A Bayesian fixed effects analysis of the Mantel-Haenszel model applied to meta-analysis

When performing a meta analysis, it is often necessary to combine results from several 2 x 2 contingency tables. The Mantel-Haenszel model assumes a common measure of association between the treatment and outcome variables across the tables. A Bayesian method is described for drawing inferences regarding the measure of association, for checking the plausibility of the Mantel-Haenszel model, and for drawing inferences regarding the success rates for the individual studies. While the methodology is readily extendable to random effects models, a fixed effects approach avoids the complex statistical modelling of a mixture distribution which is required for the good application of random effects models.