We introduce a nonparametric estimator of the conditional survival function in the mixture cure model for right censored data when cure status is partially known. The estimator is developed for the setting of a single continuous covariate but it can be extended to multiple covariates. It extends the estimator of Beran (1981), which ignores cure status information. We obtain an almost sure representation, from which the strong consistency and asymptotic normality of the estimator are derived. Asymptotic expressions of the bias and variance demonstrate a reduction in the variance with respect to Beran's estimator. A simulation study shows that, if the bandwidth parameter is suitably chosen, our estimator performs better than others for an ample range of covariate values. A bootstrap bandwidth selector is proposed. Finally, the proposed estimator is applied to a real dataset studying survival of sarcoma patients.

翻译：我们针对右删失数据下的混合治愈模型，在治愈状态部分已知的情形下，引入了一个条件生存函数的非参数估计量。该估计量针对单一连续协变量的情景开发，但可扩展至多个协变量。它扩展了Beran (1981) 未利用治愈状态信息的估计量。我们获得了几乎必然表示形式，由此推导出该估计量的强相合性和渐近正态性。偏差与方差的渐近表达式表明，相比Beran估计量，其方差有所降低。模拟研究表明，若带宽参数选择适当，该估计量在广泛的协变量取值范围内优于其他估计量。我们提出了一种自助法带宽选择器。最后，将所提出的估计量应用于研究肉瘤患者生存的真实数据集。