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

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 frequentist and MCMC techniques using simulated data under various scenarios. A publicly available dataset is employed for illustration. 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). When compared to MCMC, similar performance was achieved by our proposed VB, and, in certain scenarios, VB yielded the lowest MSE. Furthermore, the proposed VB algorithm offers a significantly reduced computational cost compared to MCMC, with an average speedup of 300 times.