Previous research has noted that many factors greatly influence the spread of COVID-19. Contrary to explicit factors that are measurable, such as population density, number of medical staff, and the daily test rate, many factors are not directly observable, for instance, culture differences and attitudes toward the disease, which may introduce unobserved heterogeneity. Most contemporary COVID-19 related research has focused on modeling the relationship between explicitly measurable factors and the response variable of interest (such as the infection rate or the death rate). The infection rate is a commonly used metric for evaluating disease progression and a state's mitigation efforts. Because unobservable sources of heterogeneity cannot be measured directly, it is hard to incorporate them into the quantitative assessment and decision-making process. In this study, we propose new metrics to study a state's performance by adjusting the measurable county-level covariates and unobservable state-level heterogeneity through random effects. A hierarchical linear model (HLM) is postulated, and we calculate two model-based metrics—the standardized infection ratio (SDIR) and the adjusted infection rate (AIR). This analysis highlights certain time periods when the infection rate for a state was high while their SDIR was low and vice versa. We show that trends in these metrics can give insight into certain aspects of a state's performance. As each state continues to develop their individualized COVID-19 mitigation strategy and ultimately works to improve their performance, the SDIR and AIR may help supplement the crude infection rate metric to provide a more thorough understanding of a state's performance.

中文翻译：

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评估国家抗击 COVID-19 大流行表现的新指标

先前的研究指出，许多因素极大地影响了 COVID-19 的传播。与人口密度、医务人员数量、每日检测率等可测量的明确因素相反，许多因素是不可直接观察的，例如文化差异和对疾病的态度，这可能会引入不可观察的异质性。大多数当代 COVID-19 相关研究都集中于对明确可测量因素与感兴趣的响应变量（例如感染率或死亡率）之间的关系进行建模。感染率是评估疾病进展和州缓解努力的常用指标。由于不可观测的异质性来源无法直接测量，因此很难将其纳入定量评估和决策过程。在这项研究中，我们提出了新的指标来通过随机效应调整可测量的县级协变量和不可观察的州级异质性来研究州的绩效。假设了分层线性模型（HLM），我们计算了两个基于模型的指标——标准化感染率（SDIR）和调整后感染率（AIR）。该分析强调了某个州的感染率较高而 SDIR 较低的某些时间段，反之亦然。我们表明，这些指标的趋势可以洞察一个州绩效的某些方面。随着每个州继续制定个性化的 COVID-19 缓解策略并最终努力提高其绩效，SDIR 和 AIR 可能有助于补充粗略的感染率指标，以更全面地了解各州的绩效。