Statistical Methods for Complex Infectious Disease Systems

对传染病的研究在加拿大和世界各地越来越重要。新冠肺炎、埃博拉、非典或口蹄疫等疾病的爆发对公共卫生和农业行业构成直接威胁，和/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是如何随着时间的推移传播的，以及是什么因素导致一些人被感染，另一些人没有。为了解决这些问题，已经开发了几个个人水平的传染病传播数学模型。这些模型具有直观和灵活的特点，并已被证明准确地描述了疾病传播动力学在时间和空间上的模式。这类模型的参数估计一般是在贝叶斯框架下进行的，使用了探索后验分布的马尔可夫链蒙特卡罗(MCMC)等技术。贝叶斯方法有许多优点，例如很容易将缺失的数据信息作为潜在变量纳入。然而，在贝叶斯框架中从这些模型进行参数估计是计算密集型的，需要大量的计算机时间来执行。这在有大量数据、有相当大比例的缺失数据或我们希望解释的数据不准确的情况下尤其明显。所有这些病例通常适用于传染病数据集。为了决定在暴发期间如何最好地控制传染病，需要迅速取得结果，并在有新数据时经常需要更新。因此，该研究计划的目的是：i)开发更准确、更可靠地模拟真实环境中发生的疾病传播的个体水平模型；ii)改进计算密集的统计推断过程，以使其更高效，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关于各种传染病的数据，以回答关于这些疾病的生物学上有趣的问题；iv)使用计算机模拟和推理来确定未来应该收集哪种传染病数据，以最有效地提供关于感染过程的信息。这一建议强调，在大规模传染病数据分析中，统计人员在解决问题方面发挥着重要作用。它还将为培训各级高素质人员提供机会。这项培训包括三个部分：方法论、计算和对真实生活数据的分析。这项研究计划的结果有望帮助医疗保健服务的利益相关者，并帮助在其他应用领域，如植物和动物疾病，根据快速和正确的统计推断做出适当的决定。

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.