  Correlated survival data are prevalent in various clinical settings and have
been extensively discussed in literature. One of the most common types of
correlated survival data is clustered survival data, where the survival times
from individuals in a cluster are associated. Our study is motivated by
invasive mechanical ventilation data from different intensive care units (ICUs)
in Ontario, Canada, forming multiple clusters. The survival times from patients
within the same ICU cluster are correlated. To address this association, we
introduce a shared frailty log-logistic accelerated failure time model that
accounts for intra-cluster correlation through a cluster-specific random
intercept. We present a novel, fast variational Bayes (VB) algorithm for
parameter inference and evaluate its performance using simulation studies
varying the number of clusters and their sizes. We further compare the
performance of our proposed VB algorithm with the h-likelihood method and a
Markov Chain Monte Carlo (MCMC) algorithm. The proposed algorithm delivers
satisfactory results and demonstrates computational efficiency over the MCMC
algorithm. We apply our method to the ICU ventilation data from Ontario to
investigate the ICU site random effect on ventilation duration.
