Titman Andrew C, Sharples Linda D
Department of Mathematics and Statistics, Lancaster University, Lancaster, UK.
Biometrics. 2010 Sep;66(3):742-52. doi: 10.1111/j.1541-0420.2009.01339.x.
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.
连续时间多状态模型广泛应用于分类响应数据，尤其是在慢性病建模中。然而，当过程仅在离散时间点被观测时，推断会很困难，因为在观测时间之间没有关于事件发生时间或类型的信息，除非做出马尔可夫假设。这种假设可能具有局限性，因为疾病状态之间的转变率可能反而取决于进入当前状态后的时间。这样的一种表述会产生一个半马尔可夫模型。我们表明，通过考虑一类具有相位型逗留分布的半马尔可夫模型，可以缓解将半马尔可夫模型拟合到面板观测数据时所涉及的计算问题。这使得隐藏马尔可夫模型的方法能够被应用。此外，还给出了对观测状态存在分类误差的模型的扩展。该方法在一个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验证。
