Better than Random: Weighted Least Squares Meta-Regression Analysis

Our study revisits and challenges two core conventional meta-regression models: the prevalent use of ‘mixed-effects’ or random-effects meta-regression analysis (RE-MRA) and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why the traditional, unrestricted weighted least squares estimator (WLS-MRA) is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias and as good as FE-MRA in all cases and better in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients with confidence intervals that are comparable to mixed-or random-effects when there is no publication bias. When there is publication selection bias, WLS-MRA dominates mixed- and random-effects, especially when there is large additive heterogeneity as assumed by the random-effects meta-regression model.