Estimation of a decreasing mean residual life based on ranked set sampling with an application to survival analysis.

IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2024-03-29 eCollection Date: 2024-11-01 DOI:10.1515/ijb-2023-0051
Elham Zamanzade, Ehsan Zamanzade, Afshin Parvardeh
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引用次数: 0

Abstract

The mean residual lifetime (MRL) of a unit in a population at a given time t, is the average remaining lifetime among those population units still alive at the time t. In some applications, it is reasonable to assume that MRL function is a decreasing function over time. Thus, one natural way to improve the estimation of MRL function is to use this assumption in estimation process. In this paper, we develop an MRL estimator in ranked set sampling (RSS) which, enjoys the monotonicity property. We prove that it is a strongly uniformly consistent estimator of true MRL function. We also show that the asymptotic distribution of the introduced estimator is the same as the empirical one, and therefore the novel estimator is obtained "free of charge", at least in an asymptotic sense. We then compare the proposed estimator with its competitors in RSS and simple random sampling (SRS) using Monte Carlo simulation. Our simulation results confirm the superiority of the proposed procedure for finite sample sizes. Finally, a real dataset from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) is used to show that the introduced technique can provide more accurate estimates for the average remaining lifetime of patients with breast cancer.

基于排序集抽样的平均剩余寿命递减估计,并应用于生存分析。
在给定的时间 t,种群中一个单位的平均剩余寿命(MRL)是在时间 t 仍存活的种群单位的平均剩余寿命。因此,改进 MRL 函数估计的一个自然方法就是在估计过程中使用这一假设。在本文中,我们在排序集抽样(RSS)中开发了一种 MRL 估计器,它具有单调性特性。我们证明它是真正 MRL 函数的强均匀一致估计器。我们还证明,引入的估计器的渐近分布与经验分布相同,因此,至少在渐近意义上,新估计器是 "免费 "获得的。然后,我们利用蒙特卡罗模拟将所提出的估计器与 RSS 和简单随机抽样 (SRS) 中的竞争对手进行了比较。我们的模拟结果证实了所提出的程序在有限样本量下的优越性。最后,我们使用了来自美国国家癌症研究所(NCI)的监测、流行病学和最终结果(SEER)项目的真实数据集,以证明所引入的技术能更准确地估计乳腺癌患者的平均剩余寿命。
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
International Journal of Biostatistics
International Journal of Biostatistics Mathematics-Statistics and Probability
CiteScore
2.30
自引率
8.30%
发文量
28
期刊介绍: The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.
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