gms | German Medical Science

The beta-binomial model has been proven a valuable statistical model for the meta-analysis of binary outcomes, especially in challenging situations with a low number of studies or events or even both. We present two variations of the model for meta-analysis, namely a “common-beta” and a “common-alpha” model. Both models have surprising connections to negative binomial regression models for count panel data used in econometrics. Using this equivalence, it is also possible to estimate an extension of these beta-binomial models with an additional multiplicative overdispersion term, while preserving the closed form likelihood, which is one of main advantages of the beta-binomial model. An additional advantage of the connection to economic models is that they can be quite easily implemented because “standard” statistical software for count panel data can be used for estimation (e.g., SAS PROC COUNTREG, Stata xtnbreg, R MASS-Package). We illustrate the methods with empirical example data. In addition, we show the results of a simulation study that compares the new models to the standard beta-binomial model (“common-rho”). The input parameters of the simulation were informed by actually performed meta-analysis. Our results suggest that the considered common-beta and the common-alpha beta-binomial models are promising extensions of the family of beta-binomial models for meta-analyses with binary outcomes.

The authors declare that an ethics committee vote is not required.