Statistics in Medicine

Gibbs sampler for the logistic model in the analysis of longitudinal binary data

Journal Article

  • Author(s): Isabelle Albert, Jean‐Philippe Jais
  • Article first published online: 05 Jan 1999
  • DOI: 10.1002/(SICI)1097-0258(19981230)17:24<2905::AID-SIM911>3.0.CO;2-G
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Abstract

Logistic mixed‐effects models constitute a natural framework to study longitudinal binary response variables when the question addressed with the data is related to covariate effects within persons. However, the computations of the likelihoods are generally tedious and require the resolution of integrals which have no analytical solution. In this paper, we study a logistic mixed‐effects model in a Bayesian framework and use the Gibbs sampler to overcome the current computational limitations. From a study of side‐effects occurring during plasma exchanges, we explore the issues of Bayesian formulation, model parametrization, choice of the prior distributions, diagnosing convergence, comparison between models and model adequacy. Finally, we show that a Bayesian random‐effects model is useful to facilitate prediction. © 1998 John Wiley & Sons, Ltd.

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