A NONPARAMETRIC-ESTIMATION PROCEDURE FOR A PERIODICALLY OBSERVED 3-STATE MARKOV PROCESS, WITH APPLICATION TO AIDS

• 成果类型: Article
• 署名作者: FRYDMAN, H
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 1992
• 页码: 853-866
• 关键词: censored survival-data; counting-processes; Consistency; MODEL

摘要

Estimation in a three-state Markov process with irreversible transitions in the presence of interval-censored data is considered. A nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented. A self-consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self-consistent estimator. This extends the idea of self-consistency introduced by Efron to the estimation of more than one parameter. An algorithm, based on self-consistency equations, is provided for the computation of the estimators. This algorithm is a generalization of an algorithm by Turnbull which yields an estimator of a distribution function for interval-censored univariate data. The methods are applied to Aids data.