This paper considers a composite nonparametric product limit estimator for estimating the distribution of survival times when the data are length-biased and right censored. Our method takes into account auxiliary information that frequently arises in survival analysis, and is easier to implement than existing methods for estimating survival functions. We derive a strong representation of the proposed estimator, establish its consistency and asymptotic normality, and derive its convergence rate of approximation. As well, we prove that auxiliary information improves the asymptotic efficiency of the proposed estimator, and provide the values of the composite weights that result in the largest efficiency gain. Our proposed estimator fares well in comparison with other more complex methods in finite samples and offers a clear advantage with respect to computational time.

中文翻译：

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估计长度偏向和右删失数据下生存时间分布的复合非参数乘积极限方法

本文考虑了一种复合非参数乘积极限估计器，用于估计数据有长度偏向和右删失时的生存时间分布。我们的方法考虑了生存分析中经常出现的辅助信息，并且比现有的估计生存函数的方法更容易实现。我们推导出所提出的估计量的强表示，建立其一致性和渐近正态性，并推导出其近似收敛速度。同样，我们证明了辅助信息提高了所提出的估计器的渐近效率，并提供了导致最大效率增益的复合权重值。