Abstract

We present a novel Bayesian nonparametric model for regression in survival analysis. Our model builds on the classical neutral to the right model of Doksum and on the Cox proportional hazards model of Kim and Lee. The use of a vector of dependent Bayesian nonparametric priors allows us to efficiently model the hazard as a function of covariates while allowing nonproportionality. The model can be seen as having competing latent risks. We characterize the posterior of the underlying dependent vector of completely random measures and study the asymptotic behavior of the model. We show how an MCMC scheme can provide Bayesian inference for posterior means and credible intervals. The method is illustrated using simulated and real data. Supplementary materials for this article are available online.

摘要

我们提出了一种新颖的贝叶斯非参数模型，用于生存分析中的回归。我们的模型建立在Doksum正确模型的经典中性和Cox 比例风险之上金和李的模特。使用依赖贝叶斯非参数先验向量使我们能够有效地将风险建模为协变量的函数，同时允许不成比例。该模型可以被视为具有竞争的潜在风险。我们描述了完全随机测量的基础依赖向量的后验，并研究了模型的渐近行为。我们展示了 MCMC 方案如何为后验均值和可信区间提供贝叶斯推理。该方法使用模拟和真实数据进行说明。本文的补充材料可在线获取。