The design of cross-over studies subject to dropout

A cross-over study is a comparitive experiment in which subjects receive a sequence of two or more treatments, one in each of a series of successive time periods, and the response of each subject is measured at the end of every period. A common problem, particularly in medicine, is that subjects fail to complete a study through dropping out during the later stages of the trial for reasons unrelated to the treatments received! Current practice is to select a design for a study on the basis of its performance under the assumption that no subjects drop out, using a criterion such as A-optimality. This is an unrealistic assumption for many medical applications. This thesis investigates how studies should be designed when it is unrealistic to assume that subjects will not drop out.A method of assessing cross-over designs is presented which judges how accurately all the pairwise treatment comparisons are estimated under the assumption that each subject has a fixed probability of dropping out during the final period, independent of treatment received and the other subjects. The method of design assessment is computationally intensive even for studies involving a relatively small number of subjects. Ways of reducing the amount of computation required are presented through establishing the link between implemented designs and a colouring problem in combinatorial theory. The reductions achieved make feasible investigations of currently used designs for cross-over studies.The results of investigations are presented for designs for the cases of particular practical importance, namely four treatment, four period and three treatment, three period studies, in which a simple carry-over model is assumed for the observations. Designs which are more robust to final period dropout than the currently favoured designs are identifie