Constrained Mixture Models in Competing Risks Problems

We consider the problem of modelling the failure-time distribution, where failure is due to two distinct causes. One approach is to adopt a two-component mixture model where the components correspond to the two di€erent causes of failure. However, routine application of this approach with typical parametric forms for the component densities proves to be inadequate in modelling the time to a re-replacement operation or death after the initial replacement of the aortic valve in the heart by a prosthesis, such as a xenograft valve. Hence we consider modi®cations to the usual mixture model approach to handle situations where there exists a strong dependency between the failure times of the distinct causes. With these modi®cations, a suitable model is able to be provided for the distribution of the time to a re-replacement operation conditional on the age of the patient at the time of the initial replacement operation. The estimate so obtained by the probability that a patient of a given age will undergo a re-replacement operation provides a useful guide to heart surgeons on the type of valve to be used in view of the patient's age. Copyright # 1999 John Wiley & Sons, Ltd.