dose Software evaluating six models: logprobit, loglogistic, Weibull, exponential, gamma, and dichotomous‐Hill. All models produced acceptable fits to either data set. The exponential model was identified as the best fitting model for both data sets. Statistical tests suggested there was no significant difference between the single exposure exponential model results and the multiple exposure exponential model results, which suggests the risk of disease is similar between the two data sets. The dose expected to cause 10% lethality was 15,600 inhaled spores and 18,200 inhaled spores for the single exposure and multiple exposure exponential dose‐response model, respectively, and the 95% lower confidence intervals were 9,800 inhaled spores and 9,200 inhaled spores, respectively.     

The Use of Multizone Models to Estimate an Airborne Chemical Contaminant Generation and Decay Profile: Occupational Exposures of Hairdressers to Vinyl Chloride in Hairspray During the 1960s and 1970s

Vinyl chloride (VC) was used as a propellant in a limited percentage of aerosol hairspray products in the United States from approximately 1967 to 1973. The question has arisen whether occupational exposures of hairdressers to VC-containing hairsprays in hair salons were sufficient to increase the risk for developing hepatic angiosarcoma (HAS). Transient two-zone and steady-state three-zone models were used to estimate the historical airborne concentration of VC for individual hairdressers using hairspray as well as estimated contributions from other hairdressers in the same salon. Concentrations of VC were modeled for small, medium, and large salons, as well as a representative home salon. Model inputs were determined using published literature, and variability in these inputs was also considered using Monte Carlo techniques. The 95th percentile for the daily time-weighted average exposure for small, medium, and large salons, assuming a market-share fraction of VC-containing hairspray use from the Monte Carlo analysis, was about 0.3 ppm, and for the home salon scenario was 0.1 ppm. The 95th percentile value for the cumulative lifetime exposure of the hairdressers was 2.8 ppm-years for the home salon scenario and 2.0 ppm-years for the small, medium, and large salon scenarios. If using the assumption that all hairsprays used in a salon contained VC, the 95th percentile of the theoretical lifetime cumulative dose was estimated to be 52–79 ppm-years. Estimated lifetime doses were all below the threshold dose for HAS of about 300 to 500 ppm-years reported in the published epidemiology literature.     

Multi-Stage Model Estimates of Lung Cancer Risk from Exposure to Diesel Exhaust, Based on a U.S. Railroad Worker Cohort

A California Environmental Protection Agency (Cal/EPA) report concluded that a reasonable and likely explanation for the increased lung cancer rates in numerous epidemiological studies is a causal association between diesel exhaust exposure and lung cancer. A version of the present analysis, based on a retrospective study of a U.S. railroad worker cohort, provided the Cal/EPA report with some of its estimates of lung cancer risk associated with diesel exhaust. The individual data for that cohort study furnish information on age, employment, and mortality for 56,000 workers over 22 years. Related studies provide information on exposure concentrations. Other analyses of the original cohort data reported finding no relation between measures of diesel exhaust and lung cancer mortality, while a Health Effects Institute report found the data unsuitable for quantitative risk assessment. None of those three works used multistage models, which this article uses in finding a likely quantitative, positive relations between lung cancer and diesel exhaust. A seven-stage model that has the last or next-to-last stage sensitive to diesel exhaust provides best estimates of increase in annual mortality rate due to each unit of concentration, for bracketing assumptions on exposure. Using relative increases of risk and multiplying by the background lung cancer mortality rates for California, the 95% upper confidence limit of the 70-year unit risks for lung cancer is estimated to be in the range 2.1 x 10(-4) (microg/m3)(-1) to 5.5 x 10(-4) (microg/m3)(-1). These risks constitute the low end of those in the Cal/EPA report and are below those reported by previous investigators whose estimates were positive using human data.     

Reanalysis of Dose-Response Data from the Iraqi Methylmercury Poisoning Episode

Applying a hockey stick parametric dose-response model to data on late or retarded development in Iraqi children exposed in utero to methylmercury, with mercury (Hg) exposure characterized by the peak Hg concentration in mothers'hair during pregnancy, Cox et al. calculated the "best statistical estimate" of the threshold for health effects as 10 ppm Hg in hair with a 95% range of uncertainty of between 0 and 13.6 ppm.⁽¹⁾A new application of the hockey stick model to the Iraqi data shows, however, that the statistical upper limit of the threshold based on the hockey stick model could be as high as 255 ppm. Furthermore, the maximum likelihood estimate of the threshold using a different parametric model is virtually zero. These and other analyses demonstrate that threshold estimates based on parametric models exhibit high statistical variability and model dependency, and are highly sensitive to the precise definition of an abnormal response. Consequently, they are not a reliable basis for setting a reference dose (RfD) for methylmercury. Benchmark analyses and statistical analyses useful for deriving NOAELs are also presented. We believe these latter analyses—particularly the benchmark analyses—generally form a sounder basis for determining RfDs than the type of hockey stick analysis presented by Cox et al. However, the acute nature of the exposures, as well as other limitations in the Iraqi data suggest that other data may be more appropriate for determining acceptable human exposures to methylmercury.     

Peak Exposures in Epidemiologic Studies and Cancer Risks: Considerations for Regulatory Risk Assessment

We review approaches for characterizing “peak” exposures in epidemiologic studies and methods for incorporating peak exposure metrics in dose–response assessments that contribute to risk assessment. The focus was on potential etiologic relations between environmental chemical exposures and cancer risks. We searched the epidemiologic literature on environmental chemicals classified as carcinogens in which cancer risks were described in relation to “peak” exposures. These articles were evaluated to identify some of the challenges associated with defining and describing cancer risks in relation to peak exposures. We found that definitions of peak exposure varied considerably across studies. Of nine chemical agents included in our review of peak exposure, six had epidemiologic data used by the U.S. Environmental Protection Agency (US EPA) in dose–response assessments to derive inhalation unit risk values. These were benzene, formaldehyde, styrene, trichloroethylene, acrylonitrile, and ethylene oxide. All derived unit risks relied on cumulative exposure for dose–response estimation and none, to our knowledge, considered peak exposure metrics. This is not surprising, given the historical linear no‐threshold default model (generally based on cumulative exposure) used in regulatory risk assessments. With newly proposed US EPA rule language, fuller consideration of alternative exposure and dose–response metrics will be supported. “Peak” exposure has not been consistently defined and rarely has been evaluated in epidemiologic studies of cancer risks. We recommend developing uniform definitions of “peak” exposure to facilitate fuller evaluation of dose response for environmental chemicals and cancer risks, especially where mechanistic understanding indicates that the dose response is unlikely linear and that short‐term high‐intensity exposures increase risk.     

Benzene Inhalation by Parts Washers: New Estimates Based on Measures of Occupational Exposure to Solvent Coaromatics

Questions persist regarding assessment of workers’ exposures to products containing low levels of benzene, such as mineral spirit solvent (MSS). This study summarizes previously unpublished data for parts‐washing activities, and evaluates potential daily and lifetime cumulative benzene exposures incurred by workers who used historical and current formulations of a recycled mineral spirits solvent in manual parts washers. Measured benzene concentrations in historical samples from parts‐washing operations were frequently below analytical detection limits. To better assess benzene exposure among these workers, air‐to‐solvent concentration ratios measured for toluene, ethylbenzene, and xylenes (TEX) were used to predict those for benzene based on a statistical model, conditional on physical‐chemical theory supported by new thermodynamic calculations of TEX and benzene activity coefficients in a modeled MSS‐type solvent. Using probabilistic methods, the distributions of benzene concentrations were then combined with distributions of other exposure parameters to estimate eight‐hour time‐weighted average (TWA) exposure concentration distributions and corresponding daily respiratory dose distributions for workers using these solvents in parts washers. The estimated 50th (95th) percentile of the daily respiratory dose and corresponding eight‐hour TWA air concentration for workers performing parts washing are 0.079 (0.77) mg and 0.0030 (0.028) parts per million by volume (ppm) for historical solvent, and 0.020 (0.20) mg and 0.00078 (0.0075) ppm for current solvent, respectively. Both 95th percentile eight‐hour TWA respiratory exposure estimates for solvent formulations are less than 10% of the current Occupational Safety and Health Administration permissible exposure limit of 1.0 ppm for benzene.     

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.     

Risk‐Based Probabilistic Approach to Assess the Impact of False Mussel Invasions on Farmed Hard Clams

The purpose of this article is to provide a risk‐based predictive model to assess the impact of false mussel Mytilopsis sallei invasions on hard clam Meretrix lusoria farms in the southwestern region of Taiwan. The actual spread of invasive false mussel was predicted by using analytical models based on advection‐diffusion and gravity models. The proportion of hard clam colonized and infestation by false mussel were used to characterize risk estimates. A mortality model was parameterized to assess hard clam mortality risk characterized by false mussel density and infestation intensity. The published data were reanalyzed to parameterize a predictive threshold model described by a cumulative Weibull distribution function that can be used to estimate the exceeding thresholds of proportion of hard clam colonized and infestation. Results indicated that the infestation thresholds were 2–17 ind clam^?1 for adult hard clams, whereas 4 ind clam^?1 for nursery hard clams. The average colonization thresholds were estimated to be 81–89% for cultivated and nursery hard clam farms, respectively. Our results indicated that false mussel density and infestation, which caused 50% hard clam mortality, were estimated to be 2,812 ind m^?2 and 31 ind clam^?1, respectively. This study further indicated that hard clam farms that are close to the coastal area have at least 50% probability for 43% mortality caused by infestation. This study highlighted that a probabilistic risk‐based framework characterized by probability distributions and risk curves is an effective representation of scientific assessments for farmed hard clam in response to the nonnative false mussel invasion.     

Economics of Disaster Risk,Social Vulnerability,and Mental Health Resilience

We investigate the relationship between exposure to Hurricanes Katrina and/or Rita and mental health resilience by vulnerability status, with particular focus on the mental health outcomes of single mothers versus the general public. We advance a measurable notion of mental health resilience to disaster events. We also calculate the economic costs of poor mental health days added by natural disaster exposure. Negative binomial analyses show that hurricane exposure increases the expected count of poor mental health days for all persons by 18.7% (95% confidence interval [CI], 7.44–31.14%), and by 71.88% (95% CI, 39.48–211.82%) for single females with children. Monthly time‐series show that single mothers have lower event resilience, experiencing higher added mental stress. Results also show that the count of poor mental health days is sensitive to hurricane intensity, increasing by a factor of 1.06 (95% CI, 1.02–1.10) for every billion (U.S.$) dollars of damage added for all exposed persons, and by a factor of 1.08 (95% CI, 1.03–1.14) for single mothers. We estimate that single mothers, as a group, suffered over $130 million in productivity loss from added postdisaster stress and disability. Results illustrate the measurability of mental health resilience as a two‐dimensional concept of resistance capacity and recovery time. Overall, we show that natural disasters regressively tax disadvantaged population strata.     

Estimating Contaminant Dose for Intermittent Dermal Contact: Model Development, Testing, and Application

Assessments of aggregate exposure to pesticides and other surface contamination in residential environments are often driven by assumptions about dermal contacts. Accurately predicting cumulative doses from realistic skin contact scenarios requires characterization of exposure scenarios, skin surface loading and unloading rates, and contaminant movement through the epidermis. In this article we (1) develop and test a finite-difference model of contaminant transport through the epidermis; (2) develop archetypal exposure scenarios based on behavioral data to estimate characteristic loading and unloading rates; and (3) quantify 24-hour accumulation below the epidermis by applying a Monte Carlo simulation of these archetypal exposure scenarios. The numerical model, called Transient Transport through the epiDERMis (TTDERM), allows us to account for variable exposure times and time between exposures, temporal and spatial variations in skin and compound properties, and uncertainty in model parameters. Using TTDERM we investigate the use of a macro-activity parameter (cumulative contact time) for predicting daily (24-hour) integrated uptake of pesticides during complex exposure scenarios. For characteristic child behaviors and hand loading and unloading rates, we find that a power law represents the relationship between cumulative contact time and cumulative mass transport through the skin. With almost no loss of reliability, this simple relationship can be used in place of the more complex micro-activity simulations that require activity data on one- to five-minute intervals. The methods developed in this study can be used to guide dermal exposure model refinements and exposure measurement study design.     

Model Uncertainty and Model Averaging in the Estimation of Infectious Doses for Microbial Pathogens

Food‐borne infection is caused by intake of foods or beverages contaminated with microbial pathogens. Dose‐response modeling is used to estimate exposure levels of pathogens associated with specific risks of infection or illness. When a single dose‐response model is used and confidence limits on infectious doses are calculated, only data uncertainty is captured. We propose a method to estimate the lower confidence limit on an infectious dose by including model uncertainty and separating it from data uncertainty. The infectious dose is estimated by a weighted average of effective dose estimates from a set of dose‐response models via a Kullback information criterion. The confidence interval for the infectious dose is constructed by the delta method, where data uncertainty is addressed by a bootstrap method. To evaluate the actual coverage probabilities of the lower confidence limit, a Monte Carlo simulation study is conducted under sublinear, linear, and superlinear dose‐response shapes that can be commonly found in real data sets. Our model‐averaging method achieves coverage close to nominal in almost all cases, thus providing a useful and efficient tool for accurate calculation of lower confidence limits on infectious doses.     

Likelihood Contour Method for the Calculation of Asymptotic Upper Confidence Limits on the Risk Function for Quantitative Responses

This article develops a computationally and analytically convenient form of the profile likelihood method for obtaining one-sided confidence limits on scalar-valued functions phi = phi(psi) of the parameters psi in a multiparameter statistical model. We refer to this formulation as the likelihood contour method (LCM). In general, the LCM procedure requires iterative solution of a system of nonlinear equations, and good starting values are critical because the equations have at least two solutions corresponding to the upper and lower confidence limits. We replace the LCM equations by the lowest order terms in their asymptotic expansions. The resulting equations can be solved explicitly and have exactly two solutions that are used as starting values for obtaining the respective confidence limits from the LCM equations. This article also addresses the problem of obtaining upper confidence limits for the risk function in a dose-response model in which responses are normally distributed. Because of normality, considerable analytic simplification is possible and solution of the LCM equations reduces to an easy one-dimensional root-finding problem. Simulation is used to study the small-sample coverage of the resulting confidence limits.     

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.