In the post-pandemic era of COVID-19, hospitalization remains a primary public health concern and wastewater surveillance has become an important tool for monitoring its dynamics at the level of community. However, there is usually no sufficient information to know the infection process that results in both wastewater viral signals and hospital admissions. That key challenge has motived a statistical framework proposed in this paper. We formulate the connection of overtime wastewater viral signals and hospitalization counts through a latent process of infection at the level of individual subject. We provide a strategy for accommodating aggregated data, a typical form of surveillance data. Moreover, we ease the conventional procedure of the statistical learning with the joint modeling using available information on the infection process, which can be under-reporting. A simulation study demonstrates that the proposed approach yields stable inference under different degrees of under-ascertainment. The COVID-19 surveillance data from Ottawa, Canada shows that the framework recovers coherent temporal patterns in infection prevalence and variant-specific hospitalization risk under several reporting assumptions.

翻译：在后疫情时代，COVID-19住院情况仍是主要的公共卫生关注点，而废水监测已成为在社区层面追踪其动态的重要工具。然而，通常缺乏足够信息来了解导致废水中病毒信号与住院人数产生的感染过程。这一关键挑战促使本文提出一个统计框架。我们通过个体层面的潜在感染过程，建立了随时间变化的废水中病毒信号与住院人数之间的关联。我们提供了一种处理聚合数据（一种典型的监测数据形式）的策略。此外，我们利用感染过程中可能存在的漏报信息，通过联合建模简化了传统的统计学习流程。模拟研究表明，所提方法在不同程度的漏报情况下均能产生稳定的推断结果。对加拿大渥太华市COVID-19监测数据的分析表明，该框架在多种报告假设下能恢复感染流行率与变异株特异性住院风险的一致时间模式。