Combining Lead Exposure Measurements and Experts’ Judgment Through a Bayesian Framework

Abstract

Objectives

CARcinogen EXposure (CAREX) is a carcinogen-surveillance system employed in many countries. To develop Korean CAREX, the intensity of exposure to lead, as an example, was estimated across industries.

Methods

Airborne-lead measurement records were extracted from the work-environment measurement database (WEMD), which is a nationwide workplace-monitoring database. Lead measurements were log-transformed; then, the log-transformed geometric means (LGMs) and log-transformed geometric standard deviations (LGSDs) were calculated for each industry. However, the data of many industries was limited. To address this shortcoming, experts' judgments of the lead exposure levels across industries were elicited. Experts provided their estimates of lead exposure levels as the boundary of the 5^th and 95^th percentiles, and it is assumed that these estimates are based on the log-normal distributions of exposure levels. Estimates of LGM and LGSD were extracted from each expert's response and then combined to quantify the experts' prior distribution. Then, the experts' prior distributions for each industry were updated with the corresponding LGMs and LGSDs calculated from the WEMD data through a Bayesian framework, yielding posterior distributions of the LGM and LGSD.

Results

The WEMD contains 83035 airborne-lead measurements that were collected between 2002 and 2007. A total of 17 occupational-hygiene professionals with >20 years of experience provided lead exposure estimates. In industries where measurement data were abundant, the measurement data dominated the posterior exposure estimates. For example, for one industry, 'Manufacture of Accumulator, Primary Cells, and Primary Batteries,' 1152 lead measurements [with a geometric mean (GM) of 14.42 µg m⁻³ and a geometric standard deviation (GSD) of 3.31] were available and 15 experts' responses (with a GM of 7.06 µg m⁻³ and a GSD of 4.15) were collected, resulting in a posterior exposure estimate of 14.41µg m⁻³ as the GM with a GSD of 3.31. For industries with a limited number of measurements available in the WEMD, experts' decisions played a significant role in determining the posterior exposure estimates. For example, for the 'Manufacture of Weapons and Ammunition' industry, 15 lead measurements (with a GM of 6.45 µg m⁻³ and a GSD of 3.37) were available and seven experts' responses (with a GM of 3.28 µg m⁻³ and a GSD of 4.54) were obtained, resulting in a posterior exposure estimate of 5.42 µg m⁻³ as the GM with a GSD of 3.73.

Conclusions

The proposed method for estimating the intensity of exposure to carcinogens may introduce an unbiased approach to the development process by simultaneously utilizing both prior knowledge of experts and measurement data. In addition, it supplies a framework for future updates.