Splitting the sample at the largest uncensored observation

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-03-01 DOI:10.3150/21-bej1417

R. Maller, S. Resnick, S. Shemehsavar

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引用次数: 3

Abstract

We calculate finite sample and asymptotic distributions for the largest censored and uncensored survival times, and some related statistics, from a sample of survival data generated according to an iid censoring model. These statistics are important for assessing whether there is sufficient follow-up in the sample to be confident of the presence of immune or cured individuals in the population. A key structural result obtained is that, conditional on the value of the largest uncensored survival time, and knowing the number of censored observations exceeding this time, the sample partitions into two independent subsamples, each subsample having the distribution of an iid sample of censored survival times, of reduced size, from truncated random variables. This result provides valuable insight into the construction of censored survival data, and facilitates the calculation of explicit finite sample formulae. We illustrate for distributions of statistics useful for testing for sufficient follow-up in a sample, and apply extreme value methods to derive asymptotic distributions for some of those. MSC 2010 subject classifications: MSC2000 Subject Classifications: Primary 62N01, 62N02, 62N03, 62E10, 62E15, 62E20, G2G05; secondary 62F03, 62F05, 62F12, 62G32.

查看原文本刊更多论文

在最大的未经审查的观察中分割样本

我们从根据iid审查模型生成的生存数据样本中计算了最大审查和未审查生存时间的有限样本和渐近分布，以及一些相关统计数据。这些统计数据对于评估样本中是否有足够的随访以确定人群中是否存在免疫或治愈个体非常重要。所获得的一个关键结构结果是，在最大未审查生存时间的值的条件下，并且知道超过该时间的审查观察的数量，样本被划分为两个独立的子样本，每个子样本具有来自截断随机变量的缩小大小的审查生存时间iid样本的分布。这一结果为截尾生存数据的构造提供了有价值的见解，并有助于显式有限样本公式的计算。我们举例说明了统计数据的分布，这些分布可用于测试样本中是否有足够的后续行动，并应用极值方法推导其中一些的渐近分布。MSC 2010主题分类：MSC2000主题分类：初级62N01、62N02、62N03、62E10、62E15、62E20、G2G05；次级62F03、62F05、62F12、62G32。

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

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.