  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 piecewise approximation technique is embedded in deriving the
VB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated and
compared with typical frequentist inferences and MCMC inference using simulated
data under various scenarios. A publicly available dataset is employed for
illustration. We demonstrate that the proposed VB algorithm can achieve good
estimation accuracy and has a lower computational cost compared with MCMC
methods.
