[The biological monitoring of those exposed to 1,1,1-trichloroethane: a longitudinal study].
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Data on long-term biological monitoring in two groups of workers engaged in cleaning operations in a wool factory and exposed to methylchloroform are presented. The longitudinal survey lasted one year and brought about 19 random systematic sampling (once or twice a month for everyone of the 13 subjects monitored). The biological marker adopted was the urinary concentration of the solvent as such, according to a previously studied method. The collected data allowed to measure: the annual average level of exposure (estimated by the long term geometric mean); the day to day variation of the true daily exposure averages (estimated by the geometric standard deviation); the probability of overexposure (daily exposures exceeding the biological exposure limit) and the yearly number of work shifts of overexposure. The usefulness of performing long-term surveys of occupational exposure to the chemical substances by mean of longitudinal biological monitoring is discussed.Keywords:
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Measurements of 8-hr time-weighted average (TWA) exposures are subject to environmental variability and collection and analytical error. Environmental variability can be represented by the geometric standard deviation (GSD) of the lognormally distributed 8-hr TWAs; analytical variability can be represented by the coefficient of variation (CV) of the normally distributed collection and analytical errors. A mathematical expression is derived for the variance of the measured 8-hr TWAs as a function of the GSD of the true daily average exposures and the total CV of the industrial hygiene method used in monitoring. For typical values of the GSD and CV, environmental variability is far more important than analytical variability in determining the variance of the measured 8-hr TWAs. A resulting policy implication is that the Occupational Safety and Health Administration inappropriately focuses on analytical variability when determining compliance with its permissible exposure limits.
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Formulae are presented for calculating the approximate sample size needed to estimate the true arithmetic mean or true geometric mean exposure for an exposure group to within a specified accuracy (±x% of the true arithmetic or geometric mean) with a specified level of confidence. These formulae are intended for use in prospective or cross-sectional occupational health studies, or when building an exposure database for use in assessing long-term changes in worker health status. They are applicable where the investigator is satisfied that the distribution of exposures within a group can be approximated by a lognormal distribution. The formulae were validated by computer simulation and show that large sample sizes are required when the existing parameter estimates were derived from a limited number of prior measurements and/or the true exposure distribution has a large geometric standard deviation. When summed across all exposure groups, an unreasonable total sample size may result. The total sample burden can be reduced in several ways: (1) A pilot study should be used to provide reasonably precise initial estimates of the distribution parameters for each exposure group. This may require 20 or more measurements per group. (2) Workers should be grouped into exposure groups where the group geometric standard deviation is two or less. (3) The desired accuracy should be kept at a reasonable level, perhaps between 20 and 30% of the true parameter. Accuracy levels less than 20% can result in large total sample size requirements.
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A measure of dispersion is a statistical tool used to define the distribution of various datasets mainly from measures of central tendency. Some notable measures of dispersion from the mean are; average deviation, mean deviation, variance, and standard deviation. However, from previousstudies, it has been established that the aforementioned measures are not absolutely perfect in estimating average variation from the mean. For instance, variance gives estimates which are of different units of measurements (squared) from the original dataset’s unit of measurement. In the case of mean deviation, it gives a large average deviation than the actual deviation due to its conformation to the triangular inequality, whereas standard deviation is affected by outliers and skewed datasets. The aim of this study was to estimate variation about the mean using a technique that would overcome the weaknesses of other global measures. The study employed the geometricaveraging technique to average deviation from the mean, which averages absolute products and not sums and it is nonresponsive to outliers and skewed datasets. The study formulated a geometric measure of variation for unweighted and weighted datasets, and probability mass and density functions. Using the formulations, the estimates of the average variation from the mean for thegiven datasets and probability distributions were computed. From the results established that the estimates obtained by the geometric measures were significantly smaller as compared to those obtained by standard deviation. In terms of efficiency, the measure was more efficient compared to standard deviation is estimating average variation about the mean for geometric, skewed and peaked datasets.
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Measure of dispersion is an important statistical tool used to illustrate the distribution of datasets.The use of this measure has allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers have been able to develop measures of dispersion from the mean such as mean deviation, mean absolute deviation, variance and standard deviation. Studies have shown that standard deviation is currently the most efficient measure of variation about the mean and the most popularly used measure of variation about the mean around the world because of its fewer shortcomings. However, studies have also established that standard deviation is not 100% efficient because the measure is affected by outlier in thedatasets and it also assumes symmetry of datasets when estimating the average deviation about the mean a factor that makes it to be responsive to skewed datasets hence giving results which are biased for such datasets. The aim of this study is to make a comparative analysis of the precision of the geometric measure of variation and standard deviation in estimating the average variationabout the mean for various datasets. The study used paired t-test to test the difference in estimates given by the two measures and four measures of efficiency (coefficient of variation, relative efficiency, mean squared error and bias) to assess the efficiency of the measure. The results determined that the estimates of geometric measure were significantly smaller than those of standard deviation and that the geometric measure was more efficient in estimating the average deviation for geometric, skewed and peaked datasets. In conclusion, the geometric measure was not affected by outliers and skewed datasets, hence it was more precise than standard deviation.
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Journal Article The Influence of the Reference Mean Prothrombin Time on the International Normalized Ratio Get access Gregory C. Critchfield, MD, MS, Gregory C. Critchfield, MD, MS 1From the Intermountain Laboratory Data Project, IHC Laboratory Services, Salt Lake City, Utah2Intermountain Laboratory Data Project, Department of Pathology, Utah Valley Regional Medical Center, Provo, Utah3Intermountain Laboratory Data Project, Department of Microbiology, Brigham Young University, Provo, Utah Search for other works by this author on: Oxford Academic Google Scholar Sterling T. Bennett, MD, MS Sterling T. Bennett, MD, MS 1From the Intermountain Laboratory Data Project, IHC Laboratory Services, Salt Lake City, Utah4Intermountain Laboratory Data Project, Department of Pathology, LDS Hospital, Salt Lake City, Utah5Intermountain Laboratory Data Project, Department of Pathology, University of Utah School of Medicine, Salt Lake City, Utah Search for other works by this author on: Oxford Academic Google Scholar American Journal of Clinical Pathology, Volume 102, Issue 6, 1 December 1994, Pages 806–811, https://doi.org/10.1093/ajcp/102.6.806 Published: 01 December 1994 Article history Received: 15 October 1993 Accepted: 21 February 1994 Published: 01 December 1994
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Day-to-day variations of occupational exposures have important implications for the industrial hygienist trying to assess compliance with an occupational exposure limit. As only a limited number of samples are taken during an observation period, extrapolations are required to estimate exposures over the unsampled period. Compliance may be evaluated using estimates of the geometric mean (GM) and the geometric standard deviation (GSD) to calculate a confidence interval around the mean exposure and compare this interval to a limit value, assuming a lognormal distribution of exposures over time. These confidence intervals are very sensitive to the estimate of GSD. Hence, the questions of when to sample and how many samples to take for a reliable assessment of exposure variability (GSD) are the focus of this paper. Analyses of simulated exposure-time series and 420 data sets of personal exposures with three or more measurements obtained from actual workplaces demonstrate that the small number of samples usually collected during surveys leads to biased estimates of the variance of the exposure distribution. There is a high likelihood of an underestimate of variance, which rapidly increases if 8-hr time-weighted average samples are collected on consecutive days or within a week. The results indicate that in 80% of the within-week exposure-time series, the estimated GSD may be too low, even up to a factor of 2. Evidence is presented that autocorrelation is a likely explanation for the bias observed. Because sampling schemes adequate for reliable decision-making require highly unrealistic observation periods and numbers of samples, it is recommended either to use a preliminary GSD (in the Netherlands, a GSD of 2.7 seems a reasonable estimate) or to proceed to a “worst-case” strategy, preferably supported by models.
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A Method for Evaluating Exposure to Nitrous Oxides by Application of Lognormal Distribution: S.S. B orjanovic , et al . Department of Work Physiology, Institute of Occupational Health “Dr Dragomir Karajovic” —A lognormal distribution adequately describes exposure to nitrous oxides in a work environment. The aim of this paper was to assign to the measured data a certain degree of variability which defines the interval in which real concentrations can be found with a given probability. Exposures may be evaluated by using estimates of the geometric mean (GM) and the geometric standard deviation (GSD), i.e. central value and dispersion index, to calculate the confidence interval (Cl) around the mean exposure and compare this interval to the occupational exposure limit. The concentration of nitrous oxides (114 random temporal measurements covering all three shifts, during 6 consecutive days) on coated electrode welding in a car manufacturing plant, was determined with colourimetric direct reading method. Statistical analysis (chi‐square and Kolmogorov‐Smirnov goodness of fit tests, lognormal and Gaussian distribution fitting and Q‐G plots) was performed. The distribution of the nitrous oxides concentration in the work environment studied closely resembled that of lognormal distribution. The geometric mean was 4.098 mg/m 3 , median 4.00 mg/m 3 , geometric standard deviation 1.829 and 95% confidence interval 3.66‐4.58 mg/m 3 . It is possible to apply the computed GSD for evaluation of exposure limits to nitrous oxides in any other work environment, even with only a few measurements.
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Epidemiologic studies examining the risk of cancer among occupational groups exposed to electric fields (EF) and or magnetic fields (MF) have relied on traditional summaries of exposure such as the time weighted arithmetic or geometric mean exposure. Findings from animal and cellular studies support the consideration of alternative measures of exposure capable of capturing threshold and intermittent measures of field strength. The main objective of this study was to identify a series of suitable exposure metrics for an ongoing cancer incidence study in a cohort of Ontario electric utility workers. Principal components analysis (PCA) and correlational analysis were used to explore the relationships within and between series of EF and MF exposure indices. Exposure data were collected using personal monitors worn by a sample of 820 workers which yielded 4247 worker days of measurement data. For both EF and MF, the first axis of the PCA identified a series of intercorrelated indices that included the geometric mean, median and arithmetic mean. A considerable portion of the variability in EF and MF exposures were accounted for by two other principal component axes. The second axes for EF and MF exposures were representative of the standard deviation (standard deviation) and thresholds of field measures. To a lesser extent, the variability in the exposure variable was explained by time dependent indices which consisted of autocorrelations at 5 min lags and average transitions in field strength. Our results suggest that the variability in exposure data can only be accounted for by using several exposure indices, and consequently, a series of metrics should be used when exploring the risk of cancer owing to MF and EF exposure in this cohort. Furthermore, the poor correlations observed between indices of MF and EF reinforce the need to be take both fields into account when assessing the risk of cancer in this occupational group. Bioelectromagnetics 19:140–151, 1998. © 1998 Wiley-Liss, Inc.
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