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Plausible Upper Bounds: Are Their Sums Plausible?

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  • Vincent James Cogliano

Abstract

Quantitative cancer risk assessments are typically expressed as plausible upper bounds rather than estimates of central tendency. In analyses involving several carcinogens, these upper bounds are often summed to estimate overall risk. This begs the question of whether a sum of upper bounds is itself a plausible estimate of overall risk. This question can be asked in two ways: whether the sum yields an improbable estimate of overall risk (that is, is it only remotely possible for the true sum of risks to match the sum of upper bounds), or whether the sum gives a misleading estimate (that is, is the true sum of risks likely to be very different from the sum of upper bounds). Analysis of four case studies shows that as the number of risk estimates increases, their sum becomes increasingly improbable, but not misleading. Though the overall risk depends on the independence, additivity, and number of risk estimates, as well as the shapes of the underlying risk distributions, sums of upper bounds provide useful information about the overall risk and can be adjusted downward to give a more plausible [perhaps probable] upper bound, or even a central estimate of overall risk.

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  • Vincent James Cogliano, 1997. "Plausible Upper Bounds: Are Their Sums Plausible?," Risk Analysis, John Wiley & Sons, vol. 17(1), pages 77-84, February.
    • Handle: RePEc:wly:riskan:v:17:y:1997:i:1:p:77-84
    DOI: 10.1111/j.1539-6924.1997.tb00845.x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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. Ian G. J. Dawson & Johnnie E. V. Johnson & Michelle A. Luke, 2013. "Helping Individuals to Understand Synergistic Risks: An Assessment of Message Contents Depicting Mechanistic and Probabilistic Concepts," Risk Analysis, John Wiley & Sons, vol. 33(5), pages 851-865, May.
    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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