Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular statistical technique, in particular when the exact transition times are not observed. The key quantities of interest are the transition rates, capturing the instantaneous risk of moving from one state to another. The main contribution of this work is to propose a joint semiparametric model for several possibly related multi-state processes (Seemingly Unrelated Multi-State, SUMS, processes), assuming a Markov structure for the transitions over time. The dependence between different processes is captured by specifying a joint random effect distribution on the transition rates of each process. We assume a flexible random effect distribution, which allows for clustering of the individuals, overdispersion and outliers. Moreover, we employ a graph structure to describe the dependence among processes, exploiting tools from the Gaussian Graphical model literature. It is also possible to include covariate effects. We use our approach to model disease progression in mental health. Posterior inference is performed through a specially devised MCMC algorithm.
翻译:在医学统计和其他领域的许多应用中,可以通过个人在一段时间内经历的多重国家(例如从健康到疾病)之间的过渡来描述。在这方面,多国家的模型是一种流行的统计技术,特别是在没有观察到确切的过渡时间的情况下。关键利息数量是过渡率,反映了从一个州向另一个州流动的瞬间风险。这项工作的主要贡献是提议一个联合半参数模型,用于若干可能相关的多国家进程(似乎没有关联的多国家、SUMS、过程),假设一个长期过渡的Markov结构。不同进程之间的依赖性通过对每个进程过渡速度的任意联合分布来捕捉。我们假设一个灵活的随机效应分布,允许个人、过度分散和异端群聚在一起。此外,我们使用一个图表结构来描述各个进程之间的依赖性,利用高斯图形模型文献中的工具。还有可能包括同化效应。我们用方法来模拟心理健康中的疾病演变。我们通过一个特别设计的MC算法来分析。