Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects

Samuel Rosa () and Radoslav Harman
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Samuel Rosa: Comenius University in Bratislava
Radoslav Harman: Comenius University in Bratislava

Statistical Papers, 2016, vol. 57, issue 4, No 13, 1077-1106

Abstract: 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.

Keywords: Approximate design; Optimal design; Treatment contrasts; Resistance to nuisance effects; Designs with small support; 62K05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00362-016-0809-0

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