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被用来预测疫情的大小，增进对传播机制的了解，并制定有效的控制战略。为了让这些模型提供有用的见解，至关重要的是，它们适合正在建模的疾病，并得到数据的良好支持。这个项目将开发必要的技术来比较和评估传染病模型，即使在没有观察到所有信息的情况下也是如此，就像实践中的典型情况一样。从历史上看，将流行病模型与数据相匹配一直是极具挑战性的，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)等数据补偿技术的出现使得重建缺失的信息并成功地将单个流行病模型与数据匹配成为可能，尽管代价是相当大的计算工作量。开发工具，使我们能够从数据中了解哪些模型最适合每种疾病，这是该项目的主题，这是一项具有挑战性的任务。这个问题将涉及三个方面：A)模型比较，B)模型评估和影响，C)通过一系列应用说明这些方法。A.模型比较技术使统计学家能够量化证据，支持相互竞争的科学假设，其中每个假设可以表示为不同的模型。例如，我们可能希望了解一个群体中的每个人是否都具有同等的传染性，或者个人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，而数据支持得最好的模型表明了我们应该相信哪个假设。不幸的是，对于使用MCMC拟合的模型，在技术上计算有利于每个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。如果没有适当的模型评估，模型比较可能具有误导性，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的模型参数具有不成比例的影响的观测，因此是使用拟合的模型进行的任何后续预测。尽管在2001年SARS疫情期间观察到少数超级传播事件在传播动态中发挥了关键作用，但目前几乎没有量化工具来确定流行病中有影响力的数据。能够确定此类事件发生的时间可能会对控制政策的有效性产生重大影响。这个项目将通过扩展最近开发的贝叶斯潜在残差的作用，并修改用于其他类型统计模型的现有方法，来开发识别流行病数据中有影响力的个人和时间段的方法。c.最后，将考虑一些值得注意的应用。新的方法对于新出现的数据特别重要，它允许探索新的流行病学层面(例如病原体遗传学)；对于对感染流行病学知之甚少的新疾病；以及对于揭示感染的季节性驱动因素。将使用现有数据集审议所有三个应用领域的实例，这些数据集在使用新方法进行分析时可能产生新的见解。这些应用将有助于传播新的技术，并将确保任何新的方法都可以很容易地应用于实践。

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.