Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based on the use of the recently developed theory of imprecise probabilities. This work draws an explicit distinction between the related but nevertheless distinct questions of inference and decision in clinical trials. The traditional question of scientific interest asks 'Which treatment offers the greater chance of success?' and is the primary reason for conducting the clinical trial. The question of decision concerns the welfare of the patients in the clinical trial, asking whether the accumulated evidence favours one treatment over the other to such an extent that the next patient should decline randomization and instead express a preference for one treatment. Consideration of the decision question within the framework of imprecise probabilities leads to a mathematical definition of equipoise and a method for governing the randomization protocol of a clinical trial. This paper describes in detail the protocol for the conduct of clinical trials based on this new method of analysis, which is illustrated in a retrospective analysis of data from a clinical trial comparing the anti-emetic drugs ondansetron and droperidol in the treatment of postoperative nausea and vomiting. The proposed methodology is compared quantitatively using computer simulation studies with conventional clinical trial designs and is shown to maintain high statistical power with reduced sample sizes, at the expense of a high type I error rate that we argue is irrelevant in some specific circumstances. Particular emphasis is placed on describing the type of medical conditions and treatment comparisons where the new methodology is expected to provide the greatest benefit.