Zero-Truncated Modelling in a Meta-Analysis on Suicide Data 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 modeling approach was developed. This approach addresses heterogeneity, both observed and unobserved, through covariate and overdispersion modeling, respectively. Additionally, through the Horvitz-Thompson estimator, an approach is 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 is achieved through a parametric bootstrapping approach.