文章基本信息

标题：ASYMPTOTIC PROPERTIES OF AALEN-JOHANSEN INTEGRALS FOR COMPETING RISKS DATA
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作者：Akio Suzukawa
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2002
卷号：32
期号：1
页码：77-93
DOI：10.14490/jjss.32.77
出版社：JAPAN STATISTICAL SOCIETY
摘要：This paper considers the competing risks problem with randomly right-censored data. Let F^(j)(t) be the cause-specific cumulative incidence function of a cause j, which is the probability of death due to a cause j by time t in the presence of other acting causes. The Aalen-Johansen estimator F^(j)_n is a nonparametric maximum likelihood estimator of F^(j). Under the assumption that all F^(j)’s and a censoring distribution are continuous, asymptotic properties of the Aalen-Johansen integral s^(j)_n=∫φdF^(j)_n are investigated. Let F be the overall lifetime distribution. We show that for any F-integrable function φ, the Aalen-Johansen integral s^(j)_n converges almost surely as n→∞. It is also shown that under some mild integrability assumptions for φ, the joint distribution of √¯ns^(j)_n’s for all causes is asymptotically multivariate normal.
关键词：Aalen-Johansen estimator;cumulative incidence function;Kaplan-Meier integral