The problem of analysing longitudinal data that are complicated by possibly informative drop-out has received considerable attention in the statistical literature. Most researchers have concentrated on either methodology or application, but we begin this paper by arguing that more attention could be given to study objectives and to the relevant targets for inference. Next we summarize a variety of approaches that have been suggested for dealing with drop-out. A long-standing concern in this subject area is that all methods require untestable assumptions. We discuss circumstances in which we are willing to make such assumptions and we propose a new and computationally efficient modelling and analysis procedure for these situations. We assume a dynamic linear model for the expected increments of a constructed variable, under which subject-specific random effects follow a martingale process in the absence of drop-out. Informal diagnostic procedures to assess the tenability of the assumption are proposed. The paper is completed by simulations and a comparison of our method and several alternatives in the analysis of data from a trial into the treatment of schizophrenia, in which approximately 50% of recruited subjects dropped out before the final scheduled measurement time.