Neither fixed nor random: weighted least squares meta-analysis

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...

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Bibliographic Details
Published in:Statistics in medicine 2015-06, Vol.34 (13), p.2116-2127
Main Authors: Stanley, T. D., Doucouliagos, Hristos
Format: Article
Language:English
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
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Summary: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.
ISSN:0277-6715
1097-0258
DOI:10.1002/sim.6481