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Biostatistics Advance Access originally published online on August 17, 2009
Biostatistics 2009 10(4):792-805; doi:10.1093/biostatistics/kxp032
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Modeling between-trial variance structure in mixed treatment comparisons

Guobing Lu* and Ae Ades

Department of Community Based Medicine, University of Bristol, Cotham House, Cotham Hill, Bristol BS6 6JL, UK guobing.lu{at}bristol.ac.uk

* To whom correspondence should be addressed.

In mixed treatment comparison (MTC) meta-analysis, modeling the heterogeneity in between-trial variances across studies is a difficult problem because of the constraints on the variances inherited from the MTC structure. Starting from a consistent Bayesian hierarchical model for the mean treatment effects, we represent the variance configuration by a set of triangle inequalities on the standard deviations. We take the separation strategy (Barnard and others, 2000) to specify prior distributions for standard deviations and correlations separately. The covariance matrix of the latent treatment arm effects can be employed as a vehicle to load the triangular constraints, which in addition allows incorporation of prior beliefs about the correlations between treatment effects. The spherical parameterization based on Cholesky decomposition (Pinheiro and Bates, 1996) is used to generate a positive-definite matrix for the prior correlations in Markov chain Monte Carlo (MCMC). Elicited prior information on correlations between treatment arms is introduced in the form of its equivalent data likelihood. The procedure is implemented in a MCMC framework and illustrated with example data sets from medical research practice.

Keywords: Bayesian hierarchical model; Between-trial heterogeneity; Equivalent prior sample method; Evidence consistency; Markov chain Monte Carlo; Mixed treatment comparison meta-analysis; Triangle inequality

Received January 10, 2008; revised October 20, 2008; revised April 8, 2009; revised May 26, 2009; revised June 22, 2009; accepted for publication July 24, 2009.


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