Skip to main content
SpringerLink
Log in

Calibration confidence regions for asbestos fibers with heteroscedasticity and interlaboratory variability

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

It is well known that asbestos exposure causes mesothelioma and asbestosis. We present statistical methodologies for analyzing airborne asbestos fiber counts measured by transmission electron microscopy. We observed from multiple laboratories that the variability of asbestos measurements increases with the true concentration levels. In order to account for the heteroscedasticity and between-laboratories variation of asbestos fiber counts, we use a two-component mixed model as well as a gamma mixed model. We construct calibration confidence regions for unknown true measurements borrowing strength from multiple laboratories. The performances of our calibration confidence regions and their robustness are studied via simulation. To illustrate our results, we analyze a real data set of amosite asbestos.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Baron, P. A. 2017. Measure of fibers. In NIOSH manual of analytical methods, ed. K. Ashley, and P. F. O’Connor, 5th ed. Atlanta, GA: NIOSH Centers for Disease Control and Prevention.

    Google Scholar 

  • Bhaumik, D. K., and R. D. Gibbons. 2005. Confidence regions for random-effects calibration curves with heteroscedastic errors. Technometrics 47:223–31. doi:10.1198/004017005000000021.

    Article  MathSciNet  Google Scholar 

  • Camus, M., J. Siemiatycki, and B. Meek. 1998. Nonoccupational exposure to chrysotile asbestos and the risk of lung cancer. New England Journal of Medicine 338:1565–71. doi:10.1056/NEJM199805283382201.

    Article  Google Scholar 

  • Carroll, R. J., and D. Ruppert. 1988. Transformation and weighting in regression. New York, NY: Champman & Hall/CRC.

    Book  Google Scholar 

  • Christensen, B. C, J. J. Godleski, C. R. Roelofs, et al. 2008. Asbestos burden predicts survival in pleural mesothelioma. Environmental Health Perspectives 116:723–26. doi:10.1289/ehp.11151.

    Article  Google Scholar 

  • Fitzmaurice, G. M., N. M. Laird, and J. H. Ware. 2004. Applied longitudinal analysis. Wiley series in probability and statistics. Hoboken, NJ: Wiley-Interscience.

    MATH  Google Scholar 

  • Gibbons, R D., and D. K. Bhaumik. 2001. Weighted random-effects regression models with application to interlaboratory calibration. Technometrics 43:192–98. doi:10.1198/004017001750386305.

    Article  MathSciNet  Google Scholar 

  • Hedeker, D., and R. D. Gibbons. 2006. Longitudinal data analysis. Hoboken, NJ: Wiley.

    MATH  Google Scholar 

  • International Agency for Research on Cancer, World Health Organization. 1998. Asbestos. IARC Monographs on the Evaluation of Carcinogenic Risks to Humans 14. Lyon, France: IARC.

    Google Scholar 

  • Krishnamoorthy, K., T. Mathew, and S. Mukherjee. 2008. Normal-based methods for a gamma distribution: Prediction and tolerance intervals and stress-strength reliability. Technometrics 50:69–78. doi:10.1198/004017007000000353.

    Article  MathSciNet  Google Scholar 

  • Lessaffre, E., and B. Spiessens. 2001. On the effects of the number of quadrature points in a logistic random-effects model: An example. Applied Statistics 50:325–35.

    MathSciNet  MATH  Google Scholar 

  • Loomis, D., J. Dement, D. Richardson, and S. Wolf. 2010. Asbestos fibre dimensions and lung cancer mortality among workers exposed to chrysotile. Occupational and Environmental Medicine 67:580–84. doi:10.1136/oem.2009.050120.

    Article  Google Scholar 

  • McCullagh, P., and J. A. Neider. 1989. Generalized linear models, 2nd ed. New York, NY: Champman & Hall/CRC.

    Book  Google Scholar 

  • Pinheiro, J. C, and D. M. Bates. 1995. Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics 4:12–35.

    Google Scholar 

  • Rocke, D. M., B. Durbin, M. Wilson, and H. D. Kahn. 2003. Modeling uncertainty in the measurement of low-level analytes in environmental analysis. Ecotoxicology and Environmental Safety 56:78–92. doi:10.1016/S0147-6513(03)00052-6.

    Article  Google Scholar 

  • Rocke, D. M., and S. Lorenzato. 1995. A two-component model for measurement error in analytical chemistry. Technometrics 37:176–84. doi:10.1080/00401706.1995.10484302.

    Article  Google Scholar 

  • Rooker, S. J., N. P. Vaughan, and J. M. Le Guen. 1982. On the visibility of fibers by phase contrast microscopy. American Industrial Hygiene Association Journal 43:505–15. doi:10.1080/15298668291410125.

    Article  Google Scholar 

  • Stayner, L., E. Kuempel, S. Gilbert, M. Hein, and J. Dement. 2008. An epidemiological study of the role of chrysotile asbestos fibre dimensions in determining respiratory disease risk in exposed workers. Occupational and Environmental Medicine 65:613–19. doi:10.1136/oem.2007.035584.

    Article  Google Scholar 

  • Stayner, L. T., D. A. Dankovic, and R. A. Lemen. 1996. Occupational exposure to Chrysotile asbestos and cancer risk: A review of the amphibole hypothesis. American Journal of Public Health 86:179–86. doi:10.2105/AJPH.86.2.179.

    Article  Google Scholar 

  • Wilson, E. B., and M. M. Hilferty. 1931. The Distribution of Chi-Squares. Proceedings of the National Academy of Sciences 17:684–688.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NORC at the University of Chicago, 55 East Monroe Street, 30th Floor, Chicago, IL, 60603, USA

    Yoonsang Kim

  2. Division of Epidemiology and Biostatistics, University of Illinois at Chicago, Chicago, Illinois, USA

    Dulal K. Bhaumik

Authors
  1. Yoonsang Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dulal K. Bhaumik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoonsang Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, Y., Bhaumik, D.K. Calibration confidence regions for asbestos fibers with heteroscedasticity and interlaboratory variability. J Stat Theory Pract 12, 635–656 (2018). https://doi.org/10.1080/15598608.2018.1449685

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2018.1449685

Keywords

AMS Subject Classification

Search

Navigation