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Computational and Mathematical Methods in Medicine
Volume 2017 (2017), Article ID 7518035, 16 pages
https://doi.org/10.1155/2017/7518035
Research Article

Estimating and Interpreting Effects from Nonlinear Exposure-Response Curves in Occupational Cohorts Using Truncated Power Basis Expansions and Penalized Splines

1Department of Mathematics and Statistics, American University, Washington, DC, USA
2Occupational Science & Technology, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

Correspondence should be addressed to Elizabeth J. Malloy; ude.nacirema@yollam

Received 31 January 2017; Revised 25 April 2017; Accepted 16 May 2017; Published 20 September 2017

Academic Editor: Ruisheng Wang

Copyright © 2017 Elizabeth J. Malloy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. R. Cox, “Regression models and life-tables,” Journal of the Royal Statistical Society, vol. 34, Series B, pp. 187–220, 1972. View at Google Scholar · View at MathSciNet
  2. S. Costello, M. C. Friesen, D. C. Christiani, and E. A. Eisen, “Metalworking fluids and malignant melanoma in autoworkers,” Epidemiology, vol. 22, no. 1, pp. 90–97, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. C. Harris-Adamson, E. A. Eisen, J. Kapellusch et al., “Biomechanical risk factors for carpal tunnel syndrome: A pooled study of 2474 workers,” Occupational and Environmental Medicine, vol. 72, no. 1, pp. 33–41, 2015. View at Publisher · View at Google Scholar · View at Scopus
  4. J. M. Kapellusch, A. Garg, S. Boda et al., “Association between lifting and use of medication for low back pain: Results from the backworks prospective cohort study,” Journal of Occupational and Environmental Medicine, vol. 56, no. 8, pp. 867–877, 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. J. M. Kapellusch, C. Harris-Adamson, F. Gerr et al., “Exposure-response relationships for force and repetition, and CTS,” Proceedings of the HFES Annual Meeting, vol. 59, no. 1, pp. 11–15, October 2015. View at Publisher · View at Google Scholar
  6. Y. Liu, Y. Rong, K. Steenland et al., “Long-term exposure to crystalline silica and risk of heart disease mortality,” Epidemiology, vol. 25, no. 5, pp. 689–696, 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. A. J. Mehta, E. J. Malloy, K. M. Applebaum, J. Schwartz, D. C. Christiani, and E. A. Eisen, “Reduced lung cancer mortality and exposure to synthetic fluids and biocide in the auto manufacturing industry,” Scandinavian Journal of Work, Environment and Health, vol. 36, no. 6, pp. 499–508, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Stayner, K. Steenland, M. Dosemeci, and I. Hertz-Picciotto, “Attenuation of exposure-response curves in occupational cohort studies at high exposure levels,” Scandinavian Journal of Work, Environment and Health, vol. 29, no. 4, pp. 317–324, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. K. Christensen, C. H. Christensen, J. M. Wright et al., “The Use of Epidemiology in Risk Assessment: Challenges and Opportunities,” Human and Ecological Risk Assessment, vol. 21, no. 6, pp. 1644–1663, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. K. Steenland and J. A. Deddens, “A practical guide to dose-response analyses and risk assessment in occupational epidemiology,” Epidemiology, vol. 15, no. 1, pp. 63–70, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. L. A. Sleeper and D. P. Harrington, “Regression splines in the Cox model with application to covariate effects in liver disease,” Journal of the American Statistical Association, vol. 85, no. 412, pp. 941–949, 1990. View at Publisher · View at Google Scholar · View at Scopus
  12. R. J. Gray, “Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis,” Journal of the American Statistical Association, vol. 87, no. 420, pp. 942–951, 1992. View at Publisher · View at Google Scholar · View at Scopus
  13. K. Steenland, R. Seals, M. Klein, J. Jinot, and H. D. Kahn, “Risk estimation with epidemiologic data when response attenuates at high-exposure levels,” Environmental Health Perspectives, vol. 119, no. 6, pp. 831–837, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Garg, J. Kapellusch, K. Hegmann et al., “The Strain Index (SI) and Threshold Limit Value (TLV) for Hand Activity Level (HAL): risk of carpal tunnel syndrome (CTS) in a prospective cohort,” Ergonomics, vol. 55, no. 4, pp. 396–414, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. R Core Team, “R: A language and environment for statistical computing,” R Foundation for Statistical Computing, Vienna, Austria, 2016; http://www.R-project.org/.
  16. D. Ruppert, M. P. Wand, and R. J. Carroll, Semiparametric Regression, Cambridge University Press, Cambridge, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. R. Bender, T. Augustin, and M. Blettner, “Generating survival times to simulate Cox proportional hazards models,” Statistics in Medicine, vol. 24, no. 11, pp. 1713–1723, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. E. J. Malloy, D. Spiegelman, and E. . Eisen, “Comparing measures of model selection for penalized splines in Cox models,” Computational Statistics & Data Analysis, vol. 53, no. 7, pp. 2605–2616, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  19. T. Therneau, “A Package for Survival Analysis in S. R package version 2.38,” 2015.
  20. C. de Boor, A Practical Guide to Splines, Springer, New York, NY, USA, 1978, http://www.springer.com/us/book/9780387953663. View at MathSciNet
  21. P. H. Eilers and B. D. Marx, “Flexible smoothing with B-splines and penalties,” Statistical Science. A Review Journal of the Institute of Mathematical Statistics, vol. 11, no. 2, pp. 89–121, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  22. H. Akaike, “Information Theory and an Extension of the Maximum Likelihood Principle,” in 2nd International Symposium on Information Theory, B. N. Petrov and F. Csaki, Eds., pp. 267–281, Akademiai Kiado, Budapest, Hungary, 1973, http://www.springer.com/us/book/9780387953663. View at Google Scholar · View at MathSciNet
  23. C. M. Hurvich, J. S. Simonoff, and C.-L. Tsai, “Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion,” Journal of the Royal Statistical Society. Series B. Statistical Methodology, vol. 60, no. 2, pp. 271–293, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  24. T. M. Therneau and P. M. Grambsch, Modeling Survival Data: Extending the Cox Model, Statistics for Biology and Health, Springer, New York, NY, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  25. J. S. Moore and A. Garg, “The strain index: a proposed method to analyze jobs for risk of distal upper extremity disorders,” American Industrial Hygiene Association Journal, vol. 56, no. 5, pp. 443–458, 1995. View at Publisher · View at Google Scholar · View at Scopus
  26. M. J. Gardner and D. G. Altman, “Confidence intervals rather than P values: estimation rather than hypothesis testing,” British Medical Journal, vol. 292, no. 6522, pp. 746–750, 1986. View at Publisher · View at Google Scholar · View at Scopus
  27. K. J. Rothman, S. Greenland, and T. L. Lash, Modern Epidemiology, Lippincott Williams & Wilkins, Philadelphia, PA, Pennsylvania, 2008.
  28. D. A. Fraser and N. Reid, “Crisis in science? Or crisis in statistics! Mixed messages in statistics with impact on science,” Journal of Statistical Research, vol. 48-50, pp. 1–9, 2016. View at Publisher · View at Google Scholar
  29. B. Ganguli, M. Naskar, E. J. Malloy, and E. A. Eisen, “Determination of the functional form of the relationship of covariates to the log hazard ratio in a Cox model,” Journal of Applied Statistics, vol. 42, no. 5, pp. 1091–1105, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. L. Desquilbet and F. Mariotti, “Dose-response analyses using restricted cubic spline functions in public health research,” Statistics in Medicine, vol. 29, no. 9, pp. 1037–1057, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. L. Meira-Machado, C. Cadarso-Suárez, F. Gude, and A. Araújo, “SmoothHR: An R package for pointwise nonparametric estimation of hazard ratio curves of continuous predictors,” Computational and Mathematical Methods in Medicine, vol. 2013, Article ID 745742, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Greenland, “Modeling and variable selection in epidemiologic analysis,” American Journal of Public Health, vol. 79, no. 3, pp. 340–349, 1989. View at Publisher · View at Google Scholar · View at Scopus
  33. S. Greenland, “Dose-response and trend analysis in epidemiology: alternatives to categorical analysis,” Epidemiology, vol. 6, no. 4, pp. 356–365, 1995. View at Publisher · View at Google Scholar · View at Scopus
  34. E. L. Lehmann and G. Casella, Theory of Point Estimation, Springer, New York, NY, USA, 2nd edition, 1998. View at MathSciNet
  35. DA. Collett, Modelling Survival Data in Medical Research, Chapman & Hall/CRC Press, Boca Raton, Fla, USA, 2003.