  Objective: We investigated the associations between risk of bias judgments
from Cochrane reviews for sequence generation, allocation concealment and
blinding and between-trial heterogeneity.
  Study Design and Setting: Bayesian hierarchical models were fitted to binary
data from 117 meta-analyses, to estimate the ratio {\lambda} by which
heterogeneity changes for trials at high/unclear risk of bias, compared to
trials at low risk of bias. We estimated the proportion of between-trial
heterogeneity in each meta-analysis that could be explained by the bias
associated with specific design characteristics.
  Results: Univariable analyses showed that heterogeneity variances were, on
average, increased among trials at high/unclear risk of bias for sequence
generation ({\lambda} 1.14, 95% interval: 0.57 to 2.30) and blinding ({\lambda}
1.74, 95% interval: 0.85 to 3.47). Trials at high/unclear risk of bias for
allocation concealment were on average less heterogeneous ({\lambda} 0.75, 95%
interval: 0.35 to 1.61). Multivariable analyses showed that a median of 37%
(95% interval: 0% to 71%) heterogeneity variance could be explained by trials
at high/unclear risk of bias for sequence generation, allocation concealment
and/or blinding. All 95% intervals for changes in heterogeneity were wide and
included the null of no difference.
  Conclusion: Our interpretation of the results is limited by imprecise
estimates. There is some indication that between-trial heterogeneity could be
partially explained by reported design characteristics, and hence adjustment
for bias could potentially improve accuracy of meta-analysis results.
