Paul Hewett

Rating Exposure Control Using Bayesian Decision Analysis

A model is presented for applying Bayesian statistical techniques to the problem of determining, from the usual limited number of exposure measurements, whether the exposure profile for a similar exposure group can be considered a Category 0, 1, 2, 3, or 4 exposure. The categories were adapted from the AIHA exposure category scheme and refer to (0) negligible or trivial exposure (i.e., the true X 0.95 < 1%OEL), (1) highly controlled (i.e., X 0.95 < 10%OEL), (2) well controlled (i.e., X 0.95 < 50%OEL), (3) controlled (i.e., X 0.95 < 100%OEL), or (4) poorly controlled (i.e., X0.95 > 1%OEL) exposures. Unlike conventional statistical methods applied to exposure data, Bayesian statistical techniques can be adapted to explicitly take into account professional judgment or other sources of information. The analysis output consists of a distribution (i.e., set) of decision probabilities: e.g., 1%, 80%, 12%, 5%, and 2% probability that the exposure profile is a Category 0, 1, 2, 3, or 4 exposure. By inspection of these decision probabilities, rather than the often difficult to interpret point estimates (e.g., the sample 95th percentile exposure) and confidence intervals, a risk manager can be better positioned to arrive at an effective (i.e., correct) and efficient decision. Bayesian decision methods are based on the concepts of prior, likelihood, and posterior distributions of decision probabilities. The prior decision distribution represents what an industrial hygienist knows about this type of operation, using professional judgment; company, industry, or trade organization experience; historical or surrogate exposure data; or exposure modeling predictions. The likelihood decision distribution represents the decision probabilities based on an analysis of only the current data. The posterior decision distribution is derived by mathematically combining the functions underlying the prior and likelihood decision distributions, and represents the final decision probabilities. Advantages of Bayesian decision analysis include: (a) decision probabilities are easier to understand by risk managers and employees; (b) prior data, professional judgment, or modeling information can be objectively incorporated into the decision-making process; (c) decisions can be made with greater certainty; (d) the decision analysis can be constrained to a more realistic “parameter space” (i.e., the range of plausible values for the true geometric mean and geometric standard deviation); and (e) fewer measurements are necessary whenever the prior distribution is well defined and the process is fairly stable. Furthermore, Bayesian decision analysis provides an obvious feedback mechanism that can be used by an industrial hygienist to improve professional judgment. For example, if the likelihood decision distribution is inconsistent with the prior decision distribution then it is likely that either a significant process change has occurred or the industrial hygienists initial judgment was incorrect. In either case, the industrial hygienist should readjust his judgment regarding this operation.

An Accurate Substitution Method for Analyzing Censored Data

When analyzing censored datasets, where one or more measurements are below the limit of detection (LOD), the maximum likelihood estimation (MLE) method is often considered the gold standard for estimating the GM and GSD of the underlying exposure profile. A new and relatively simple substitution method, called β -substitution, is presented and compared with the MLE method and the common substitution methods (LOD/2 and LOD/√2 substitution) when analyzing a left-censored dataset with either single or multiple censoring points. A computer program was used to generate censored exposure datasets for various combinations of true geometric standard deviation (1.2 to 4), percent censoring (1% to 50%), and sample size (5 to 19 and 20 to 100). Each method was used to estimate four parameters of the lognormal distribution: (1) the geometric mean, GM; (2) geometric standard deviation, GSD; (3) 95th percentile, and (4) Mean for the censored datasets. When estimating the GM and GSD, the bias and root mean square error (rMSE) for the β -substitution method closely matched those for the MLE method, differing by only a small amount, which decreased with increasing sample size. When estimating the Mean and 95th percentile the β -substitution method bias results closely matched or bettered those for the MLE method. In addition, the overall imprecision, as indicated by the rMSE, was similar to that of the MLE method when estimating the GM, GSD, 95th percentile, and Mean. The bias for the common substitution methods was highly variable, depending strongly on the range of GSD values. The β-substitution method produced results comparable to the MLE method and is considerably easier to calculate, making it an attractive alternative. In terms of bias it is clearly superior to the commonly used LOD/2 and LOD/√2 substitution methods. The rMSE results for the two substitution methods were often comparable to rMSE results for the MLE method, but the substitution methods were often considerably biased.

Desktop Study of Occupational Exposure Judgments: Do Education and Experience Influence Accuracy?

This study examines the impact of several experience and education determinants on exposure judgment accuracy. The study used desktop assessments performed on several different tasks with different exposure profiles to identify correlations between determinants and judgment accuracy using logistic regression models. The exposure judgments were elicited from industrial hygienists with varying levels of experience, education, and training. Videos and written and oral information about the exposure tasks were presented to all participants as they documented a series of qualitative and quantitative exposure judgment probabilities in four exposure categories. Participants (n = 77) first documented their qualitative and then their quantitative exposure assessments after receiving the series of sampling data points. Data interpretation tests and training in simple rules-of-thumb for data interpretation were also given to each participant to investigate the impact of data interpretation skills on exposure judgment accuracy. Logistic regression analysis indicated “years of exposure assessment experience” (p < 0.05), “highest EHS degree” (p < 0.05), and a participants “data interpretation test score” (p < 0.05) directly impacted qualitative exposure judgment accuracy. Logistic regression models of quantitative judgment accuracy showed positive correlation with “greater than 10 years of exposure assessment experience” (p < 0.05), “highest EHS degree” (p < 0.05), a participants “data interpretation test score” (p < 0.001), rules-of-thumb data interpretation training (p < 0.001), and the number of sample data points available for a judgment (p < 0.005). Analyzing judgments in subsets for participants with less or more than 10 years’ experience indicated additional correlations with Certified Industrial Hygienist and Certified Safety Professional certifications, total number of task exposure assessments, and career number of air surveys. The correlation of qualitative and quantitative exposure judgment accuracy with “greater than 10 years experience” supports similar research findings from other fields. The results of this study indicate that several determinants of experience, education, and training, in addition to the availability of sampling data, significantly impact the accuracy of exposure assessments. The findings also suggest methods for enhancing exposure judgment accuracy through statistical tools, mathematical exposure modeling, and specific training.

Cohort Mortality Study of Roofing Granule Mine and Mill Workers. Part II. Epidemiologic Analysis, 1945–2004

The mortality of 2650 employees (93.4% males) in the mine and mill production of roofing granules at four plants was examined between 1945 and 2004. Hypotheses focused on diseases associated with exposure to silica: nonmalignant respiratory disease, lung cancer, and nonmalignant renal disease. Study eligibility required ≥ 1 year of employment by 2000. Work history and vital status were followed through 2004 with < 1% lost to follow-up. Industrial hygiene sampling data (1871 sampling measurements over a 32-year period) and professional judgment were used to construct 15 respirable crystalline silica exposure categories. A category was assigned to all plant-, department-, and time-dependent standard job titles. Cumulative respirable crystalline silica exposure (mg/m3-years) was calculated as the sum of the product of time spent and the average exposure for each plant-, department-, job-, and calendar-year combination. The cohort geometric mean was 0.17 mg/m3-years (geometric standard deviation 4.01) and differed by plant. Expected deaths were calculated using U.S. (entire cohort) and regional (each plant) mortality rates. Poisson regression was used for internal comparisons. For the entire cohort, 772 deaths (97.4% males) were identified (standardized mortality ratio 0.95, 95% CI 0.88–1.02). There were 50 deaths from nonmalignant respiratory diseases (1.14, 95% CI 0.85–1.51). Lagging exposure 15 years among the male cohort, the relative risks for nonmalignant respiratory disease were 1.00 (reference), 0.80, 1.94, and 2.03 (p value trend = 0.03) when cumulative exposure was categorized < 0.1, 0.1–<0.5, 0.5–<1.0, and ≥ 1.0 mg/m3-years, respectively. There was a total of 77 lung cancer deaths (1.11, 95% CI 0.88–1.39). Lagging exposure 15 years, the relative risks for males were 1.00 (reference), 1.83, 1.83, and 1.05 (p value trend = 0.9). There were 16 deaths from nonmalignant renal disease (1.76, 95% CI 1.01–2.86). This exposure-response trend was suggestive but imprecise. The study results are consistent with other cohorts with similar levels of exposure to respirable crystalline silica.

Exposure data from multi-application, multi-industry maintenance of surfaces and joints sealed with asbestos-containing gaskets and packing.

Fluid sealing devices (gaskets and packing) containing asbestos are manufactured and blended with binders such that the asbestos fibers are locked in a matrix that limits the potential for fiber release. Occasionally, fluid sealing devices fail and need to be replaced or are removed during preventive maintenance activities. This is the first study known to pool over a decades worth of exposure assessments involving fluid sealing devices used in a variety of applications. Twenty-one assessments of work activities and air monitoring were performed under conditions with no mechanical ventilation and work scenarios described as “worst-case” conditions. Frequently, the work was conducted using aggressive techniques, along with dry removal practices. Personal and area samples were collected and analyzed in accordance with the National Institute for Occupational Safety and Health Methods 7400 and 7402. A total of 782 samples were analyzed by phase contrast microscopy, and 499 samples were analyzed by transmission electron microscopy. The statistical data analysis focused on the overall data sets which were personal full-shift time-weighted average (TWA) exposures, personal 30-min exposures, and area full-shift TWA values. Each data set contains three estimates of exposure: (1) total fibers; (2) asbestos fibers only but substituting a value of 0.0035 f/cc for censored data; and (3) asbestos fibers only but substituting the limit of quantification value for censored data. Censored data in the various data sets ranged from 7% to just over 95%. Because all the data sets were censored, the geometric mean and geometric standard deviation were estimated using the maximum likelihood estimation method. Nonparametric, Kaplan-Meier, and lognormal statistics were applied and found to be consistent and reinforcing. All three sets of statistics suggest that the mean and median exposures were less than 25% of 0.1 f/cc 8-hr TWA sample or 1.0 f/cc 30-min samples, and that there is at least 95% confidence that the true 95th percentile exposures are less than 0.1 f/cc as an 8-hr TWA.

Cohort Mortality Study of Roofing Granule Mine and Mill Workers. Part I: Estimation of Historical Crystalline Silica Exposures

A study was conducted to construct a job exposure matrix for the roofing granule mine and mill workers at four U.S. plants. Each plant mined different minerals and had unique departments and jobs. The goal of the study was to generate accurate estimates of the mean exposure to respirable crystalline silica for each cell of the job exposure matrix, that is, every combination of plant, department, job, and year represented in the job histories of the study participants. The objectives of this study were to locate, identify, and collect information on all exposure measurements ever collected at each plant, statistically analyze the data to identify deficiencies in the database, identify and resolve questionable measurements, identify all important process and control changes for each plant-department-job combination, construct a time line for each plant-department combination indicating periods where the equipment and conditions were unchanged, and finally, construct a job exposure matrix. After evaluation, 1871 respirable crystalline silica measurements and estimates remained. The primary statistic of interest was the mean exposure for each job exposure matrix cell. The average exposure for each of the four plants was 0.042 mg/m3 (Belle Mead, N.J.), 0.106 mg/m3 (Corona, Calif.), 0.051 mg/m3 (Little Rock, Ark.), and 0.152 mg/m3 (Wausau, Wis.), suggesting that there may be substantial differences in the employee cumulative exposures. Using the database and the available plant information, the study team assigned an exposure category and mean exposure for every plant-department-job and time interval combination. Despite a fairly large database, the mean exposure for >95% of the job exposure matrix cells, or specific plant-department-job-year combinations, were estimated by analogy to similar jobs in the plant for which sufficient data were available. This approach preserved plant specificity, hopefully improving the usefulness of the job exposure matrix.

Corrigenda - Models for nearly every occasion: Part II - Two box models

In volume 14, issue 1 of Journal of Occupational and Environmental Hygiene, an incorrect equation is shown in “Models for Nearly Every Occasion: Part II - Two Box Models”, by Gary H. Ganser and Pau...

Models for nearly every occasion: Part III – One box decreasing emission models

ABSTRACT New one box “well-mixed room” decreasing emission (DE) models are introduced that allow for local exhaust or local exhaust with filtered return, as well the recirculation of a filtered (or cleaned) portion of the general room ventilation. For each control device scenario, a steady state and transient model is presented. The transient equations predict the concentration at any time t after the application of a known mass of a volatile substance to a surface, and can be used to predict the task exposure profile, the average task exposure, as well as peak and short-term exposures. The steady state equations can be used to predict the “average concentration per application” that is reached whenever the substance is repeatedly applied. Whenever the beginning and end concentrations are expected to be zero (or near zero) the steady state equations can also be used to predict the average concentration for a single task with multiple applications during the task, or even a series of such tasks. The transient equations should be used whenever these criteria cannot be met. A structured calibration procedure is proposed that utilizes a mass balance approach. Depending upon the DE model selected, one or more calibration measurements are collected. Using rearranged versions of the steady state equations, estimates of the model variables—e.g., the mass of the substance applied during each application, local exhaust capture efficiency, and the various cleaning or filtration efficiencies—can be calculated. A new procedure is proposed for estimating the emission rate constant.