Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.

中文翻译：

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死因数据随机缺失的危害函数估计

危害函数估计是生存分析的重要组成部分。兴趣通常集中在估计与特定死因相关的危险函数上。我们为风险函数提出了三个非参数核估计器，当死亡时间受到随机审查并且审查指标可能随机丢失时，所有这些估计器都是合适的。具体来说，我们提出了一个回归替代估计量、一个插补估计量和一个逆概率加权估计量。所有三个估计量都一致强一致且渐近正态。我们推导出这些估计器的均方误差和均方积分误差的渐近表示，并讨论了数据驱动的带宽选择方法。模拟研究，用于评估有限样本行为，表明建议的危险估计器表现相对较好。我们通过对一些血管疾病数据的分析来说明我们的方法。