DOI link for Introduction
In a completely randomized, or parallel groups, trial, each experimental unit is randomized to receive one experimental treatment. Such experimental designs are the foundation of much research, particularly in medicine and the health sciences. A good general introduction to experimental design is given by Cox and Reid (2000), while Pocock (1983), Friedman et al. (1998), Armitage (1996) and DeMets (2002) consider trial design and related issues in a clinical setting. A cross-over trial is distinguished from such a parallel groups study by each unit, or subject, receiving a sequence of experimental treatments. Typically, however, the aim is still to compare the effects of individual treatments, not the sequences themselves. There are many possible sets of sequences that might be used in a design, depending on the number of treatments, the length of the sequences and the aims of the trial. The simplest design is the two-period two-treatment or 2×2 design. In this design each subject receives two different treatments which we conventionally label as A and B. Half the subjects receive A first and then, after a suitably chosen period of time, cross over to B. The remaining subjects receive B first and then cross over to A. A typical example of such a trial is given in Example 1.1.