Estimation in the single change-point hazard function for interval-censored data with a cure fraction.

In reliability or survival analysis, the hazard function plays a significant part for it can display the instantaneous failure rate at any time point. In practice, the abrupt change in hazard function at an unknown time point may occur after a maintenance activity or major operation. Under these circumstances, identifying the change point and estimating the size of the change are meaningful. In this paper, we assume that the hazard function is piecewise constant with a single jump at an unknown time. We propose the single change-point model for interval-censored survival data with a cure fraction. Estimation methods for the proposed model are investigated, and large-sample properties of the estimators are established. Simulation studies are carried out to evaluate the performance of the estimating method. The liver cancer data and breast cancer data are analyzed as the applications.