Semi-Markov Models with Phase-Type Sojourn Distributions
Semi-Markov Models with Phase-Type Sojourn Distributions
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DOI：
10.1111/j.1541-0420.2009.01339.x
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发表时间：
2010-09-01
期刊：
影响因子：
1.9
通讯作者：
Sharples, Linda D.
中科院分区：
文献类型：
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作者：
Titman, Andrew C.;Sharples, Linda D.
连续时间多状态模型广泛用于分类反应数据，特别是在慢性疾病的建模中。然而，当过程只在离散的时间点观察时，没有关于时间或观察时间之间事件类型的信息，除非做出马尔可夫假设，否则推理是困难的。这种假设可能是有限的，因为疾病状态之间的转换率可能取决于进入当前状态后的时间。这样的公式得到半马尔可夫模型。我们表明，考虑一类具有相型逗留分布的半马尔可夫模型，可以减轻与面板观测数据拟合半马尔可夫模型相关的计算问题。这允许应用隐马尔可夫模型的方法。此外，还对观测状态存在分类误差的模型进行了扩展。该方法在与肺移植后患者闭塞性细支气管炎综合征发展相关的数据集上得到了证明。
Continuous-time multistate models are widely used for categorical response data, particularly in the modeling of chronic diseases. However, inference is difficult when the process is only observed at discrete time points, with no information about the times or types of events between observation times, unless a Markov assumption is made. This assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state. Such a formulation results in a semi-Markov model. We show that the computational problems associated with fitting semi-Markov models to panel-observed data can be alleviated by considering a class of semi-Markov models with phase-type sojourn distributions. This allows methods for hidden Markov models to be applied. In addition, extensions to models where observed states are subject to classification error are given. The methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post-lung-transplantation patients.