Nathoo F, Dean C B
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada.
Biometrics. 2007 Sep;63(3):881-91. doi: 10.1111/j.1541-0420.2007.00752.x.
Studies of recurring infection or chronic disease often collect longitudinal data on the disease status of subjects. Two-state transitional models are useful for analysis in such studies where, at any point in time, an individual may be said to occupy either a diseased or disease-free state and interest centers on the transition process between states. Here, two additional features are present. The data are spatially arranged and it is important to account for spatial correlation in the transitional processes corresponding to different subjects. In addition there are subgroups of individuals with different mechanisms of transitions. These subgroups are not known a priori and hence group membership must be estimated. Covariates modulating transitions are included in a logistic additive framework. Inference for the resulting mixture spatial Markov regression model is not straightforward. We develop here a Monte Carlo expectation maximization algorithm for maximum likelihood estimation and a Markov chain Monte Carlo sampling scheme for summarizing the posterior distribution in a Bayesian analysis. The methodology is applied to a study of recurrent weevil infestation in British Columbia forests.
对复发性感染或慢性疾病的研究通常会收集有关研究对象疾病状态的纵向数据。两状态转换模型对于此类研究的分析很有用，在这类研究中，在任何时间点，个体都可被认为处于患病或无病状态，且关注点在于状态之间的转换过程。在此，还存在另外两个特征。数据是按空间排列的，在对应不同研究对象的转换过程中考虑空间相关性很重要。此外，存在具有不同转换机制的个体亚组。这些亚组事先并不知晓，因此必须估计组成员身份。调节转换的协变量包含在逻辑加性框架中。对所得混合空间马尔可夫回归模型进行推断并非易事。我们在此开发了一种用于最大似然估计的蒙特卡罗期望最大化算法，以及一种用于在贝叶斯分析中总结后验分布的马尔可夫链蒙特卡罗抽样方案。该方法应用于对不列颠哥伦比亚省森林中象鼻虫反复侵扰的一项研究。
