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OBJECTIVES: To investigate the statistical efficiency of strategies for sampling upper arm elevation data, which differed with respect to sample sizes and sample allocations within and across measurement days. The study was also designed to compare standard theoretical predictions of sampling efficiency, which rely on several assumptions about the data structure, with 'true' efficiency as determined by bootstrap simulations.

METHODS: Sixty-five sampling strategies were investigated using a data set containing minute-by-minute values of average right upper arm elevation, percentage of time with an arm elevated <15°, and percentage of time with an arm elevated >90° in a population of 23 house painters, 23 car mechanics, and 26 machinists, all followed for four full working days. Total sample times per subject between 30 and 240 min were subdivided into continuous time blocks between 1 and 240 min long, allocated to 1 or 4 days per subject. Within day(s), blocks were distributed using either a random or a fixed-interval principle. Sampling efficiency was expressed in terms of the variance of estimated mean exposure values of 20 subjects and assessed using standard theoretical models assuming independence between variables and homoscedasticity. Theoretical performance was compared to empirical efficiencies obtained by a nonparametric bootstrapping procedure.

RESULTS: We found the assumptions of independence and homoscedasticity in the theoretical model to be violated, most notably expressed through an autocorrelation between measurement units within working days. The empirical variance of the mean exposure estimates decreased, i.e. sampling efficiency increased, for sampling strategies where measurements were distributed widely across time. Thus, the most efficient allocation strategy was to organize a sample into 1-min block collected at fixed time intervals across 4 days. Theoretical estimates of efficiency generally agreed with empirical variances if the sample was allocated into small blocks, while for larger block sizes, the empirical 'true' variance was considerably larger than predicted by theory. Theory overestimated efficiency in particular for strategies with short total sample times per subject.

CONCLUSIONS: This study demonstrates that when exposure data are autocorrelated within days-which we argue is the major reason why theory overestimates sampling performance-sampling efficiency can be improved by distributing the sample widely across the day or across days, preferably using a fixed-interval strategy. While this guidance is particularly valid when small proportions of working days are assessed, we generally recommend collecting more data than suggested by theory if a certain precision of the resulting exposure estimate is needed. More data per se give a better precision and sampling larger proportion(s) of the working day(s) also alleviate the negative effects of possible autocorrelation in data.

Background: Information on exposure variability, expressed as exposure variance components, is of vital use in occupational epidemiology, including informed risk control and efficient study design. While accurate and precise estimates of the variance components are desirable in such cases, very little research has been devoted to understanding the performance of data sampling strategies designed specifically to determine the size and structure of exposure variability. The aim of this study was to investigate the accuracy and precision of estimators of between-subjects, between-days and within-day variance components obtained by sampling strategies differing with respect to number of subjects, total sampling time per subject, number of days per subject and the size of individual sampling periods.

Methods: Minute-by-minute values of average elevation, percentage time above 90 degrees and percentage time below 15 degrees were calculated in a data set consisting of measurements of right upper arm elevation during four full shifts from each of 23 car mechanics. Based on this parent data, bootstrapping was used to simulate sampling with 80 different combinations of the number of subjects (10, 20), total sampling time per subject (60, 120, 240, 480 minutes), number of days per subject (2, 4), and size of sampling periods (blocks) within days (1, 15, 60, 240 minutes). Accuracy (absence of bias) and precision (prediction intervals) of the variance component estimators were assessed for each simulated sampling strategy.

Results: Sampling in small blocks within days resulted in essentially unbiased variance components. For a specific total sampling time per subject, and in particular if this time was small, increasing the block size resulted in an increasing bias, primarily of the between-days and the within-days variance components. Prediction intervals were in general wide, and even more so at larger block sizes. Distributing sampling time across more days gave in general more precise variance component estimates, but also reduced accuracy in some cases.

Conclusions: Variance components estimated from small samples of exposure data within working days may be both inaccurate and imprecise, in particular if sampling is laid out in large consecutive time blocks. In order to estimate variance components with a satisfying accuracy and precision, for instance for arriving at trustworthy power calculations in a planned intervention study, larger samples of data will be required than for estimating an exposure mean value with a corresponding certainty.

Ergonomics studies comparing working postures and movements between independent groups are often based on observations. The present paper derives and exemplifies procedures for estimating the statistical power of such studies, addressing the effect of different strategies for allocating observations within and between observers. In the simple case of one observer rating the postures of all subjects in the study one or multiple times, a simple t-test is appropriate for testing the group difference, while statistical models acknowledging rating differences between observers are needed when multiple observers are involved. In the one-observer case, analytical power calculations are feasible, while a parametric bootstrapping approach is suggested and practiced in the paper for the multiple-observers case. Using empirical data from a previous study of postures among hairdressers observed from video recordings (percentages of time with the right upper arm elevated less than 15° and more than 90°), the study demonstrates that a considerable gain in power can be obtained by having one observer doing multiple repeated observations as compared to rating postures only once. Distributing a certain number of video recordings between multiple observers resulted in a loss of power when a simple t-test was used to test the group difference, but the comparison could be accomplished without loss of power if all observers were involved in rating both of the compared groups and the statistical model used to analyze data acknowledged variability in rating between observers. When different observers assessed the two compared groups, power decreased considerably. Thus, the study gives guidance for efficient design of posture observation studies comparing groups, as well as for appropriate statistical procedures for analyzing the data.

Objectives: Many occupational exposure variables can be measured using different instruments, of which some can be considered inferior in terms of precision and/or accuracy while others have a superior performance. Thus, working postures can be assessed by observation, which is known to be associated with errors, while direct measurements using inclinometers are assumed to represent a “golden standard”. A possible bias in results obtained by the ”inferior” instrument can be corrected using regression calibration, but the statistical consequences of this procedure are not fully understood. This paper develops procedures for evaluating the precision of an estimate of “true” exposure after calibration, and illustrates them using data from a study of observed upper arm elevation versus corresponding inclinometer measurements.

Methods: Three random coefficient models for estimating the relationship between inferior (observations) and superior (inclinometer) measurements were constructed, taking methodological (observer) variability into account to different extents. Expressions for estimating the uncertainty of a calibrated exposure (posture) mean value were derived, which identify the specific contributions from sample uncertainty and uncertainty associated with determining the calibration parameters.

Results: In the example of posture observations, calibration introduced an uncertainty that outweighed the size of the observation bias. Thus, this proved to be an example of calibration not always being appropriate, i.e. in case the trade-off between bias correction and increased uncertainty is unfavorable.

Conclusions: Calibration of inferior measurements can be a viable tool to correct for bias, but it may add a considerable uncertainty to the eventual mean exposure estimate. Thus, the trade-off between these two calibration effects needs to be considered in each specific case, and further research is needed on the determinants of the trade-off.