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Meta-analysis is a well-established method for integrating results fromseveral independent studies to estimate a common quantity of interest. However,meta-analysis is prone to selection bias, notably when particular studies aresystematically excluded. This can lead to bias in estimating the quantity ofinterest. Motivated by a meta-analysis to estimate the rate of completedsuicide after bariatric surgery, where studies which reported no suicides wereexcluded, a novel zero-truncated count modelling approach was developed. Thisapproach addresses heterogeneity, both observed and unobserved, throughcovariate and overdispersion modelling, respectively. Additionally, through theHorvitz-Thompson estimator, an approach was developed to estimate the number ofexcluded studies, a quantity of potential interest for researchers. Uncertaintyquantification for both estimation of suicide rates and number of excludedstudies was achieved through a parametric bootstrapping approach.

Zero-Truncated Modelling Meta-Analysis for When Studies with No Events  Are Systematically Excluded: Estimating Completed Suicide After Bariatric  Surgery