The log-logistic regression model is one of the most commonly used accelerated failure time (AFT) models in survival analysis, for which statistical inference methods are mainly established under the frequentist framework. Recently, Bayesian inference for log-logistic AFT models using Markov chain Monte Carlo (MCMC) techniques has also been widely developed. In this work, we develop an alternative approach to MCMC methods and infer the parameters of the log-logistic AFT model via a mean-field variational Bayes (VB) algorithm. A piece-wise approximation technique is embedded in deriving the update equations in the VB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated and compared with typical frequentist inferences using simulated data under various scenarios, and a publicly available dataset is employed for illustration. We demonstrate that the proposed VB algorithm can achieve good estimation accuracy and is not sensitive to sample sizes, censoring rates, and prior information.
翻译:log-logistic回归模型是生存分析中最常用的加速失效时间(AFT)模型之一,统计推断方法主要是在频率主义框架下建立的。最近,也已经广泛发展了使用马尔科夫链蒙特卡罗(MCMC)技术进行log-logistic AFT模型的贝叶斯推断。在本文中,我们提出一种MCMC方法的替代方法,并通过均值场变分贝叶斯(VB)算法推断log-logistic AFT模型的参数。嵌入分段逼近技术以推导VB算法中的更新方程来实现共轭。使用模拟数据在不同情况下评估并与典型的频率主义推断进行比较,并使用公开数据集进行说明。我们证明了提出的VB算法可以实现良好的估计精度,并且对样本量,截断率和先验信息不敏感。