Lambert Philippe, Eilers Paul H C
Institut de statistique, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
Stat Med. 2005 Dec 30;24(24):3977-89. doi: 10.1002/sim.2396.
One can fruitfully approach survival problems without covariates in an actuarial way. In narrow time bins, the number of people at risk is counted together with the number of events. The relationship between time and probability of an event can then be estimated with a parametric or semi-parametric model. The number of events observed in each bin is described using a Poisson distribution with the log mean specified using a flexible penalized B-splines model with a large number of equidistant knots. Regression on pertinent covariates can easily be performed using the same log-linear model, leading to the classical proportional hazard model. We propose to extend that model by allowing the regression coefficients to vary in a smooth way with time. Penalized B-splines models will be proposed for each of these coefficients. We show how the regression parameters and the penalty weights can be estimated efficiently using Bayesian inference tools based on the Metropolis-adjusted Langevin algorithm.
人们可以以精算的方式有效地处理无协变量的生存问题。在狭窄的时间区间内，对处于风险中的人数和事件数进行计数。然后，可以使用参数模型或半参数模型估计时间与事件概率之间的关系。每个区间内观察到的事件数使用泊松分布来描述，对数均值使用具有大量等距节点的灵活惩罚B样条模型来指定。使用相同的对数线性模型可以轻松地对相关协变量进行回归，从而得到经典的比例风险模型。我们建议通过允许回归系数随时间平滑变化来扩展该模型。将为每个系数提出惩罚B样条模型。我们展示了如何使用基于Metropolis调整Langevin算法的贝叶斯推理工具有效地估计回归参数和惩罚权重。
