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.

中文翻译：

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减肥手术后自杀数据荟萃分析中的零截断模型

Meta 分析是一种行之有效的方法，用于整合几项独立研究的结果以估计共同的关注量。然而，meta 分析容易出现选择偏倚，特别是当特定研究被系统性排除时。这可能会导致在估计感兴趣的数量时出现偏差。在一项荟萃分析的推动下，估计减肥手术后自杀完成的比率，其中排除了没有报告自杀的研究，开发了一种新的零截断计数建模方法。这种方法分别通过协变量和超离散建模来解决观察到的和未观察到的异质性。此外，通过 Horvitz-Thompson 估计器，开发了一种方法来估计被排除的研究数量，这是研究人员可能感兴趣的数量。自杀率估计和排除研究数量的不确定性量化是通过参数化引导方法实现的。