Annals of Occupational Hygiene Advance Access originally published online on March 2, 2006
Annals of Occupational Hygiene 2006 50(4):343-357; doi:10.1093/annhyg/mel006
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Original Article |
A Meta-Analytic Approach for Characterizing the Within-Worker and Between-Worker Sources of Variation in Occupational Exposure
The University of Texas School of Public Health at Houston, 1200 Herman Pressler Drive, Houston, TX 77030, USA
* Author to whom correspondence should be addressed. Tel: +1-713-500-9238; fax: +1-713-500-9249; e-mail: Elaine.Symanski{at}uth.tmc.edu
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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While many studies have quantified the sources of variation in exposure to workplace contaminants for individual groups of workers, patterns of exposure variability have not been investigated since a comprehensive evaluation was carried out over 10 years ago. Therefore, a systematic review of the literature was conducted to identify studies that applied the one-way random-effects model to describe exposure profiles of groups of workers classified on the basis of the kind of work performed and where it was performed. Quantitative estimates of the sources of variation in exposure along with information related to the workplace, contaminant and sampling strategy were compiled. For subsets of the data, based upon the classification scheme used to group workers, weighted empirical cumulative distribution functions were constructed and compared using the non-parametric Kolomogorov–Smirnov two-sample test. Further stratifications evaluated differences by industry, agent and characteristics of the sampling strategy. The review identified nearly 60 studies that examined the within-worker and between-worker sources of variation in exposure to workplace contaminants. In pooling results across studies, the between-worker variability increased as workers were aggregated across jobs and locations. The within-worker variability for an occupational group of workers was generally larger than the between-worker variability, although the differences in the variation in exposures across work shifts relative to the variation among workers' mean exposure levels diminished as groups were combined across jobs and locations. On average, gaseous exposures were more homogeneous than exposures to aerosols or dermal agents as were exposures in the chemical industry compared with the non-chemical industry. The design of sampling strategies also plays an important role with greater variability among groups of workers who were sampled randomly rather than systematically; in addition, differences were detected on the basis of the study period and sample size. In evaluating key features of the design and methods of the studies identified in the review, several methodological issues emerged given the heterogeneity in terms of how censored data were handled, which estimation method was applied and whether underlying assumptions of the models were met. Notwithstanding the utility of quantifying sources of variation in exposure, several challenges lie ahead with regard to ensuring quality in the collection, analysis and reporting of exposure monitoring data that would enhance efforts to accurately assess exposure.
Keywords: exposure assessment • exposure variability • meta-analysis • variance components
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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In the first comprehensive evaluation of exposure variability, Kromhout et al. (1993)
compiled a database of nearly 14 000 personal sampling measurements collected on more than 1500 workers from myriad industries in the UK, The Netherlands, the US, Sweden and the People's Republic of China. Apart from its size, a unique characteristic of the database limited inclusion to groups of workers (classified by job title and factory) that had repeated measurements on at least five individuals. Following application of the one-way random-effects model, this data structure allowed for characterization of the intra-individual and inter-individual sources of variation in exposure vis-à-vis estimates of the within-worker and between-worker variance components, respectively. Several important findings emerged in the study. First, among the 165 occupational groups of workers that were examined, the within-worker variance component was generally larger than the between-worker variance component, indicating more variation in exposure between work shifts than between workers who shared the same job title at a common workplace. Second, results indicated that there were nearly equal numbers of groups of workers characterized either by rather homogenous or heterogeneous exposures. This latter finding challenged the assumption that workers' exposure levels within an occupational group, classified on the basis of the kind of work performed and where it was performed, were necessarily similar. Third, their findings suggested differences in the extent to which exposures vary between and within workers on the basis of characteristics related to the workplace, contaminant and sampling strategy, although some results were based upon relatively small numbers of job groups.
Since its publication 13 years ago, numerous investigations have been carried out that extend the work conducted by Kromhout and collaborators (Burdorf and van Tongeren, 2003) by focusing on workplaces outside the chemical manufacturing sector and in evaluating sources of variation in exposure to dermal agents (Kromhout and Vermeulen, 2001) and in biological measures of exposure (Symanski and Greeson, 2002). Additionally, methodological developments have further examined effects of exposure variability on epidemiological studies (Rappaport et al., 1995a; Symanski et al., 2001a), expanded the one-way random-effects model to account for temporal effects (Symanski et al., 1996, 2001b; Peretz et al., 1997) and varied determinants of exposure (e.g. Burstyn and Kromhout, 2000; Peretz et al., 2002; McClean et al., 2004; Vermeulen et al., 2004) and evaluated the assumptions underpinning the models that have been applied (Symanski et al., 1996, 2001a; Weaver et al., 2001).
Given the plethora of studies that have been published over the past 10 years, there was an opportunity to expand the assessment of exposure variability beyond the 165 groups of workers that were originally examined (Kromhout et al., 1993). Following a systematic review of the literature, data were compiled on nearly 600 occupational groups for which quantitative estimates of the within-worker and between-worker sources of variation in exposure had been obtained. In this paper, we describe the methods used to conduct the literature review, compile the database and assess patterns of variability evident in workplace exposure, as well as discuss methodological lessons learned during the course of the investigation.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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Systematic review of the literature
Two of the authors independently searched the literature using Science Citation Index and Medline to identify potentially eligible peer-reviewed publications that characterized the between-worker and within-worker sources of variation in exposure. Initially, the search criteria included the following keywords: between-worker variance, within-worker variance, between-worker variability and within-worker variability. A second search was performed to assess whether all studies on this topic had been identified using combinations of relevant keywords (variance components, random-effects model, mixed-effects model, attenuation, and measurement error coupled with exposure, occupational, workplace and worker). Both searches were restricted to articles written in English. Additional strategies to identify relevant studies included evaluating articles cited in publications retrieved in the literature review, as well as manually searching the following journals between 1993 and August 2005: American Industrial Hygiene Association Journal, The Annals of Occupational Hygiene, Applied Occupational and Environmental Hygiene, International Archives of Occupational and Environmental Health and the Journal of Occupational and Environmental Hygiene.
Data extraction and compilation
The retrieved articles were examined to identify studies for exclusion based upon the following criteria:
- Studies that evaluated variability in electromagnetic fields, noise or ergonomic factors.
- Studies that relied upon biological monitoring because additional factors contribute to intra-individual and inter-individual sources of variability in biomarkers of exposure that do not affect variation in external exposures (e.g. individual differences in the rates of uptake, metabolism or elimination).
- Studies that relied exclusively on mixed-effects models or two-way random-effects models because results are not directly comparable with those generated under a one-way random-effects model.
- Studies published prior to 1993.
For each group of workers, quantitative estimates of the within-worker and between-worker sources of variation in exposure were extracted (i.e. the within-worker and between-worker variance components of the log-transformed data 
and 
) and functions thereof). The method used for obtaining estimates of the variance components was also noted. Information on the type of contaminant, the units of measurement, the industrial sector, the numbers of workers and measurements and the duration of sampling (short-term or full-shift sampling) were extracted from the individual studies. Full-shift sampling extended to measurements collected over periods of 4 h or longer. Information was noted if investigators used data collected over both ‘short’ and ‘long’ periods of time to generate estimates of the variance components. Finally, the location where each group performed work (e.g. building, factory or plant) was extracted. Specific questions focused on whether groups were classified by job or across jobs and by location or across locations.
When available, the nature of the sampling strategy (random versus campaign), duration of the study and the geographical location (country of origin) where work occurred were extracted. If reported, arithmetic and geometric mean levels and the geometric standard deviations were noted, along with the percentage of values above the limit of detection. If a study did not report the percentage of values below the limit of detection on a group by group basis, another variable recorded information on any stated criteria in the study that restricted analyses to groups with no more than a fixed percentage of non-detectable values.
Following the compilation of the extracted data, additional variables were added to the database. For each group, the 
values were computed from estimated values of the variance components [i.e. 
and 
= 
], which represent the estimated ratios of the 97.5th percentile to the 2.5th percentile of the corresponding lognormal distributions of the individual worker's shift-long exposures and of the individual workers' mean exposure levels, respectively (Rappaport, 1991). If studies only reported the values, no computation was made. Based upon the industrial sector in which work was performed, industry was classified using the International Standard Industrial Classification of All Economic Activities codes (ISIC, version 3.1) (Department of Economic and Social Affairs Statistical Division, 2002). Industrial processes involving production of chemicals, chemical products, refining and petrochemical products (industrial divisions 23–25) were classified as ‘chemical industry’ while the remaining processes were classified as ‘non-chemical industry’ (divisions 1–22 and 26–93). Each airborne contaminant was coded as a gas/vapor or an aerosol. Exposures to dermal agents were classified separately. Categorical variables were created for the number of workers (<5, 5–8, >8), the number of measurements per group (<10, 10–25, >25) and the duration of the study (
1 year and >1 year).
Final inclusion criteria
Studies were considered eligible for inclusion in this review if the following a priori criteria were met: (i) Workers were classified on the basis of the kind of work performed and where it was performed; (ii) the period of sampling for all measurements extended over a full-shift (
4 h); and (iii) at least 5 workers with 10 or more measurements were sampled per group. For studies that applied both random-effects and mixed-effects models, only results on groups of workers examining exposure variability using one-way random-effects models were included. Finally, the studies were scrutinized to identify multiple publications that described the same data so that duplicates could be eliminated. In instances when the data were similar but not identical, studies that reported more complete data (in terms of numbers of groups, numbers of workers and/or measurements or duration of the sampling period) were selected.
Statistical analyses
Given differences in the schemes that were used to classify groups of workers, which may affect the degree of variation within and between workers, four subsets of the data were identified: (i) Groups classified by job and location; (ii) Groups classified by job and across multiple locations; (iii) Groups classified across jobs at a single location; and (iv) Groups classified across jobs at multiple locations.
Empirical cumulative distribution plots for the and 
values were generated for each classification of groups, as well as for subsets of the data stratified by type of industry, type of agent and by characteristics related to the sampling strategy. Since the sample sizes per group varied widely, the numbers of measurements collected on each occupational group (N) were used as weights to construct the distributions. That is, for each stratum, each group was assumed to carry a probability weight of the ratio of the group's sample size to the total sample size across all groups. In other words, the data from each job group was treated as a cluster sample. As such, it was assumed that the information contained in an estimate of the variance increases with sample size, which is consistent with the assumptions that underlie cluster sampling (Levy and Lemeshow, 1999).
The non-parametric Kolmogorov–Smirnov two-sample test (Gibbons and Chakraborti, 2003) was used to compare the empirical cumulative distribution functions for subsets of the weighted data. In our application, each distribution was equal to a weighted sum of ‘chi-squared type’ random variables; thus, there was no assumption that their distributional shapes were the same functional form. The Kolmogorov–Smirnov test was evaluated at a significance level of 0.05 when data were stratified into two groups; the Bonferroni procedure for multiple comparisons was applied when three or more groups were compared (Conover, 1999). All statistical analyses were carried out in SAS (version 8.2, SAS Institute, Cary, NC, USA).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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Description of the database
Following the review of the literature, a total of 56 potentially eligible studies (with data reported on 1207 groups of workers) were examined. After checking for duplicate publication of data, 261 job groups were eliminated. Another 260 groups were excluded because of concerns about unreliable estimates of the variance components owing to small sample sizes (i.e. <5 workers or <10 measurements per group). Additional groups were eliminated on the basis of absence of information on sample size (n = 16), classification by exposure level (n = 6), task-based sampling (n = 70) and short or mixed sampling times (n = 23). Following these exclusions, 571 job groups from 39 studies remained.
Table 1 profiles the studies deemed eligible for inclusion in the review by providing information about the industrial sector in which the study was conducted, the specific agent that was monitored, the study location and the classification scheme used to group workers. Details regarding the method of estimation used to generate the variance components and whether studies reported the percentage of values below the detection limit on a group by group basis are also tabulated. In stratifying the studies by type of agent, there were 30 different compounds classified as aerosols, 25 compounds classified as gases/vapors and six compounds classified as dermal agents. Benzene, toluene, styrene and organic vapors (otherwise unspecified) were the most frequently sampled gases/vapors and ‘dust’ and ‘particulate matter’ (as they were noted in the original studies) were the most commonly measured aerosol. For dermal agents, the most commonly sampled compounds were aromatic hydrocarbons in the form of cyclohexane soluble fraction. Information regarding the method of estimation used to generate the variance components could be ascertained in all but one study. The method of moments estimation method (the so-called ‘ANOVA’ estimation method) was applied more frequently (n = 24 studies) than restricted maximum likelihood (REML) (n = 14). Information on the percentage of values below the limit of detection for all groups of workers on whom variance components were reported was available in less than one-third of the studies (11/39).
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Table 2 provides a breakdown of the data based upon the classification used to group workers. Over half of the groups (54%) were classified by job and location, with nearly equal proportions classified by job across locations (22%) or across jobs by location (20%) and the smallest proportion of groups classified across jobs and locations (4%). Sample sizes, on average, tended to increase as groups of workers were collapsed across jobs or across locations. In each grouping, however, the range in numbers of measurements and workers per group varied widely. Most, but not all, of the groups had information on both the between-worker and within-worker sources of variation in exposure. For 49 groups, only the between-worker variance component was reported; for one group, only the within-worker variance component was reported.
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Table 3 profiles each classification of job groups on the basis of characteristics related to the industrial sector, the type of agent and the sampling strategy. More groups arose in the non-chemical sector with aerosols more frequently monitored than gases/vapors. Across each classification, the majority of the groups arose in the manufacturing sector with relatively few (or no) groups in the construction or agricultural sectors. For those groups with known geographical locations, the majority originated in Europe, particularly in The Netherlands. Data on the length of the study period and on the nature of the sampling strategy were missing for significant proportions of groups in each category. The geometric mean was more commonly reported (60% of all groups across the four classifications) than the arithmetic mean exposure level (52%) (data not shown).
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Patterns of the within-worker and between-worker sources of variation in exposure
Table 4 shows selected percentiles of the weighted empirical cumulative distribution functions for the
and values for groups stratified on the basis of grouping strategy. Given the possibility of undue influence of three groups with the largest number of measurements (n = 5076, n = 1162 and n = 1139) coupled with evidence of non-stationary exposures at the workplace where the monitoring data were collected (Symanski et al., 1996), the empirical cumulative distribution functions of groups classified by job and by location were re-generated with these groups excluded. Following the exclusions, notable effects were observed (Table 4), particularly on the distribution of the values. Thus, a decision was made to perform all other analyses excluding the data reported on these three groups (in Kromhout et al., 1993) since the variance component estimates are probably biased owing to having been generated under the one-way random-effects that assumes no changes in the mean exposure level over time.
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In comparing the degree of variability of exposures across classifications, the variation in exposure between workers, on average, tended to increase as workers were aggregated across jobs and location. Median
values ranged from 4.8 in groups classified by job and location to 65.0 for groups classified across jobs and locations. In contrast, the median values appeared more stable across the four classifications of workers. As expected, the range of values of the distributions tended to broaden as the classification of workers became less homogeneous.
Effect of type of industry and agent on exposure variability
For groups classified by job and location, Fig. 1 represents the weighted empirical cumulative distributions of the and values for groups stratified by industry and type of agent. For groups stratified by industry (top of the figure), statistically significant differences in the distributions of the values were detected with an interquartile range (IQR) of 6.5 for the chemical industry and 13 for the non-chemical industry (median values of 4.1 versus 5.1). Differences in the distributions of the values were also detected; the median value was shifted slightly towards higher values for the chemical (32.9) versus non-chemical (26.2) industry with an IQR of 63.5 versus 57, respectively. In stratifying groups on the basis of type of agent (bottom of the figure), the weighted cumulative distribution function of the values for groups exposed to dermal agents is shifted towards higher values as compared with the distribution for groups exposed to gases/vapors or aerosols (median values of 9.6, 4.1 and 3.6, respectively). All three pair-wise comparisons were significantly different from each other. The degree of within-worker variability for groups exposed to gases/vapors was much greater than for groups exposed to aerosols or dermal agents (median values of 54.9, 25.8 and 13.7, respectively) with significant differences detected in all cases.
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Table 5 provides a breakdown of selected percentiles of the weighted empirical cumulative distribution functions of
and values for groups classified by job and location stratified on the basis of industry and agent together, as well as characteristics of the sampling strategy. While all pair-wise comparisons were statistically significant, most notable effects were observed for groups of workers exposed to gases/vapors who experienced considerably greater variation within workers in the chemical industry as compared with the non-chemical industry. Interestingly, aerosol exposures were less variable (within and between workers) across groups in the chemical sector as compared with the non-chemical sector whereas the opposite trend was observed for gases/vapors. Differences in the distributions describing the within-worker source of variation were also readily apparent for groups stratified on the basis of sample size and length of the sampling period.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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Based upon a comprehensive review of the literature, patterns in exposure variability were evaluated for almost 600 occupational groups of workers representing 14 246 workers on whom a total of 49 807 measurements had been collected with broad coverage in terms of the agent to which workers were exposed and the industrial sector in which work was performed. Consistent with previous studies (Kromhout et al., 1993
; Rappaport et al., 1993), our findings indicate that the day-to-day variation in exposures generally exceeded the variation between workers, although the difference in the variation in exposures across work shifts relative to the variation among workers' mean exposure levels diminished as workers were collapsed across jobs and locations. Our results also confirm that aggregating workers on the basis of job title and location do not necessarily yield homogeneously exposed groups. The implication of these and earlier findings suggest that observational approaches for classifying workers should be validated with sampling data that allow for a quantitative assessment of the relative magnitude of the within-worker and between-worker sources of variation in exposure. Support for this approach is reiterated by the American Industrial Hygiene Association in their recommendation that industrial hygienists recognize situations for which misclassification would present a significant risk and then ‘make an effort to generate exposure monitoring data to check the homogeneity of the groupings and refine worker exposure classifications as appropriate’ (Mulhausen and Damiano, 1998, p. 54).
On average, gaseous exposures were more homogeneous than exposures to aerosols or dermal agents, as were exposures in the chemical industry compared with the non-chemical industry. In comparing distributions using the concept of stochastic order (Casella and Berger, 2002, p. 44), the distribution is (approximately) stochastically greater for groups in the chemical industry than in the non-chemical industry (because the cumulative distribution function lies below or is shifted to the right for all cumulative probability values except at the very uppermost tail). A similar pattern was not evident for the distribution functions of the values given the crossover that occurred at about the 35th percentile. In making similar comparisons by type of agent, the distribution for dermal agents appears stochastically greater than the distribution function for gases/vapors whereas the distribution is stochastically smaller.
Our finding of greater within-worker variability for gases/vapors than for aerosols may be due, in part, to a greater degree of variation from day to day in factors that influence the emission of gases/vapors (e.g. temperature and pressure) compared with those factors that govern the emission of aerosols (e.g. mechanical and physical forces) (Vincent, 1995; Mulhausen and Damiano, 1998). Once emitted, the agent's physical and chemical characteristics also play a role in affecting variation in exposure (particularly variation between workers) where the dispersion of gases/vapors is largely governed by convection and diffusion processes (Roach, 1991; Mulhausen and Damiano, 1998) as compared with the dispersion of aerosols that are subject to gravitational and inertial forces, thermophoresis, electrophoresis, coagulation and break-up (Vincent, 1995).
In focusing on aerosol exposures, there was greater within-worker variability, but less between-worker variability, for exposures received via inhalation than by dermal absorption. Dermal exposures would be expected to exhibit different patterns of variability than inhalation exposures because they are influenced by determinants that affect the interaction of the skin with contaminants present in the environment (Kromhout and Vermeulen, 2001; Rajan-Sithamparanadarajah et al., 2004). However, there was more than a 2-fold difference in the number of groups with inhalation as compared with dermal exposures and additional work is warranted to further evaluate this issue.
Effects related to increasing numbers of measurements per group and increasing numbers of workers were more apparent for the within-worker source of variation. Increasing sample size may reflect sampling over longer periods, during which either the full range of exposures were more likely to have been monitored or changes in the process or the workplace occurred (Symanski et al., 1996). In fact, the majority of the groups with more than 25 measurements were collected over periods longer than 1 year. In evaluating study duration directly, groups with longer monitoring periods were characterized by significantly higher levels of within-worker variability. The observed effects on the within-worker source of variation owing to the number of workers is more difficult to explain, although it may be possible that as the groups become larger the workers differ not only in their mean exposure levels but also in the degree to which exposures vary from day to day. If this is indeed the case then the assumption (of the variance component models typically applied in the occupational arena) that workers in a group (however defined) experience the same level of variation across sampling periods is open to question.
There are important differences in the methodological approaches used to conduct the current investigation as compared with the study by Kromhout et al. (1993). Rather than compile individual exposure measurements and pertinent information about the workplace or the job group on which data were collected, our investigation followed a line of inquiry in which a body of work is synthesized (Pettiti, 1999) and was, thereby, limited by the information provided in the individual studies. Notwithstanding the merits of both approaches to answer questions about exposure variability, careful methods need to be elaborated in compiling the data in either case to enhance reliability and validity, and reduce bias.
In total, 56 potentially eligible studies were examined that included data reported on 1207 groups of workers. Based upon the eligibility criteria established in this study, 636 groups of workers (and 17 studies) were eliminated because of duplication, short or mixed sampling periods, small sample sizes or the grouping strategy used to classify workers. A larger than expected proportion of the data was excluded on the basis of too few measurements (<10) or too few workers (<5), which calls into question the application of random-effects models to characterize exposures in the face of insufficient data. Moreover, we identified several studies that combined measurements of mixed sampling times in a single analysis. Such a practice seems injudicious given that exposures experienced over short periods are probably dissimilar to exposures experienced over full work shifts. Thus, investigators are encouraged in the future to employ sampling strategies that collect enough data over common sampling intervals to allow meaningful inferences about exposure to be made.
While the inclusion criteria that were applied ensure a minimum standard of quality of the studies included in the systematic review, several limitations remain. Measurement error may have been introduced during sample collection or laboratory analysis. Also, the protocols for handling the data may have introduced additional sources of error. While most of the studies in our review, for example, provided information about the limit of detection of the analytical methods that were applied, they oftentimes did not report the percentage of non-detectable values on a group by group basis (or indicate a cut point above which data were not analyzed). This omission is notable given concerns related to the effects of highly censored data on estimates of the variance components. In addition, there was rarely indication in the studies included in this review that the data were examined to evaluate whether changes or trends in exposure levels have occurred. Since biased estimates of the variance components can result when a variance component model is improperly specified (Symanski et al., 1996), an inspection of the data for non-stationary behavior should become routine in any exposure assessment. Such results would then be coupled with knowledge about changes in the process or in production levels over time and used to select an appropriate model to characterize variability and, thereby, minimize potential sources of error due to model mis-specification.
Another issue in pooling results across studies relates to differences in the method used to obtain estimates of the within-worker and between-worker variance components. Two methods were applied in the studies included in our review, namely a method of moments estimation method (ANOVA) and REML. Since the ANOVA method is unbiased and REML is asymptotically unbiased, our exclusion of groups with small samples suggests that the estimators that were applied often shared the desirable property of unbiasedness. Further, we reduced the influence of any potential deviation between values generated using the two estimation methods by utilizing a weighted approach in comparing empirical cumulative distribution functions and, thus, it is not likely that the original authors' selection of different estimation methods adversely influenced our results.
In a more general context, the question as to which method of estimation is preferable may depend upon which property or set of properties of an estimator is viewed as more important. In the balanced case, ANOVA and REML estimators are identical and share both unbiasedness and minimum variance properties (under normality). For unbalanced data, Searle et al. (1992) prefer maximum likelihood estimators (ML or REML) over ANOVA estimators because they are consistent, asymptotically normal and have known asymptotic sampling dispersion matrices (no preference is indicated for ML over REML or vice versa). Features of the data themselves could also play a role and investigators are encouraged to consider them (along with those properties of an estimator deemed important) when making decisions about the optimal method of estimation to apply in their studies.
In making pair-wise comparisons in the distributions of the values stratified on the basis of type of agent, industry or sampling characteristic, we chose to use the Kolmogorov–Smirnov test because it does not assume that the groups being compared have the same distributional form. This test is different from the Wilcoxon's rank sum test, which is used to compare distributions that differ only in their location shift (i.e. to test differences in the median values). Under the scenario that two distributions have the same median, but a different distributional form, the Wilcoxon's rank sum test may falsely accept the null hypothesis that two distributions are the same whereas the Kolmogorov–Smirnov test would not. Given the lack of evidence in the literature that the groups compared in our study have the same distributional form, we chose to apply the Kolmogorov–Smirnov test.
Finally, weighted rather than un-weighted analyses were employed in the current investigation. Here, the numbers of measurements collected on each occupational group of workers were used as weights in constructing and comparing empirical cumulative distribution functions, which provided a means of adjusting the relative contribution of each group on the basis of sample size. To illustrate the impact of possible differences based upon which approach is utilized, our data were examined using un-weighted analyses. For groups classified by job and location, the IQR of the distribution of the values increased from 7.8 in the weighted analysis to 12.8 in the un-weighted analysis with little effect on the median values (4.8 and 5.0, respectively). In making a similar comparison of the distribution of values from the weighted and un-weighted analyses, respectively, effects were observed in the median values (26.2 and 15.8) and the IQR (48.6 and 56).
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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A considerable number of studies have been carried out that have examined variation in occupational exposure by applying random-effects and mixed-effects models. Clearly, the utility of this approach lies in the information it provides about the magnitude of the within-worker source of variation relative to the between-worker source of variation that has applications in both occupational hygiene and epidemiological studies. Nevertheless, results from our literature review suggest that variance component models have sometimes been inappropriately applied in the face of insufficient or unsuitable data. Moreover, we noted inconsistencies across studies in the degree of information provided regarding the study population, the sampling protocols and the statistical methods applied, as well as in the summary statistics presented to describe any particular group of workers. Several challenges lie ahead to minimize potential sources of error and bias in the collection, analysis and reporting of exposure monitoring data.
Notwithstanding the aforementioned methodological issues, our investigation provides evidence that, as expected, the between-worker source of variation in exposure, on average, increases as workers are aggregated across jobs and locations. Within-worker variability for an occupational group of workers was generally larger than between-worker variability, although the difference in the within-worker source of variation relative to the between-worker variation diminished as workers were collapsed across jobs and locations. On average, gaseous exposures were more homogeneous than exposures to aerosols or dermal agents, as were exposures in the chemical industry compared with the non-chemical industry. The design of sampling strategies also appears to play an important role with effects detected based upon whether workers' exposures were monitored systematically versus randomly, with greater frequency, in larger groups or over longer periods of time.
Received November 20, 2005; in final form January 23, 2006
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