A further design which can require fewer patients than the corresponding parallel group design is known as the cross-over trial. Here, every patient receives all the treatments under investigation (which may include a placebo), but the order in which they receive them is randomized. The general, simplified, design of a cross-over trial is shown in Fig. 4.6. In the case of a two-treatment cross-over trial, eligible patients are randomized to receive either A followed by B or B followed by A. An example is given by a trial in patients with chronic cancer-related pain , in which patients were randomized to receive contolled-release oxycodone or morphine for seven days, then switched to the alternative treatment for the next seven days. Pain levels were recorded by the patients on a 0-100 mm visual analogue scale, and within-patient differences in pain levels on the two treatments compared.
The benefit of such a design is that each patient acts as their own control, effectively halving the number of patients required when compared to a conventional parallel group design. In addition, because comparisons are made within-patients, intra-patient variability is eliminated which can also lead to a requirement for a smaller sample size. A further benefit is that the patients are in a position to express a treatment preference, having experienced both.
In a trial such as this where each patient is intended to receive two or more treatments in succession, and where the efficiency of the design requires that patients do so, there are naturally constraints. It is only appropriate for chronic conditions, which are stable at least over the time period of the study; there must be a negligible risk of death whilst
on study. It cannot involve treatments which cure the condition, they must only alleviate symptoms, and finally the treatment effects must be short-lasting, such that the effect is ended by the time the next treatment starts. In practice, this is achieved by having a 'wash-out' period between the treatments.
There are a number of potential problems with this design which can mean that only the first period of treatment can be used. These include:
♦ drop-out after the first treatment, which may be related to treatment,
♦ carry-over of treatment effect from the first period which is not eliminated by the wash-out period,
♦ treatment by period interaction - in which the effect of a treatment is substantially different in the two periods - making their combination inappropriate.
Where these problems exist, data from the first period can be used, but the trial effectively becomes a parallel group trial and the sample size is effectively halved - thus, as for the factorial design, the final treatment comparison can be underpowered. Hills and Armitage  provided a general rule for determining whether to use a parallel group or cross-over design:
♦ if an unequivocal result is required from a clinical trial and enough patients are available, then a simple parallel trial should be carried out (this will be approximately twice the size of the cross-over trial to have the same statistical power);
♦ if the number of patients available is limited and a cross-over design is chosen, results should be presented giving evidence that the basic assumptions are fulfilled and if necessary, basing conclusions on the first period only.
The design requirements make cross-over trials inappropriate for most comparisons of cytotoxic treatments for cancer and there are few examples to be found. However, it can potentially be a useful design when evaluating treatments for symptoms which are either chronic or occur at predictable times such as treatment-related nausea. Detailed discussion of cross-over trials can be found in the book by Senn .
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