Second-order accurate likelihood inference for meta-analysis of comparative studies with binary outcomes

We apply modern likelihood asymptotics to one-step methods for meta-analysis of comparative studies with binary outcomes. This approach requires a complete statistical model for the original data, rather than just a model to combine the summary statistics of individual studies as in two-step methods. We illustrate the advantages of calculating accurate confidence intervals in the common case where meta-analysis combines a limited number of studies and thus ordinary first-order accurate likelihood methods may yield incorrect inferential conclusions.