Bias in risk estimates from variability of exposure to postural load on the back in occupational

BURDORFA. Bias in risk estimates from variability of exposure to postural load on the back in oc cupational groups. Scand J Work Environ Health 1993;19:50-4. Variability of exposure can be a source of information bias in studies with exposure assessment based on the use of a sample of work ers in each occupational group under study. This paper presents a method to assess the rate of expo sure misclassification from the magnitude of overlap of exposure distributions and, consequently, to evaluate the bias to risk estimates in cross-sectional and prospective studies. The percentage of work time with trunk flexion and rotation was studied in five occupational groups. The rate of misclassifi cation of exposure to trunk flexion and rotation varied from 0.03 to 0.35. Misclassification below0.10 was found only for occupational groups with at least a 14-fold difference in mean exposure. Higher rates of misclassification can easily bias the risk estimates up to 50%. In the cross-sectional design the odds ratio was more sensitive to bias than the prevalence rate ratio. The estimate of the relative risk in a prospective study design was the least biased.

How ever, information bias can als o occur as a result of the mea surement strategy applied. Th e common approach in cross -sectional studies on low-back pain is to monitor a sample of workers in each occupational group under stud y. When expos ure assessment is not possible for each individu al, measurement s of postural load are used to assi gn expo sure categories to the occupational groups, often on the basis of the workers' mean exposure (2). Subsequently, the prevalen ce of low-back pain is compa red amon g groups with different expos ure status . In th is grouping strategy, inherent mi sclassifi cation of expo sure will occur if the occ upationa l groups sho w overl apping distribution s of mean ex posures in each occupational group. A similar problem may ari se in prospective studies on incident cas es of low-back pain in occupational groups when a random sample of workers in eac h occup ational group is being mon itored .
Therefore, va riability of expo sur e among worke rs with in an occupational group can be described in term s of nond ifferential m isclassification of exposure. Hence, it is important to know the magnitude of overlap of the exposure distributions. In th is paper, the rate of nondifferential mi sclassification of expo sure due to variabil ity of the expos ure among workers has been deri ved from the magnitude of the overl ap in exposure exper ience of two occupational groups. Its imp act on the estimate of the association betw een postural load and low-back pain was investigat ed. The purpose of the analysis was to assess the potential magnitude of bias caused to the risk estimat e by exposure asse ssm ent based on grouping strategi es in cross-sec tional and prospe cti ve studies . health status, the subjects with low-back pain and the subjects without low-back pain have the same exposure sensitivity and specificity. Moreover, in this approach, the exposure sensitivity and specificity are assumed to be equal and can be derived directly from the obtained rate of misclassification. Given the true distribution of the cases and referents by exposure status, and the common value S for exposure sensitivity and specificity, the observed values of the cell frequencies can be calculated by the following equations:

Methods
In cross-sectional studies, the prevalence odds ratio is frequently used to derive a measure of association between exposure and disease. Some authors give preference to the prevalence rate ratio when the prevalence of disease is rather high (10). Since this condition is often true in studies of low-back disorders, for the purpose of the discussion, the effect of exposure misclassification on both measures of risk have been presented.
Exposure misclassification is expressed in table I by a 2 x 2 table of conditional probabilities (II). On the assumption of nondifferential misclassification with regard to exposure status, the probability of being classified correctly as exposed (PI) should be equal to the probability of being classified correctly as unexposed (P(0) . P II is often referred to as exposure sensitivity, and P00 as exposure specificity (II). Under the assumption that the correct classification rate of the exposed and unexposed will be equal (that is P I' = p tX ) , the magnitude of nondifferential misclassification due to exposure variability can be derived from the overlap of exposure distributions of the two occupational groups compared. The probability of a measurement among the unexposed subjects exceeding or equaling a specific value is supposed to be the same as the probability of a measurement among the exposed subjects falling below this value. Essential for estimating this probability is inference about the underlying distributions. The distribution of measurements of aspects of postural load on the back is described best by the log-normal distribution, characterized by the geometric mean (GM) and the geometric standard deviation (GSD) (12). Thus the probability can be obtained by the following equation: The biased prevalence rate ratio is estimated by: In these equations the rate of misclassification is estimated by I -S. The observed values of the cell frequencies can be used to obtain the observed risk estimates. The biased odds ratio is estimated by: A similar approach can be described for a hypothetical prospective study , as pre sented in table 3. A group of workers with high exposure to postural load on the back is compared with an occupational group of workers with low exposure to postural load. Suppose the true incidence rates of low-back pain are 70 per 1000 person-years in the high-exposure group and 30 per 1000 person-years in the low-exposure group. The true distributions of cases and personyears are presented in table 3. Given these figures The value of '«corresponds to the percentile of the distribution of the one-sided Student's t-statistic (13,14). The corresponding probability of a measurement exceeding or equaling this percentile presents the estimate of the misclassification rate y. Note that the misclassification rate y is equal to I-P 11" As a simple illustration of the effect of exposure rnisclassification, consider the hypothetical data presented for a cross-sectional study in table 2. An occupational group of 200 (11,) subjects with high exposure to postural load on the back is compared with an occupational group of 200 (11 0) subjects with low exposure to postural load on the back. The measure of disease is the 12-month prevalence of low-back pain . In this example the overall prevalence of lowback pain is 40% among the total population. The prevalence of low-back pain among the subjects with high exposure is atn ; among the subjects with low exposure it is cln o. By definition, when the exposure misclassification is nondifferential with regard to Table 3. True distribution of incident cases of low-back pain and exposure to postural load in a prospectivedesign. and the common value S for expos ure sen sit ivity and spec ifici ty, the obs erved number of cases and subsequent person-years of exposure can be calculated by the follo wing equations:

Exposure status
High (1) Low (0) the group with the lowest exposure being used as the reference.
To invest igate the effect of exposure miscl assification on the risk estimates in a cross-sectional stud y, an overall prevalence of low-back pain of 40% among the 200 subjects in the high-exposure group and 200 subjects in the low-exposure group was used . Different distributions of workers with lowba ck pain by ex pos ure status were evaluated, which yie lded values of true odd s ratios clo se to 1.50, 2.25, and 3.00, and associated true pre valence rate ratios .
For three rat es of misclassification the biased odd s ratio s and prev alence rate ratios were calculated. An ana logous analysis was made for a prospective desig n using hypothetical dat a accord ing to the format of table 3. The true relative risks were 1.50, 2.33, and 3.00, and the same thr ee rate s of miscl assification were evaluated.
Th e bia sed relative risk is estimated by : Empirical data of a survey on workers ' distributions of exposure to po stural load in five different occupational groups have been used to estimate different rates of misclassification. The principle measure of exposure was th e percentage of worktime with trunk flexion or trunk rotation (12). Straddlecarrier dr ivers were found to be the occ upationa l group with the lo west ex pos ure to trunk flexion , and crane oper ators formed the occupational group with the lowest exposure to trunk rotation. Th e magnitude of the overlap of the workers' ex posure distributions has been ca lculated for each occup ational title group,

Results
In tabl e 4 the workers ' di stributi on s of expo sure to trunk fle xion and trunk rotation are presen ted , charact erized by their geometric mean and geometric standard deviation. With regard to ex pos ure to trunk flexion , the group of straddle-carrier driver s was used for referen ce. When the four occupational title groups were compared with this reference group, the application of equ ation 1 yielded rates of miscl assification varying from 0.15 to 0.35, For exposure to trunk rotation the rat es of misclassification varied from 0.03 to 0.31, when the four occupational titl e groups we re compared with the group of crane operato rs. It can also be noted that considerable rat es of miscla ssific ation can occur, although the occupational title gro ups can have cle arly different values of worke rs' mean expo sure to trunk fle xion or trunk rot ation.
In tabl e 5 hypothetical data sim ilar to the data giv en in tabl e 2 have been used to illu str ate the ex-  status. In this approach the nondifferential misclassification is solely due to the variability in exposure within an occupational group.
In this study the rates of misclassification of exposure to trunk flexion and rotation varied from 0.03 to 0.35. Misclassification below 10% was found only in compari sons of occupational groups with at least a 14-fold level of exposure, compared with the lowexposure group. The high rates of miscla ssification reflect the considerable variance in exposure between workers in the same group and between parts of a shift within workers (12). Under the assumption that the exposure variability and the concomitant concept of a log-normal distribution can be generalized to other occupational group s and work situations, misclassification of postural load due to nonneutral postures is easily obtained .
Attenuation of the risk estimate caused by exposure misclassification is demonstrated in tables 5 and 6. In the cross-sectional approach the odds ratio was more sensitive to bias than the prevalence rate ratio. The relative risk in the prospective approach showed the least bias. In the case of a dichotomous exposure categorization nondifferential misclassification of exposure always biases a true effect toward the null value. The foregoing approach to estimate the amount of bias can be extended to the more general case of more than two exposure categories. In specific cases it can be demon strated that the bias due to nondifferential misclassification of exposure is not necessarily downward when a polychotomous exposure measure is used (6).
In this study the misclassification of exposure was limited to a main measure of exposure to postural load and its effect on the risk estimate for this exposure . In many occupational situation s workers are exposed to several risk factors of postural load, such as rotation of the trunk , lifting, and forceful movements. There is no reason to belie ve that miscla ssification of exposure to these confounding factors will not occur. An assessment of the possible effect of confounder misclassification can be achieved with a similar approach for evaluating the nondifferential misclassification of the main exposure variable. Recently, Ahlborn & Steineck (15) pointed out that misclassification of the confounding (exposure ) factor can be of particular importance. In their example control for a confounding variable, subject to a considerable amount of misclassification, led to a strong overestimate of the true exposure-dise ase association tent of bias due to nondifferential misclassification of exposure in a cross-sectional study. The true odds ratio for low-back pain due to aspects of postural load was obtained simply from the marginal totals of a 2 x 2 table. When nondifferential misclassification of exposure is accounted for, the true odds ratio markedly decrease s. For example, the true odds ratio is 2.23, whereas the observed odds ratio under the condition of 10% misclassification of exposure is only 1.89. Two points are noteworthy. First, when the true odds ratio increase s, the bias introdu ced by the misclassification of exposure also increases. Second, higher rates of misclassification more strongly bias the odds ratio towards unity. With regard to the true prevalence rate ratio, the magnitude of the bias to the prevalence rate ratio also depends on the actual prevalence of the health outcome . The degree to which the prevalence rate ratio is underestimated is smaller than the bias in the odds ratio.
In table 6 the bias to the relative risk in a prospective study design is illustrated . Again , the observed relative risk decrea ses with a higher rate of misclassification . The magnitude of the bias in the estimated relative risk in the prospective design is slightly less than that of the bias in the estimated prevalence rate ratio in the cross-sectional design.

Discussion
Frequently, in occupational epidemiology on lowback disorders, the prevalence of these disorders is compared between occupational title groups. Whenever objective measurement techniques for postural load have been used, a random sample of workers in each occupational group is often monitored. The average values of the parameters measured are used to chara cterize the exposure to postural load in the occupational title groups (2). In fact , worker s who have not been monitored are assigned the mean exposure of their occupational group .
Two occupational groups can have significantly different values for their mean exposure and thereby suggest a clear difference in exposure status. However , large variability of exposure within each group can result in overlapping exposure distributions and thus in misclassification of exposure. The variability of exposure within each occupational group is due to within-worker and between -worker variance. Information on the underlying distributions is essential for estimating the magnitude of the overlap. An extensive measurement program of the percentage workt ime spent in trunk flexion and trunk rotation in five different occupational groups revealed that these aspects of exposure to postural load were best described by log-normal distributions (12). Hence , it was possible to draw inferences about the magnitude of overlap between two exposure distributions. The area of overlap presents a fruitful estimate of the rate of misclassification of exposure that is nondifferential to both exposure status and disease Scand J Work Environ Health 1993, vol 19, no I measured by the incidence rate ratio. This observation clearly shows that the influence of the variability of exposure on misclassification must not be restricted to the main exposure variable of interest, but should also include the confounding exposure variables. This paper has attempted to demonstrate a practical approach for assessing possible bias in cross-sectional and prospective studies on the basis of a comparison of two occupational groups with overlapping exposure distributions. The approach is only valid when the exposure sensitivity and specificity are assumed to be equal. If this assumption is being met, the presented method allows a direct estimation of the extent of misclassification of exposure and its effect on the attenuation of the risk estimate. This approach only requires empirical data on the distributions of exposure in the occupational groups under study. The primary importance of the procedure is that the assessment of exposure misclassification may guide researchers towards improving measurement strategies to decrease the estimated rate of misclassification. In some studies the conclusion could be inevitable that grouping by job title is inadequate. In other studies it may be necessary to collect exposure data on the individual level. Of less importance is the application of this procedure to adjust or "correct" the observed effect estimate for the amount of exposure misclassification due to exposure variability. Simultaneous presentation of the observed risk estimates and the adjusted "true" risk estimates offers the reader insight into the bias associated with the sources of variability.