Using Bayesian inference to perform meta-analysis

Bayesian modeling offers an elegant approach to meta-analysis that efficiently incorporates all sources of variability and relevant quantifiable external information. It provides a more informative summary of the likely value of parameters after observing the data than do non-Bayesian approaches. This leads to direct probabilistic inference about model parameters such as the average treatment effect, the between-study variance, and individual study treatment effects. The latter are weighted averages of the common mean and individual study means with weights reflecting the amount of information provided by each study relative to the others. Homogeneity among these posterior study estimates indicates that pooling these studies is appropriate; heterogeneity suggests that some cause of between-study variation should be explored. The author describes the construction of such models and shows how to use them to estimate a common mean and regression slopes. Two examples illustrate the additional inferences available with the Bayesian methodology.