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The log-logistic regression model is one of the most commonly usedaccelerated failure time (AFT) models in survival analysis, for whichstatistical inference methods are mainly established under the frequentistframework. Recently, Bayesian inference for log-logistic AFT models usingMarkov chain Monte Carlo (MCMC) techniques has also been widely developed. Inthis work, we develop an alternative approach to MCMC methods and infer theparameters of the log-logistic AFT model via a mean-field variational Bayes(VB) algorithm. A piecewise approximation technique is embedded in deriving theVB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated andcompared with typical frequentist inferences and MCMC inference using simulateddata under various scenarios. A publicly available dataset is employed forillustration. We demonstrate that the proposed VB algorithm can achieve goodestimation accuracy and has a lower computational cost compared with MCMCmethods.

Variational Bayesian analysis of survival data using a log-logistic accelerated failure time model