Bayesian Regularisation in Structured Additive Regression Models for Survival Data
Bayesian Regularisation in Structured Additive Regression Models for Survival Data
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DOI：
10.5282/ubm/epub.5732
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发表时间：
2008-08
期刊：
影响因子：
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通讯作者：
Susanne Konrath;T. Kneib;L. Fahrmeir
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文献类型：
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作者：
Susanne Konrath;T. Kneib;L. Fahrmeir
近年来，惩罚似然方法在半参数回归和高维回归模型的正则化方面引起了广泛的兴趣。在本文中，我们介绍了贝叶斯公式，允许联合收割机两个方面到一个联合回归模型，重点是生存时间的风险回归。虽然贝叶斯惩罚样条形成了估计非参数和灵活时变效应的基础，但高维协变量向量的正则化是基于法线先验的尺度混合。这类先验允许在模型的预测阶段保持回归系数的（条件）高斯先验，但为高斯方差引入合适的混合分布以实现正则化。这种尺度混合属性允许设备通用和自适应马尔可夫链蒙特卡罗模拟算法，用于拟合各种风险回归模型。特别地，基于迭代加权最小二乘建议的统一算法可以用于正则化和惩罚半参数函数估计。由于基于抽样的估计不再具有频率论分析中Lasso众所周知的变量选择属性，因此我们还考虑了尖峰和平板先验，它们引入了进一步的混合阶段，允许区分有影响力的参数和冗余的参数。我们用三种模拟设置展示了不同的收缩属性，并将这些方法应用于PBC肝脏数据集。
During recent years, penalized likelihood approaches have attracted a lot of interest both in the area of semiparametric regression and for the regularization of high-dimensional regression models. In this paper, we introduce a Bayesian formulation that allows to combine both aspects into a joint regression model with a focus on hazard regression for survival times. While Bayesian penalized splines form the basis for estimating nonparametric and flexible time-varying effects, regularization of high-dimensional covariate vectors is based on scale mixture of normals priors. This class of priors allows to keep a (conditional) Gaussian prior for regression coefficients on the predictor stage of the model but introduces suitable mixture distributions for the Gaussian variance to achieve regularization. This scale mixture property allows to device general and adaptive Markov chain Monte Carlo simulation algorithms for fitting a variety of hazard regression models. In particular, unifying algorithms based on iteratively weighted least squares proposals can be employed both for regularization and penalized semiparametric function estimation. Since sampling based estimates do no longer have the variable selection property well-known for the Lasso in frequentist analyses, we additionally consider spike and slab priors that introduce a further mixing stage that allows to separate between influential and redundant parameters. We demonstrate the different shrinkage properties with three simulation settings and apply the methods to the PBC Liver dataset.