Public health researchers may have to decide whether to perform a meta-analysis including only high-quality randomized clinical trials (RCTs) or whether to include a mixture of all the available evidence, namely RCTs of varying quality and observational studies (OS). The main hurdle when combining disparate evidence in a meta-analysis is that we are not only combining results of interest but we are also combining multiple biases. Therefore, commonly applied meta-analysis methods may lead to misleading conclusions. In this paper, we present a new Bayesian hierarchical model, called the bias-corrected (BC) meta-analysis model, to combine different study types in meta-analysis. This model is based on a mixture of two random effects distributions, where the first component corresponds to the model of interest and the second component to the hidden bias structure. In this way, the resulting model of interest is adjusted by the internal validity bias of the studies included in a systematic review. We illustrate the BC model with two meta-analyses: The first one combines RCTs and OS to assess effectiveness of vaccination to prevent invasive pneumococcal disease. The second one investigates the effectiveness of stem cell treatment in heart disease patients. Our results show that ignoring internal validity bias in a meta-analysis may lead to misleading conclusions. However, if a meta-analysis model contemplates a bias adjustment, then RCTs results may increase their precision by including OS in the analysis. The BC model has been implemented in JAGS and R, which facilitate its application in practice.
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