MULTISCALE BAYESIAN SURVIVAL ANALYSIS

• 成果类型: Article
• 署名作者: Castillo, Ismael; van der Pas, Stephanie
• 署名单位: Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Vrije Universiteit Amsterdam; University of Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2097
• 发表日期: 2021
• 页码: 3559-3582
• 关键词: von-mises theorem; confidence bands; models; rates; contraction; inference

摘要

We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for 'many' functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein-von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, we show optimal posterior contraction rates for the hazard in terms of the supremum norm. In medical studies, a popular approach is to model hazards a priori as random histograms with possibly dependent heights. This and more general classes of arbitrarily smooth prior distributions are considered as applications of our theory. A sampler is provided for possibly dependent histogram posteriors. Its finite sample properties are investigated on both simulated and real data experiments.