Random-effects meta-analysis: the number of studies matters

This paper investigates the impact of the number of studies on meta-analysis and meta-regression within the random-effects model framework. It is frequently neglected that inference in random-effects models requires a substantial number of studies included in meta-analysis to guarantee reliable conclusions. Several authors warn about the risk of inaccurate results of the traditional DerSimonian and Laird approach especially in the common case of meta-analysis involving a limited number of studies. This paper presents a selection of likelihood and non-likelihood methods for inference in meta-analysis proposed to overcome the limitations of the DerSimonian and Laird procedure, with a focus on the effect of the number of studies. The applicability and the performance of the methods are investigated in terms of Type I error rates and empirical power to detect effects, according to scenarios of practical interest. Simulation studies and applications to real meta-analyses highlight that it is not possible to identify an approach uniformly superior to alternatives. The overall recommendation is to avoid the DerSimonian and Laird method when the number of meta-analysis studies is modest and prefer a more comprehensive procedure that compares alternative inferential approaches. R code for meta-analysis according to all of the inferential methods examined in the paper is provided.