Neither fixed nor random: weighted least squares meta-analysis

• Published in: Statistics in medicine Vol. 34; no. 13; pp. 2116 - 2127
• Main Authors: Stanley, T. D., Doucouliagos, Hristos
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 15.06.2015; Wiley Subscription Services, Inc
• Subjects: Bias; Computer Simulation; Confidence Intervals; Estimating techniques; fixed effect; Humans; Least-Squares Analysis; Markov Chains; Meta-analysis; Meta-Analysis as Topic; meta-regression; Publication Bias; random effects; Regression analysis; Simulation; Statistical methods; weighted least squares; random effects; fixed effect; meta-analysis; weighted least squares; meta-regression
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.6481

This study challenges two core conventional meta‐analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random‐effects meta‐analysis when there is publication (or small‐sample) bias and better than a fixed‐effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small‐sample) bias and identical to fixed‐effect meta‐analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed‐effect meta‐analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects. Copyright © 2015 John Wiley & Sons, Ltd.