Craig Bruce A, Sendi Peter P
Department of Statistics, 1399 Mathematical Sciences, Purdue University, West Lafayette, IN 47907-1399, USA.
Health Econ. 2002 Jan;11(1):33-42. doi: 10.1002/hec.654.
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.
离散时间马尔可夫链已成功用于研究慢性病的治疗方案和医疗保健协议。在这些情况下，描述疾病自然进展的转移矩阵通常是根据以固定间隔观察的队列进行估计的。然而，由于转移概率之间的复杂关系，矩阵的估计常常变得复杂。本文总结了在模型的周期长度与观察间隔一致、周期长度与观察间隔不一致以及观察间隔长度不相等时，获取转移矩阵最大似然估计的方法。此外，还讨论了自助法，作为一种评估最大似然估计不确定性以及为转移矩阵的函数（如预期生存率）构建置信区间的方法。
