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.     

A measurement error model for time-series studies of air pollution and mortality

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.     

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.     

Correcting for measurement error in individual ancestry estimates in structured association tests

We present theoretical explanations and show through simulation that the individual admixture proportion estimates obtained by using ancestry informative markers should be seen as an error-contaminated measurement of the underlying individual ancestry proportion. These estimates can be used in structured association tests as a control variable to limit type I error inflation or reduce loss of power due to population stratification observed in studies of admixed populations. However, the inclusion of such error-containing variables as covariates in regression models can bias parameter estimates and reduce ability to control for the confounding effect of admixture in genetic association tests. Measurement error correction methods offer a way to overcome this problem but require an a priori estimate of the measurement error variance. We show how an upper bound of this variance can be obtained, present four measurement error correction methods that are applicable to this problem, and conduct a simulation study to compare their utility in the case where the admixed population results from the intermating between two ancestral populations. Our results show that the quadratic measurement error correction (QMEC) method performs better than the other methods and maintains the type I error to its nominal level.     

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.     

On the effect of misclassification on bias of perfectly measured covariates in regression

This note clarifies under what conditions a naive analysis using a misclassified predictor will induce bias for the regression coefficients of other perfectly measured predictors in the model. An apparent discrepancy between some previous results and a result for measurement error of a continuous variable in linear regression is resolved. We show that similar to the linear setting, misclassification (even when not related to the other predictors) induces bias in the coefficients of the perfectly measured predictors, unless the misclassified variable and the perfectly measured predictors are independent. Conditional and asymptotic biases are discussed in the case of linear regression, and explored numerically for an example relating birth weight to the weight and smoking status of the mother.     

Biasing Factors for Simple Soil Ingestion Estimates in Mass Balance Studies of Soil Ingestion

Soil ingestion estimates from mass balance soil ingestion studies can be used in Monte Carlo Risk assessment. We develop and describe a simulation model based on four mass balance soil ingestion studies that enables food ingestion, soil ingestion, and transit time to be mimicked. We use the simulation to evaluate potential biases that exist in current estimates of the distribution of daily soil ingestion in children (constructed from subject specific average daily estimates). The simulation identifies the importance of the study duration on the bias in the upper percentile soil ingestion estimates, indicating that the 95% soil ingestion estimate may be positively biased by over 100%. Misspecification of play areas for soil sampling is shown to have no biasing effect, and absorption of trace elements in food of up to 30% is shown to bias the soil ingestion distribution by less than 20 mg/d. The results, based on Al and Si trace element estimates, define the limits of previously published soil ingestion estimates, and provide insight for future study design and estimation methods.     

Insights on bias and information in group-level studies

Ecological and aggregate data studies are examples of group-level studies. Even though the link between the predictors and outcomes is not preserved in these studies, inference about individual-level exposure effects is often a goal. The disconnection between the level of inference and the level of analysis expands the array of potential biases that can invalidate the inference from group-level studies. While several sources of bias, specifically due to measurement error and confounding, may be more complex in group-level studies, two sources of bias, cross-level and model specification bias, are a direct consequence of the disconnection. With the goal of aligning inference from individual versus group-level studies, I discuss the interplay between exposure and study design. I specify the additional assumptions necessary for valid inference, specifically that the between- and within-group exposure effects are equal. Then cross-level inference is possible. However, all the information in the group-level analysis comes from between-group comparisons. Models where the group-level analysis provides even a small percentage of information about the within-group exposure effect are most susceptible to model specification bias. Model specification bias can be even more serious when the group-level model isn't derived from an individual-level model.     

Equilibrating errors: reliable estimation of information transmission rates in biological systems with spectral analysis-based methods

Shannon’s seminal approach to estimating information capacity is widely used to quantify information processing by biological systems. However, the Shannon information theory, which is based on power spectrum estimation, necessarily contains two sources of error: time delay bias error and random error. These errors are particularly important for systems with relatively large time delay values and for responses of limited duration, as is often the case in experimental work. The window function type and size chosen, as well as the values of inherent delays cause changes in both the delay bias and random errors, with possibly strong effect on the estimates of system properties. Here, we investigated the properties of these errors using white-noise simulations and analysis of experimental photoreceptor responses to naturalistic and white-noise light contrasts. Photoreceptors were used from several insect species, each characterized by different visual performance, behavior, and ecology. We show that the effect of random error on the spectral estimates of photoreceptor performance (gain, coherence, signal-to-noise ratio, Shannon information rate) is opposite to that of the time delay bias error: the former overestimates information rate, while the latter underestimates it. We propose a new algorithm for reducing the impact of time delay bias error and random error, based on discovering, and then using that size of window, at which the absolute values of these errors are equal and opposite, thus cancelling each other, allowing minimally biased measurement of neural coding.     

Thyroid cancer following scalp irradiation: a reanalysis accounting for uncertainty in dosimetry

In the 1940s and 1950s, over 20,000 children in Israel were treated for tinea capitis (scalp ringworm) by irradiation to induce epilation. Follow-up studies showed that the radiation exposure was associated with the development of malignant thyroid neoplasms. Despite this clear evidence of an effect, the magnitude of the dose-response relationship is much less clear because of probable errors in individual estimates of dose to the thyroid gland. Such errors have the potential to bias dose-response estimation, a potential that was not widely appreciated at the time of the original analyses. We revisit this issue, describing in detail how errors in dosimetry might occur, and we develop a new dose-response model that takes the uncertainties of the dosimetry into account. Our model for the uncertainty in dosimetry is a complex and new variant of the classical multiplicative Berkson error model, having components of classical multiplicative measurement error as well as missing data. Analysis of the tinea capitis data suggests that measurement error in the dosimetry has only a negligible effect on dose-response estimation and inference as well as on the modifying effect of age at exposure.     

Use of deterministic sampling for exploring likelihoods in linkage analysis for quantitative traits

Deterministic sampling was used to numerically evaluate the expected log-likelihood surfaces of QTL-marker linkage models in large pedigrees with simple structures. By calculating the expected values of likelihoods, questions of power of experimental designs, bias in parameter estimates, approximate lower-bound standard errors of estimates and correlations among estimates, and suitability of statistical models were addressed. Examples illustrated that bracket markers around the QTL approximately halved the standard error of the recombination fraction between the QTL and the marker, although they did not affect the standard error of the QTL's effect, that overestimation of the distance between the markers caused overestimation of the distance between the QTL and marker, that more parameters in the model did not affect the accuracy of parameter estimates, that there was a moderate positive correlation between the estimates of the QTL effect and its recombination distance from the marker, and that selective genotyping did not introduce bias into the estimates of the parameters. The method is suggested as a useful tool for exploring the power and accuracy of QTL linkage experiments, and the value of alternative statistical models, whenever the likelihood of the model can be written explictly.     

Approximate maximum likelihood estimation for logistic regression with covariate measurement error

In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)‐InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC‐InterAct Study under a sensitivity analysis framework.     

Estimation in the Cox survival regression model with covariate measurement error and a changepoint

The Cox regression model is a popular model for analyzing the relationship between a covariate vector and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulation-extrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM₁₀ and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 and MPPLE.     

Statistical issues in a metaregression analysis of randomized trials: impact on the dietary sodium intake and blood pressure relationship

In a meta-analysis of randomized trials of the effects of dietary sodium interventions on blood pressure, we found substantial heterogeneity among the studies. We were interested in evaluating whether measurement error, known to be a problem for dietary sodium measures, publication bias, or confounding factors could be responsible for the heterogeneity. A measurement error correction was developed that corrects both the slope and the intercept and takes into account the sample size of each study and the number of measurements taken on an individual. The measurement error correction had a minimal effect on the estimates, although it performed well in simulated data. A smoothed scatter plot was used to assess publication bias. Metaregressions provide a convenient way to jointly assess the effects of several factors, but care must be taken to fit an appropriate model.     

Process and measurement errors of population size: their mutual effects on precision and bias of estimates for demographic parameters

Knowing the parameters of population growth and regulation is fundamental for answering many ecological questions and the successful implementation of conservation strategies. Moreover, detecting a population trend is often a legal obligation. Yet, inherent process and measurement errors aggravate the ability to estimate these parameters from population time-series. We use numerical simulations to explore how the lengths of the time-series, process and measurement error influence estimates of demographic parameters. We first generate time-series of population sizes with given demographic parameters for density-dependent stochastic population growth, but assume that these population sizes are estimated with measurement errors. We then fit parameters for population growth, habitat capacity, total error and long-term trends to the ‘measured’ time-series data using non-linear regression. The length of the time-series and measurement error introduce a substantial bias in the estimates for population growth rate and to a lesser degree on estimates for habitat capacity, while process error has little effect on parameter bias. The total error term of the statistical model is dominated by process error as long as the latter is larger than the measurement error. A decline in population size is difficult to document as soon as either error becomes moderate, trends are not very pronounced, and time-series are short (<10–15 seasons). Detecting an annual decline of 1% within 6-year reporting periods, as required for the European Union for the species of Community Interest, appears unachievable.     

Air pollution and daily mortality in London: 1987-92.

OBJECTIVE--To investigate whether outdoor air pollution levels in London influence daily mortality. DESIGN--Poisson regression analysis of daily counts of deaths, with adjustment for effects of secular trend, seasonal and other cyclical factors, day of the week, holidays, influenza epidemic, temperature, humidity, and autocorrelation, from April 1987 to March 1992. Pollution variables were particles (black smoke), sulphur dioxide, ozone, and nitrogen dioxide, lagged 0-3 days. SETTING--Greater London. OUTCOME MEASURES--Relative risk of death from all causes (excluding accidents), respiratory disease, and cardiovascular disease. RESULTS--Ozone levels (same day) were associated with a significant increase in all cause, cardiovascular, and respiratory mortality; the effects were greater in the warm seasons (April to September) and were independent of the effects of other pollutants. In the warm season an increase of the eight hour ozone concentration from the 10th to the 90th centile of the seasonal change (7-36 ppb) was associated with an increase of 3.5% (95% confidence interval 1.7 to 5.3), 3.6% (1.04 to 6.1), and 5.4% (0.4 to 10.7) in all cause, cardiovascular, and respiratory mortality respectively. Black smoke concentrations on the previous day were significantly associated with all cause mortality, and this effect was also greater in the warm season and was independent of the effects of other pollutants. For black smoke an increase from the 10th to 90th centile in the warm season (7-19 microg/m3) was associated with an increase of 2.5% (0.9 to 4.1) in all cause mortality. Significant but smaller and less consistent effects were also observed for nitrogen dioxide and sulphur dioxide. CONCLUSION--Daily variations in air pollution within the range currently occurring in London may have an adverse effect on daily mortality.     

Propagating Uncertainty in Plot-based Estimates of Forest Carbon Stock and Carbon Stock Change

Ecosystem science increasingly relies on highly derived metrics to synthesize across large datasets. However, full uncertainty associated with these metrics is seldom quantified. Our objective was to evaluate measurement error and model uncertainty in plot-based estimates of carbon stock and carbon change. We quantified the measurement error associated with live stems, deadwood and plot-level variables in temperate rainforest in New Zealand. We also quantified model uncertainty for height–diameter allometry, stem volume equations and wood-density estimates. We used Monte Carlo simulation to assess the net effects on carbon stock and carbon change estimated using data from 227 plots from throughout New Zealand. Plot-to-plot variation was the greatest source of uncertainty, amounting to 9.1% of mean aboveground carbon stock estimates (201.11 MgC ha^?1). Propagation of the measurement error and model uncertainty resulted in a 1% increase in uncertainty (0.1% of mean stock estimate). Carbon change estimates (mean ?0.86 MgC ha^?1 y^?1) were more uncertain, with sampling error equating to 56% of the mean, and when measurement error and model uncertainty were included this uncertainty increased by 35% (22.1% of the mean change estimate). For carbon change, the largest sources of measurement error were missed/double counted stems and fallen coarse woody debris. Overall, our findings show that national-scale plot-based estimates of carbon stock and carbon change in New Zealand are robust to measurement error and model uncertainty. We recommend that calculations of carbon stock and carbon change incorporate both these sources of uncertainty so that management implications and policy decisions can be assessed with the appropriate level of confidence.     

Classification based upon gene expression data: bias and precision of error rates

MOTIVATION: Gene expression data offer a large number of potentially useful predictors for the classification of tissue samples into classes, such as diseased and non-diseased. The predictive error rate of classifiers can be estimated using methods such as cross-validation. We have investigated issues of interpretation and potential bias in the reporting of error rate estimates. The issues considered here are optimization and selection biases, sampling effects, measures of misclassification rate, baseline error rates, two-level external cross-validation and a novel proposal for detection of bias using the permutation mean. RESULTS: Reporting an optimal estimated error rate incurs an optimization bias. Downward bias of 3-5% was found in an existing study of classification based on gene expression data and may be endemic in similar studies. Using a simulated non-informative dataset and two example datasets from existing studies, we show how bias can be detected through the use of label permutations and avoided using two-level external cross-validation. Some studies avoid optimization bias by using single-level cross-validation and a test set, but error rates can be more accurately estimated via two-level cross-validation. In addition to estimating the simple overall error rate, we recommend reporting class error rates plus where possible the conditional risk incorporating prior class probabilities and a misclassification cost matrix. We also describe baseline error rates derived from three trivial classifiers which ignore the predictors. AVAILABILITY: R code which implements two-level external cross-validation with the PAMR package, experiment code, dataset details and additional figures are freely available for non-commercial use from http://www.maths.qut.edu.au/profiles/wood/permr.jsp     

Deaths and Medical Visits Attributable to Environmental Pollution in the United Arab Emirates

Background

This study estimates the potential health gains achievable in the United Arab Emirates (UAE) with improved controls on environmental pollution. The UAE is an emerging economy in which population health risks have shifted rapidly from infectious diseases to chronic conditions observed in developed nations. The UAE government commissioned this work as part of an environmental health strategic planning project intended to address this shift in the nature of the country’s disease burden.

Methods and Findings

We assessed the burden of disease attributable to six environmental exposure routes outdoor air, indoor air, drinking water, coastal water, occupational environments, and climate change. For every exposure route, we integrated UAE environmental monitoring and public health data in a spatially resolved Monte Carlo simulation model to estimate the annual disease burden attributable to selected pollutants. The assessment included the entire UAE population (4.5 million for the year of analysis). The study found that outdoor air pollution was the leading contributor to mortality, with 651 attributable deaths (95% confidence interval [CI] 143–1,440), or 7.3% of all deaths. Indoor air pollution and occupational exposures were the second and third leading contributors to mortality, with 153 (95% CI 85–216) and 46 attributable deaths (95% CI 26–72), respectively. The leading contributor to health-care facility visits was drinking water pollution, to which 46,600 (95% CI 15,300–61,400) health-care facility visits were attributed (about 15% of the visits for all the diseases considered in this study). Major study limitations included (1) a lack of information needed to translate health-care facility visits to quality-adjusted-life-year estimates and (2) insufficient spatial coverage of environmental data.

Conclusions

Based on international comparisons, the UAE’s environmental disease burden is low for all factors except outdoor air pollution. From a public health perspective, reducing pollutant emissions to outdoor air should be a high priority for the UAE’s environmental agencies.     

Sharing is caring? Measurement error and the issues arising from combining 3D morphometric datasets

Geometric morphometrics is routinely used in ecology and evolution and morphometric datasets are increasingly shared among researchers, allowing for more comprehensive studies and higher statistical power (as a consequence of increased sample size). However, sharing of morphometric data opens up the question of how much nonbiologically relevant variation (i.e., measurement error) is introduced in the resulting datasets and how this variation affects analyses. We perform a set of analyses based on an empirical 3D geometric morphometric dataset. In particular, we quantify the amount of error associated with combining data from multiple devices and digitized by multiple operators and test for the presence of bias. We also extend these analyses to a dataset obtained with a recently developed automated method, which does not require human‐digitized landmarks. Further, we analyze how measurement error affects estimates of phylogenetic signal and how its effect compares with the effect of phylogenetic uncertainty. We show that measurement error can be substantial when combining surface models produced by different devices and even more among landmarks digitized by different operators. We also document the presence of small, but significant, amounts of nonrandom error (i.e., bias). Measurement error is heavily reduced by excluding landmarks that are difficult to digitize. The automated method we tested had low levels of error, if used in combination with a procedure for dimensionality reduction. Estimates of phylogenetic signal can be more affected by measurement error than by phylogenetic uncertainty. Our results generally highlight the importance of landmark choice and the usefulness of estimating measurement error. Further, measurement error may limit comparisons of estimates of phylogenetic signal across studies if these have been performed using different devices or by different operators. Finally, we also show how widely held assumptions do not always hold true, particularly that measurement error affects inference more at a shallower phylogenetic scale and that automated methods perform worse than human digitization.