A Non-parametric \Trim and Fill" Method of Assessing Publication Bias in Meta-analysis

Meta-analysis collects and synthesizes results from individual studies to estimate an overall eeect size. If published studies are chosen, say through a literature review, an inherent selection bias may arise, since for example, studies may tend to be published more readily if they are statistically signiicant, or deemed to be morèinteresting' in terms of the impact of their outcomes. We develop a simple rank-based data augmentation technique, formalizing the use of funnel plots, to estimate and adjust for the numbers and outcomes of missing studies. Several non-parametric estimators are proposed for the number of missing studies, and their properties are developed analytically and through simulations. We apply the method to simulated and epidemiological data sets, and show it is both eeective and consistent with other criteria in the literature.