Intrinsic meta-analysis of contingency tables

Meta-analysis has a natural formulation as a Bayesian hierarchical model. The main theoretical difficulty is the construction of a sensible relationship between the parameters of the individual statistical experiments and the meta-parameter. Since that prior information on such a relationship is typically not available, we argue that this relationship should be dictated by the structure of the model at hand. We then propose a novel procedure based on intrinsic priors which we fully develop for the case of meta-analysis of 2 x 2 contingency tables. Illustrations on real and artificial tables are given.