Crossover designs in clinical trials
by
Nye John
University of Waikato, New Zealand

Many diseases and conditions are studied using a crossover design in a clinical trial. In such trials, subjects receive a sequence of treatments, specified by the design, over successive periods of time. Treatments can then be compared using repeated measurements taken on each subject. A difficulty is that the effect of a treatment applied in one period may persist into the following period. In order to estimate the treatment effects free of these carry-over effects, it will be necessary to make important assumptions about the model.

A simple model is one that assumes that a carry-over effect is additive, in the sense that it is unaffected by the current treatment or by the period in which it is applied. This model has been the basis for much theoretical research and, more recently, the development of computer optimisation algorithms for the construction of efficient crossover designs. However, despite its widespread use, it has been criticized for taking a simplistic view of how pharmaceutical treatments produce their effects. Often additivity cannot be assumed, as a treatment by carry-over interaction is likely to be present. While the full set of interactions can be modelled, a simple and potentially realistic alternative is to allow an additional set of carry-over effects when a treatment carries over into itself. Other self-adjacency models have also been proposed. The simple model may also be inappropriate when one or more of the treatments are placebos. A consequence of such criticisms is that designs chosen on the basis of the simple model are unlikely to be adequate under alternative and more realistic modelling assumptions.

Some limited work has been carried out to construct designs using other models. However, no general theory or construction algorithm exists, partly because of the complexity of the estimating equations of the alternative models. In this paper a unified theory for the construction of efficient crossover designs will be developed for a wide range of models, through the establishment of a link between the crossover design and a surrogate row-column design. It will be shown that updating formulae can be applied to the estimating equations of the surrogate design to give a fast interchange algorithm for constructing efficient crossover designs. Some examples will be presented.

This work has been carried out in collaboration with Ken Russell of the University of Wollongong and my colleague David Whitaker.

Date received: May 3, 2002