Integrated likelihood inference for risk difference in meta-analysis with sparse data

We propose the use of the integrated likelihood based on the zero-score expectation nuisance parameter for inference on a common risk difference for stratified binomial settings, typically arising in meta-analyses of comparative studies with binary outcomes. The proposal is built upon the Mantel-Haenszel estimator. It produces accurate inferences and, at the same time, resolves the numerical issues arising in sparse-data settings, without requiring any continuity correction or other changes to the original data. The same methodology extends to other risk measures, such as relative risk or log-odds ratio, and can be viewed as a general, unified solution for inference on stratified 2 × 2 tables.