左截断右删失数据下非参数估计方法的研究

The Study of Nonparametric Estimate Method for Left Truncated and Right Censored Data

目的针对左截断右删失数据,现有的非参极大似然估计法(NPMLE)和Breslow-Fleming-Harrington估计法(BFH)都对小风险集情形极为敏感,此时生存率会出现急速下降,本文除了提出校正精度的新估计法,同时对现有方法进行比较研究。方法基于现有NPMLE和BFH,结合Lai-Ying加权思想和条件概率,介绍加权NPMLE和条件NPMLE法,并提出加权BFH法。利用绝对误差积分(IAE)和平均宽度积分(IAW)指标,通过模拟研究比较上述方法的估计精度。结果模拟结果显示NPMLE、BFH、加权NPMLE、加权BFH和条件NPMLE法的IAE值依次递增,而IAW值显示加权BFH法最小,NPMLE法最大,BFH、条件NPMLE和加权NPMLE法在高低删失率下IAW大小相互逆转。结论结合模拟结果和实际例子,存在小风险集时推荐使用加权BFH法,其次加权NPMLE法;没有小风险集时5种方法基本一致。

Objective Nonparametric maximum likelihood estimate （NPMLE） and Breslow-Fleming-Harrington estimate （BFH）are extremely sensitive to small risk set for left truncated and right censored data, this study aims to develop estimation methods to improve the estimation accuracy and compare the existing methods. Methods We introduced the NPMLE, weighted NPMLE, conditional NPMLE, BFH and a new weighted BFH estimate. Simulation studies were carried out to compare five methods via the integrated absolute error（IAE） and integrated average width（IAW）. Results The IAE of NPMLE, BFH, weighted NPMLE,weighted BFH and conditional NPMLE is ascending in turn;The IAW of weighted BFH is the lowest and NPMLE is the largest, BFH, conditional NPMLE and weighted NPMLE is reversed under different censored rate. Conclusion According to the results of simulation and example, weighted BFH and weighted NPMLE is recommended in turn when the risk set is small. Otherwise, the results of five methods would be consistent.