title: Modelling heterogeneity variances in multiple treatment comparison meta-analysis--are informative priors the better solution?
abstract: BACKGROUND
  Multiple treatment comparison (MTC) meta-analyses are commonly modeled in a Bayesian framework, and weakly informative priors are typically preferred to mirror familiar data driven frequentist approaches. Random-effects MTCs have commonly modeled heterogeneity under the assumption that the between-trial variance for all involved treatment comparisons are equal (i.e., the 'common variance' assumption). This approach 'borrows strength' for heterogeneity estimation across treatment comparisons, and thus, ads valuable precision when data is sparse. The homogeneous variance assumption, however, is unrealistic and can severely bias variance estimates. Consequently 95% credible intervals may not retain nominal coverage, and treatment rank probabilities may become distorted. Relaxing the homogeneous variance assumption may be equally problematic due to reduced precision. To regain good precision, moderately informative variance priors or additional mathematical assumptions may be necessary.
  
  
  METHODS
  In this paper we describe four novel approaches to modeling heterogeneity variance - two novel model structures, and two approaches for use of moderately informative variance priors. We examine the relative performance of all approaches in two illustrative MTC data sets. We particularly compare between-study heterogeneity estimates and model fits, treatment effect estimates and 95% credible intervals, and treatment rank probabilities.
  
  
  RESULTS
  In both data sets, use of moderately informative variance priors constructed from the pair wise meta-analysis data yielded the best model fit and narrower credible intervals. Imposing consistency equations on variance estimates, assuming variances to be exchangeable, or using empirically informed variance priors also yielded good model fits and narrow credible intervals. The homogeneous variance model yielded high precision at all times, but overall inadequate estimates of between-trial variances. Lastly, treatment rankings were similar among the novel approaches, but considerably different when compared with the homogenous variance approach.
  
  
  CONCLUSIONS
  MTC models using a homogenous variance structure appear to perform sub-optimally when between-trial variances vary between comparisons. Using informative variance priors, assuming exchangeability or imposing consistency between heterogeneity variances can all ensure sufficiently reliable and realistic heterogeneity estimation, and thus more reliable MTC inferences. All four approaches should be viable candidates for replacing or supplementing the conventional homogeneous variance MTC model, which is currently the most widely used in practice.
authors: Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, ON, Canada. thorluk@mcmaster.ca
authors: Kristian
authors: K
authors: Thorlund
authors: Lehana
authors: L
authors: Thabane
authors: Edward J
authors: EJ
authors: Mills
mesh_terms: D000704:Analysis of Variance; D001499:Bayes Theorem; D006801:Humans; D015201:Meta-Analysis as Topic; D015203:Reproducibility of Results; D012107:Research Design / Q000592:standards*; D018401:Sample Size; D016896:Treatment Outcome