Optimal Designs for the Carryover Model with Random Interactions Between Subjects and Treatments

Andrea Bludowsky, Joachim Kunert, John Stufken

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The paper considers a model for crossover designs with carryover effects and a random interaction between treatments and subjects. Under this model, two observations of the same treatment on the same subject are positively correlated and therefore provide less information than two observations of the same treatment on different subjects. The introduction of the interaction makes the determination of optimal designs much harder than is the case for the traditional model. Generalising the results of Bludowsky's thesis, the present paper uses Kushner's method to determine optimal approximate designs. We restrict attention to the case where the number of periods is less than or equal to the number of treatments. We determine the optimal designs in the important special cases that the number of periods is 3, 4 or 5. It turns out that the optimal designs depend on the variance of the random interactions and in most cases are not binary. However, we can show that neighbour balanced binary designs are highly efficient, regardless of the number of periods and of the size of the variance of the interaction effects.

Original languageEnglish (US)
Pages (from-to)517-533
Number of pages17
JournalAustralian and New Zealand Journal of Statistics
Volume57
Issue number4
DOIs
StatePublished - Dec 1 2015

Keywords

  • Carryover effects
  • Crossover design
  • Treatment effects
  • Universally optimal designs

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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