Fast Variational Bayesian Inference for Correlated Survival Data: An Application to Invasive Mechanical Ventilation Duration Analysis.

Correlated survival data are prevalent in various clinical settings and have been extensively discussed in the literature. A common example is clustered survival data, where survival times are associated due to shared characteristics within clusters. In our study, we analyze invasive mechanical ventilation data collected from multiple intensive care units (ICUs) across Ontario, Canada. Patients within the same ICU exhibit similarities in clinical profiles and mechanical ventilation settings, leading to a correlation in their ventilation durations. 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 ICU ventilation data from Ontario to investigate the ICU-site random effect on ventilation duration.