Estimation of the transition matrix of a discrete-time Markov chain
Estimation of the transition matrix of a discrete-time Markov chain
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DOI：
10.1002/hec.654
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发表时间：
2002-01-01
期刊：
影响因子：
2.1
通讯作者：
Sendi, PP
中科院分区：
文献类型：
--
作者：
Craig, BA;Sendi, PP
离散时间马尔可夫链已被成功地用于研究慢性病的治疗方案和保健方案。在这些情况下，描述疾病自然发展的转移矩阵通常是根据以共同间隔观察的队列来估计的。然而，矩阵的估计往往由于转移概率之间的复杂关系而变得复杂。本文总结了当模型周期长度与观测区间重合、周期长度与观测区间不一致以及观测区间长度不相等时，转移矩阵的极大似然估计的求取方法。此外，还讨论了Bootstrap作为一种方法来评估最大似然估计的不确定性，以及为转移矩阵的函数(如期望存活率)构造可信区间。版权所有(C)2002 John Wiley Sons，Ltd.
Discrete-time Markov chains have been successfully used to investigate treatment programs and health care protocols for chronic diseases. In these situations, the transition matrix, which describes the natural progression of the disease, is often estimated from a cohort observed at common intervals. Estimation of the matrix, however, is often complicated by the complex relationship among transition probabilities. This paper summarizes methods to obtain the maximum likelihood estimate of the transition matrix when the cycle length of the model coincides with the observation interval, the cycle length does not coincide with the observation interval, and when the observation intervals are unequal in length. In addition, the bootstrap is discussed as a method to assess the uncertainty of the maximum likelihood estimate and to construct confidence intervals for functions of the transition matrix such as expected survival. Copyright (C) 2002 John Wiley Sons, Ltd.