In failure time studies involving a chronic disease such as cancer, several competing causes of mortality may be operating. Commonly, the conventional statistical technique of Kaplan–Meier, which is only meaningfully interpreted by assuming independence of failure types and the censoring mechanism, is employed in clinical research involving competing risks data. Some authors have advocated the use of a cause-specific cumulative incidence function which takes into account the existence of other events within a competing risks framework, without making any assumption about independence. Lunn and McNeil have proposed an approach based on an extension of the Cox proportional hazards regression, which enables direct comparisons between failure types. We have extended this approach to estimate cause-specific cumulative incidence. As it is often not easy to follow competing risks methodology in the literature, this paper sets out systematically the assumptions made and the steps taken to implement four different methods of analysing competing risks data using cumulative incidence rates or the Kaplan–Meier estimates of cause-specific failure probabilities. The data obtained from a randomized trial of patients with osteosarcoma were used to compare these four approaches. As illustrated using the osteosarcoma data, the estimates of the classical Kaplan–Meier methods have larger numerical values than the cause-specific cumulative incidence. On the other hand, estimates of the cause-specific cumulative incidence rates from the conventional method and the modified Cox method are highly comparable. Copyright © 2001 John Wiley & Sons, Ltd.