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 identified.