title: Meta-regression approximations to reduce publication selection bias.
abstract: 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.
authors.affiliation: Economics, Hendrix College, 1600 Washington St., Conway, AR, 72032, USA.
authors.forename: T D
authors.initials: TD
authors.lastname: Stanley
authors.affiliation: School of Accounting, Economics, and Finance and Alfred Deakin Research Institute, Deakin University, 221 Burwood Highway, Burwood, 3125, Victoria, Australia.
authors.forename: Hristos
authors.initials: H
authors.lastname: Doucouliagos
mesh_terms: D002986:Clinical Trials as Topic / Q000145:classification / Q000706:statistics & numerical data*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D019317:Evidence-Based Medicine; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D011237:Predictive Value of Tests; D017594:Publication Bias / Q000706:statistics & numerical data*; D012044:Regression Analysis
keywords: meta-regression; publication selection bias; systematic reviews, truncation