Dauxois Jean-Yves, Guilloux Agathe, Kirmani Syed N U A
Université de Toulouse-INSA, IMT, UMR CNRS 5219, 135, Avenue de Rangueil, 31077 , Toulouse cedex 4, France,
Lifetime Data Anal. 2014 Apr;20(2):276-302. doi: 10.1007/s10985-013-9248-6. Epub 2013 Mar 3.
What population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time t(0) represents not the target density f (t) but its length-biased version proportional to t f (t), for t > 0. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent censoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators.
该样本代表的是哪些人群？在持续时间研究中估计生存函数时，这个问题的答案至关重要。众所周知，在一个稳定的人群中，在时间t(0)从该人群中抽取的横截面样本所获得的生存数据，对于t > 0而言，代表的不是目标密度f(t)，而是与t f(t)成比例的长度偏倚版本。在存在竞争风险和删失的情况下，从这种长度偏倚样本中估计生存函数的问题变得更加复杂且有趣。本文提出了一种与混合泊松过程相关的抽样方案，并在假设两个独立竞争风险具有成比例风险率的情况下，开发了目标人群生存函数的非参数估计量。考虑了两种情况：在长度偏倚抽样之前有无独立删失。在每种情况下，都证明了所提出估计量生成的过程的弱收敛性。一项关于政治领导人掌权持续时间的著名研究被用来阐述我们的结果。最后，进行了一项模拟研究，以评估我们估计量的有限样本行为。
