Background
Meta-analyses are used to summarize the results of several studies to 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 case of binary data, the “common-rho” beta-binomial model has shown good results in situations with spare 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 “common-rho” beta-binomial model and several other beta-binomial models to standard meta-analyses models including generalised linear mixed models and several inverse variance random effects models.
Methods
We conducted a simulation study in which beta-binomial models and various standard meta-analysis methods were compared. The design of the simulation aimed to consider meta-analytic situations occurring in practice.
Results
In summary, 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 the “common-rho” beta-binomial model performed at least slightly better than other models, whereas performance was not improved by the beta-binomial model respecting randomisation.
Conclusion
The “common-rho” beta-binomial appears to be a good option for meta-analyses of very few studies. Because residual concerns about the consequences of disrespecting the randomisation may still exist, we recommend a sensitivity analysis with a standard meta-analysis method that respects randomisation.