gms | German Medical Science

Introduction: Meta analysis is commonly performed based on a random effects model in order to account for both the measurement uncertainty as well as the heterogeneity between data sources. This usually implies a model including two parameters: the main effect that is of primary interest, and the heterogeneity, which constitutes a nuisance parameter [1]. A Bayesian approach to this problem is particularly useful in this context due to its easy interpretability, the straightforward inclusion of information external to the data, and the avoidance of commonly encountered pathologies like zero heterogeneity estimates [2]. On the other hand, a Bayesian approach usually requires the evaluation of complicated multi-dimensional integrals.

Material and Methods: While in general this problem may be approached e.g. via Markov chain Monte Carlo methods, in this particular case it is possible to decompose the problem so that it may be solved partly analytically and numerically [3]. While some approximation still needs to be employed, we are also able to provide a handle on the numerical accuracy by bounding the the discrepancy between the true posterior and its approximation.

Results: We demonstrate a user friendly implementation of the model, where the input arguments consist of data as well as (prior density) functions, and the output are point estimates as well as several functions like joint and marginal posterior density functions, distribution functions etc. The functionality of the approach is illustrated using real data examples.

Discussion: The presented implementation allows to approach the common problem of random-effects meta-analysis via a Bayesian model, without the necessity for the user to delve into the details of numerical or stochastic integration methods. Easy application and fast computation make the Bayesian toolbox available to a wider audience, and also allow for quick simulations or sensitivity checks.