Efficiency of the Breslow estimator in semiparametric transformation models.

IF 1.2 3区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Lifetime Data Analysis Pub Date : 2024-04-01 Epub Date: 2023-11-26 DOI:10.1007/s10985-023-09611-w
Theresa P Devasia, Alexander Tsodikov
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引用次数: 0

Abstract

Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we derive the relative efficiency of the Breslow estimator and consider the properties of the two estimators using simulations and real data on prostate cancer survival.

Abstract Image

半参数变换模型中Breslow估计量的效率。
失效时间数据的半参数转换模型由参数回归成分和未指定的累积基线危险组成。累积基线危害的非参数极大似然估计量(NPMLE)可以用引入加权布雷斯洛估计量(Weighted Breslow)的权重来概括。在任何给定的时间点,权重调用累积基线风险的未来积分,这提出了理论和计算上的挑战。一个更简单的非mle Breslow型估计器(Breslow)是早先从鞅估计方程(MEE)中推导出来的,在过去的历史条件下,观察到的和期望的故障计数相等。尽管有许多成功的理论和计算发展,但更简单的Breslow估计器仍然被普遍使用,作为简单性和感知到的完全效率损失之间的折衷。本文推导了Breslow估计器的相对效率,并利用前列腺癌生存的模拟和真实数据考虑了这两种估计器的性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Lifetime Data Analysis
Lifetime Data Analysis 数学-数学跨学科应用
CiteScore
2.30
自引率
7.70%
发文量
43
审稿时长
3 months
期刊介绍: The objective of Lifetime Data Analysis is to advance and promote statistical science in the various applied fields that deal with lifetime data, including: Actuarial Science – Economics – Engineering Sciences – Environmental Sciences – Management Science – Medicine – Operations Research – Public Health – Social and Behavioral Sciences.
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