Semiparametric random censorship models for survival data with long-term survivors

In this article, we study a semiparametric random censorship model for survival data in the presence of long-term survivors. Local likelihood method is employed to estimate the conditional mean regression function of binary random variables. The proposed estimators for the survival function and the cure rate, as well as their asymptotic properties, are investigated based on empirical and U-statistical processes. In particular, the proposed estimator for the cure rate is shown to be superior over the previous estimator considered by Maller and Zhou in the sense of having a smaller asymptotic variance. This semiparametric random censorship model with related estimation methods provide an efficient alternative for survival analysis with long-term survivors.