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Comparing Experimental Designs for Benchmark Dose Calculations for Continuous Endpoints

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  • Kristi Kuljus
  • Dietrich Von Rosen
  • Salomon Sand
  • Katarina Victorin

Abstract

The BMD (benchmark dose) method that is used in risk assessment of chemical compounds was introduced by Crump (1984) and is based on dose‐response modeling. To take uncertainty in the data and model fitting into account, the lower confidence bound of the BMD estimate (BMDL) is suggested to be used as a point of departure in health risk assessments. In this article, we study how to design optimum experiments for applying the BMD method for continuous data. We exemplify our approach by considering the class of Hill models. The main aim is to study whether an increased number of dose groups and at the same time a decreased number of animals in each dose group improves conditions for estimating the benchmark dose. Since Hill models are nonlinear, the optimum design depends on the values of the unknown parameters. That is why we consider Bayesian designs and assume that the parameter vector has a prior distribution. A natural design criterion is to minimize the expected variance of the BMD estimator. We present an example where we calculate the value of the design criterion for several designs and try to find out how the number of dose groups, the number of animals in the dose groups, and the choice of doses affects this value for different Hill curves. It follows from our calculations that to avoid the risk of unfavorable dose placements, it is good to use designs with more than four dose groups. We can also conclude that any additional information about the expected dose‐response curve, e.g., information obtained from studies made in the past, should be taken into account when planning a study because it can improve the design.

Suggested Citation

  • Kristi Kuljus & Dietrich Von Rosen & Salomon Sand & Katarina Victorin, 2006. "Comparing Experimental Designs for Benchmark Dose Calculations for Continuous Endpoints," Risk Analysis, John Wiley & Sons, vol. 26(4), pages 1031-1043, August.
    • Handle: RePEc:wly:riskan:v:26:y:2006:i:4:p:1031-1043
    DOI: 10.1111/j.1539-6924.2006.00798.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. W. Slob & M. N. Pieters, 1998. "A Probabilistic Approach for Deriving Acceptable Human Intake Limits and Human Health Risks from Toxicological Studies: General Framework," Risk Analysis, John Wiley & Sons, vol. 18(6), pages 787-798, December.
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    1. Fereshteh Kalantari & Joakim Ringblom & Salomon Sand & Mattias Öberg, 2017. "Influence of Distribution of Animals between Dose Groups on Estimated Benchmark Dose and Animal Distress for Quantal Responses," Risk Analysis, John Wiley & Sons, vol. 37(9), pages 1716-1728, September.
    2. Joakim Ringblom & Fereshteh Kalantari & Gunnar Johanson & Mattias Öberg, 2018. "Influence of Distribution of Animals between Dose Groups on Estimated Benchmark Dose and Animal Welfare for Continuous Effects," Risk Analysis, John Wiley & Sons, vol. 38(6), pages 1143-1153, June.

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