Background: Fixed-effect and random-effects models may lack consistency when heterogeneity is present. When systematic bias causes heterogeneity both models may perform poorly.

Objectives: To incorporate bias-risk adjustment in meta-analyses with heterogeneity.

Material: We searched The Cochrane Library for neonatal, cardiovascular, and hepato-biliary meta-analyses including at least two trials with adequate allocation concealment and a minimum of 800 participants in one of those. Thirty meta-analyses were identified.

Methods: We defined a hybrid-effects model under the assumption that heterogeneity was due to high bias-risk trials only. Under the model we derived a moment estimate of the between-study variance and added this to the sample variances of high bias-risk trials only. A detailed presentation of the statistical framework will be given. The meta-analyses were analysed using fixed-effect, randomeffects, and hybrid-effects models. Trials using adequate allocation concealment were considered low bias-risk; trials with unclear/inadequate allocation concealment high bias-risk. We used the estimate of the largest low risk trial as the 'true' intervention effect. For each meta-analysis we calculated the absolute percentile deviation [APD] between the 'true' intervention effect and the pooled estimates of the models. Data were analysed in subgroups of meta-analyses with heterogeneity (I2>=25%) and homogeneity (I2<25%) using Friedman's test for analysis of variance and Wilcoxon's test for pairwise comparisons of the models' APDs.

Results: Among homogeneous meta-analyses no discrepancies were detected between models. Among heterogeneous metaanalyses the APDs were 21%, 31%, and 15% for fixed-effect, random-effects, and hybrid-effects models (P=0.01). Hybrid-effects model versus random-effects model (P=0.006) and versus fixed-effect model (P=0.062).

Conclusions: The hybrid-effects model offers a flexible way of incorporating bias-risk adjustment in meta-analysis - regardless of the sources of bias. In our study, the hybrid-effects model compared to the random-effects model reduces systematic bias introduced by unclear/inadequate allocation concealment and enhances the precision of pooled estimates.