Nonparametric regression estimates with censored data: Local linear smoothers and their applications

For censored time-to-event data, Beran (unpublished manuscript), followed by Doksum and Yandell (1982, Properties of Regression Estimates Based on Censored Survival Data) and Dabrowska (1987, Scandinavian Journal of Statistics 14, 181-197), suggested a nonparametric regression technique based on the kernel method to estimate the conditional survival function. We propose to improve the bias term and boundary effects of their procedure by using local linear fits. This is illustrated in this paper with simulated and real data. Moreover, consistency results for the local linear-based estimates of the conditional survival, cumulative hazard, mean, and median functions are also established.