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Role of the Standard Deviation in the Estimation of Benchmark Doses with Continuous Data

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  • David W. Gaylor
  • William Slikker

Abstract

For continuous data, risk is defined here as the proportion of animals with values above a large percentile, e.g., the 99th percentile or below the 1st percentile, for the distribution of values among control animals. It is known that reducing the standard deviation of measurements through improved experimental techniques will result in less stringent (higher) doses for the lower confidence limit on the benchmark dose that is estimated to produce a specified risk of animals with abnormal levels for a biological effect. Thus, a somewhat larger (less stringent) lower confidence limit is obtained that may be used as a point of departure for low‐dose risk assessment. It is shown in this article that it is important for the benchmark dose to be based primarily on the standard deviation among animals, sa, apart from the standard deviation of measurement errors, sm, within animals. If the benchmark dose is incorrectly based on the overall standard deviation among average values for animals, which includes measurement error variation, the benchmark dose will be overestimated and the risk will be underestimated. The bias increases as sm increases relative to sa. The bias is relatively small if sm is less than one‐third of sa, a condition achieved in most experimental designs.

Suggested Citation

  • David W. Gaylor & William Slikker, 2004. "Role of the Standard Deviation in the Estimation of Benchmark Doses with Continuous Data," Risk Analysis, John Wiley & Sons, vol. 24(6), pages 1683-1687, December.
    • Handle: RePEc:wly:riskan:v:24:y:2004:i:6:p:1683-1687
    DOI: 10.1111/j.0272-4332.2004.559_1.x
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    References listed on IDEAS

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    1. Kenny S. Crump, 1995. "Calculation of Benchmark Doses from Continuous Data," Risk Analysis, John Wiley & Sons, vol. 15(1), pages 79-89, February.
    2. David W. Gaylor & William Slikker, 1994. "Modeling for Risk Assessment of Neurotoxic Effects," Risk Analysis, John Wiley & Sons, vol. 14(3), pages 333-338, June.
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    1. Susan Dekkers & Jan Telman & Monique A. J. Rennen & Marco J. Appel & Cees De Heer, 2006. "Within‐Animal Variation as an Indication of the Minimal Magnitude of the Critical Effect Size for Continuous Toxicological Parameters Applicable in the Benchmark Dose Approach," Risk Analysis, John Wiley & Sons, vol. 26(4), pages 867-880, August.
    2. Signe M. Jensen & Felix M. Kluxen & Christian Ritz, 2019. "A Review of Recent Advances in Benchmark Dose Methodology," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2295-2315, October.

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