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Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects

Author

Listed:
  • Samuel Rosa

    (Comenius University in Bratislava)

  • Radoslav Harman

    (Comenius University in Bratislava)

Abstract

Suppose that we intend to perform an experiment consisting of a set of independent trials. The mean value of the response in each trial is assumed to be equal to the sum of the effect of the treatment selected for that trial and some nuisance effects, e.g., the effect of a time trend or blocking. In this model, we examine optimal approximate designs for the estimation of a system of treatment contrasts, with respect to a wide range of optimality criteria. We show that it is necessary for any optimal design to attain the optimal treatment proportions, which may be obtained from the marginal model that excludes the nuisance effects. Moreover, we prove that for a design to be optimal, it is sufficient that it attains the optimal treatment proportions and satisfies the conditions for resistance to nuisance effects. For selected natural choices of treatment contrasts and optimality criteria, we calculate the optimal treatment proportions and provide an explicit form of optimal designs. In particular, we obtain optimal treatment proportions for the comparison of a set of test treatments with a set of controls. Once the optimal treatment proportions are determined, the results allow us to construct a method of calculating optimal approximate designs with small support sizes through linear programming. Consequently, we can construct efficient exact designs using a simple heuristic.

Suggested Citation

  • Samuel Rosa & Radoslav Harman, 2016. "Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects," Statistical Papers, Springer, vol. 57(4), pages 1077-1106, December.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0809-0
    DOI: 10.1007/s00362-016-0809-0
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    References listed on IDEAS

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    1. Katarzyna Filipiak & Augustyn Markiewicz & Anna Szczepańska, 2009. "Optimal designs under a multivariate linear model with additional nuisance parameters," Statistical Papers, Springer, vol. 50(4), pages 761-778, August.
    2. Radoslav Harman, 2004. "Minimal efficiency of designs under the class of orthogonally invariant information criteria," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 137-153, September.
    3. Mike Jacroux, 1990. "Some optimal designs for comparing a set of test treatments with a set of controls," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 173-185, March.
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    Citations

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    Cited by:

    1. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    2. Harman, Radoslav & Rosa, Samuel, 2019. "Removal of the points that do not support an E-optimal experimental design," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 83-89.
    3. Samuel Rosa, 2018. "Optimal designs for treatment comparisons represented by graphs," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 479-503, October.
    4. Samuel Rosa, 2019. "Equivalence of weighted and partial optimality of experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 719-732, August.
    5. Samuel Rosa & Radoslav Harman, 2017. "Optimal approximate designs for comparison with control in dose-escalation studies," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 638-660, September.

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