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：对数逻辑斯蒂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，其统计推断方法主要建立在频率学派框架下。近年来，基于马尔可夫链蒙特卡洛（MCMC）技术的对数逻辑斯蒂AFT模型贝叶斯推断也得到了广泛发展。本研究提出一种替代MCMC方法的新途径，通过平均场变分贝叶斯（VB）算法推断对数逻辑斯蒂AFT模型参数。在推导VB算法中的更新方程时，嵌入分段逼近技术以实现共轭性。通过多种情景下的模拟数据对所提出的VB算法进行评估，并与典型频率学派推断方法进行比较，同时采用公开数据集进行实例说明。研究表明，所提出的VB算法能够实现良好的估计精度，且对样本量、删失率及先验信息不敏感。