Chain Event Graphs and Applications to Longitudinal Studies

链事件图是一种基于阶段树、有色概率树的统计模型和演绎推理工具，是一个发展迅速、应用广泛的研究领域。该项目旨在进一步发展与CEGS及其动态对应机构相关的现有理论和软件。这些应用也可以探索，CEGS已经被用于公共卫生、法医学、旅游业和犯罪激进化等领域。我已经分析了一个关于早期癫痫和单次癫痫发作治疗的数据集。这项工作侧重于分析在1年内发生强直-阵挛发作的可能性，这取决于个体的基线变量以及他们是否接受了抗癫痫药物的治疗。这项调查开辟了新的分析方法的研究领域，并对现有方法进行了潜在的改进。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在一起。例如，癫痫发作之间的时间是连续的，动态脑电地形图(DCEG)中考虑了这一点。一段时间内的癫痫发作次数将通过假设一年中癫痫发作的次数遵循泊松过程来建模。目前，在纳入这类数据方面所做的工作很少，除了在DCEG中纳入持有时间，这只是一种可能性。因此，我将把CEGS推广到一种新的形式，称为泊松CEG(PCEG)，其中响应变量将被假设为来自泊松过程，我将深入研究这个新模型的理论、方法和应用。在许多可以假设响应变量来自泊松过程的应用中，零、零计数的观测值比预期的要多。这是零通胀的一个例子，可以用零膨胀泊松(ZIP)分布来建模。这一观点的核心是，并非所有的零都是生而平等的；一些人永远不会有非零计数，因此被认为是“零风险”，而另一些人可能有零计数，但仍然“有风险”，如果观察足够长的时间，就会有非零计数。ZIP的目标是估计处于风险中的个人的比例，然后估计他们的潜在利率，如果不考虑零通胀，潜在利率将被低估。我将讨论通过引入潜在风险状态变量将这种零通胀纳入CEG的方法，该状态变量将PCEG扩展为零膨胀泊松CEG(ZIPCEG)。随着协变量的数量增加，从而树的大小增加，这导致树的后面部分的边缘计数稀疏，特别是当总体样本量不足时。这些分析边缘计数可能导致错误和不可靠的结论。我将提出各种方法来解决和减轻稀疏边计数，最终形成新的中间CEG，其中断言条件独立关系以减小树的大小。这些方法将使用真实世界的数据进行演示。为了促进CEGS的发展，R中的现有软件和软件包必须便于用户使用，特别是为了拟合CEGS和绘制CEGS图。CEG是关注CEGS的主要R包之一，它有几个错误，没有积极维护。我计划发布我自己的包，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.