Zhao Lihui, Hu X Joan
Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA.
Can J Stat. 2013 Jun;41(2):237-256. doi: 10.1002/cjs.11176.
The semi-Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end-point of the support of the censoring time is strictly less than the right end-point of the support of the semi-Markov kernel, the transition probability of the semi-Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi-Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study.
对于具有多个状态的事件分析，半马尔可夫过程通常比经典马尔可夫过程提供了一个更好的框架。本文有两个目的。首先，我们表明，在存在右删失的情况下，当删失时间支持集的右端点严格小于半马尔可夫核支持集的右端点时，半马尔可夫过程的转移概率是不可识别的，并且文献中提出的估计量通常是不一致的。我们基于删失数据推导出转移概率的所有可达到值的集合，并使用该集合提出一种转移概率的非参数推断程序。其次，构建置信带的传统方法不适用于半马尔可夫核和逗留时间分布。我们提出新的扰动重采样方法来构建这些置信带。在构建过程中探索了不同的权重和变换。我们使用模拟来检验我们的提议，并通过最近一项癌症幸存者研究中的住院数据对其进行说明。
