Statistical Machine Learning for Emergency Hospital Admissions

这项博士工作将加入与NHS苏格兰正在进行的合作，寻求预测急诊入院的风险，以帮助医疗保健专业人员优先考虑具有复杂护理需求的患者，最终目的是减少急诊住院率。这既有利于改善患者的治疗效果，也有利于节省医疗服务的潜在成本。有一个人口水平的数据集，提供纵向诊断和患者水平的数据，为整个苏格兰人口，使用了国民保健服务医院（约360万人）。到目前为止，以前的工作只涉及一系列逻辑回归模型，这些模型是基于人群中熟练引出的患者队列。这些模型使用一个简单的未学习的规则进行组合。因此，本博士将寻求开发新的统计方法，其灵感来自于明确关注解决上述应用问题。早期工作将研究现有无监督学习（或聚类）方法的效果，以在没有专家干预的情况下从数据中学习患者队列。这将迅速发展并扩展到一个完全有原则的贝叶斯分析，其中需要开发新的方法来实现患者队列和逻辑回归模型参数的联合推断，属于所谓的专家建模混合领域。实现这一目标可能需要扩展现有的计算统计方法：尽管目前存在基于模型的聚类和逻辑回归方法，但在文献中，在本文所需的规模（超过2700万例患者反应观察）下，对结合聚类和风险评分预测的联合模型进行全面推断的工作较少。这将包括探索许多最近所谓的“大数据”蒙特卡罗方法的扩展，包括实现收敛到正确的贝叶斯后验的方法，同时只需要访问任何给定算法迭代的数据子样本。这一最初的里程碑将实现改进的风险评分预测和洞察哪些人群队列经历了急诊入院的同质协变量效应。NHS特别感兴趣的是将这些与以前专业引发的集群进行比较。从这个意义上说，第一阶段工作的聚类和风险评分方面仍然是完全可解释的，不仅可能提供准确的风险评分，而且还可能为GP提供诊断帮助。第二个问题是，如果牺牲完全可解释性（所谓的黑盒建模），风险评分可以提高多少。这项工作将继续将联合推理任务扩展到更现代的统计机器学习方法，如梯度提升机器，同时保留估计患者队列的目标，从而保留一些可解释性，同时利用机器学习的最新进展。这些现代方法的灵活性意味着需要仔细开发一个模型惩罚方案，以确保患者队列发现-也就是说，例如惩罚梯度增强中的轮数。这意味着在每个队列中，可以提高准确性，同时保留队列估计，而不是简单地将整个建模工作变成一个黑盒子。特别是，在模型的规模方面，将有计算统计学的挑战需要克服，因为更复杂的机器学习模型的完全贝叶斯方法仍然是一个非常活跃的研究领域。

This PhD work will join an ongoing collaboration with NHS Scotland seeking to predict risk of emergency hospital admission to assist healthcare professionals in prioritising patients with complex care needs, with the ultimate aim of reducing emergency hospital attendance. This facilitates both better patient outcomes and potential cost savings for the health service. There is a population level dataset, providing longitudinal diagnostic and patient level data for the full Scottish population that has used an NHS hospital (~3.6 million individuals). Prior work to date has only involved a collection of logistic regression models which were based on expertly elicited cohorts of patients in the population. These models were combined using a simple unlearned rule. Therefore, this PhD will seek to develop new statistical methodology inspired by a clear focus on addressing the above applied question.Early work will examine the effect of existing unsupervised learning (or clustering) methods to learn patient cohorts from the data without expert intervention. This will quickly move on and extend to a fully principled Bayesian analysis where new methodology will need to be developed to enable joint inference of both patient cohorts and logistic regression model parameters, falling in the domain of so-called mixture of expert modelling. Achieving this goal will likely require extension of existing computational statistics methods: although methods currently exist for model based clustering and logistic regression separately, less work has been done in the literature on full inference of a joint model incorporating both clustering and risk score prediction for models at the scale required here (in excess of 27 million patient-response observations). This will include exploring extension of many recent so-called "big data" Monte Carlo methods, including approaches that achieve convergence to the correct Bayesian posterior whilst only requiring access to subsamples of the data on any given iteration of the algorithm.This initial milestone will enable both improved risk score prediction and insight into which population cohorts experience homogeneous covariate effects for emergency admission. It is of particular interest to the NHS to compare these to the previously expertly elicited clusters. In this sense both clustering and risk scoring aspects of the first stage of work are still fully interpretable, potentially providing not only accurate risk scoring but also diagnostic assistance to GPs.A second question is how much better risk scoring can be made if full interpretability is sacrificed (so-called black box modelling). The work will move on to extend the joint inference task to more modern statistical machine learning methods such as gradient boosting machines, whilst retaining the goal of estimating patient cohorts, thereby retaining some modicum of interpretability whilst leveraging the latest advances in machine learning. The flexibility of these modern methods means that careful development of a model penalisation scheme will be required to ensure patient cohort discovery -- that is, for example penalising the number of rounds in gradient boosting. This will mean that within each cohort accuracy can be improved whilst retaining cohort estimation, rather than simply turning the entire modelling exercise into a black box. In particular, there will be computational statistics challenges to overcome in the scale of the model, since fully Bayesian approaches to more complex machine learning models is still an area of very active research.