Current status and right-censored data structures when observing a marker at the censoring time

• 成果类型: Article
• 署名作者: Van der Laan, MJ; Jewell, NP
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 512-535
• 关键词: survival sacrifice experiments; nonparametric-estimation; onset; lifetime; AGE

摘要

We study nonparametric estimation with two types of data structures. In the first data structure n i.i.d. copies of (C, N(C)) are observed, where N is a finite state counting process jumping at time-variables of interest and C a random monitoring time. In the second data structure n i.i.d. copies of (C boolean AND T, I(T less than or equal to C), N (C boolean AND T)) are observed, where N is a counting process with a final jump at time T (e.g., death). This data structure includes observing right-censored data on T and a marker variable at the censoring time. In these data structures, easy to compute estimators, namely (weighted)pool-adjacent-violator estimators for the marginal distributions of the unobservable time variables, and the Kaplan-Meier estimator for the time T till the final observable event, are available. These estimators ignore seemingly important information in the data. In this paper we prove that, at many continuous data generating distributions the ad hoc estimators yield asymptotically efficient estimators of rootn-estimable parameters.