Novel Bayesian methods for comparing and evaluating infectious disease models in the light of partially observed data.

传染病传播的数学模型用于预测流行病的规模，增进对传播机制的了解，并制定有效的控制战略。要使这些模型提供有用的见解，至关重要的是它们适合所建模的疾病并得到数据的充分支持。这个项目将发展比较和评价传染病模型所需的技术，即使不是所有的信息都已被观察到，这在实践中是典型的情况。从历史上看，将流行病模型与数据拟合是极具挑战性的，因为疾病传播的关键特征，如感染时间和谁感染了谁，很少为人所知。马尔可夫链蒙特卡罗（MCMC）等数据输入技术的出现，使重建这些缺失的信息成为可能，并成功地将单一流行病模型拟合到数据中，尽管需要付出相当大的计算努力。开发工具，使我们能够从数据中了解哪种模型最适合每种疾病，这一具有挑战性的任务是本项目的主题。这个问题将涉及三个方面：A)模型比较，B)模型评价和影响，C)通过一系列应用说明这些方法。模型比较技术允许统计学家量化证据，以支持相互竞争的科学假设，其中每个假设都可以表示为不同的模型。例如，我们可能希望了解群体中的每个个体是否具有相同的传染性，或者个体之间的传染性是否存在异质性。这些假设中的每一个都可以用一个流行病模型来表示，而数据最支持的模型表明我们应该相信哪个假设。遗憾的是，对于使用MCMC拟合的模型来说，计算支持每种模型的证据在技术上是非常具有挑战性的，因此需要针对流行病的新方法以及对现有通用方法的改进。模型评估技术可用于量化单个模型与数据的拟合程度（以及在哪些领域）。如果没有适当的模型评估，模型比较可能会产生误导，例如，如果考虑的模型都不能充分解释数据。有影响的数据是对拟合模型参数有不成比例影响的观测数据，因此对使用拟合模型所作的任何后续预测也有不成比例的影响。目前很少有定量工具来确定流行病中有影响的数据，尽管在2001年SARS流行期间，人们观察到少数超级传播事件在传播动态中发挥了关键作用。能够识别此类事件何时发生可能对控制政策的有效性产生重大影响。该项目将通过扩大最近发展的贝叶斯潜在残差的作用，并调整用于其他类型统计模型的现有方法，发展确定流行病数据中有影响的个人和时间段的方法。最后，将考虑几个值得注意的应用。新方法对于新出现的数据尤其重要，它允许探索新的流行病学层面（例如病原体遗传学）；对于新出现的疾病，当对感染的流行病学知之甚少时；并发现了感染的季节性驱动因素。来自所有三个应用领域的例子将被考虑使用现有的数据集，当用新的方法分析时，这些数据集可以产生新的见解。这些应用将有助于传播新技术，并将确保任何新方法都能在实践中容易地应用。

Mathematical models for the spread of infectious diseases are used to make predictions of the size of the epidemic, to improve understanding of the mechanisms of transmission and to develop effective strategies for control. For such models to provide useful insights it is vital that they are appropriate for the disease being modelled and well supported by data. This project will develop the techniques necessary to compare and evaluate infectious disease models, even when not all of the information has been observed, as is typically the case in practice.Historically it has been extremely challenging to fit epidemic models to data due to the fact that key characteristics of disease transmission, such as infection times and who infected whom, are rarely known. The advent of data imputation techniques such as Markov chain Monte Carlo (MCMC) have made it possible to reconstruct this missing information and successfully fit a single epidemic model to data, albeit at the cost of considerable computational effort. The challenging task of developing tools that enable us to learn from data which models are the most appropriate for each disease is the subject of this project. Three aspects of this question will be addressed: A) model comparison, B) model evaluation and influence, and C) the illustration of these methods through a series of applications.A. Model comparison techniques allow statisticians to quantify the evidence in favour of competing scientific hypotheses, where each hypothesis can be represented as a different model. For example we might wish to learn whether every individual in a population is equally infectious or if there is heterogeneity in infectivity between individuals. Each of these hypotheses can be represented by an epidemic model and the model that is best supported by the data indicates which hypothesis we should believe. Unfortunately for models fitted using MCMC it is technically very challenging to calculate the evidence in favour of each model and so new methods specific to epidemics, as well as refinements to existing generic methods, are needed.B. Model evaluation techniques can be used to quantify how well (and in what areas) a single model fits the data. Without proper model assessment, model comparison can be misleading, if for example none of the models being considered adequately explain the data. Influential data are observations that have a disproportionate influence over the fitted model parameters, and therefore any subsequent predictions made using the fitted model. Currently there are few quantitative tools for identifying influential data in epidemics, despite the fact that during the SARS epidemic in 2001 it was observed that a small number of super-spreading events played a key role in the transmission dynamics. Being able to identify when such events occur can have major repercussions on the effectiveness of control policies. This project will develop methods to identify influential individuals and time periods in epidemic data by extending the role of the recently developed Bayesian latent residuals and adapting existing methods used for other types of statistical models.C. Finally, several notable applications will be considered. The new methodology is particularly important for emerging data, which allows new epidemiological dimensions (e.g. pathogen genetics) to be explored; for emerging diseases, when little is known about the epidemiology of infection; and for uncovering seasonal drivers of infection. Examples from all three application areas will be considered using existing datasets that could yield new insights when analysed with the new methodology. These applications will help to disseminate the new techniques and will ensure that any new methodology can be readily applied in practice.