An efficient estimate for the change point in the hazard function is obtained. This is based on a Bayesian estimator which uses equations concerning the parameters of a recently proposed hazard function. It is found through a simulation study that the proposed estimator is more efficient than the traditional estimators in many cases. Furthermore, experimental results that use data of breast cancer patients and some lymphoma data show that the proposed estimator is also practical in applications. (c) 2006 Elsevier B.V. All rights reserved.