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A Simple Upper Limit for the Sum of the Risks of the Components in a Mixture

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  • David W. Gaylor
  • James J. Chen

Abstract

Natural or manufactured products may contain mixtures of carcinogens and the human environment certainly contains mixtures of carcinogens. Various authors have shown that the total risk of a mixture can be approximated by the sum of the risks of the individual components under a variety of conditions at low doses. Under these conditions, summing the individual estimated upper bound risks, as currently often done, is too conservative because it is unlikely that all risks for a mixture are at their maximum levels simultaneously. In the absence of synergism, a simple procedure is proposed for estimating a more appropriate upper bound of the additive risks for a mixture of carcinogens. These simple limits also apply to noncancer endpoints when the risks of the components are approximately additive.

Suggested Citation

  • David W. Gaylor & James J. Chen, 1996. "A Simple Upper Limit for the Sum of the Risks of the Components in a Mixture," Risk Analysis, John Wiley & Sons, vol. 16(3), pages 395-398, June.
    • Handle: RePEc:wly:riskan:v:16:y:1996:i:3:p:395-398
    DOI: 10.1111/j.1539-6924.1996.tb01473.x
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    References listed on IDEAS

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    1. Wout Slob, 1994. "Uncertainty Analysis in Multiplicative Models," Risk Analysis, John Wiley & Sons, vol. 14(4), pages 571-576, August.
    2. Ralph L. Kodell & Daniel Krewski & Jan M. Zielinski, 1991. "Additive and Multiplicative Relative Risk in the Two‐Stage Clonal Expansion Model of Carcinogenesis," Risk Analysis, John Wiley & Sons, vol. 11(3), pages 483-490, September.
    3. James J. Chen & David W. Gaylor & Ralph L. Kodell, 1990. "Estimation of the Joint Risk from Multiple‐Compound Exposure Based on Single‐Compound Experiments," Risk Analysis, John Wiley & Sons, vol. 10(2), pages 285-290, June.
    4. Charles C. Brown & Kenneth C. Chu, 1989. "Additive and Multiplicative Models and Multistage Carcinogenesis Theory," Risk Analysis, John Wiley & Sons, vol. 9(1), pages 99-105, March.
    5. Herman J. Gibb & Chao W. Chen, 1986. "Multistage Model Interpretation of Additive and Multiplicative Carcinogenic Effects," Risk Analysis, John Wiley & Sons, vol. 6(2), pages 167-170, June.
    6. Ralph L. Kodell & James J. Chen, 1994. "Reducing Conservatism in Risk Estimation for Mixtures of Carcinogens," Risk Analysis, John Wiley & Sons, vol. 14(3), pages 327-332, June.
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    Cited by:

    1. Vincent James Cogliano, 1997. "Plausible Upper Bounds: Are Their Sums Plausible?," Risk Analysis, John Wiley & Sons, vol. 17(1), pages 77-84, February.
    2. Jing‐Shiang Hwang & James J. Chen, 1999. "An Evaluation of Risk Estimation Procedures for Mixtures of Carcinogens," Risk Analysis, John Wiley & Sons, vol. 19(6), pages 1071-1076, December.

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