In most clinical trials, some patients do not complete their intended follow-up according to protocol, for a variety of reasons, and are often described as having 'dropped out' before the conclusion of the trial. Their subsequent measurements are missing, and this makes the analysis of the trial's repeated measures data more difficult. In this paper we briefly review the reasons for patient drop-out, and their implications for some commonly used methods of analysis. We then propose a class of models for modelling both the response to treatment and the drop-out process. Such models are readily fitted in a Bayesian framework using non-informative priors with the software BUGS. The results from such models are then compared with the results of standard methods for dealing with missing data in clinical trials, such as last observation carried forward. We further propose the use of a time transformation to linearize an asymptotic pattern of repeated measures over time and therefore simplify the modelling. All these ideas are illustrated using data from a five-arm asthma clinical trial.