Higher‐order likelihood inference in meta‐analysis and meta‐regression

This paper investigates the use of likelihood methods for meta-analysis, within the random-effects models framework. We show that likelihood inference relying on first-order approximations, while improving common meta-analysis techniques, can be prone to misleading results. This drawback is very evident in the case of small sample sizes, which are typical in meta-analysis. We alleviate the problem by exploiting the theory of higher-order asymptotics. In particular, we focus on a second-order adjustment to the log-likelihood ratio statistic. Simulation studies in meta-analysis and meta-regression show that higher-order likelihood inference provides much more accurate results than its first-order counterpart, while being of a computationally feasible form. We illustrate the application of the proposed approach on a real example.