Variational Bayesian analysis for joint models of longitudinal and failure time data with interval censoring

Abstract

Alzheimer’s Disease (AD) progression is marked by a gradual decline in cognitive function, with significant events often occurring within uncertain intervals. To comprehensively understand AD, it is essential to jointly model longitudinal cognitive assessments and interval-censored survival data. However, current methodologies have certain limitations when applied to joint models. Maximum Likelihood Estimation often neglects parameter and model uncertainty, while Bayesian methods permit uncertainty quantification but rely on traditional Markov Chain Monte Carlo algorithms, which suffer from slow convergence and high memory demands. To address these challenges, we propose variational Bayesian methods as a more computationally efficient and scalable alternative. Specifically, we focus on two approaches: the Non-Conjugate Variational Message Passing method and the Non-Conjugate Variational Laplace Approximation method. These techniques effectively approximate complex posterior distributions while minimizing the excessive computational demands typically associated with traditional Bayesian techniques. Additionally, we introduce a variational Bayesian framework for local influence analysis and outlier detection, utilizing sparse priors to enhance the model’s robustness against data anomalies. Through simulation studies and an application to the Alzheimer’s Disease Neuroimaging Initiative dataset, we demonstrate the effectiveness of our variational Bayesian joint modeling approach. Our results underscore the advantages of these methods in terms of computational efficiency and scalability, making them well-suited for analyzing complex longitudinal and interval-censored data in AD research.