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IJE Advance Access originally published online on February 28, 2007
International Journal of Epidemiology 2007 36(1):195-202; doi:10.1093/ije/dyl289
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Published by Oxford University Press on behalf of the International Epidemiological Association © The Author 2007; all rights reserved.

Bayesian perspectives for epidemiological research. II. Regression analysis

Sander Greenland

Departments of Epidemiology and Statistics, University of California, Los Angeles, CA 90095-1772, USA.

E-mail: lesdomes{at}ucla.edu


  Abstract

This article describes extensions of the basic Bayesian methods using data priors to regression modelling, including hierarchical (multilevel) models. These methods provide an alternative to the parsimony-oriented approach of frequentist regression analysis. In particular, they replace arbitrary variable-selection criteria by prior distributions, and by doing so facilitate realistic use of imprecise but important prior information. They also allow Bayesian analyses to be conducted using standard regression packages; one need only be able to add variables and records to the data set. The methods thus facilitate the use of Bayesian solutions to problems of sparse data, multiple comparisons, subgroup analyses and study bias. Because these solutions have a frequentist interpretation as ‘shrinkage’ (penalized) estimators, the methods can also be viewed as a means of implementing shrinkage approaches to multiparameter problems.

Keywords Bayesian methods, biostatistics, odds ratio, relative risk, risk assessment

Accepted 15 August 2006


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