Spatial Modeling of Air Pollution in Studies of Its Short‐Term Health Effects

Summary In studies that estimate the short‐term effects of air pollution on health, daily measurements of pollution concentrations are often available from a number of monitoring locations within the study area. However, the health data are typically only available in the form of daily counts for the entire area, meaning that a corresponding single daily measure of pollution is required. The standard approach is to average the observed measurements at the monitoring locations, and use this in a log‐linear health model. However, as the pollution surface is spatially variable this simple summary is unlikely to be an accurate estimate of the average pollution concentration across the region, which may lead to bias in the resulting health effects. In this article, we propose an alternative approach that jointly models the pollution concentrations and their relationship with the health data using a Bayesian spatio‐temporal model. We compare this approach with the simple spatial average using a simulation study, by investigating the impact of spatial variation, monitor placement, and measurement error in the pollution data. An epidemiological study from Greater London is then presented, which estimates the relationship between respiratory mortality and four different pollutants.     

Survival Analysis with Error‐Prone Time‐Varying Covariates: A Risk Set Calibration Approach

Summary Occupational, environmental, and nutritional epidemiologists are often interested in estimating the prospective effect of time‐varying exposure variables such as cumulative exposure or cumulative updated average exposure, in relation to chronic disease endpoints such as cancer incidence and mortality. From exposure validation studies, it is apparent that many of the variables of interest are measured with moderate to substantial error. Although the ordinary regression calibration (ORC) approach is approximately valid and efficient for measurement error correction of relative risk estimates from the Cox model with time‐independent point exposures when the disease is rare, it is not adaptable for use with time‐varying exposures. By recalibrating the measurement error model within each risk set, a risk set regression calibration (RRC) method is proposed for this setting. An algorithm for a bias‐corrected point estimate of the relative risk using an RRC approach is presented, followed by the derivation of an estimate of its variance, resulting in a sandwich estimator. Emphasis is on methods applicable to the main study/external validation study design, which arises in important applications. Simulation studies under several assumptions about the error model were carried out, which demonstrated the validity and efficiency of the method in finite samples. The method was applied to a study of diet and cancer from Harvard's Health Professionals Follow‐up Study (HPFS).     

Hierarchical bivariate time series models: a combined analysis of the effects of particulate matter on morbidity and mortality

In this paper we develop a hierarchical bivariate time series model to characterize the relationship between particulate matter less than 10 microns in aerodynamic diameter (PM10) and both mortality and hospital admissions for cardiovascular diseases. The model is applied to time series data on mortality and morbidity for 10 metropolitan areas in the United States from 1986 to 1993. We postulate that these time series should be related through a shared relationship with PM10. At the first stage of the hierarchy, we fit two seemingly unrelated Poisson regression models to produce city-specific estimates of the log relative rates of mortality and morbidity associated with exposure to PM10 within each location. The sample covariance matrix of the estimated log relative rates is obtained using a novel generalized estimating equation approach that takes into account the correlation between the mortality and morbidity time series. At the second stage, we combine information across locations to estimate overall log relative rates of mortality and morbidity and variation of the rates across cities. Using the combined information across the 10 locations we find that a 10 microg/m3 increase in average PM10 at the current day and previous day is associated with a 0.26% increase in mortality (95% posterior interval -0.37, 0.65), and a 0.71% increase in hospital admissions (95% posterior interval 0.35, 0.99). The log relative rates of mortality and morbidity have a similar degree of heterogeneity across cities: the posterior means of the between-city standard deviations of the mortality and morbidity air pollution effects are 0.42 (95% interval 0.05, 1.18), and 0.31 (95% interval 0.10, 0.89), respectively. The city-specific log relative rates of mortality and morbidity are estimated to have very low correlation, but the uncertainty in the correlation is very substantial (posterior mean = 0.20, 95% interval -0.89, 0.98). With the parameter estimates from the model, we can predict the hospitalization log relative rate for a new city for which hospitalization data are unavailable, using that city's estimated mortality relative rate. We illustrate this prediction using New York as an example.     

Quantifying personal exposure to air pollution from smartphone‐based location data

Personal exposure assessment is a challenging task that requires both measurements of the state of the environment as well as the individual's movements. In this paper, we show how location data collected by smartphone applications can be exploited to quantify the personal exposure of a large group of people to air pollution. A Bayesian approach that blends air quality monitoring data with individual location data is proposed to assess the individual exposure over time, under uncertainty of both the pollutant level and the individual location. A comparison with personal exposure obtained assuming fixed locations for the individuals is also provided. Location data collected by the Earthquake Network research project are employed to quantify the dynamic personal exposure to fine particulate matter of around 2500 people living in Santiago (Chile) over a 4‐month period. For around 30% of individuals, the personal exposure based on people movements emerges significantly different over the static exposure. On the basis of this result and thanks to a simulation study, we claim that even when the individual location is known with nonnegligible error, this helps to better assess personal exposure to air pollution. The approach is flexible and can be adopted to quantify the personal exposure based on any location‐aware smartphone application.     

Air pollution combustion emissions: characterization of causative agents and mechanisms associated with cancer, reproductive, and cardiovascular effects

Combustion emissions account for over half of the fine particle (PM(2.5)) air pollution and most of the primary particulate organic matter. Human exposure to combustion emissions including the associated airborne fine particles and mutagenic and carcinogenic constituents (e.g., polycyclic aromatic compounds (PAC), nitro-PAC) have been studied in populations in Europe, America, Asia, and increasingly in third-world counties. Bioassay-directed fractionation studies of particulate organic air pollution have identified mutagenic and carcinogenic polycyclic aromatic hydrocarbons (PAH), nitrated PAH, nitro-lactones, and lower molecular weight compounds from cooking. A number of these components are significant sources of human exposure to mutagenic and carcinogenic chemicals that may also cause oxidative and DNA damage that can lead to reproductive and cardiovascular effects. Chemical and physical tracers have been used to apportion outdoor and indoor and personal exposures to airborne particles between various combustion emissions and other sources. These sources include vehicles (e.g., diesel and gasoline vehicles), heating and power sources (e.g., including coal, oil, and biomass), indoor sources (e.g., cooking, heating, and tobacco smoke), as well as secondary organic aerosols and pollutants derived from long-range transport. Biomarkers of exposure, dose and susceptibility have been measured in populations exposed to air pollution combustion emissions. Biomarkers have included metabolic genotype, DNA adducts, PAH metabolites, and urinary mutagenic activity. A number of studies have shown a significant correlation of exposure to PM(2.5) with these biomarkers. In addition, stratification by genotype increased this correlation. New multivariate receptor models, recently used to determine the sources of ambient particles, are now being explored in the analysis of human exposure and biomarker data. Human studies of both short- and long-term exposures to combustion emissions and ambient fine particulate air pollution have been associated with measures of genetic damage. Long-term epidemiologic studies have reported an increased risk of all causes of mortality, cardiopulmonary mortality, and lung cancer mortality associated with increasing exposures to air pollution. Adverse reproductive effects (e.g., risk for low birth weight) have also recently been reported in Eastern Europe and North America. Although there is substantial evidence that PAH or substituted PAH may be causative agents in cancer and reproductive effects, an increasing number of studies investigating cardiopulmonary and cardiovascular effects are investigating these and other potential causative agents from air pollution combustion sources.     

Corrections for measurement error due to delayed onset of illness for case-crossover designs

Epidemiologic studies of the short-term effects of ambient particulate matter (PM) on the risk of acute cardiovascular or cerebrovascular events often use data from administrative databases in which only the date of hospitalization is known. A common study design for analyzing such data is the case-crossover design, in which exposure at a time when a patient experiences an event is compared to exposure at times when the patient did not experience an event within a case-control paradigm. However, the time of true event onset may precede hospitalization by hours or days, which can yield attenuated effect estimates. In this article, we consider a marginal likelihood estimator, a regression calibration estimator, and a conditional score estimator, as well as parametric bootstrap versions of each, to correct for this bias. All considered approaches require validation data on the distribution of the delay times. We compare the performance of the approaches in realistic scenarios via simulation, and apply the methods to analyze data from a Boston-area study of the association between ambient air pollution and acute stroke onset. Based on both simulation and the case study, we conclude that a two-stage regression calibration estimator with a parametric bootstrap bias correction is an effective method for correcting bias in health effect estimates arising from delayed onset in a case-crossover study.     

Measurement error caused by spatial misalignment in environmental epidemiology

In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.     

Molecular epidemiology studies of carcinogenic environmental pollutants. Effects of polycyclic aromatic hydrocarbons (PAHs) in environmental pollution on exogenous and oxidative DNA damage

Exposure to high levels of environmental air pollution is known to be associated with an increased carcinogenic risk. The individual contribution to this risk derived from specific carcinogenic chemicals within the complex mixture of air pollution is less certain, but may be explored by the use of molecular epidemiological techniques. Measurements of biomarkers of exposure, of effect and of susceptibility provide information of potential benefit for epidemiological and cancer risk assessment. The application of such techniques has been mostly concerned in the past with the carcinogenic polycyclic aromatic hydrocarbons (c-PAHs) that are associated with particulate matter in air pollution, and has showed clear evidence of genotoxic effects, such as DNA adducts, chromosome aberrations (CA) and ras oncogene overexpression, in environmentally exposed Czech and Polish populations. We are currently extending these studies by an investigation of populations exposed to environmental pollution in three European countries, Czech Republic, Slovak Republic and Bulgaria. This pays particular attention to PAHs, but also investigates the extent of radically induced (oxidative) DNA damage in the exposed populations. Policemen, bus drivers and controls, who carried personal monitors to determine their exposures to PAHs have been studied, and blood and urine were collected. Antioxidant and dietary status were assessed in these populations. Stationary monitors were also used for ambient air monitoring. Amongst the parameters studied in the biological samples were: (a) exposure biomarkers, such as PAH adducts with DNA, p53 and p21(WAF1) protein levels, (b) oxidative DNA damage, (c) the biological effect of the exposure by measurement of chromosome damage by fluorescence in situ hybridisation (FISH) or conventional methods, and (d) polymorphisms in carcinogen metabolising and DNA repair enzymes. Repair ability was also measured by the Comet assay. In vitro systems are being evaluated to characterise the genotoxicity of the organic compounds adsorbed to air particles.     

Estimating the acute health effects of coarse particulate matter accounting for exposure measurement error

In air pollution epidemiology, there is a growing interest in estimating the health effects of coarse particulate matter (PM) with aerodynamic diameter between 2.5 and 10 μm. Coarse PM concentrations can exhibit considerable spatial heterogeneity because the particles travel shorter distances and do not remain suspended in the atmosphere for an extended period of time. In this paper, we develop a modeling approach for estimating the short-term effects of air pollution in time series analysis when the ambient concentrations vary spatially within the study region. Specifically, our approach quantifies the error in the exposure variable by characterizing, on any given day, the disagreement in ambient concentrations measured across monitoring stations. This is accomplished by viewing monitor-level measurements as error-prone repeated measurements of the unobserved population average exposure. Inference is carried out in a Bayesian framework to fully account for uncertainty in the estimation of model parameters. Finally, by using different exposure indicators, we investigate the sensitivity of the association between coarse PM and daily hospital admissions based on a recent national multisite time series analysis. Among Medicare enrollees from 59 US counties between the period 1999 and 2005, we find a consistent positive association between coarse PM and same-day admission for cardiovascular diseases.     

Air pollution and the lung: epidemiological approach

Epidemiological evidence has concurred with clinical and experimental evidence to correlate current levels of ambient air pollution, both indoors and outdoors, with respiratory effects. In this respect, the use of specific epidemiological methods has been crucial. Common outdoor pollutants are particulate matter, nitrogen dioxide, carbon monoxide, volatile organic compounds and ozone. Short-term effects of outdoor air pollution include changes in lung function, respiratory symptoms and mortality due to respiratory causes. Increase in the use of health care resources has also been associated with short-term effects of air pollution. Long-term effects of cumulated exposure to urban air pollution include lung growth impairment, chronic obstructive pulmonary disease (COPD), lung cancer, and probably the development of asthma and allergies. Lung cancer and COPD have been related to a shorter life expectancy. Common indoor pollutants are environmental tobacco smoke, particulate matter, nitrogen dioxide, carbon monoxide, volatile organic compounds and biological allergens. Concentrations of these pollutants can be many times higher indoors than outdoors. Indoor air pollution may increase the risk of irritation phenomena, allergic sensitisation, acute and chronic respiratory disorders and lung function impairment. Recent conservative estimates have shown that 1.5-2 million deaths per year worldwide could be attributed to indoor air pollution. Further epidemiological research is necessary to better evaluate the respiratory health effects of air pollution and to implement protective programmes for public health.     

Oxidative stress-induced DNA damage by particulate air pollution

Exposure to ambient air particulate matter (PM) is associated with pulmonary and cardiovascular diseases and cancer. The mechanisms of PM-induced health effects are believed to involve inflammation and oxidative stress. The oxidative stress mediated by PM may arise from direct generation of reactive oxygen species from the surface of particles, soluble compounds such as transition metals or organic compounds, altered function of mitochondria or NADPH-oxidase, and activation of inflammatory cells capable of generating ROS and reactive nitrogen species. Resulting oxidative DNA damage may be implicated in cancer risk and may serve as marker for oxidative stress relevant for other ailments caused by particulate air pollution. There is overwhelming evidence from animal experimental models, cell culture experiments, and cell free systems that exposure to diesel exhaust and diesel exhaust particles causes oxidative DNA damage. Similarly, various preparations of ambient air PM induce oxidative DNA damage in in vitro systems, whereas in vivo studies are scarce. Studies with various model/surrogate particle preparations, such as carbon black, suggest that the surface area is the most important determinant of effect for ultrafine particles (diameter less than 100 nm), whereas chemical composition may be more important for larger particles. The knowledge concerning mechanisms of action of PM has prompted the use of markers of oxidative stress and DNA damage for human biomonitoring in relation to ambient air. By means of personal monitoring and biomarkers a few studies have attempted to characterize individual exposure, explore mechanisms and identify significant sources to size fractions of ambient air PM with respect to relevant biological effects. In these studies guanine oxidation in DNA has been correlated with exposure to PM(2.5) and ultrafine particles outdoor and indoor. Oxidative stress-induced DNA damage appears to an important mechanism of action of urban particulate air pollution. Related biomarkers and personal monitoring may be useful tools for risk characterization.     

Short-term effects of ambient sulphur dioxide and particulate matter on mortality in 12 European cities: results from time series data from the APHEA project. Air Pollution and Health: a European Approach.

OBJECTIVES: To carry out a prospective combined quantitative analysis of the associations between all cause mortality and ambient particulate matter and sulphur dioxide. DESIGN: Analysis of time series data on daily number of deaths from all causes and concentrations of sulphur dioxide and particulate matter (measured as black smoke or particles smaller than 10 microns in diameter (PM10)) and potential confounders. SETTING: 12 European cities in the APHEA project (Air Pollution and Health: a European Approach). MAIN OUTCOME MEASURE: Relative risk of death. RESULTS: In western European cities it was found that an increase of 50 micrograms/m3 in sulphur dioxide or black smoke was associated with a 3% (95% confidence interval 2% to 4%) increase in daily mortality and the corresponding figure for PM10 was 2% (1% to 3%). In central eastern European cities the increase in mortality associated with a 50 micrograms/m3 change in sulphur dioxide was 0.8% (-0.1% to 2.4%) and in black smoke 0.6% (0.1% to 1.1%). Cumulative effects of prolonged (two to four days) exposure to air pollutants resulted in estimates comparable with the one day effects. The effects of both pollutants were stronger during the summer and were mutually independent. CONCLUSIONS: The internal consistency of the results in western European cities with wide differences in climate and environmental conditions suggest that these associations may be causal. The long term health impact of these effects is uncertain, but today''s relatively low levels of sulphur dioxide and particles still have detectable short term effects on health and further reductions in air pollution are advisable.     

Linking exposure to environmental pollutants with biological effects

Exposure to ambient air pollution has been associated with cancer. Ambient air contains a complex mixture of toxics, including particulate matter (PM) and benzene. Carcinogenic effects of PM may relate both to the content of PAH and to oxidative DNA damage generated by transition metals, benzene, metabolism and inflammation. By means of personal monitoring and biomarkers of internal dose, biologically effective dose and susceptibility, it should be possible to characterize individual exposure and identify air pollution sources with relevant biological effects. In a series of studies, individual exposure to PM(2.5), nitrogen dioxide (NO(2)) and benzene has been measured in groups of 40-50 subjects. Measured biomarkers included 1-hydroxypyrene, benzene metabolites (phenylmercapturic acid (PMA) and trans-trans-muconic acid (ttMA)), 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodG) in urine, DNA strand breaks, base oxidation, 8-oxodG and PAH bulky adducts in lymphocytes, markers of oxidative stress in plasma and genotypes of glutathione transferases (GSTs) and NADPH:quinone reductase (NQO1). With respect to benzene, the main result indicates that DNA base oxidation is correlated with PMA excretion. With respect to exposure to PM, biomarkers of oxidative damage showed significant positive association with the individual exposure. Thus, 8-oxodG in lymphocyte DNA and markers of oxidative damage to lipids and protein in plasma associated with PM(2.5) exposure. Several types of DNA damage showed seasonal variation. PAH adduct levels, DNA strand breaks and 8-oxodG in lymphocytes increased significantly in the summer period, requiring control of confounders. Similar seasonal effects on strand breaks and expression of the relevant DNA repair genes ERCC1 and OGG1 have been reported.In the present setting, biological effects of air pollutants appear mainly related to oxidative stress via personal exposure and not to urban background levels. Future developments include personal time-resolved monitors for exposure to ultrafine PM and PM(2.5,) use of GPS, as well as genomics and proteomics based biomarkers.     

Bayesian distributed lag models: estimating effects of particulate matter air pollution on daily mortality

Summary .  A distributed lag model (DLagM) is a regression model that includes lagged exposure variables as covariates; its corresponding distributed lag (DL) function describes the relationship between the lag and the coefficient of the lagged exposure variable. DLagMs have recently been used in environmental epidemiology for quantifying the cumulative effects of weather and air pollution on mortality and morbidity. Standard methods for formulating DLagMs include unconstrained, polynomial, and penalized spline DLagMs. These methods may fail to take full advantage of prior information about the shape of the DL function for environmental exposures, or for any other exposure with effects that are believed to smoothly approach zero as lag increases, and are therefore at risk of producing suboptimal estimates. In this article, we propose a Bayesian DLagM (BDLagM) that incorporates prior knowledge about the shape of the DL function and also allows the degree of smoothness of the DL function to be estimated from the data. We apply our BDLagM to its motivating data from the National Morbidity, Mortality, and Air Pollution Study to estimate the short-term health effects of particulate matter air pollution on mortality from 1987 to 2000 for Chicago, Illinois. In a simulation study, we compare our Bayesian approach with alternative methods that use unconstrained, polynomial, and penalized spline DLagMs. We also illustrate the connection between BDLagMs and penalized spline DLagMs. Software for fitting BDLagM models and the data used in this article are available online.     

Estimating Mortality Derived from Indoor Exposure to Particles of Outdoor Origin

Following an extensive review of the literature, we further analyze the published data to examine the health effects of indoor exposure to particulate matter (PM) of outdoor origin. We obtained data on all-cause, cardiovascular, and respiratory mortality per 10 μg/m³ increase in outdoor PM₁₀ or PM_2.5; the infiltration factors for buildings; and estimated time spent outdoors by individuals in the United States, Europe, China, and globally. These data were combined log-linear exposure–response model to estimate the all-cause, cardiovascular, and respiratory mortality of exposure to indoor PM pollution of outdoor origin. Indoor PM pollution of outdoor origin is a cause of considerable mortality, accounting for 81% to 89% of the total increase in mortality associated with exposure to outdoor PM pollution for the studied regions. The findings suggest that enhancing the capacity of buildings to protect occupants against exposure to outdoor PM pollution has significant potential to improve public health outcomes.     

Stochastic Dynamic Model for Estimation of Rate Constants and Their Variances from Noisy and Heterogeneous PET Measurements

Tissue heterogeneity, radioactive decay and measurement noise are the main error sources in compartmental modeling used to estimate the physiologic rate constants of various radiopharmaceuticals from a dynamic PET study. We introduce a new approach to this problem by modeling the tissue heterogeneity with random rate constants in compartment models. In addition, the Poisson nature of the radioactive decay is included as a Poisson random variable in the measurement equations. The estimation problem will be carried out using the maximum likelihood estimation. With this approach, we do not only get accurate mean estimates for the rate constants, but also estimates for tissue heterogeneity within the region of interest and other possibly unknown model parameters, e.g. instrument noise variance, as well. We also avoid the problem of the optimal weighting of the data related to the conventionally used weighted least-squares method. The new approach was tested with simulated time–activity curves from the conventional three compartment – three rate constants model with normally distributed rate constants and with a noise mixture of Poisson and normally distributed random variables. Our simulation results showed that this new model gave accurate estimates for the mean of the rate constants, the measurement noise parameter and also for the tissue heterogeneity, i.e. for the variance of the rate constants within the region of interest.     

Zero-inflated Poisson models with measurement error in the response

Zero-inflated count data arise frequently from genomics studies. Analysis of such data is often based on a mixture model which facilitates excess zeros in combination with a Poisson distribution, and various inference methods have been proposed under such a model. Those analysis procedures, however, are challenged by the presence of measurement error in count responses. In this article, we propose a new measurement error model to describe error-contaminated count data. We show that ignoring the measurement error effects in the analysis may generally lead to invalid inference results, and meanwhile, we identify situations where ignoring measurement error can still yield consistent estimators. Furthermore, we propose a Bayesian method to address the effects of measurement error under the zero-inflated Poisson model and discuss the identifiability issues. We develop a data-augmentation algorithm that is easy to implement. Simulation studies are conducted to evaluate the performance of the proposed method. We apply our method to analyze the data arising from a prostate adenocarcinoma genomic study.     

Risk of adult street vendor exposure to traffic-related air pollution in Bangkok,Thailand

Traffic-related air pollution (TRAP), including particulate matter (PM) in respirable coarse and fine size fractions (PM10 and PM2.5), is known to have exposure effects on human health and environment. Real-time PM10 and PM2.5 concentrations were collected from the study locations in Bangkok, Thailand, using TSI AM510 particle counters. Temperature and % relative humidity (%RH) were also collected. Data were compared to data from the closest station of the Pollution Control Department (PCD), Thailand. Real-time mean concentration varied from 86 to 1107 µg/m³ (PM10) and varied from 25 to 664 µg/m³ (PM2.5). In addition, real-time mean PM10 (223.1 µg/m³) was nearly four times greater than that measured by the PCD station, 60 µg/m³. Temperature and %RH from real-time air monitoring and PCD station were comparable. In each study location (five locations, two in morning and afternoon/evening), there were significant positive correlations between PM10 and PM2.5 concentrations and significant negative correlations between temperature and RH%. Results suggested that outdoor TRAP via measured real-time PM concentrations were more realistic exposure concentration estimates among street vendors as related to respiratory and other symptoms than data obtained from PCD station. Nevertheless, PM10 as measured by the PCD station might be a reasonable surrogate for estimated outdoor PM2.5 exposure.     

Probability and Persistence of High Pollutant Concentrations in Soils: A Modeling Study and Implications for Exposure and Risk Assessment

Risk assessments for environmental pollutants have relied upon steady-state models that do not represent the variability of pollutant transport and fate processes, thus predictions are unlikely to reflect the true variability in pollutant concentrations. Such models cannot be used to estimate the probability, magnitude and duration of short- to intermediate-term and high-concentration events that might lead to adverse acute impacts. In this study, a numerical model is used to simulate pollutant accumulation in surface soils at six U.S. locations that result from atmospheric deposition and leaching. Historical (50 year) precipitation data drive the model. Model predictions are filtered and analyzed to identify high pollution events (exceeding specific concentration thresholds) and their occurrence probability and duration. Predicted concentrations at each site varied by a factor of 100 over time and by a factor of five among the six locations. The frequency and duration of high pollution events also differed by locations and concentration threshold. In general, larger thresholds lead to less frequent events and shorter durations. The proposed method allows estimates of the probability of occurrence and duration of high pollution events, providing information that complements the steady-state methods.     

Control for confounding in the presence of measurement error in hierarchical models

Hierarchical modeling is becoming increasingly popular in epidemiology, particularly in air pollution studies. When potential confounding exists, a multilevel model yields better power to assess the independent effects of each predictor by gathering evidence across many sub-studies. If the predictors are measured with unknown error, bias can be expected in the individual substudies, and in the combined estimates of the second-stage model. We consider two alternative methods for estimating the independent effects of two predictors in a hierarchical model. We show both analytically and via simulation that one of these gives essentially unbiased estimates even in the presence of measurement error, at the price of a moderate reduction in power. The second avoids the potential for upward bias, at the price of a smaller reduction in power. Since measurement error is endemic in epidemiology, these approaches hold considerable potential. We illustrate the two methods by applying them to two air pollution studies. In the first, we re-analyze published data to show that the estimated effect of fine particles on daily deaths, independent of coarse particles, was downwardly biased by measurement error in the original analysis. The estimated effect of coarse particles becomes more protective using the new estimates. In the second example, we use published data on the association between airborne particles and daily deaths in 10 US cities to estimate the effect of gaseous air pollutants on daily deaths. The resulting effect size estimates were very small and the confidence intervals included zero.