A LOOK BEHIND SURVIVAL DATA: UNDERLYING PROCESSES AND QUASI-STATIONARITY
A LOOK BEHIND SURVIVAL DATA: UNDERLYING PROCESSES AND QUASI-STATIONARITY
复制标题
生存数据背后的一瞥：潜在过程和准平稳性
DOI：
10.1142/9789812795250_0015
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发表时间：
2003
影响因子：
1.2
通讯作者：
H. Gjessing
中科院分区：
文献类型：
--
作者：
O. Aalen;H. Gjessing
在生存和事件历史分析中，重点通常是事件的发生。没有太多的重点放在了解导致这些事件的过程。原因很简单，因为这些过程通常是无法观察到的。然而，人们可以考虑可能的基本过程的结构，并从中得出一些一般性的结论。这里使用的一个重要概念是准平稳分布。这些出现在瞬态空间的概率质量不断丢失到一些吸收状态集的限制分布。由于概率质量的这种泄漏，极限分布在条件意义上只是静止的，即以非吸收为条件。准平稳性是随机过程理论中的一个研究主题，虽然没有做太多的工作，但已经有了一些确定的结果。准平稳分布作为个体潜在过程集合上的吸引子，可以作为理解风险率形状的工具，我们将解释这个概念在生存分析中的应用。将提到基于马尔可夫链、扩散过程和Lévy过程的随机模型。
In survival and event history analysis the focus is usually on the mere occurrence of events. Not much emphasis is placed on understanding the processes leading up to these events. The simple reason for this is that these processes are usually unobserved. However, one may consider the structure of possible underlying processes and draw some general conclusions from this. One important concept being of use here is quasi-stationary distributions. These arise as limiting distributions on transient spaces where probability mass is continuously being lost to some set of absorbing states. Due to this leaking of probability mass, the limiting distribution is just stationary in a conditional sense, that is, conditioned on non-absorption. Quasi-stationarity is a research theme in stochastic process theory, with several established results, although not too much work has been done. Quasi-stationary distributions act as attractors on the set of individual underlying processes, and can be a tool for understanding the shape of the hazard rate.We shall explain the use of this concept in survival analysis. Stochastic models based on Markov chains, diffusion processes and Lévy processes will be mentioned.