A beta-binomial model respecting randomization and its comparison to the standard beta-binomial model that ignores randomization for the meta-analysis of rare events

Background: One of the suggested models for meta-analysis with rare events is the beta-binomial model (BBM).

The main advantage of this model compared to inverse-variance models, is that it uses information from zero cells without needing a continuity correction.

A disadvantage of the standard BBM is that it ignores randomization.

Here we introduce a BBM that respects randomization.

Methods: The main idea to preserve randomization is using a common-beta BBM.

We illustrate that randomization is preserved by conditioning on the total sum of counts in a studys four-fold table when estimating the model parameters.

We perform a simulation study reflecting real-world meta-analyses to compare the models.

In addition, we explore in which situations ignoring randomization could be problematic.

Results: The BBM that respects randomization performs well in the simulation study that mirrors real meta-analyses in Cochrane and non-Cochrane reviews, respectively.

Ignoring randomization appears to be problematic in situations with very different sample sizes of the studies included in the meta-analysis.

However, the BBM ignoring randomization tended to perform better when heterogeneity was high.

Conclusion: The results show that using the standard BBM, which ignores randomization is usually not biased when the randomization is balanced and the size of studies included in the meta-analysis is not very different.

However, as possible ecological bias due to ignoring randomization is an inherent disadvantage of the model and the BBM that respects randomization shows very similar results in the simulation study, it may be generally preferred.

Key words Beta-binomial model, generalized linear mixed models, meta-analyses, simulation study, rare events, zero events