title: A bound for publication bias based on the fraction of unpublished studies.
abstract: Publication bias in meta-analysis is usually modeled in terms of an accept/reject selection procedure in which the selected studies are the "published" studies and the rejected studies are the "unpublished" studies. One possible selection mechanism is to suppose that only studies that report an estimated treatment effect exceeding (or falling short of) some threshold are accepted. We show that, with appropriate choice of thresholds, this attains the maximum bias among all selection mechanisms in which the probability of selection increases with study size. It is impossible to estimate the selection mechanism from the observed studies alone: this result leads to a "worst-case" sensitivity analysis for publication bias, which is remarkably easy to implement in practice. The method is illustrated using data on the effectiveness of prophylactic corticosteroids.
authors.affiliation: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK. J.B.Copas@warwick.ac.uk
authors.forename: John
authors.initials: J
authors.lastname: Copas
authors.forename: Dan
authors.initials: D
authors.lastname: Jackson
mesh_terms: D000305:Adrenal Cortex Hormones / Q000494:pharmacology; D001699:Biometry; D005260:Female; D006801:Humans; D007231:Infant, Newborn; D015201:Meta-Analysis as Topic; D007752:Obstetric Labor, Premature / Q000517:prevention & control; D011247:Pregnancy; D017594:Publication Bias / Q000706:statistics & numerical data*
chemical_list: D000305:Adrenal Cortex Hormones