Performance of several types of beta-binomial models in comparison to standard approaches for meta-analyses with very few studies

Meta-analyses are used to summarise the results of several studies on a specific research question. Standard methods for meta-analyses, namely inverse variance random effects models, have unfavourable properties if only very few (2 - 4) studies are available. Therefore, alternative meta-analytic methods are needed. In the case of binary data, the "common-rho" beta-binomial model has shown good results in situations with sparse data or few studies. The major concern of this model is that it ignores the fact that each treatment arm is paired with a respective control arm from the same study. Thus, the randomisation to a study arm of a specific study is disrespected, which may lead to compromised estimates of the treatment effect. Therefore, we extended this model to a version that respects randomisation. The aim of this simulation study was to compare the "common-rho" beta-binomial model and several other beta-binomial models with standard meta-analyses models, including generalised linear mixed models and several inverse variance random effects models. We conducted a simulation study comparing beta-binomial models and various standard meta-analysis methods. The design of the simulation aimed to consider meta-analytic situations occurring in practice. No method performed well in scenarios with only 2 studies in the random effects scenario. In this situation, a fixed effect model or a qualitative summary of the study results may be preferable. In scenarios with 3 or 4 studies, most methods satisfied the nominal coverage probability. The "common-rho" beta-binomial model showed the highest power under the alternative hypothesis. The beta-binomial model respecting randomisation did not improve performance. The "common-rho" beta-binomial appears to be a good option for meta-analyses of very few studies. As residual concerns about the consequences of disrespecting randomisation may still exist, we recommend a sensitivity analysis with a standard meta-analysis method that respects randomisation.