John Mulhausen

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.

Exposure Modeling in Occupational Hygiene Decision Making

The primary objective was to develop a framework for using exposure models in conjunction with two-dimensional Monte Carlo methods for making exposure judgments in the context of Bayesian decision analysis. The AIHA exposure assessment strategy will be used for illustrative purposes, but the method has broader applications beyond these specific exposure assessment strategies. A two-dimensional Monte Carlo scheme by which the exposure model output can be represented in the form of a decision chart is presented. The chart shows the probabilities of the 95th percentile of the exposure distribution lying in one of the four exposure categories relative to the occupational exposure limit (OEL): (1) highly controlled (<10% of OEL), (2) well controlled (10–50% of OEL), (3) controlled (50–100% of OEL), and (4) poorly controlled (>100% of OEL). Such a decision chart can be used as a “prior” in the Bayesian statistical framework, which can be updated using monitoring data to arrive at a final decision chart. Hypothetical examples using commonly used exposure models are presented, along with a discussion of how this framework can be used given a hierarchy of exposure models.

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.

Effect of training on exposure judgment accuracy of industrial hygienists.

Results are presented from a study that investigated the effect of data interpretation training on exposure judgment accuracy of industrial hygienists across several companies in different industry sectors. Participating companies provided monitoring information on specific exposure tasks. Forty-nine hygienists from six companies participated in the study, and 22 industrial tasks were evaluated. The number of monitoring data points for individual tasks varied between 5 and 24. After reviewing all available basic characterization information for the job, task, and chemical, hygienists were asked to provide their judgment on the probability of the 95th percentile of the underlying exposure distribution being located in one of four exposure categories relative to the occupational exposure limit as outlined in the AIHA® exposure assessment strategy. Ninety-three qualitative judgments (i.e., without reviewing monitoring data) and 2142 quantitative judgments (i.e., those made after reviewing monitoring data) were obtained. Data interpretation training, with simple rules of thumb for estimating 95th percentiles, was provided to all hygienists. A data interpretation test was administered before and after training. All exposure task judgments were collected before and after training. Data interpretation test accuracy for the hygienists increased from 48% to 67% after training (p < 0.001) and a significant underestimation bias was removed. Hygienist quantitative task judgment accuracy improved from 46% to 69% (p < 0.001) post-training. Accuracy results showed good improvement in industrial hygienists’ quantitative judgments as a result of training. Hence, the use of statistical tools is promoted to improve judgments based on monitoring data and provide feedback and calibration to improve qualitative judgments. It may be worthwhile to develop standard training programs to improve exposure judgments.