Variations in exposure to inhalable wood dust in the Danish furniture industry. Within- and between-worker and factory components estimated from passive dust sampling

Variability of exposure to wood dust at large factories in the Danish furniture industry was studied. Three repeated exposure measurements of 292 workers at 38 factories were included in the study. The measurements were carried out by use of personal passive dust monitors. The components of variance were estimated by means of a random effects ANOVA model. The ratio of within- to between-worker variance was 1.07. Based on this result, and three repeated exposure measurements, the observed relation between health outcome and exposure will be attenuated to 74% of the true value. Grouping by factory showed very poor exposure contrast, as the contrast in exposure level among factories was as low as 0.15.     

Sources of variance in exposure to postural load on the back in occupational groups.

The variability of exposure to postural load on the back was studied in five occupational groups. A random sample of workers in each group was observed for two periods of 30 min during a shift, their posture being classified every 20 s. The estimated percentage of time spent in trunk flexion and rotation formed the principal measures of exposure. The partitioning of the total variability of exposure showed that occupational group status was the principal source of variance. The between-group variance accounted for 47 and 72% of the total variability of exposure to trunk flexion and rotation, respectively. The corresponding percentages were 29 and 16% for the within-worker variance of trunk flexion and rotation and 24 and 12% for the between-worker variance. This type of analysis of the sources of exposure variability may help to establish appropriate measurement strategies for exposure to postural load on the back in epidemiologic studies on low-back pain.     

Attenuation in risk estimates in logistic and Cox proportional-hazards models due to group-based exposure assessment strategy

In occupational epidemiology, it is often possible to obtain repeated measurements of exposure from a sample of subjects (workers) who belong to exposure groups associated with different levels of exposure. Average exposures from a sample of workers can be assigned to all members of that group including those who are not sampled, leading to a group-based exposure assessment. We discuss how this group-based exposure assessment leads to approximate Berkson error model when the number of subjects with exposure measurements in each group is large, and how the error variance approximates the between-worker variability. Under the normality assumption of exposures and with moderately large number of workers in each group, there is attenuation in the estimate of the association parameter, the magnitude of which depends on the sizes of the between-worker variability and the true association parameter. Approximate equations for attenuation have been derived in logistic and Cox proportional-hazards models. These equations show that the attenuation in Cox proportional-hazards models is generally more severe than in logistic regression. Furthermore, when the between-worker variability is large, our simulation study found that the approximation by equation is poor for the Cox proportional-hazards model. If the number of subjects is small, the approximation does not hold for either model.     

Improved non-negative estimation of variance components for exposure assessment.

Hygiene surveys of pollutants exposure data can be analyzed by analysis of variance (ANOVA) model with a random worker effect. Typically, workers are classified into homogeneous exposure groups, so it is very common to obtain a zero or negative ANOVA estimate of the between-worker variance (sigma2B). Negative estimates are not sensible and also pose problems for estimating the probability (theta) that in a job group, a randomly selected worker's mean exposure exceeds the occupational exposure standard. Therefore, it was suggested by Rappaport et al. to replace a non-positive estimate with an approximate one-sided 60% upper confidence bound. This article develops an alternative estimator, based on the upper tolerance interval suggested by Wang and Iyer. We compared the performance of the two methods using real data and simulations with respect to estimating both the between-worker variance and the probability of overexposure in balanced designs. We found that the method of Rappaport et al. has three main disadvantages: (i) the estimated sigma2B remains negative for some data sets; (ii) the estimator performs poorly in estimating sigma2B and theta with two repeated measures per worker and when true sigma2B is quite small, which are quite common situations when studying exposure; (iii) the estimator can be extremely sensitive to small changes in the data. Our alternative estimator offers a solution to these problems.     

Exposure to benzene in fuel distribution installations: monitoring and prevention

The authors used a mixed-effects model on a cohort of 258 randomly chosen workers in 7 fuel-distribution facilities to examine the association between airborne benzene exposure and task and timing factors. During an 8-y period, 692 repeated personal measurements were performed. Filler task, warm month, Tuesday, credit day, and time period (1992-1996) were associated significantly with higher exposures to benzene. The authors controlled for the time period, and task type strongly affected the between-worker variance; therefore, two exposure groups (i.e., fillers and nonfillers) were adequate for purposes of exposure grouping strategy. Timing factors (after controlling for task and period effects) strongly affected the high within-worker variance (> 2 than between-worker variance). Long-term exposure would be better represented if the sample was stratified by warm/nonwarm months and if measurement days were selected randomly.     

Exposure to Benzene in Fuel Distribution Installations: Monitoring and Prevention

The authors used a mixed-effects model on a cohort of 258 randomly chosen workers in 7 fuel-distribution facilities to examine the association between airborne benzene exposure and task and timing factors. During an 8-y period, 692 repeated personal measurements were performed. Filler task, warm month, Tuesday, credit day, and time period (1992-1996) were associated significantly with higher exposures to benzene. The authors controlled for the time period, and task type strongly affected the between-worker variance; therefore, two exposure groups (i.e., fillers and nonfillers) were adequate for purposes of exposure grouping strategy. Timing factors (after controlling for task and period effects) strongly affected the high within-worker variance (> 2 than between-worker variance). Long-term exposure would be better represented if the sample was stratified by warm/non-warm months and if measurement days were selected randomly.     

Application of mixed-effects models for exposure assessment

The benefits of using linear mixed-effects models for occupational exposure assessment were studied by re-analysing three data sets from two published surveys with repeated exposure measurements. The relative contributions of particular characteristics affecting exposure levels were assessed as in a multiple regression model, while controlling for the correlation between repeated measurements. While one-way ANOVA allows one only to estimate unconditioned variance components, a mixed model enables estimation of between- and within-worker variance components of exposure levels while accounting for the fixed effects of work characteristics. Consequently, we can identify the work characteristics affecting each variance component. Mixed models were applied to the data sets with repeated measurements and auxil iary information on work characteristics. The between-worker variance components were reduced by 35, 66 and 80%, respectively, in the three data sets when work characteristics were taken into account. The within-worker (day-to-day) variability was reduced only in the pig farmer data set, by 25%, when accounting for work activities. In addition, coefficients of work characteristics from the mixed model were compared with coefficients resulting from originally published multiple linear regression models. In the rubber manufacturing data, the coefficients of the mixed model showed similar relative importance, but were generally smaller than the coefficients from regression models. However, in the pig farm data, only the coefficients of work activities were somewhat reduced. The mixed model is a helpful tool for estimating factors affecting exposure and suitable variance components. Identifying the factors in the working environment that affect the between-worker variability facilitates a posteriori grouping of workers into more uniformly exposed groups. Identifying the factors that affect the within-worker variance is helpful for hazard control and in designing efficient sampling schemes with reference to time schedule.     

Combining expert ratings and exposure measurements: a random effect paradigm

The aim of this paper is to present a paradigm for combining ordinal expert ratings with exposure measurements while accounting for a between-worker effect when estimating exposure group (EG)-specific means for epidemiological purposes. Expert judgement is used to classify the EGs into a limited number of exposure levels independently of the exposure measurements. The mean exposure of each EG is considered to be a random deviate from a central exposure rating-specific value. Combining this approach with the standard between-worker random effect model, we obtain a nested two-way model. Using Gibbs sampling, we can fit such models incorporating prior information on components of variance and modelling options to the rating-specific means. An approximate formula is presented estimating the mean exposure of each EG as a function of the geometric mean of the measurements in this EG, between and within EG standard deviations and the overall geometric mean, thus borrowing information from other EGs. We apply this paradigm to an actual data set of dust exposure measurements in a steel producing factory. Some EG-specific means are quite different from the estimates including the ratings. Rating-specific means could be estimated under different hypotheses. It is argued that when setting up an expert rating of exposures it is best done independently of existing exposure measurements. The present model is then a convenient framework in which to combine the two sources of information.     

Exposure assessment of monoterpenes and styrene: a comparison of air sampling and biomonitoring

Background: Within- and between-worker variance components have seldom been reported for both environmental and biological data collected from the same persons.

Aims: To estimate these variance components and their ratio for air contaminants and urinary metabolites in two different work environments and to predict the attenuation of exposure-response relationships based on these measures.

Methods: Parallel measurements of air and urine were performed among workers exposed to monoterpenes in sawmills (urinary metabolite: verbenol) and styrene in reinforced plastics factories (urinary metabolite: mandelic acid).

Results: Among the sawmill workers, variance components of the air and urinary verbenol results were similar; for the reinforced plastics workers the estimated between-worker variance component was greater for styrene in air than mandelic acid in urine. This suggests that attenuation bias would be about equal if air or biological monitoring were employed for monoterpene exposures, but would be greater if urinary mandelic acid were used instead of airborne styrene in an investigation of styrene exposure.

Conclusions: Personal air samplers provide data with similar or superior quality to urinary metabolites as measures of exposure to these monoterpenes in sawmills and styrene in reinforced plastics factories.

     

Heterogeneity in sources of exposure variability among groups of workers exposed to inorganic mercury.

Many exposure assessment strategies rely on the occupational group as the unit of analysis in which workers are classified on the basis of job title, location, or on other characteristics related to the workplace or the job. Although statistical methods that combine exposure data collected on workers from different occupational groups are more efficient, the underlying assumption that the degree of variation over time and among workers is the same for all groups has yet to be fully investigated. Given the utility of different modeling approaches when assessing exposures, we investigated assumptions of homogeneity of variance within and between workers using both random- and mixed-effects models. In our study of four groups of workers exposed to inorganic mercury (Hg) at a chloralkali plant, there was no evidence of significant heterogeneity in the levels of variation over time or between workers for air Hg levels. For the biological monitoring data, however, our findings indicate that groups did not share common levels of variability and that it was not appropriate to pool the data and obtain single estimates of the within- and between-worker variance components. Classification of job group as a random or fixed effect had no effect on the results and yielded the same conclusions when the models were compared. To illustrate effects related to the proper specification of a model, the likelihood of exceeding certain levels (which is a function of the parameters of the underlying distribution of the natural log-transformed exposures) was evaluated using the results obtained from the different models. Although the probability that workers' mean exposures exceeded occupational exposure limits for air, urine and blood Hg was generally low (<10%) for all groups except maintenance workers, the estimated values sometimes varied depending upon the particular model that was applied. Given the growing use of random- and mixed-effects models that combine data across occupational groups, additional studies are warranted to evaluate whether it is reasonable to assume common variances and covariances among measurements collected on workers from different groups.     

Variability of exposure and estimation of cumulative exposure in a manually operated coal mine

This study aims at estimating variability in exposure to respirable dust and assessing whether the a priori grouping by job team is appropriate for an exposure-response study on respiratory effects among workers in a manually operated coal mine in Tanzania. Furthermore, estimated exposure levels were used to calculate cumulative exposure. Full-shift personal respirable dust samples (n = 204) were collected from 141 randomly chosen workers at underground and surface work sites. The geometric mean exposure for respirable dust varied from 0.07 mg m(-3) for office workers to 1.96 mg m(-3) for the development team. The analogous range of respirable quartz exposure was 0.006-0.073 mg m(-3). Variance components were estimated using random effect models. For most job teams the within-worker variance component was considerably higher than the between-worker variance component. For respirable dust the estimated attenuation of the linear exposure-response relationship was low (5.9%) when grouping by job team. Grouping by job team was considered appropriate for studying the association between current dust exposure and respiratory effects. Based on the estimated worker-specific mean exposure in the job teams, the arithmetic mean cumulative exposure for the 299 workers who participated in the epidemiological part of the study was 38.1 mg* yr m(-3) for respirable dust and 2.0 mg* yr m(-3) for quartz.     

Within-day variability of magnetic fields among electric utility workers: consequences for measurement strategies

Occupational exposure to 50-Hz magnetic fields was surveyed among electric utility workers to investigate (1) components of exposure variability, (2) patterns of autocorrelation between short-term measurements, and (3) imprecision and misclassification due to short-term measurements. Spot measurements every 10 seconds during 81 working days were analyzed for 42 electric utility workers from 10 occupational subgroups and during 8 working days for 4 office workers from the same company. For the 8-hour time-weighted average (TWA) magnetic fields, the variability was partitioned into its components: within workers, between workers, and between groups. For spot measurements of magnetic fields, the within-day variance component also was examined. Autocorrelation functions were determined and numbers of short-term measurements necessary for reliable estimates of 8-hour TWA magnetic fields were assessed. Spot measurements of magnetic fields, as well as 8-hour TWA magnetic fields, were approximately log normally distributed among workers. The mean exposure to magnetic fields was 0.47 microT (n = 81 days) in electric utility workers and 0.12 microT (n = 8 days) in office workers. A large fraction, 76% of the spot measurements total variance, could be attributed to variability within days. For the 8-hour TWA magnetic fields, between-group variability was small and of the same magnitude as between-worker variability. Significant autocorrelations between short-term averages of 7.5, 15, and 30 minutes were present, when taken within periods of 30 minutes. One-hour averages showed no autocorrelation. Simulations showed that, due to high within-day variability and autocorrelation, a limited number of short-term measurements of magnetic fields in electric utility workers are likely to result in imprecise estimates of 8-hour TWA magnetic fields. Measurement strategies relying on short-term (spot) measurements are therefore likely to result in misclassification of exposure and consequently absent or spurious exposure-response relations.     

Variability in quartz exposure in the construction industry: implications for assessing exposure-response relations

The aims of this study were to determine implications of inter- and intraindividual variation in exposure to respirable (quartz) dust and of heterogeneity in dust characteristics for epidemiologic research in construction workers. Full-shift personal measurements (n = 67) from 34 construction workers were collected. The between-worker and day-to-day variances of quartz and respirable dust exposure were estimated using mixed models. Heterogeneity in dust characteristics was evaluated by electron microscopic analysis and electron spin resonance. A grouping strategy based on job title resulted in a 2- and 3.5-fold reduction in expected attenuation of a hypothetical exposure-response relation for respirable dust and quartz exposure, respectively, compared to an individual based approach. Material worked on explained most of the between-worker variance in respirable dust and quartz exposure. However, for risk assessment in epidemiology, grouping workers based on the materials they work on is not practical. Microscopic characterization of dust samples showed large quantities of aluminum silicates and large quantities of smaller particles, resulting in a D(50) between 1 and 2 microm. For risk analysis, job title can be used to create exposure groups, although error is introduced by the heterogeneity of dust produced by different construction workers activities and by the nonuniformity of exposure groups. A grouping scheme based on materials worked on would be superior, for both exposure and risk assessment, but is not practical when assessing past exposure. In dust from construction sites, factors are present that are capable of influencing the toxicological potency.     

Estimating the association between blood pressure variability and cardiovascular disease: An application using the ARIC Study

The association between visit-to-visit systolic blood pressure variability and cardiovascular events has recently received a lot of attention in the cardiovascular literature. But, blood pressure variability is usually estimated on a person-by-person basis and is therefore subject to considerable measurement error. We demonstrate that hazard ratios estimated using this approach are subject to bias due to regression dilution, and we propose alternative methods to reduce this bias: a two-stage method and a joint model. For the two-stage method, in stage one, repeated measurements are modelled using a mixed effects model with a random component on the residual standard deviation (SD). The mixed effects model is used to estimate the blood pressure SD for each individual, which, in stage two, is used as a covariate in a time-to-event model. For the joint model, the mixed effects submodel and time-to-event submodel are fitted simultaneously using shared random effects. We illustrate the methods using data from the Atherosclerosis Risk in Communities study.     

Effects of model misspecification in the estimation of variance components and intraclass correlation for paired data

Paired data occur in many experimental situations. When one views the subjects as a random sample from some large population, it may seem reasonable to model the data according to the typical one-way random effects analysis of variance (ANOVA). It is then usually of interest to estimate variance components and intraclass correlation. These estimators can be biased if key assumptions are violated, leading to erroneous interpretations and conclusions. We focus upon assumptions about the equality or inequality of means and/or variances of the two measures on each subject. In the framework of the one-way random effects ANOVA model, and three generalizations of it, we document estimators obtained as solutions to the likelihood equations. We consider the potentially serious effects of mistaken assumptions. Our findings suggest that the most general model considered is most desirable if consistent and efficient estimation of the between-subject variance component and intraclass correlation is the main goal. We also briefly connect our exposition to the study of reliability or agreement.     

Variability of task-based dermal exposure measurements from a variety of workplaces

INTRODUCTION: The RISKOFDERM project collected task-based estimates of potential dermal exposure from a wide range of industries and services from around Europe. A formal statistical analysis was carried out to explore the main components of variability in dermal exposure levels. The central research question was to what extent dermal exposure levels could be explained by generic grouping variables like 'exposure scenarios' and 'dermal exposure operation units' (DEOs) (grouping of scenarios on the basis of similarity in exposure patterns). METHODS: Mixed effect linear models were used to estimate variance components of potential dermal exposure for DEOs or scenarios and for factories, workers and time. In addition within- and between-worker variance components were estimated for single groups of workers performing a specific scenario in a specific location with potential dermal exposure to a specific agent. RESULTS: Variability in potential dermal exposure is very large. Differences in geometric mean potential dermal exposure can range over 3-5 orders of magnitude both for DEOs and scenarios. The range depends on how dermal exposure is expressed (amount or rate). Both DEOs and scenarios explain a considerable amount of variability, but large differences in dermal exposure still existed within DEOs and scenarios. In contrast, between-worker variability in mean potential dermal exposure is minimal for a given scenario carried out within a specific location with exposure to a particular agent. Temporal variability, however, is considerable, most likely due to the event-based nature of the dermal exposure process. CONCLUSION: The classification of tasks in DEOs and scenarios has proven to be useful since large differences in average dermal exposure estimates exist between DEOs and between scenarios. However, large differences also exist between scenarios within a DEO and even within a scenario. These differences are governed by local conditions determined by the actual handling of the agent, the agent's physical and chemical properties, its intrinsic toxicity, control measures taken and training and attitude of workers. For the time being, actual dermal exposure measurements and a better understanding of actual determinants of dermal exposure seem to be a necessity in order to evaluate dermal exposure hazards properly.     

Metamodels of bias in Cox proportional-hazards and logistic regressions with heteroscedastic measurement error under group-level exposure assessment

In occupational epidemiology, group-based exposure assessment entails estimating the average exposure level in a group of workers and assigning the average to all members of the group. The assigned exposure values can be used in epidemiological analyses and have been shown to produce virtually unbiased relative-risk estimates in many situations. Although the group-based exposure assessment continues to be used widely, it is unclear whether it produces unbiased relative-risk estimates in all circumstance, specifically in Cox proportional-hazards and logistic regressions when between-worker variance is not constant but proportional to the true group mean. This question is important because (i) between-worker variance has been shown to differ among exposure groups in occupational epidemiological studies and (ii) recent theoretical work has suggested that bias may exist in such situations. We conducted computer simulations of occupational epidemiological studies to address this question and analysed simulation results using 'metamodelling'. The results indicate that small-to-negligible bias can be expected to result from heteroscedastic between-worker variance. Cox proportional-hazards models can produce attenuated risk estimates, while logistic regression may result in overestimation of risk gradient. Bias caused by ignoring the heteroscedastic measurement error is unlikely to be large enough to alter the conclusion about the direction of exposure-disease association in occupational epidemiology.     

Biases in estimating the effect of cumulative exposure in log-linear models when estimated exposure levels are assigned

OBJECTIVES: Exposure-response trends in occupational studies of chronic disease are often modeled via log-linear models with cumulative exposure as the metric of interest. Exposure levels for most subjects are often unknown, but can be estimated by assigning known job-specific mean exposure levels from a sample of workers to all workers. Such assignment results in (nondifferential) measurement error of the Berkson type, which does not bias the estimate of exposure effect in linear models but can result in substantial bias in log-linear models with dichotomous outcomes. This bias was explored in estimated exposure-response trends using cumulative exposure. METHODS: Simulations were conducted under the assumptions that (i) exposure level is assigned to all workers based on the job-specific means from a sample of workers, (ii) exposure level and duration are log-normal, (iii) the true exposure-response model is log-linear for cumulative exposure, (iv) the disease is rare, and (v) the variance of job-specific exposure level increases with its job-specific mean. Results Assignment of job-specific mean exposure levels from a sample of workers causes an upward bias in the estimated exposure-response trend when there is little variance in the duration of exposure but causes a downward bias when duration has a large variance. This bias can be substantial (eg, 30-50%). CONCLUSIONS: Berkson errors in exposure result in little bias in estimating exposure-response trends when the standard deviation of duration is approximately equal to its mean, which is common in many occupational studies. No bias occurs when the variance of exposure level is constant across jobs, but such conditions are probably uncommon.     

Temporal, personal and spatial variability in dermal exposure

A database of dermal exposure measurements (DERMDAT) comprising data from 20 surveys was created. The majority of dermal exposure measurements were from agricultural settings in which workers' exposure to pesticides was investigated. Other data came from studies of workers exposed to polycyclic aromatic hydrocarbons (e.g. coke-oven workers and paving workers) and from studies of subjects exposed to complex mixtures (rubber industry). The database contains approximately 6400 observations. Grouping the workers by job title, factory and body location and excluding groups with more than 25% data below the limit of detection, or with less than two workers with at least two repeats, resulted in 283 groups with 1065 workers and 2716 measurements. Analyses of variability showed median values of the total, within- and between-worker geometric standard deviations of respectively 2.55, 1.98 and 1.47, strikingly similar to what has been published previously for respiratory exposure. Within-worker variability ((w)S(2)y) was in general higher than between-worker variability ((b)S(2)y) in dermal exposure levels. Agricultural groups of re-entry workers showed very little to no between-worker variability, while industrial groups did show some variability in individual mean exposures (range (b)S(2)y=0.15-0.29). When the between-body-location component (bl)S(2)y) was also addressed, it turned out to be the most prominent component (median (b)S(2)y=0.004; median (w)S(2)y=0.12; median (bl)S(2)y=0.34). In agriculture the between-body-location component was smaller than in industry. Day-to-day variability in dermal exposure levels appeared to be significant for specific locations, but not for the average of several body-location. Underlying exposure scenarios (transfer and deposition) also played an important role.     

Maximum likelihood estimation of correction for dilution bias in simple linear regression using replicates from subjects with extreme first measurements

The least-squares estimator of the slope in a simple linear regression model is biased towards zero when the predictor is measured with random error. A corrected slope may be estimated by adding data from a reliability study, which comprises a subset of subjects from the main study. The precision of this corrected slope depends on the design of the reliability study and estimator choice.Previous work has assumed that the reliability study constitutes a random sample from the main study. A more efficient design is to use subjects with extreme values on their first measurement. Previously, we published a variance formula for the corrected slope, when the correction factor is the slope in the regression of the second measurement on the first. In this paper we show that both designs improve by maximum likelihood estimation (MLE). The precision gain is explained by the inclusion of data from all subjects for estimation of the predictor's variance and by the use of the second measurement for estimation of the covariance between response and predictor. The gain of MLE enhances with stronger true relationship between response and predictor and with lower precision in the predictor measurements. We present a real data example on the relationship between fasting insulin, a surrogate marker, and true insulin sensitivity measured by a gold-standard euglycaemic insulin clamp, and simulations, where the behavior of profile-likelihood-based confidence intervals is examined. MLE was shown to be a robust estimator for non-normal distributions and efficient for small sample situations. Copyright (c) 2008 John Wiley & Sons, Ltd.