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Parallel, AA/BB, AB/BA and Balaam's design: efficient and maximin choices when testing the treatment effect in a mixed effects linear regression


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Math J. J.M. Candel, Department Methodology and Statistics, Maastricht University, P.O. Box 616, 6200 MD,Maastricht, The Netherlands.



When examining the effect of treatment A versus B, there may be a choice between a parallel group design, an AA/BB design, an AB/BA cross-over and Balaam's design. In case of a linear mixed effects regression, it is examined, starting from a flexible function of the costs involved and allowing for subject dropout, which design is most efficient in estimating this effect. For no carry-over, the AB/BA cross-over design is most efficient as long as the dropout rate at the second measurement does not exceed /(1 + ρ), ρ being the intraclass correlation. For steady-state carry-over, depending on the costs involved, the dropout rate and ρ, either a parallel design or an AA/BB design is most efficient. For types of carry-over that allow for self carry-over, interest is in the direct treatment effect plus the self carry-over effect, with either an AA/BB or Balaam's design being most efficient. In case of insufficient knowledge on the dropout rate or ρ, a maximin strategy is devised: choose the design that minimizes the maximum variance of the treatment estimator. Such maximin designs are derived for each type of carry-over. Copyright © 2012 John Wiley & Sons, Ltd.

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