Fast variational Bayesian inference for correlated survival data: an application to invasive mechanical ventilation duration analysis

TL;DR

This paper introduces a fast variational Bayesian method for analyzing correlated survival data, specifically applied to ICU ventilation duration, improving computational efficiency over traditional methods.

Contribution

The study develops a novel variational Bayes algorithm for shared frailty models in correlated survival data, demonstrating its effectiveness and efficiency compared to existing methods.

Findings

The VB algorithm provides accurate parameter estimates.

It is computationally faster than MCMC methods.

Application to ICU data reveals significant ICU site effects.

Abstract

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.