Abstract

In survival analysis naturally observed lifetimes are not of large size and so the most commonly used maximum likelihood (ML) estimator that is often biased needs to be corrected in the sense of bias. In this paper, exact expression for the Fisher Information matrix under progressive type-I interval censoring (PTIC) scheme is given. Using the method proposed by Cox and Snell (J. Royal Stat. Soc. B., 30:248–265, 1968), we construct the first-order bias corrected maximum likelihood (BML) estimator under PTIC scheme. As an application, performance of the ML and BML estimators are compared by simulations when generated realizations under PTIC scheme follow Chen distribution. Furthermore, performance of the BML estimator is demonstrated through three sets of real data.

摘要

在生存分析中，自然观察到的生命周期并不大，因此最常用的最大似然 (ML) 估计量通常存在偏差，需要在偏差的意义上进行校正。本文给出了渐进I型区间删失（PTIC）方案下Fisher信息矩阵的精确表达式。使用 Cox 和 Snell (J. Royal Stat. Soc. B., 30:248–265, 1968) 提出的方法，我们构建了 PTIC 方案下的一阶偏差校正最大似然 (BML) 估计器。作为一个应用程序，当 PTIC 方案下生成的实现遵循 Chen 分布时，通过模拟比较了 ML 和 BML 估计器的性能。此外，通过三组真实数据证明了 BML 估计器的性能。