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

Meta-analysis is a well-established method for integrating results from several independent studies to estimate a common quantity of interest. However, meta-analysis is prone to selection bias, notably when particular studies are systematically excluded. This can lead to bias in estimating the quantity of interest. Motivated by a meta-analysis to estimate the rate of completed suicide after bariatric surgery, where studies which reported no suicides were excluded, a novel zero-truncated count modelling approach was developed. This approach addresses heterogeneity, both observed and unobserved, through covariate and overdispersion modelling, respectively. Additionally, through the Horvitz-Thompson estimator, an approach was developed to estimate the number of excluded studies, a quantity of potential interest for researchers. Uncertainty quantification for both estimation of suicide rates and number of excluded studies was achieved through a parametric bootstrapping approach.