We present a nonparametric study of current status data in the presence of death. Such data arise from biomedical investigations in which patients are examined for the onset of a certain disease, for example, tumor progression, but may die before the examination. A key difference between such studies on human subjects and the survival–sacrifice model in animal carcinogenicity experiments is that, due to ethical and perhaps technical reasons, deceased human subjects are not examined, so that the information on their disease status is lost. We show that, for current status data with death, only the overall and disease‐free survival functions can be identified, whereas the cumulative incidence of the disease is not identifiable. We describe a fast and stable algorithm to estimate the disease‐free survival function by maximizing a pseudo‐likelihood with plug‐in estimates for the overall survival rates. It is then proved that the global rate of convergence for the nonparametric maximum pseudo‐likelihood estimator is equal to O_p(n^−1/3) or the convergence rate of the estimated overall survival function, whichever is slower. Simulation studies show that the nonparametric maximum pseudo‐likelihood estimators are fairly accurate in small‐ to medium‐sized samples. Real data from breast cancer studies are analyzed as an illustration.

中文翻译：

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存在死亡时的非参数识别和当前状态数据估计

我们提出了存在死亡时当前状态数据的非参数研究。此类数据来自生物医学研究，在生物医学研究中，应检查患者是否患有某种疾病，例如肿瘤进展，但可能在检查之前死亡。此类针对人类受试者的研究与动物致癌性实验中的生存牺牲模型之间的主要区别在于，由于伦理或技术上的原因，未对已故的人类受试者进行检查，从而失去了有关其疾病状况的信息。我们显示，对于具有死亡的当前状态数据，只能确定总体和无疾病生存功能，而无法确定疾病的累积发生率。我们描述了一种快速稳定的算法，通过使用总生存率的插件估算值最大化伪似然性来估算无病生存功能。然后证明，非参数最大伪拟似然估计的全局收敛速度等于O _p（n ^-1/3）或估计的总体生存函数的收敛速度，以较慢者为准。仿真研究表明，在中小型样本中，非参数最大伪似然估计量非常准确。分析来自乳腺癌研究的真实数据作为例证。