Chain Event Graphs and Applications to Longitudinal Studies

链事件图（Chain Event Graphs，CEG）是一种基于阶段树的统计模型和演绎推理工具，是一种彩色概率树，是一个快速发展的研究领域，具有广泛的应用。该项目旨在进一步发展与CEG及其动态对应物相关的现有理论和软件。这些应用也可以探索，CEG已经被用于公共卫生，法医学，旅游和犯罪激进化等领域。我已经分析了早期癫痫和单次癫痫发作治疗的数据集。这项工作的重点是分析1年内发生强直-阵挛性癫痫发作的概率，取决于个体的基线协变量以及他们是否接受抗癫痫药物治疗。这项调查开辟了新的分析方法和现有方法的潜在改进的研究领域。这些新方法之一是将连续数据或潜在的无限离散数据和响应变量结合起来。例如，癫痫发作之间的时间是连续的，并已在动态CEG（DCEG）中考虑。将通过假设一年内发作次数遵循泊松过程，对一个时期内的发作次数进行建模。目前，在纳入这些数据方面所做的工作很少，除了将DCEG的持有时间包括在内，这只是一种可能性。因此，我将CEG扩展到一个新的形式称为泊松CEG（PCEG），其中的响应变量将被假定为来自泊松过程，我将深入研究这个新模型的理论，方法和应用。在许多应用中，响应变量可以假设为来自泊松过程，有更多的观测值为零，零计数，比预期的要多。这是零膨胀的一个例子，可以用零膨胀泊松（zero-inflated Poisson，ZIP）分布来建模。这是集中在这样一个想法，即不是所有的零都是平等的;有些人永远不会有非零计数，因此被认为是“无风险”，而其他人可能有零计数，但仍然是“有风险”，如果观察足够长的时间，就会有非零计数。ZIP旨在估计处于风险中的个人的比例，并随后估计其基本比率，如果不考虑零通货膨胀，这将被低估。我将讨论通过引入潜在风险状态变量将零通货膨胀纳入CEG的方法，该变量将PCEG扩展为零通货膨胀泊松CEG（ZIPCEG）。 随着协变量数量的增加，树的大小也会增加，这会导致树后面部分的边缘计数稀疏，特别是当总样本量不足时。这些解析边计数可能导致虚假和不可靠的结论。我将提出各种方法来解决和减轻稀疏边缘计数，最终在新的中间CEG，条件独立关系断言，以减少树的大小。这些方法将使用真实的世界数据进行演示。 为了进一步开发CEG，R中现有的软件和包必须对用户友好，特别是为了拟合和绘制CEG。其中一个主要的R包专注于CEG，ceg，有几个bug，并且没有积极维护。我计划发布我自己的软件包pcegr，它使用ceg的绘图方法，但具有适合CEG，PCEG和ZIPCEG的功能，以及执行变量离散化。

Chain Event Graphs (CEGs) are a form of statistical model and deductive reasoning tool based on staged trees, a coloured probability tree, and are a rapidly growing research field with a wide range of applications. This project aims to further develop on the existing theory and software associated with CEGs and their dynamic counterparts. These applications can also be explored, with CEGs already being used in fields such as public health, forensic science, tourism and criminal radicalisation. I have already analysed a dataset on the treatment of early epilepsy and single seizures. This work focused on analysing the probability of a tonic-clonic seizure occurring within 1 year, dependent on the individual's baselines covariates and whether they received treatment with anti-epileptic drugs or not. This investigation opened up further areas of research on new approaches to analysis, and potential improvements to existing methods. One of these new approaches is to incorporate continuous data or potentially infinite discrete data and response variables. For example, time between seizures is continuous and has been considered in Dynamic CEGs (DCEGs). Number of seizures in a period will be modelled by assuming the number of seizures suffered in a year follows a Poisson process. Currently, there is very little work being done on incorporating such data, except for including holding times in DCEGs, which is only one possibility. As such, I will extend CEGs to a new form called a Poisson CEG (PCEG), where the response variable will be assumed to come from a Poisson process, and I will delve into the theory, methods, and applications of this new model. In many of the applications where the response variable could be assumed to come from a Poisson process, there are a greater number of observations of zero, zero counts, than would be expected. This is an example of zero-inflation, and can be modelled with a zero-inflated Poisson (ZIP) distribution. This is centred on the idea that not all zeroes are created equal; some individuals will never have a nonzero count, and thus considered "risk free", while others may have a zero count but still be "at risk" and would have a nonzero count if observed for long enough. The ZIP aims to estimate the proportion of at risk individuals and subsequently estimate their underlying rate, which would be underestimated if zero-inflation was not accounted for. I will discuss methods used to incorporate this zero-inflation into the CEG through the introduction of a latent risk state variable, which extends the PCEG to a Zero-inflated Poisson CEG (ZIPCEG). As the number of covariates increases and thus the size of the tree grows, this leads to sparse edge counts in the later parts of the tree, particularly when the overall sample size is insufficient. These parse edge counts can lead to spurious and unreliable conclusions. I will propose various methods to address and alleviate sparse edge counts, culminating in the novel intermediate CEG, where conditional independence relations are asserted in order to decrease the size of the tree. These methods will be demonstrated using real world data. In order to further the development of CEGs, the existing software and packages in R must be made user friendly, particularly for the purposes of fitting and graphing CEGs. One of the main R packages focused on CEGs, ceg, has several bugs and is not actively maintained. I plan to publish my own package, pcegr, which uses the graphing methods of ceg but with the functionality to fit CEGs, PCEGs and ZIPCEGs, as well as perform variable discretisation.