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Bayesian Analysis of Silica Exposure and Lung Cancer Using Human and Animal Studies

Bartell, Scott M.; Hamra, Ghassan Badri; Steenland, Kyle

doi: 10.1097/EDE.0000000000000602
Occupational Epidemiology

Background: Bayesian methods can be used to incorporate external information into epidemiologic exposure–response analyses of silica and lung cancer.

Methods: We used data from a pooled mortality analysis of silica and lung cancer (n = 65,980), using untransformed and log-transformed cumulative exposure. Animal data came from chronic silica inhalation studies using rats. We conducted Bayesian analyses with informative priors based on the animal data and different cross-species extrapolation factors. We also conducted analyses with exposure measurement error corrections in the absence of a gold standard, assuming Berkson-type error that increased with increasing exposure.

Results: The pooled animal data exposure–response coefficient was markedly higher (log exposure) or lower (untransformed exposure) than the coefficient for the pooled human data. With 10-fold uncertainty, the animal prior had little effect on results for pooled analyses and only modest effects in some individual studies. One-fold uncertainty produced markedly different results for both pooled and individual studies. Measurement error correction had little effect in pooled analyses using log exposure. Using untransformed exposure, measurement error correction caused a 5% decrease in the exposure–response coefficient for the pooled analysis and marked changes in some individual studies.

Conclusion: The animal prior had more impact for smaller human studies and for one-fold versus three- or 10-fold uncertainty. Adjustment for Berkson error using Bayesian methods had little effect on the exposure–response coefficient when exposure was log transformed or when the sample size was large. See video abstract at,

Supplemental Digital Content is available in the text.

From the aProgram in Public Health, Department of Statistics, and Department of Epidemiology, University of California, Irvine, Irvine, CA; bEnvironmental and Occupational Health Program, Dornsife School of Public Health, Drexel University, Philadelphia, PA; and cDepartment of Environmental Health, Rollins School of Public Health, Emory University, Atlanta, GA.

Submitted 17 November 2015; accepted 21 November 2016.

Dr. Steenland’s study on this project was supported by the International Agency for Research on Cancer through a Visiting Scientist appointment and by NIEHS Environmental Health Sciences Core Center P30 ES019776.

The authors report no conflicts of interest.

Data and code for replication are available from Dr. Steenland (

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

Correspondence: Scott M. Bartell, Program in Public Health, 2032 Anteater Instruction & Research Building, University of California, Irvine, Irvine, CA 92697. E-mail:

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