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We have demonstrated that our proposed Variational Bayes (VB) algorithm consistently produces satisfactory estimation results and, in most scenarios, outperforms the likelihood-based method in terms of empirical mean squared error (MSE). A publicly available dataset is employed for illustration. The proposed VB algorithm is evaluated and compared with frequentist and MCMC techniques using simulated data under various scenarios. A piecewise approximation technique is embedded in deriving the VB algorithm to achieve conjugacy. 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. Recently, Bayesian inference for log-logistic AFT models using Markov chain Monte Carlo (MCMC) techniques has also been widely developed. 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.

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