title: Variational methods for fitting complex Bayesian mixed effects models to health data.
abstract: We consider approximate inference methods for Bayesian inference to longitudinal and multilevel data within the context of health science studies. The complexity of these grouped data often necessitates the use of sophisticated statistical models. However, the large size of these data can pose significant challenges for model fitting in terms of computational speed and memory storage. Our methodology is motivated by a study that examines trends in cesarean section rates in the largest state of Australia, New South Wales, between 1994 and 2010. We propose a group-specific curve model that encapsulates the complex nonlinear features of the overall and hospital-specific trends in cesarean section rates while taking into account hospital variability over time. We use penalized spline-based smooth functions that represent trends and implement a fully mean field variational Bayes approach to model fitting. Our mean field variational Bayes algorithms allow a fast (up to the order of thousands) and streamlined analytical approximate inference for complex mixed effects models, with minor degradation in accuracy compared with the standard Markov chain Monte Carlo methods.
authors.affiliation: School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales, 2007, Australia.
authors.forename: Cathy Yuen Yi
authors.initials: CY
authors.lastname: Lee
authors.affiliation: School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales, 2007, Australia.
authors.forename: Matt P
authors.initials: MP
authors.lastname: Wand
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D056808:Biostatistics / Q000379:methods*; D002585:Cesarean Section / Q000706:statistics & numerical data / Q000639:trends; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D011247:Pregnancy; D012044:Regression Analysis
keywords: Bayesian inference; Markov chain Monte Carlo; group-specific curves; longitudinal and multilevel data; mean field variational Bayes approximation; semiparametric regression