Statistical methods for characterising the severity of an emerging pathogen: case studies of the COVID-19 pandemic

对一种新病原体的持续流行进行建模提出了若干特殊挑战，特别是当这些病例往往没有症状或容易被误认为是感冒或流感等常见疾病时。传染病的数学模型依赖于数据的输入，在COVID-19大流行开始时，研究人员可以获得的数据集非常有限。这导致估计存在较大偏差，包括较大的不确定性间隔，或者需要假设不同国家的病毒严重程度相同。这一假设在当时是必要的，但使结果非常值得怀疑，例如，当使用来自高收入国家的数据来模拟低收入或中等收入国家的流行病时。数据带来的另一个问题是数据收集的延迟。对正在发生的流行病的监测需要每天监测新病例或死亡人数，但由于报告的延误，这往往是不可能的，因为许多医院工作人员不堪重负，无法及时在线更新数据。这导致有系统地少报该流行病的真实情况。我博士项目的主要主题是缩小这些数据差距，减少数据中的偏差。在第一个项目中，我们根据住院数据对巴西COVID-19流行的常见流行病学分布（如发病至死亡时间）进行了估计。我们的估计在拟合分布中提供了空间异质性的证据。在第二个项目中，我们提出了一种利用潜在高斯过程（GPs）纠正数据报告延迟的新方法，并展示了该方法对巴西COVID-19死亡率数据的适用性。

Modelling of an ongoing epidemic of a new pathogen poses several particular challenges, especially when the cases are often symptomless or easy to mistake for a common disease such as a cold or flu. Mathematical models of infectious diseases rely on the input of data, and at the beginning of the COVID-19 pandemic very limited datasets were available to the researchers. This caused the estimates to have large biases, including large uncertainty intervals or the need to assume the severity of the virus across different countries was the same. This assumption was necessary at the time but made the results highly questionable e.g. when data from a high-income country were used to model the epidemic in a low- or middle-income country.An additional problem posed by the data was the delay with which they were collected. Surveillance of an ongoing epidemic requires daily monitoring of the numbers of new cases or deaths, but this was often impossible due to the reporting delays, as a lot of hospital staff was overwhelmed with the number of patients and unable to promptly update the data online. This led to systematic underreporting of the true state of the epidemic.The main topic of my PhD projects is closing some of those data gaps and decreasing the bias in the data. In the first project, we provided estimates of common epidemiological distributions, such as onset-to-death time, for the COVID-19 epidemic in Brazil based on hospitalisation data. Our estimates gave evidence of spatial heterogeneity in the fitted distributions. In the second project, we proposed a new approach to correcting the delays in data reporting using latent Gaussian processes (GPs) and presented the applicability of the method to the COVID-19 mortality data in Brazil.