Bayesian hierarchical modeling of longitudinal glaucomatous visual fields using a two-stage approach

Susan R Bryan, Paul H C Eilers, Joost van Rosmalen, Dimitris Rizopoulos, Koenraad A Vermeer, Hans G Lemij, Emmanuel M E H Lesaffre

Research output: Contribution to journalArticleResearchpeer-review


The Bayesian approach has become increasingly popular because it allows to fit quite complex models to data via Markov chain Monte Carlo sampling. However, it is also recognized nowadays that Markov chain Monte Carlo sampling can become computationally prohibitive when applied to a large data set. We encountered serious computational difficulties when fitting an hierarchical model to longitudinal glaucoma data of patients who participate in an ongoing Dutch study. To overcome this problem, we applied and extended a recently proposed two-stage approach to model these data. Glaucoma is one of the leading causes of blindness in the world. In order to detect deterioration at an early stage, a model for predicting visual fields (VFs) in time is needed. Hence, the true underlying VF progression can be determined, and treatment strategies can then be optimized to prevent further VF loss. Because we were unable to fit these data with the classical one-stage approach upon which the current popular Bayesian software is based, we made use of the two-stage Bayesian approach. The considered hierarchical longitudinal model involves estimating a large number of random effects and deals with censoring and high measurement variability. In addition, we extended the approach with tools for model evaluation. Copyright © 2017 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)1735-1753
Number of pages19
JournalStatistics in Medicine
Issue number11
Publication statusPublished - 20 May 2017


  • Adolescent
  • Adult
  • Aged
  • Aged, 80 and over
  • Bayes Theorem
  • Data Interpretation, Statistical
  • Disease Progression
  • Female
  • Glaucoma/pathology
  • Humans
  • Longitudinal Studies
  • Male
  • Markov Chains
  • Middle Aged
  • Models, Statistical
  • Monte Carlo Method
  • Prospective Studies
  • Visual Fields
  • Young Adult


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