Meta‐regression approximations to reduce publication selection bias.

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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 tothe 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 mostcases and to outperform conventional meta-analysis estimators, often by a great deal. Monte Carlo simulationsalso demonstrate how a new hybrid estimator that conditionally combines PEESE and the Egger regressionintercept can provide a practical solution to publication selection bias. PEESE is easily expanded to accom-modate systematic heterogeneity along with complex and differential publication selection bias that is relatedto moderator variables. By p roviding an intuitive reason for these approximations, we can also explain why theEgger regression works so well and when it does not. These meta-regression methods are applied to severalpolicy-relevant areas of research including antidepressant effectiveness, the value of a statistical life, theminimum wage, and nicotine replacement therapy.