论文标题
重建Kaplan-估计器作为M估计器及其信心带
Reconstruct Kaplan--Meier Estimator as M-estimator and Its Confidence Band
论文作者
论文摘要
Kaplan--Meier（KM）估计量提供了用于事件时间数据的生存功能的非参数估计值，它在临床研究，工程，经济学和其他领域中广泛应用。广泛研究了KM估计量（包括其一致性和渐近分布）的理论特性。我们通过基于一致性最大化二次M-功能来重建KM估计器作为M估计量，该二次M-功能可以使用期望 - 最大化（EM）算法来计算。结果表明，EM算法的收敛点与传统的KM估计器一致，从而将KM估计器作为M估计器提供了新的解释。使用M估计理论建立了包括大样本差异和限制KM估计器的限制分布的理论特性。两个真实数据集上的仿真和应用表明，所提出的M估计器完全等同于KM估计器，而置信区间和频段也可以得出。
The Kaplan--Meier (KM) estimator, which provides a nonparametric estimate of a survival function for time-to-event data, has wide application in clinical studies, engineering, economics and other fields. The theoretical properties of the KM estimator including its consistency and asymptotic distribution have been extensively studied. We reconstruct the KM estimator as an M-estimator by maximizing a quadratic M-function based on concordance, which can be computed using the expectation--maximization (EM) algorithm. It is shown that the convergent point of the EM algorithm coincides with the traditional KM estimator, offering a new interpretation of the KM estimator as an M-estimator. Theoretical properties including the large-sample variance and limiting distribution of the KM estimator are established using M-estimation theory. Simulations and application on two real datasets demonstrate that the proposed M-estimator is exactly equivalent to the KM estimator, while the confidence interval and band can be derived as well.
