Summary: When a woman diagnosed as having breast cancer has a tumour removed, it is important to try and predict whether she is likely to relapse within, say, the next three years. In the paper, the performance of a neural network classifier trained on a number of prognostic indicators is shown to be better than that of the clinical experts working with the same information. To obtain meaningful statistics with the relatively small dataset available, the network is trained using a modified form of the leave-one-out method. A procedure is also introduced for investigating how much ${\it $independent} information each input parameter contributes. This shows that, in this type of retrospective study, the type of therapy given to the woman does not significantly affect the network’s prediction of whether or not she will relapse within three years. Finally, since this problem, in common with many other medical problems, is plagued by a shortage of data, the final section of the paper reports on an investigation of whether or not multi-centre databases might be feasible.