A Hierarchical Framework for Correcting Under-Reporting in Count Data

Tuberculosis poses a global health risk and Brazil is among the top 20 countries by absolute mortality. However, this epidemiological burden is masked by under-reporting, which impairs planning for effective intervention. We present a comprehensive investigation and application of a Bayesian hierarchical approach to modeling and correcting under-reporting in tuberculosis counts, a general problem arising in observational count data. The framework is applicable to fully under-reported data, relying only on an informative prior distribution for the mean reporting rate to supplement the partial information in the data. Covariates are used to inform both the true count-generating process and the under-reporting mechanism, while also allowing for complex spatio-temporal structures. We present several sensitivity analyses based on simulation experiments to aid the elicitation of the prior distribution for the mean reporting rate and decisions relating to the inclusion of covariates. Both prior and posterior predictive model checking are presented, as well as a critical evaluation of the approach. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

结核病（Tuberculosis）是全球公共卫生领域的重大威胁，巴西的结核病绝对死亡率位列全球前二十国家之列。然而，该疾病的流行病学负担因低报行为被掩盖，这一情况会阻碍有效干预措施的规划与制定。本文针对结核病计数数据的低报问题——该问题是观测计数数据中普遍存在的一类共性问题，全面介绍了贝叶斯分层建模方法（Bayesian hierarchical approach）的研究与应用，用于对结核病计数的低报情况进行建模与校正。该框架仅需借助针对平均报告率（mean reporting rate）的信息先验分布，即可补充数据中蕴含的部分信息，适用于完全低报的数据集。协变量（Covariates）可用于辅助刻画真实计数生成过程与低报机制，同时允许模型纳入复杂的时空结构。本文通过多组模拟实验开展了多项敏感性分析，以辅助确定平均报告率的先验分布，并辅助做出协变量纳入相关的决策。此外，本文还介绍了先验与后验预测模型检验方法，并对该方法进行了批判性评价。本文的补充材料，包括可用于复现本研究的材料的标准化说明，可作为在线补充材料获取。