In epidemiological studies, the capture-recapture (CRC) method is a powerful tool that can be used to estimate the number of diseased cases or potentially disease prevalence based on data from overlapping surveillance systems. Estimators derived from log-linear models are widely applied by epidemiologists when analyzing CRC data. The popularity of the log-linear model framework is largely associated with its accessibility and the fact that interaction terms can allow for certain types of dependency among data streams. In this work, we shed new light on significant pitfalls associated with the log-linear model framework in the context of CRC using real data examples and simulation studies. First, we demonstrate that the log-linear model paradigm is highly exclusionary. That is, it can exclude, by design, many possible estimates that are potentially consistent with the observed data. Second, we clarify the ways in which regularly used model selection metrics (e.g., information criteria) are fundamentally deceiving in the effort to select a best model in this setting. By focusing attention on these important cautionary points and on the fundamental untestable dependency assumption made when fitting a log-linear model to CRC data, we hope to improve the quality of and transparency associated with subsequent surveillance-based CRC estimates of case counts.

翻译：在流行病学研究中，捕获-再捕获（CRC）方法是一种强大的工具，可用于基于重叠监测系统的数据估计病例数或疾病患病率。流行病学家在分析CRC数据时广泛使用基于对数线性模型的估计量。对数线性模型框架的普及主要归因于其易用性，以及交互项可允许数据流之间存在某些类型的依赖性这一事实。在本研究中，我们通过实际数据示例和模拟研究，揭示了在CRC背景下对数线性模型框架存在的重大陷阱。首先，我们证明了对数线性模型范式具有高度排他性——即其设计本身会排除许多可能与观测数据一致的估计值。其次，我们阐明了在此场景下，常规使用的模型选择指标（如信息准则）在选择最优模型时本质上具有欺骗性。通过聚焦这些重要的警示要点，以及对拟合CRC数据的对数线性模型时所作的基本不可检验的依赖性假设，我们期望提升后续基于监测的CRC病例数估计的质量与透明度。