Modeling between-trial variance structure in mixed treatment comparisons

Biostatistics. 2009 Oct;10(4):792-805. doi: 10.1093/biostatistics/kxp032. Epub 2009 Aug 17.


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.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Analysis of Variance
  • Bayes Theorem
  • Biostatistics / methods*
  • Clinical Trials as Topic / statistics & numerical data*
  • Gastroesophageal Reflux / drug therapy
  • Humans
  • Likelihood Functions
  • Markov Chains
  • Meta-Analysis as Topic*
  • Models, Statistical*
  • Monte Carlo Method
  • Smoking Cessation / statistics & numerical data