Statistica Sinica 19 (2009), 377-390

A CHANGE-POINT MODEL FOR SURVIVAL

DATA WITH LONG-TERM SURVIVORS

Xiaobing Zhao$^1$, Xianyi Wu$^2$ and Xian Zhou$^3$

$^1$Jiang Nan University, $^2$East China Normal University and

$^3$Macquarie University

Abstract: Change-point hazard models have been extensively investigated by many authors, but the literature on change-point problems with survival data subject to censoring is rather small. In an earlier example provided by Matthews and Farewell (1982), a set of nonlymphoblastic leukemia data were fitted by using a change-point model. But for that data set, the Kaplan-Meier estimator of the distribution function levels off well below 1, which indicates the presence of ``long-term survivors'' in the data. In this paper, we propose a new change-point model for survival data that accounts for long-term survivors. Estimation methods for the proposed model are investigated, and large-sample properties of the estimators are established. A simulation study is carried out to evaluate the performance of the estimating methods. As an application, the nonlymphoblastic leukemia data are re-analyzed using the new model.

Key words and phrases: Change-point hazard model, long-term survivors, pseudo-maximum likelihood, random censoring.