Geoadditive survival models
Geoadditive survival models
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DOI：
10.1198/016214506000000348
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发表时间：
2006-09-01
影响因子：
3.7
通讯作者：
Fahrmeir, Ludwig
中科院分区：
文献类型：
--
作者：
Hennerfeind, Andrea;Brezger, Andreas;Fahrmeir, Ludwig
生存数据通常包含小区域的地理或空间信息，例如个人的居住地。在许多情况下，这种空间效应对灾害率的影响具有相当大的实质性意义。因此，扩展已知的生存或风险率模型的空间模型已被建议。大多数情况下，空间分量被添加到考克斯模型的常用线性预测因子中。本文提出了一种灵活的连续时间geoaddivive模型，在应用中经常需要的几个方面扩展了考克斯模型。将常见的线性预测因子推广为加性预测因子，包括对数基线风险的非参数分量、时变效应和连续协变量或其他时间尺度的可能非线性效应，以及地理效应的空间分量。此外，可以合并不相关的脆弱性效应或非线性双向相互作用。推理是在一个统一的完全贝叶斯框架内开发的。惩罚回归样条和马尔可夫随机场建议作为基本的积木，地质统计（克里金）模型也被认为是。后验分析使用计算效率高的马尔可夫链蒙特卡罗抽样方案。平滑参数是模型不可分割的一部分，并且会自动估计。适当的后验显示在相当一般的条件下，和实际性能进行了研究，通过模拟研究。我们的方法是适用于数据从一个案例研究在伦敦和埃塞克斯，旨在估计影响居住面积和进一步的协变量对等待时间的冠状动脉旁路移植术。结果提供了明确的证据，非线性随时间变化的影响，以及相当大的空间变异的等待时间旁路移植术。
Survival data often contain small-area geographical or spatial information, such as the residence of individuals. In many cases, the impact of such spatial effects on hazard rates is of considerable substantive interest. Therefore, extensions of known survival or hazard rate models to spatial models have been suggested. Mostly, a spatial component is added to the usual linear predictor of the Cox model. In this article flexible continuous-time geoaddifive models are proposed, extending the Cox model with respect to several aspects often needed in applications. The common linear predictor is generalized to an additive predictor, including nonparametric components for the log-baseline hazard, time-varying effects, and possibly nonlinear effects of continuous covariates or further time scales, and a spatial component for geographical effects. In addition, uncorrelated frailty effects or nonlinear two-way interactions can be incorporated. Inference is developed within a unified fully Bayesian framework. Penalized regression splines and Markov random fields are suggested as basic building blocks, and geostatistical (kriging) models are also considered. Posterior analysis uses computationally efficient Markov chain Monte Carlo sampling schemes. Smoothing parameters are an integral part of the model and are estimated automatically. Propriety of posteriors is shown under fairly general conditions, and practical performance is investigated through simulation studies. Our approach is applied to data from a case study in London and Essex that aims to estimate the effect of area of residence and further covariates on waiting times to coronary artery bypass grafting. Results provide clear evidence of nonlinear time-varying effects, and considerable spatial variability of waiting times to bypass grafting.