### Abstract

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., X_{0.95} >100%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 hygienist's initial judgment was incorrect. In either case, the industrial hygienist should readjust his judgment regarding this operation.

Original language | English (US) |
---|---|

Pages (from-to) | 568-581 |

Number of pages | 14 |

Journal | Journal of Occupational and Environmental Hygiene |

Volume | 3 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bayesian statistics
- Exposure assessment
- Exposure rating

### ASJC Scopus subject areas

- Public Health, Environmental and Occupational Health

### Cite this

*Journal of Occupational and Environmental Hygiene*,

*3*(9), 568-581. https://doi.org/10.1080/15459620600914641

**Rating exposure control using Bayesian decision analysis.** / Hewett, Paul; Logan, Perry; Mulhausen, John; Ramachandran, Gurumurthy; Banerjee, Sudipto.

Research output: Contribution to journal › Article

*Journal of Occupational and Environmental Hygiene*, vol. 3, no. 9, pp. 568-581. https://doi.org/10.1080/15459620600914641

}

TY - JOUR

T1 - Rating exposure control using Bayesian decision analysis

AU - Hewett, Paul

AU - Logan, Perry

AU - Mulhausen, John

AU - Ramachandran, Gurumurthy

AU - Banerjee, Sudipto

PY - 2006/9/1

Y1 - 2006/9/1

N2 - 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 X0.95 ≤1%OEL), (1) highly controlled (i.e., X 0.95 ≤10%OEL), (2) well controlled (i.e., X0.95 ≤50%OEL), (3) controlled (i.e., X0.95 ≤100%OEL), or (4) poorly controlled (i.e., X0.95 >100%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 hygienist's initial judgment was incorrect. In either case, the industrial hygienist should readjust his judgment regarding this operation.

AB - 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 X0.95 ≤1%OEL), (1) highly controlled (i.e., X 0.95 ≤10%OEL), (2) well controlled (i.e., X0.95 ≤50%OEL), (3) controlled (i.e., X0.95 ≤100%OEL), or (4) poorly controlled (i.e., X0.95 >100%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 hygienist's initial judgment was incorrect. In either case, the industrial hygienist should readjust his judgment regarding this operation.

KW - Bayesian statistics

KW - Exposure assessment

KW - Exposure rating

UR - http://www.scopus.com/inward/record.url?scp=84875636736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875636736&partnerID=8YFLogxK

U2 - 10.1080/15459620600914641

DO - 10.1080/15459620600914641

M3 - Article

C2 - 16998991

AN - SCOPUS:84875636736

VL - 3

SP - 568

EP - 581

JO - Journal of Occupational and Environmental Hygiene

JF - Journal of Occupational and Environmental Hygiene

SN - 1545-9624

IS - 9

ER -