生存模型的贝叶斯自助法

中文摘要 AI 辅助

生存分析被广泛用于分析事件发生时间数据，但在存在删失、样本量有限和异质人群的情况下，不确定性量化往往颇具挑战性。现有贝叶斯生存方法为整合先验信息提供了框架，但通常需要指定完整的概率似然，这使得推断对分布假设敏感，且有时计算要求较高。我们提出一种用于生存分析的贝叶斯方法，将贝叶斯自助法与广义贝叶斯（吉布斯）更新相结合。贝叶斯自助法首先通过狄利克雷权重生成生存估计量上的分布，对抽样不确定性提供非参数化表征。随后在广义贝叶斯框架内利用损失函数整合模型参数的先验信息，得到后验分布的推断。该方法与模型无关，可应用于广泛类别的生存估计量。作为示例，我们为Cox比例风险模型开发了该框架，生成回归系数的后验推断，同时保留了风险比的熟悉特性与解释。模拟研究表明，所提方法能提供稳健的不确定性量化，且可有效整合先验信息。对右删失生存数据的应用进一步说明了其实用性。开源R包BayesBoots实现了所提方法。

英文摘要

Survival inference often requires uncertainty quantification under censoring and limited sample sizes, while prior information may be available but difficult to incorporate without specifying a full likelihood. Likelihood-based Bayesian survival methods provide prior-informed inference but may be sensitive to distributional assumptions and computationally demanding for complex survival models. The Bayesian bootstrap provides a likelihood-free, nonparametric approach to uncertainty quantification, but by itself does not provide a general mechanism for incorporating priors on model parameters. We propose a general Bayesian method for survival models that combines the generalized Bayesian (Gibbs) updating with Bayesian bootstrap. The Bayesian bootstrap generates a distribution over a target survival estimator through Dirichlet weights, while generalized Bayesian updating incorporates parameter-specific prior information through a loss function. The resulting posterior provides a flexible alternative to likelihood-based Bayesian inference and can be applied to a broad class of survival estimators. We develop the method for the Cox proportional hazards model and obtain posterior inference for regression coefficients and hazard ratios. Simulation studies demonstrate uncertainty quantification and prior-data learning across varying sample sizes. An application to right-censored survival data illustrates its practical utility. The methodology is implemented in the open-source \texttt{R} package \texttt{BayesBoots}.

发表机构

• The University of Sydney（悉尼大学）
• Kids Research Institute, The Children’s Hospital at Westmead（西梅德儿童医院儿童研究所）

机构由 AI 辅助整理，请以论文原文为准。