title: A selection model for accounting for publication bias in a full network meta-analysis.
abstract: Copas and Shi suggested a selection model to explore the potential impact of publication bias via sensitivity analysis based on assumptions for the probability of publication of trials conditional on the precision of their results. Chootrakool et al. extended this model to three-arm trials but did not fully account for the implications of the consistency assumption, and their model is difficult to generalize for complex network structures with more than three treatments. Fitting these selection models within a frequentist setting requires maximization of a complex likelihood function, and identification problems are common. We have previously presented a Bayesian implementation of the selection model when multiple treatments are compared with a common reference treatment. We now present a general model suitable for complex, full network meta-analysis that accounts for consistency when adjusting results for publication bias. We developed a design-by-treatment selection model to describe the mechanism by which studies with different designs (sets of treatments compared in a trial) and precision may be selected for publication. We fit the model in a Bayesian setting because it avoids the numerical problems encountered in the frequentist setting, it is generalizable with respect to the number of treatments and study arms, and it provides a flexible framework for sensitivity analysis using external knowledge. Our model accounts for the additional uncertainty arising from publication bias more successfully compared to the standard Copas model or its previous extensions. We illustrate the methodology using a published triangular network for the failure of vascular graft or arterial patency.
authors.affiliation: Department of Hygiene and Epidemiology, University of Ioannina School of Medicine, Ioannina, Greece; Department of Primary Education, University of Ioannina, Ioannina, Greece.
authors.forename: Dimitris
authors.initials: D
authors.lastname: Mavridis
authors.forename: Nicky J
authors.initials: NJ
authors.lastname: Welton
authors.forename: Alex
authors.initials: A
authors.lastname: Sutton
authors.forename: Georgia
authors.initials: G
authors.lastname: Salanti
mesh_terms: D001241:Aspirin / Q000627:therapeutic use; D001499:Bayes Theorem; D004176:Dipyridamole / Q000627:therapeutic use; D004338:Drug Combinations; D006801:Humans; D008390:Markov Chains; D015201:Meta-Analysis as Topic; D010919:Placebos; D010975:Platelet Aggregation Inhibitors / Q000627:therapeutic use; D017594:Publication Bias; D016032:Randomized Controlled Trials as Topic / Q000379:methods; D012107:Research Design; D018401:Sample Size
chemical_list: D004338:Drug Combinations; D010919:Placebos; D010975:Platelet Aggregation Inhibitors; D004176:Dipyridamole; D001241:Aspirin
keywords: consistency; mixed treatment comparison; propensity for publication; publication bias; study design