Estimation and adjustment of bias in randomized evidence by using mixed treatment comparison meta‐analysis

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.