Statistical Methods for Complex Infectious Disease Systems

传染病的研究在加拿大和世界各地越来越重要。COVID-19、埃博拉、SARS或口蹄疫等疾病的爆发对公共卫生和农业产业构成直接威胁，并╱或产生严重的经济影响。为了迅速控制这种疾病的爆发，重要的是要了解疾病如何随着时间的推移而传播，以及哪些因素导致一些人感染而另一些人没有感染。为了解决这些问题，已经开发了几个传染病传播的个体水平的数学模型。这些模型具有直观和灵活的特点，并已被证明可以准确地描述疾病在时间和空间上的传播动态模式。这些模型的参数估计通常在贝叶斯框架中进行，使用诸如马尔可夫链蒙特卡罗（MCMC）的技术，其探索后验分布。贝叶斯方法提供了许多优点，例如容易将缺失的数据信息作为潜在变量合并。然而，在贝叶斯框架中从这些模型的参数估计是计算密集型的，需要大量的计算机时间来执行。这在数据量大、数据缺失比例大或我们希望解释的数据不准确的情况下尤其明显。所有这些情况通常都适用于传染病数据集。 为了决定如何在疫情爆发期间最好地控制传染病，需要快速获得结果，并在获得新数据时经常进行更新。因此，本研究计划的目的是：i）开发个人层面的模型，更准确和可靠地模拟疾病在真实的环境中的传播; ii）改进计算密集型统计推断过程，使其更有效，例如使用高斯过程仿真和流行病分类技术; iii）将新模型应用于收集的各种传染病数据，以回答有关这些疾病的生物学问题; iv）利用电脑模拟及推论，以决定日后应收集哪类传染病资料，才能最有效地提供有关感染过程的资料。这一建议强调了统计人员在解决大规模传染病数据分析问题中的重要作用。它还将为培训各级高素质人员提供机会。这种培训有三个组成部分：方法，计算和分析真实的生活数据。这项研究计划的成果预计将有助于医疗保健服务的利益相关者，并有助于在其他应用领域（如植物和动物疾病）基于快速和正确的统计推断做出适当的决策。

Studies of infectious diseases are increasingly important in Canada and around the world. Outbreaks of diseases such as COVID-19, Ebola, SARS, or foot-and-mouth disease pose direct threats to public health and agriculture industries, and/or have serious economic effects. To quickly control such disease outbreaks, it is important to understand how the disease spreads over time and what factors lead some individuals to become infected and some not. To address these issues, several individual-level mathematical models for infectious disease transmission have been developed. These models have intuitive and flexible characteristics and have been shown to accurately describe the patterns of disease spread dynamics over time and space. The parameter estimation of such models is in general carried out in a Bayesian framework, using techniques such as Markov chain Monte Carlo (MCMC), which explores the posterior distribution. The Bayesian approach offers many advantages, such as the easy incorporation of missing data information as latent variables. However, the parameter estimation from these models in a Bayesian framework are computationally intensive, requiring substantial computer time to carry out. This is especially apparent in cases with large amounts of data, a substantial proportion of missing data, or inaccuracies in the data that we wish to account for. All of these cases typically apply with infectious disease data sets. To decide how best to control an infectious disease during the course of an outbreak, results are needed quickly and updates needed often as new data are available. The purpose of this research program is therefore to: i)develop individual-level models that more accurately and reliably model disease transmission as it occurs in real settings; ii)improve the computationally intensive statistical inference process to make it more efficient, for example using Gaussian process emulation and epidemic classification techniques; iii)apply new models to data collected about various infectious diseases to answer biologically interesting questions about those diseases; iv)use computer simulation and inference to determine what sort of infectious disease data should be collected in the future to provide information most efficiently about the infection process. This proposal emphasizes that statisticians play an important role in solving problems in the analysis of large scale infectious disease data. It will also provide opportunities for training highly qualified personnel at all levels. This training has three components: methodology, computation, and analysis of real life data. The outcomes of this research program are expected to aid stakeholders in health care services, and to aid in making proper decisions based on quick and correct statistical inferences in other areas of applications such plant and animal disease.