EMBRACE: An EM-based bias reduction approach through Copas-model estimation for quantifying the evidence of selective publishing in network meta-analysis.

Systematic reviews and meta-analyses synthesize results from well-conducted studies to optimize healthcare decision-making. Network meta-analysis (NMA) is particularly useful for improving precision, drawing new comparisons, and ranking multiple interventions. However, recommendations can be misled if published results are a selective sample of what has been collected by trialists, particularly when publication status is related to the significance of the findings. Unfortunately, the missing-not-at-random nature of this problem and the numerous parameters involved in modeling NMAs pose unique computational challenges to quantifying and correcting for publication bias, such that sensitivity analysis is used in practice. Motivated by this important methodological gap, we developed a novel and stable expectation-maximization (EM) algorithm to correct for publication bias in the network setting. We validate the method through simulation studies and show that it achieves substantial bias reduction in small to moderately sized NMAs. We also calibrate the method against a Bayesian analysis of a published NMA on antiplatlet therapies for maintaining vascular patency.