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Low dose risk estimation via simultaneous statistical inferences

Author

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  • Walter W. Piegorsch
  • R. Webster West
  • Wei Pan
  • Ralph L. Kodell

Abstract

Summary. The paper develops and studies simultaneous confidence bounds that are useful for making low dose inferences in quantitative risk analysis. Application is intended for risk assessment studies where human, animal or ecological data are used to set safe low dose levels of a toxic agent, but where study information is limited to high dose levels of the agent. Methods are derived for estimating simultaneous, one‐sided, upper confidence limits on risk for end points measured on a continuous scale. From the simultaneous confidence bounds, lower confidence limits on the dose that is associated with a particular risk (often referred to as a bench‐mark dose) are calculated. An important feature of the simultaneous construction is that any inferences that are based on inverting the simultaneous confidence bounds apply automatically to inverse bounds on the bench‐mark dose.

Suggested Citation

  • Walter W. Piegorsch & R. Webster West & Wei Pan & Ralph L. Kodell, 2005. "Low dose risk estimation via simultaneous statistical inferences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 245-258, January.
    • Handle: RePEc:bla:jorssc:v:54:y:2005:i:1:p:245-258
    DOI: 10.1111/j.1467-9876.2005.00481.x
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    Cited by:

    1. Sanyu Zhou, 2017. "One-sided hyperbolic simultaneous confidence bands for multiple and polynomial regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 187-200, February.
    2. Liu, W. & Hayter, A.J. & Piegorsch, W.W. & Ah-Kine, P., 2009. "Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1432-1439, August.
    3. Lizhen Lin & Walter W. Piegorsch & Rabi Bhattacharya, 2015. "Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 713-731, September.
    4. Sanyu Zhou & Defa Wang & Jingjing Zhu, 2020. "Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region," Statistical Papers, Springer, vol. 61(3), pages 1335-1346, June.
    5. Mitchell J. Small, 2008. "Methods for Assessing Uncertainty in Fundamental Assumptions and Associated Models for Cancer Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1289-1308, October.
    6. Christopher Withers & Saralees Nadarajah, 2012. "Maximum modulus confidence bands," Statistical Papers, Springer, vol. 53(4), pages 811-819, November.
    7. Walter W. Piegorsch, 2010. "Translational benchmark risk analysis," Journal of Risk Research, Taylor & Francis Journals, vol. 13(5), pages 653-667, July.
    8. Jamshidian, Mortaza & Liu, Wei & Bretz, Frank, 2010. "Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1475-1483, June.

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