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. Copyright © 2011 John Wiley & Sons, Ltd.