Wang Chunjie, Sun Jianguo, Sun Liuquan, Zhou Jie, Wang Dehui
Mathematics School and Institute of Jilin University, Changchun, 130012, People's Republic of China.
Lifetime Data Anal. 2012 Oct;18(4):434-45. doi: 10.1007/s10985-012-9223-7. Epub 2012 Jun 27.
This paper discusses nonparametric estimation of a survival function when one observes only current status data (McKeown and Jewell, Lifetime Data Anal 16:215-230, 2010; Sun, The statistical analysis of interval-censored failure time data, 2006; Sun and Sun, Can J Stat 33:85-96, 2005). In this case, each subject is observed only once and the failure time of interest is observed to be either smaller or larger than the observation or censoring time. If the failure time and the observation time can be assumed to be independent, several methods have been developed for the problem. Here we will focus on the situation where the independent assumption does not hold and propose two simple estimation procedures under the copula model framework. The proposed estimates allow one to perform sensitivity analysis or identify the shape of a survival function among other uses. A simulation study performed indicates that the two methods work well and they are applied to a motivating example from a tumorigenicity study.
本文讨论了在仅观察当前状态数据时生存函数的非参数估计（麦基翁和朱厄尔，《生存数据分析》16:215 - 230，2010；孙，《区间删失失效时间数据的统计分析》，2006；孙和孙，《加拿大统计学杂志》33:85 - 96，2005）。在这种情况下，每个受试者仅被观察一次，并且感兴趣的失效时间被观察到小于或大于观察或删失时间。如果可以假定失效时间和观察时间是独立的，针对该问题已经开发了几种方法。在此我们将关注独立假设不成立的情况，并在Copula模型框架下提出两种简单的估计程序。所提出的估计值允许人们进行敏感性分析或识别生存函数的形状等其他用途。进行的模拟研究表明这两种方法效果良好，并将它们应用于一个来自致瘤性研究的激励示例。
