Pan W, Chappell R
Division of Biostatistics, University of Minnesota, Minneapolis, USA.
Lifetime Data Anal. 1998;4(2):187-202. doi: 10.1023/a:1009637624440.
It is well-known that the nonparametric maximum likelihood estimator (NPMLE) may severely under-estimate the survival function with left truncated data. Based on the Nelson estimator (for right censored data) and self-consistency we suggest a nonparametric estimator of the survival function, the iterative Nelson estimator (INE), for arbitrarily truncated and censored data, where only few nonparametric estimators are available. By simulation we show that the INE does well in overcoming the under-estimation of the survival function from the NPMLE for left-truncated and interval-censored data. An interesting application of the INE is as a diagnostic tool for other estimators, such as the monotone MLE or parametric MLEs. The methodology is illustrated by application to two real world problems: the Channing House and the Massachusetts Health Care Panel Study data sets.
众所周知，非参数极大似然估计器（NPMLE）对于左截断数据可能会严重低估生存函数。基于纳尔逊估计器（用于右删失数据）和自一致性，我们针对任意截断和删失数据提出了一种生存函数的非参数估计器——迭代纳尔逊估计器（INE），而在这种情况下可用的非参数估计器很少。通过模拟，我们表明INE在克服NPMLE对左截断和区间删失数据的生存函数低估方面表现良好。INE的一个有趣应用是作为其他估计器（如单调MLE或参数MLE）的诊断工具。通过应用于两个实际问题（钱宁之家和马萨诸塞州医疗保健小组研究数据集）来说明该方法。
