Several key metrics in public health convey the probability that a primary event will lead to a more serious secondary event in the future.Several key metrics in public health convey the probability that a primary event will lead to a more serious secondary event in the future. These "severity rates" can change over the course of an epidemic in response to shifting conditions like new therapeutics, variants, or public health interventions. In practice, time-varying parameters such as the case-fatality rate are typically estimated from aggregate count data. Prior work has demonstrated that commonly-used ratio-based estimators can be highly biased, motivating the development of new methods. In this paper, we develop an adaptive deconvolution approach based on approximating a Poisson-binomial model for secondary events, and we regularize the maximum likelihood solution in this model with a trend filtering penalty to produce smooth but locally adaptive estimates of severity rates over time. This enables us to compute severity rates both retrospectively and in real time. Experiments based on COVID-19 death and hospitalization data show that our deconvolution estimator is generally more accurate than the standard ratio-based methods, and displays reasonable robustness to model misspecification.

翻译：公共卫生领域的若干关键指标用于衡量初始事件未来导致更严重二次事件的概率。这些"严重率"会随着疫情发展而变化，以响应新型疗法、病毒变异或公共卫生干预等条件变迁。实践中，病死率等时变参数通常通过聚合计数数据进行估计。已有研究表明，常用的比值估计方法可能存在显著偏差，这推动了新方法的研发。本文基于对二次事件的泊松-二项模型近似，提出一种自适应反卷积方法，并通过趋势过滤惩罚项对模型中的最大似然解进行正则化，从而生成随时间平滑但局部自适应的严重率估计。该方法可同时支持回顾性和实时严重率计算。基于COVID-19死亡与住院数据的实验表明，我们的反卷积估计器通常比标准比值方法更准确，并对模型设定偏差表现出合理的鲁棒性。