Summary There is good empirical evidence that specific flaws in the conduct of randomized controlled trials are associated with exaggeration of treatment effect estimates. Mixed treatment comparison meta-analysis, which combines data from trials on several treatments that form a network of comparisons, has the potential both to estimate bias parameters within the synthesis and to produce bias-adjusted estimates of treatment effects. We present a hierarchical model for bias with common mean across treatment comparisons of active treatment versus control. It is often unclear, from the information that is reported, whether a study is at risk of bias or not. We extend our model to estimate the probability that a particular study is biased, where the probabilities for the ‘unclear’ studies are drawn from a common beta distribution. We illustrate these methods with a synthesis of 130 trials on four fluoride treatments and two control interventions for the prevention of dental caries in children. Whether there is adequate allocation concealment and/or blinding are considered as indicators of whether a study is at risk of bias. Bias adjustment reduces the estimated relative efficacy of the treatments and the extent of between-trial heterogeneity.
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