In earlier chapters we have considered parallel group designs, where each subject is randomised to receive one of a number of alternative treatments. By contrast, in cross-over trials, subjects are randomised to receive different sequences of treatments, with the outcome being assessed for each treatment period. As before, we have a choice in analysis between fixed effects models and random effects models. In this context, we describe the treatment effect as being crossed with a random effect (subjects).

The vast majority of cross-over trials which are carried out in practice have the same basic design. Every subject receives each of the treatments being evaluated, for a standard period of time, with the outcome variables being assessed in the same way in each period of treatment. The simplest and most commonly encountered such design employs just two treatments, and is often referred to as a 2 x 2 cross-over trial, or as an AB/BA design. The use of this design with normally distributed data will be covered in some depth in Section 7.3. The use of more than two treatments with patients receiving every treatment is known as a higher order complete block design and is covered in Section 7.4. More complicated designs are considered in Sections 7.5 and 7.6. In Section 7.7 we will show how covariance pattern models can be employed in the analysis of cross-over trials. The following two sections (7.8 and 7.9) will give examples of the analysis of binary data and categorical data in the setting of cross-over trials. Data following Poisson distributions are not directly covered, but follow the same generalised linear mixed model approach used for binary data. Section 7.10 will consider the use of information from random effects models in the planning of future studies. The chapter finishes with a discussion of some general points in relation to the analysis of cross-over trials (Section 7.11).

Applied Mixed Models in Medicine, Second Edition H. Brown and R. Prescott © 2006 John Wiley & Sons, Ltd ISBN: 0-470-02356-2

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