Methods to calculate uncertainty in the estimated overall effect size from a random-effects meta-analysis

Meta-analyses are an important tool within systematic reviews to estimate the overall effect size and its confidence interval for an outcome of interest. If heterogeneity between the results of the relevant studies is anticipated, then a random-effects model is often preferred for analysis. In this model, a prediction interval for the true effect in a new study also provides additional useful information. However, the DerSimonian and Laird method - frequently used as the default method for meta-analyses with random effects - has been long challenged due to its unfavourable statistical properties. Several alternative methods have been proposed that may have better statistical properties in specific scenarios. In this paper, we aim to provide a comprehensive overview of available methods for calculating point estimates, confidence intervals and prediction intervals for the overall effect size under the random-effects model. We indicate whether some methods are preferable than others by considering the results of comparative simulation and real-life data studies.