Exposure Variability: Concepts and Applications in Occupational Epidemiology

Transcription

1 AMERICAN JOURNAL OF INDUSTRIAL MEDICINE 45: (2004) Exposure Variability: Concepts and Applications in Occupational Epidemiology Dana Loomis, PhD 1 and Hans Kromhout, PhD 2 Background Standard approaches to assessing exposures for epidemiologic studies tend to concentrate resources on obtaining detailed data for each study participant at the expense of characterizing within-person variability. Methods This paper presents some basic, generalizeable concepts concerning exposure and its variability, describes methods that can be used to analyze, describe, and understand that variability, and reviews related implications for the design and interpretation of epidemiologic studies. Results and Conclusions Insufficient attention to the balance of within- and betweenperson variation in exposure can reduce the efficiency of measurement efforts and attenuate estimates of exposure-disease association. Exposure variability should consequently be considered carefully in the planning, analysis, and interpretation of epidemiologic studies. Greater attention to these matters can lead to more meaningful characterization of exposure itself, and, most importantly, improve the chances that epidemiologic studies can identify and accurately characterize health hazards. Am. J. Ind. Med. 45: , ß 2003 Wiley-Liss, Inc. KEY WORDS: exposure; within-individual variability; between-individual variability; epidemiology; methods INTRODUCTION As used in epidemiology, the term exposure is understood to refer to either proximity and/or contact with a source of a disease agent or the amount of a factor to which a group or individual was exposed [Last, 2001]. In the first definition, exposure is treated as an attribute of individuals that is either present or absent. In this case, measuring exposure becomes a problem of assigning people to exposed and unexposed groups that are assumed to be essentially homogeneous. This basic approach may be 1 Departments of Epidemiology and Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 2 Environmental and Occupational Health Division, Institute for Risk Assessment Sciences, Utrecht University, Utrecht,The Netherlands *Correspondence to: Dr. Dana Loomis, Department of Epidemiology, CB 7435, School of Public Health, UNC-CH, Chapel Hill, NC Dana.Loomis@unc.edu Accepted 24 September 2003 DOI /ajim Published online in Wiley InterScience ( extended to incorporate the second definition, in which exposure has to do with the quantity of the agent, by creating ordinal categories, also treated as homogeneous. In another variation, quantitative exposure measurements are taken and used to assign exposure scores to each category. All of these standard approaches classify individuals in groups with different exposures, but impose implicit assumptions that individuals within groups are uniformly exposed, and frequently that each individual s exposure is fixed over time, as well. These standard simplifying assumptions can mask complex variation that should often be accounted for in the design, conduct, and interpretation of studies. On those occasions when exposure is measured on an individual basis, it is often treated as an invariable fixed attribute of an individual. Concepts and methods for working with complex exposure information have been developed through epidemiological research on nutritional and occupational exposures [Willett, 1990; Rappaport, 1991; Boleij et al., 1995], but are still not in common use. Here we will present some basic, generalizable concepts concerning exposure and its ß2003Wiley-Liss,Inc.

2 114 Loomis and Kromhout variation among people and over time, describe methods that can be used to analyze, describe, and understand that variability, and consider implications for design and interpretation of epidemiological studies. Although our discussion focuses on occupational and environmental exposures, the concepts and methods have applications to a wider range of epidemiological problems. DIMENSIONS OF EXPOSURE VARIABILITY From the standpoint of epidemiologic research, variation in exposure has two fundamental dimensions: person and time. Because epidemiologic studies generally require comparison of the health experience of groups or populations, the notion that exposure varies between groups of people is fundamental to epidemiologic research. Exposure may also vary within groups of people. In occupational studies, groups are frequently defined by existing structures, such as job titles or work areas. Thus, workers employed in the same plant are assumed to have different exposures determined by their job titles and work areas. However, exposures of workers with the same job in a work area might vary as a result of differences in tasks, work styles, ventilation, and personal protective equipment. Figure 1 depicts this situation for two automobile manufacturing workers performing the same job (painting car bodies) in the same well-controlled spray booth: despite the apparent similarity of these workers tasks and environment, their mean exposures to isopropanol differed by a factor of 2.7. When exposure groups are selected or created for study, some aggregate measure of exposure is normally applied to all individuals in a given group. A statistical measure of central tendency, such as the arithmetic or geometric mean, is typically used when the exposure variable is quantitative. Although metrics of this type are based on explicit statistical assumptions about the distribution of exposure within the group, standard practices treat every individual s exposure as if it were equal to the mean. For categorical exposure variables, an arbitrary score (e.g., 0 or 1 for binary data) is usually applied as a metric of exposure. Metrics of this type do not explicitly presume variability within groups. Nevertheless, it is normally the case that exposure does vary within categories treated as uniform. For example, the quantitative level of lifetime exposure to tobacco smoke may vary widely among those who are classified as smokers by a binary indicator for ever having consumed cigarettes. Classical statistical methods for the analysis of exposure-disease associations do not facilitate formal consideration of the variability within groups, so it is frequently ignored. Nevertheless, within-group variability has important implications, including the potential for exposure measurement error and misclassification. FIGURE 1. Daily mean exposures to isopropanol (IPA) for two workers preparing automobile bodies for painting in a ventilated booth (diamonds, worker 1; squares, worker 2). Data from [Flynn and George, 1996]: Applied Occupational and Environmental Hygiene, A field evaluation of a mathematical model to predict worker exposure to solvent vapors, 11(10), pages1212^1216. Copyright1996. Cincinnati OH. Reprintedwithpermission.

3 Exposure Variability: Concepts and Applications 115 Time is the basic dimension of exposure variability at the individual level: people change jobs, quit smoking, retire, and experience other changes. Indeed, congenital attributes may be the only exposures that are truly fixed at the individual level. Many methods of analyzing epidemiological data nevertheless require that exposure be treated as fixed, rather than as time-dependent, for each person. Case-control studies, for example, typically use an exposure estimate based on the exposure accumulated at the time of the cases diagnosis [e.g., Sanderson et al., 2001]. The temporal variability of exposure can be considered on different time scales. Figure 2 illustrates this phenomenon for workers exposed to magnetic fields. The two workers shown in Figure 2a had different average exposures in each decade, and each worker s exposures declined by approximately 0.5 mt over the time interval. When worker 2 s exposure is examined on a day-to-day basis, however, the range of daily mean exposures is greater by a factor of 10, and no secular trend is evident (Fig. 2b). The fluctuation of exposure within a single day is greater still (Fig. 2c). As this example suggests, developments in measurement technology can make it possible to measure exposure on progressively finer time scales. Nevertheless, decisions about which time scale is relevant should still be biologically based, since there FIGURE 2. a^c: Variation in individual occupational exposure to magnetic fields (a) by year, by day within1work week (b) andby10-s interval within1day (c). Figure 2c from van der Woord et al. [2000].Within-day variability of magnetic fields among electric utility workers: consequencesformeasurementstrategies. AmIndHygAssocJ61:31^38.Copyright2000by theamericanindustrial HygieneAssociation. Reprintedwithpermission.

4 116 Loomis and Kromhout is no reason to assume that any exposure that can be measured must be important. ANALYSIS AND DESCRIPTION OF EXPOSURE VARIABILITY A description of the dimensions and determinants of exposure variability can be useful for a number of purposes, including planning exposure measurements, assigning estimates of exposure to study participants, and predicting and controlling future exposures. Mathematical Description Simple conceptual models can be developed to describe exposures, taking account of variability associated with various factors. For example, if exposure varies between groups, between people within groups, and from time-totime for each person as described above, the instantaneous exposure X(t) of a person at time t can be described by: X ij ðtþ ¼fð þ i þ ij þ ij ðtþþ, where m is the long-term, overall mean exposure level, and a,, and g, respectively, represent deviations from m associated with being a member of group i, being the jth person in that group, and temporal fluctuation of exposure at time t. Statistical Models Random-effects analysis of variance (ANOVA) models are a useful tool for quantitatively describing variability in exposure by partitioning it into variance components associated with different factors [Heederik et al., 1991]. Timevarying exposures within a population can be analyzed using a simple one-way random effects ANOVA model: X ij ¼ þ i þ " ij, where X ij is the observed exposure of person i at time j, m is the long-term, population mean exposure, i is the random deviation of the ith person s exposure from the population mean, and e ij represents a random deviation on the jth day from person i s mean exposure. This model assumes that i and e ij are normally distributed and independent. By fitting the ANOVA model to the observed exposure data, the variance components 2 b and s 2 w associated with exposure variability between people and within people, respectively, can be estimated. The total variance in exposure, 2 T is simply the sum 2 b þ 2 w. Because the distribution of occupational exposures tends to be lognormal, the ANOVA model is usually fit to log-transformed data. In this case, the model is written as Y ij ¼ lnðx ij Þ¼þ i þ " ij, where Y ij is the log-transformed individual exposure, X ij. The estimated geometric standard deviations exp(s b ) and exp(s w ) are then used to describe the variability between and within people, respectively. In Figure 3 an example is presented of within- and betweenindividual variability in exposure to cutting fumes for six workers demolishing a railway bridge. The basic random-effects ANOVA model can be expanded for the analysis of more complex situations by adding terms for additional explanatory factors or sources of variability. For example, the variability of exposure among several populations might be analyzed using the model FIGURE 3. Exposuretocuttingfumesofsixdemolitionworkersduring4consecutivedays.Thedifferencesbetweenindividualsoutweigh theday-to-dayvariability(77%between-individualvariability vs.23%within-individualvariability).estimatedgeometricstandarddeviations exp(s b )andexp(s w )are2.00and1.46,respectively,correspondingtoa b R 0.95 of15anda w R 0.95 of4.4.

5 Exposure Variability: Concepts and Applications 117 X ijk ¼ þ i þ ij þ " ijk, in which X ijk is the observed instantaneous exposure at day k of a person j in group i, i represents the random deviation of group i s exposure from the global mean, m, g ij is the random deviation of person j s exposure from the mean of group i, and e ijk is a random error component consisting of temporal variability for person j. This model assumes a hierarchical variance structure, with each successive source of variability nested within the one before it. The formulation is analogous to the conceptual model above, with exposure varying between groups, between people within groups, and within people over time [Kromhout and Heederik, 1995]. In some situations, it can be useful to employ a multilevel mixed effects regression model that allows exposures to be modeled as a function of a combination of random and fixed factors [Burton et al., 1998]. For example, groups defined by job title or work area might be entered as fixed effects, while the effect corresponding to individual workers within groups and temporal effects are modeled as random factors [Nylander-French et al., 1999; Burstyn and Kromhout, 2000]. PLANNING EXPOSURE ASSESSMENTS FOR EPIDEMIOLOGICAL STUDIES Who, What, and When to Measure The structure and magnitude of exposure variability have important practical implications for planning the assessment of exposure in an epidemiologic study. Among the first steps in planning a study are decisions about who and what to measure. Exposure variability should be considered along with other issues when selecting a study population. It can be shown that the distribution of a population s exposure can effect study efficiency, with less variable exposures generally requiring larger numbers of subjects to achieve the same study power [White et al., 1994; Armstrong, 1996] Exposure variability, and thereby efficiency, can be augmented by carefully selecting populations to increase exposure ranges or expand the overall variance of exposure [McKeown-Eyssen and Thomas, 1985; Armstrong, 1996]. Causal models are the preferred starting point for decisions about what to measure, but the balance of withinand between-person exposure variability can be an important, practical consideration with ramifications for both validity and efficiency [Rappaport et al., 1995]. Exposure Measurement Strategies Consideration of the relative magnitude of between- and within-person components of exposure variability can yield useful insights about the type of exposure measurement strategy most likely to yield valid, precise estimates of true exposure for study participants. Two extreme cases illustrate the principles involved. If exposure varied only over time, but not among people, then monitoring a single individual would be sufficient to characterize the exposure of a population. Because of temporal variability, however, either continuous monitoring of that individual s exposure over the entire time period of interest or multiple, shorter-term measurements distributed randomly over that interval would be required to accurately characterize the exposure. The optimal exposure assessment program for this situation would maximize the amount of data collected for an individual subject. At the opposite extreme, a single instantaneous measurement for each person in the study would be sufficient if exposure varied only between people and not over time. The optimum allocation of measurement effort in this situation would maximize the number of randomly selected individuals monitored, but taking more measurements per individual would add nothing. Studies of the relation of childhood cancer to exposure to residential magnetic fields provide a useful example from environmental epidemiology. Initial attempts to estimate exposure quantitatively in the 1980s were based on shortterm spot measurements a few minutes in duration in participants homes [Savitz et al., 1988]. In subsequent studies conducted in the 1990s, researchers employed new technology in attempts to improve the estimation of exposure by monitoring residential magnetic field levels over a longer period of 24 hr [London et al., 1991; Linet et al., 1997] and by restricting studies to participants with stable addresses in order to reduce the number of houses involved and thereby make it more feasible to obtain a quantitative exposure measurement for every subject [Linet et al., 1997]. A recent methodological study showed that spot measurements resulted in a misclassification rate of 36%, and the authors concluded that these measurements were not to be recommended because of high-diurnal variability [Banks et al., 2002]. The magnetic field investigators approach to improving exposure estimation illustrates a common decision that emphasizes obtaining data for every participant at the expense of assessing temporal variability. For most situations, however, the optimal exposure assessment strategy would involve distributing the sampling effort to achieve a balance between maximizing the number of people monitored to account for between-person variability and maximizing the temporal detail of the data collected for each person monitored to capture within-person variation [Phillips and Smith, 1993]. Meta-analyses of research on magnetic fields and childhood cancer suggest that the effort to improve the quality of exposure data in this research area may have achieved some success. An authoritative review issued in 1997 noted a paradoxical finding that in the studies then available, cancer risk was associated less strongly with quantitative indicators of magnetic field intensity based on short-term quantitative measurements than with a surrogate indicator derived from

6 118 Loomis and Kromhout outdoor wiring configurations [National Research Council, 1997]. The paradox appeared to be resolved by later studies that estimated individual exposures from 24 hr residential monitoring data, which would presumably be more temporally stable than spot measurements. Whereas, on average, studies that estimated exposure from spot measurements suggested no association with childhood leukemia (odds ratio 1.0), those using 24 hr measurements yielded odds ratios between 1.3 and 1.7 [Loomis et al., 1999]. Although these results suggest that the adoption of 24-hr monitoring improved the quality of exposure assessment, even this strategy would be optimal only if magnetic field levels did not vary on a time scale longer than 1 day. If there were significant dayto-day variation, it would be preferable to obtain several exposure measurements on different days for each participant. Banks et al. [2002] showed that a 2-week measurement regime improved exposure classification slightly when compared to 24 hr measurements, but concluded that the added intrusiveness and cost were likely to outweigh the improvement in precision. Pilot studies are an excellent way to gather the information needed to optimize exposure assessment strategies. These pilot studies should include assessment of a representative sample of the study population, with participants chosen among all relevant exposure categories and repeated random sampling of each individual. This allows a preliminary analysis of the components of exposure variability before undertaking a large field study. A final exposure assessment strategy can then be developed based on the pilot study findings. A detailed discussion of the principles of designing exposure assessment studies for epidemiologic research is beyond the scope of this paper, but exceptionally clear explanations were given as early as the 1950s [Oldham and Roach, 1952; Ashford, 1958]. ASSIGNING EXPOSURE ESTIMATES Once exposure information is obtained, it must be used to assign estimates of exposure to study participants. Exposure values can be assigned in many forms, ranging from binary to fully quantitative. The sources and magnitude of exposure variability are among the factors that should be considered in selecting the exposure assignment method. Individual- Versus Group-Based Assignments The situation where quantitative exposure data are available for each individual, although not always realized in practice, provides the clearest illustration of the principles involved. When exposure has been assessed for each subject, there are two basic options for assigning estimated exposures. The most intuitively transparent is the individualbased strategy, in which the exposure of each subject is estimated directly using his or her own data alone. This type of exposure assignment strategy is the norm in studies when the investigators have been able to contact each participant to obtain exposure information by measurement or interview, as in many case-control and prospective cohort studies. The principal alternative is a group-based exposure assignment strategy. With this method, subgroups of people are constructed based on common factors like job title, task, or plant. Each subgroup s mean exposure is then estimated from a sample and this metric is applied to all individuals in the subgroup. This method of assigning exposures is common in occupational studies where historical design or logistical problems prevent measurement of each worker. In such cases, the use of group exposure assessments based on such characteristics as job title, task, or environment is the norm [Checkoway et al., 1986]. Although group-based designs are well-known when dealing with quantitative exposure data, the same principle has also been used for interview data, for instance when population-based jobexposure matrices are elaborated from exposure scores from interviews with individuals sharing the same job [Kromhout et al., 1992; Post et al., 1994]. It is often assumed that individual-based methods of assigning exposure are preferable whenever the requisite data are available. However, estimates of exposure-disease association can be severely attenuated when the temporal component of exposure variability within people is large relative to that between people. Different methods for exposure assignment were compared in a recent study on exposure to carbon black and lung function among manufacturing workers [van Tongeren et al., 1999]. The overall betweenworker variability was smaller than the temporal (day-today) variability in exposure concentrations and it was estimated that the observed slope would be attenuated by 38% for inhalable dust and 59% for respirable dust with exposure assigned on an individual basis. On the contrary, group-based assignments resulted in negligible attenuation. This relationship may be shown by the equation ¼ =ð1 þ =nþ, where b and b* are, respectively, the regression coefficients on true and observed exposure, n is the number of exposure measurements per person, and l is the ratio of the within- and between-person components of exposure variance, 2 w /2 b [Cochran, 1968; Liu et al., 1978]. The potential magnitude of the resulting attenuation was illustrated by analyses by Heederik and Attfield [2000] using data from a study of coal miners that provided an average of 31 individual exposure measurements for each worker. When the lung function data were re-analyzed using only a sample of the repeated exposure measurements for each worker, the observed 11-year decrement in lung function associated with a 1 mg/m 3 average coal dust exposure became progressively more attenuated as the number of exposure measurements was reduced (Table I). This type of attenuation can be re-

7 Exposure Variability: Concepts and Applications 119 TABLE I. Attenuation of the Regression Coefficient Expressing the Association of Individual Mean Coal Dust Exposure and Change in Lung Function (FEV 1 ) in Relation to the Number of Exposure Measurements Available per Worker Dust measurements per worker FEV 1 (ml) per mg/m 3 (b) SE a b/se a All available (n ffi 36,000) Based on National Study of Coal Workers Pneumoconiosis, 1969^1981, a study of 1,105 coal miners with adjustments for age, height, and smoking [from Heederik and Attfield, 2000]. a SE, standard error; b, regression coefficient for change in FEV 1 (ml) per mg/m 3 of coal dust exposure. duced in the design phase by minimizing the ratio l/n, either by increasing the number of exposure measurements per person, n, or by increasing 2 b by selecting the study population so that the inter-individual range in exposure is broadened. Substitution of a group-based exposure-assignment scheme in the analysis phase of the study may be more effective, especially when temporal variability is large. Recent methodological research shows that in most cases validity can be substantially improved by reducing attenuation though the use of group-, rather than individual-based exposure assignments [Kromhout et al., 1996; 1997; Tielemans et al., 1998]. Group-based strategies may also be preferable for practical reasons, as they tend to be logistically less demanding than individual measurement. Group-based exposure assignments are often the only kind possible in historical studies of occupational cohorts, where the available exposure data consist exclusively of area measurements representing the average exposure of groups of workers in the same section of a plant or company [e.g., Dement et al., 1983; Burstyn et al., 2000]. A disadvantage of group-based assignments, however, is that they may provide poorer statistical precision than an individual assignment using the same data [Preller et al., 1995; Seixas and Sheppard, 1996]. Validity of the exposure response relation is the more important consideration, however [Kupper, 1984]. Seixas and Sheppard [1996] proposed an alternative exposure estimator based on an empirical-bayes approach, which weights individual and group estimates of mean exposure to obtain a single exposure indicator with optimal precision and bias. Although this indicator has not been tested extensively, a study by Vermeulen et al. [2002] demonstrates how it combines the strengths of both assignment strategies. Modeling Exposures Empirical statistical modeling can sometimes be used to improve the estimation of exposure in situations where direct measurements are sparse or unstable. To obtain such exposure estimates, multiple regression models are constructed to predict measured exposure (typically log-transformed) as a function of readily observable determinants like location, activity, or job title. The predicted values from these regressions are then assigned as estimates of exposure. As an example, Preller et al. [1995] found large withinperson variation in pig farmers exposure to endotoxins due to the non-routine nature of the farmers work schedules. They then used information on tasks performed and workplace characteristics (flooring, feeding system, etc.) from activity diaries and repeated measurements of endotoxins to develop statistical models that explained the temporal variability in exposure. Consequently, information from activity diaries, which were kept for several weeks, and the statistical models were used to estimate more precise longterm average exposures. The modeled exposure estimates yielded clear exposure response relationships with lung function, whereas no exposure response relationship was observed when individual exposure measurements were used directly. Wameling et al. [2000] recently provided theoretical proof for the use of this method. INTERPRETING RESULTS Exposure variability can influence the quantitative results of an epidemiologic study when data on exposure and health outcomes are finally linked and analyzed to elucidate the relationship of exposure and risk. Observed indicators of exposure-disease association, like the rate ratio or odds ratio, can be affected by the sources and magnitude of variation of exposure in the populations under study, as well as by the way in which that variability is handled in assigning exposure estimates. The statistical and epidemiological literature concerning measurement error provides important concepts and methods for understanding exposure variability and its consequences. As used in the literature, the term measurement error actually describes two distinct phenomena. Classical, statistical measurement error refers to uncertainty introduced by natural, random variation of the quantity being measured. In epidemiologic research, this type of error is associated with the sampling process. For example, if samples taken on several randomly selected days are used to estimate an individual s mean dermal exposure to pesticides, that estimate will be associated with a certain amount of uncertainty about the mean that can be described by the variance of the measurements. This uncertainty is an important component of the total error in measuring exposure and consequently a potentially important source of bias in epidemiologic results.

8 120 Loomis and Kromhout Analytical error, the second class of measurement error, is a tendency of measuring instruments to produce incorrect values, whose distribution may be random or systematic. Systematic analytical error can, for example, be introduced by the inability to measure exposures below a minimum detectable value. For most environmental measurements, analytical error is small relative to the imprecision resulting from natural temporal and spatial variation. In the absence of analytical error, a high ratio of within- to between-person exposure variability can attenuate estimated exposure-disease associations, as shown in Table I. The dust levels in the coal mines investigated in that example are highly variable over time and space, so the ability of the study to detect an effect depends on having a large number of exposure measurements for each worker. To illustrate, if only three exposure measurements per worker had been available, the regression coefficient would have been non-statistically significant and so severely attenuated as to compromise the sensitivity of the study [Heederik and Attfield, 2000]. Although inadequate, three exposure measurements per worker is nevertheless more than the number available in most studies. The potential effect of insufficient exposure information is usually difficult to gauge directly because of the limited data available for each person. Many epidemiologic studies use categorical, rather than continuous, exposure scores in the analysis. In such studies, the mechanism of misclassification is relevant [Copeland et al., 1977]. Misclassification is a special case of measurement error that applies when the exposure variable used in the analysis is categorical; it can arise from both classical, random statistical error [Flegal et al., 1991] and from analytical inaccuracy. When those estimates are used in turn to assign individuals to exposure categories, the probability that they will be misclassified depends in part on the magnitude of the underlying within-person variability. To illustrate this dependence, we computed the probabilities of correctly classifying the exposures of a simulated population of 1,000 workers, assuming a dichotomous exposure variable and a range of values for S b and S w. For any given level of variability between people, larger withinperson variability is associated with lower sensitivity and specificity, and thereby increased probability that an individual will be misclassified (Table II). Greater variability between people has the opposite effect: for a given level of within-person variability, greater between-person variability is associated with higher probabilities of correct classification (Table II). The probability of misclassification can also be reduced by taking more measurements for each person, but pattern of effects associated with the balance of S b and S w remains the same. When categorical exposure variables are assigned with error, as in Table II, the resulting misclassification can be differential by disease status if true exposure and disease risk are quantitatively related [Flegal et al., 1991]. Such differential misclassification often causes estimates of exposure-disease association to be attenuated, but exaggeration and reversal of associations are also possible [Brenner and Loomis, 1994; Wacholder, 1995]. Knowledge about the TABLE II. Influence of Within-Person Exposure Variability on Probability of Exposure Misclassification, When Long-Term True Mean Exposure for an Individual Is Estimated From Short-Term Measurements Probability of correct classification a Cutpoint 0.0 Cutpoint1.0 S w ¼ 0.5 S w ¼1.0 S w ¼ 2.0 S w ¼ 0.5 S w ¼1.0 S w ¼ 2.0 S b b ¼ 0.5 Se c Sp c S b ¼1.0 Se Sp S b ¼ 2.0 Se Sp a Simulated data assuming normally distributed exposure with mean ¼ 0 and standard deviation S b, with exposure for each person measured on one randomly selected day. Exposure groups formed by dichotomizing observed individual means at cutpoints of 0.0 and1.0. b S w, within-person component of exposure standard deviation; S b, between-person component of exposure standard deviation. c Sensitivity, Se, and specificity, Sp, of exposure classification, defined as the proportion classified as exposed among those with true exposure exceeding the cutpoint (sensitivity), and the proportion classified as unexposed among those with true exposures below the cutpoint (specificity).

9 Exposure Variability: Concepts and Applications 121 relative magnitude of exposure variability within and between people can be used to qualitatively assess the chances that exposure will be misclassified when individuals are assigned to exposure groups. In this discussion, we have focused on the consequences of error in measuring and assigning exposure in an epidemiologic study. Covariates of exposure can vary in similar ways and can also be measured with error, but we have not considered errors in covariates because the principles involved are the same. It should be noted, however, that error in measuring covariates that act as confounders may result in residual confounding and biased estimation of the exposure-disease association [Greenland, 1980]. CONCLUSIONS Exposure levels vary along several dimensions defined by person, space, and time. The existence of a gradient of exposure between populations is essential to many types of epidemiologic research. Nevertheless, the structure and magnitude of exposure variation on other dimensions are not always recognized or exploited to full advantage. In particular, the existence of a range of exposures within study groups and of temporal variation of exposure levels within individuals are often neglected. As a result, investigators sometimes concentrate resources on obtaining exposure data for each study participant at the expense of characterizing within-person variability. Exposure variability should be considered carefully in the planning, analysis, and interpretation of epidemiologic studies. Failure to do so can reduce study sensitivity and efficiency and may introduce bias. Attention to exposure variation and its multiple dimensions can lead to more meaningful characterization of exposure itself, and, most importantly, improve the chances that epidemiologic studies identify and accurately characterize health hazards. 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