Survival models based on the Ornstein-Uhlenbeck process
Survival models based on the Ornstein-Uhlenbeck process
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DOI：
10.1007/s10985-004-4775-9
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发表时间：
2004-12-01
影响因子：
1.3
通讯作者：
Gjessing, HK
中科院分区：
文献类型：
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作者：
Aalen, OO;Gjessing, HK
在对生存数据进行建模时，想象导致相关事件的潜在过程可能会很有趣。奥恩斯坦-乌伦贝克过程是在生物学背景下考虑的自然模型，因为它稳定在某个平衡点附近。这与生物学中经常观察到的稳态相对应，在某种程度上也与社会科学中观察到的稳态相对应。首先，我们研究 Ornstein-Uhlenbeck 过程的首次通过时间分布，特别关注所谓的准平稳性和危险率的各种形状。接下来，我们考虑一个模型，其中个体风险率是 Ornstein-Uhlenbeck 过程的平方函数。我们扩展了该模型的已知结果。准平稳性的结果与最近关于死亡率高原的讨论相关。此外，我们指出了与金融模型中的短期利率模型的联系。
When modelling survival data it may be of interest to imagine an underlying process leading up to the event in question. The Ornstein-Uhlenbeck process is a natural model to consider in a biological context because it stabilizes around some equilibrium point. This corresponds to the homeostasis often observed in biology, and also to some extent in the social sciences. First, we study the first-passage time distribution of an Ornstein-Uhlenbeck process, focussing especially on what is termed quasi-stationarity and the various shapes of the hazard rate. Next, we consider a model where the individual hazard rate is a squared function of an Ornstein-Uhlenbeck process. We extend known results on this model. The results on quasi-stationarity are relevant for recent discussions about mortality plateaus. In addition, we point out a connection to models for short-term interest rates in financial modeling.