Finite sample and asymptotic distributions of a statistic for sufficient follow-up in cure models

Pub Date : 2023-04-19 DOI:10.1002/cjs.11771
Ross Maller, Sidney Resnick, Soudabeh Shemehsavar
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Abstract

The existence of immune or cured individuals in a population and whether there is sufficient follow-up in a sample of censored observations on their lifetimes to be confident of their presence are questions of major importance in medical survival analysis. Here we give a detailed analysis of a statistic designed to test for sufficient follow-up in a sample. Assuming an i.i.d. censoring model, we obtain exact finite-sample and asymptotic distributions for the statistic, and use these to calculate the power of a test based on it. A particularly useful finding is that the asymptotic distribution of the test statistic is parameter-free in the null case when follow-up is insufficient. The methods are illustrated with application to a glioma cancer dataset.

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治疗模型中足够随访的统计量的有限样本和渐近分布
人口中是否存在免疫或痊愈的个体,以及在对这些个体的一生进行删减观测的样本中是否有足够的随访来确信这些个体的存在,是医学生存分析中非常重要的问题。在此,我们将详细分析一种旨在检验样本中是否有足够随访的统计量。假定存在 i.i.d. 普查模型,我们将得到该统计量的精确有限样本分布和渐近分布,并利用这些分布计算基于该统计量的检验功率。一个特别有用的发现是,在随访不充分的无效情况下,检验统计量的渐近分布是无参数的。这些方法将应用于胶质瘤癌症数据集。
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