Meta-regression approximations to reduce publication selection bias

• Published in: Research synthesis methods Vol. 5; no. 1; pp. 60 - 78
• Main Authors: Stanley, T. D., Doucouliagos, Hristos
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 01.03.2014; Wiley-Blackwell; Wiley; Wiley Subscription Services, Inc
• Subjects: Algebra; Applied sciences; Approximation; Bias; Clinical Trials as Topic - classification; Clinical Trials as Topic - statistics & numerical data; Computer science; control theory; systems; Computer Simulation; Data Interpretation, Statistical; Error of Measurement; Evidence-Based Medicine; Exact sciences and technology; Information systems. Data bases; Linear inference, regression; Mathematical Formulas; Mathematics; Memory organisation. Data processing; Meta Analysis; Meta-Analysis as Topic; meta-regression; Models, Statistical; Monte Carlo Methods; Polynomials; Predictive Value of Tests; Probability and statistics; Publication Bias - statistics & numerical data; publication selection bias; Regression (Statistics); Regression Analysis; Sciences and techniques of general use; Software; Statistical Bias; Statistics; systematic reviews; systematic reviews, truncation; truncation; Policy; Therapy; Polynomial approximation; Bias; publication selection bias; Systematic review; Modeling; Mean square error; Metaanalysis; meta-regression; Heterogeneity; Model matching; Quadratic approximation; Metamodel; truncation; Monte Carlo method; Wage; Statistical analysis; Empirical method; Replacement; Regression analysis; Standards; Truncated shape; systematic reviews; Integrity; systematic reviews, truncation
• DOI: 10.1002/jrsm.1095
• ISSN: 1759-2879

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta‐regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision‐effect estimate with standard error (PEESE), is shown to have the smallest bias and mean squared error in most cases and to outperform conventional meta‐analysis estimators, often by a great deal. Monte Carlo simulations also demonstrate how a new hybrid estimator that conditionally combines PEESE and the Egger regression intercept can provide a practical solution to publication selection bias. PEESE is easily expanded to accommodate systematic heterogeneity along with complex and differential publication selection bias that is related to moderator variables. By providing an intuitive reason for these approximations, we can also explain why the Egger regression works so well and when it does not. These meta‐regression methods are applied to several policy‐relevant areas of research including antidepressant effectiveness, the value of a statistical life, the minimum wage, and nicotine replacement therapy. Copyright © 2013 John Wiley & Sons, Ltd.