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On efficient exact experimental designs for ordered treatments

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  • Singh, Satya Prakash
  • Davidov, Ori

Abstract

In a recent paper Singh and Davidov (2019) derive approximate optimal designs for experiments with ordered treatments. Specifically, maxi–min and intersection–union designs were explored. These designs, which address different types of hypothesis testing problems, provide a substantial improvement over standard designs in terms of power, or equivalently, sample size requirements. In practice however, exact, not approximate designs are used. Therefore, in this paper, we develop methods for finding efficient exact designs for the testing problems considered in Singh and Davidov (2019). The proposed designs are compared numerically to some well known existing designs and it is shown that the new designs require fewer experimental units to attain prespecified power. A thorough sensitivity analysis shows that the proposed designs are robust against possible misspecification of the parameters under the alternative and the order relation among the treatment groups.

Suggested Citation

  • Singh, Satya Prakash & Davidov, Ori, 2021. "On efficient exact experimental designs for ordered treatments," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:csdana:v:164:y:2021:i:c:s0167947321001390
    DOI: 10.1016/j.csda.2021.107305
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    References listed on IDEAS

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    1. L. Imhof & J. Lopez‐Fidalgo & W. K. Wong, 2001. "Efficiencies of Rounded Optimal Approximate Designs for Small Samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 301-318, November.
    2. Satya Prakash Singh & Ori Davidov, 2019. "On the design of experiments with ordered treatments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(5), pages 881-900, November.
    3. Shyamal D. Peddada & Joseph K. Haseman & Xiaofeng Tan & Greg Travlos, 2006. "Tests for a simple tree order restriction with application to dose–response studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 493-506, August.
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    Cited by:

    1. Belmiro P. M. Duarte & Anthony C. Atkinson & Satya P. Singh & Marco S. Reis, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," Statistical Papers, Springer, vol. 64(2), pages 587-615, April.
    2. Duarte, Belmiro P.M. & Atkinson, Anthony C. & P. Singh, Satya & S. Reis, Marco, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," LSE Research Online Documents on Economics 115187, London School of Economics and Political Science, LSE Library.

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