An investigation into the use of shrinkage methods to alleviate over-fitting of prognostic models for independent and clustered data with few events

临床医生、卫生服务研究人员和流行病学家经常希望预测患者和公众未来的健康结果。这些结果的例子包括冠心病的发展，手术后住院死亡率的发生，以及抑郁症的发作。临床医生使用这些预测来确定患者的预后，以计划他们的治疗，检测高风险患者，并为患者提供信息，使他们能够做出关于他们的治疗选择的决定。政策制定者经常使用这些预测来评估医院和全科诊所的绩效，并识别绩效不佳的机构。通常使用基于患者临床和人口统计学特征的统计模型来进行这些预测。这些模型被称为预测模型。为了开发这种模型，收集了关于患者或相关受试者的信息，包括他们的风险因素和他们经历的健康结果。风险因素和结果之间的关系使用统计模型进行量化，然后可以用于预测新患者。模型通常以风险算法的形式呈现。然后在新患者身上测试该算法，以确保其做出可靠的预测。如果发现其性能令人满意，则建议临床医生在实践中使用。在实践中使用的风险算法的例子包括预测冠心病10年风险的Fragrance风险评分，预测心脏手术后住院死亡率的Euroscore和预测抑郁症风险的PREDICT评分。当感兴趣的健康结果是罕见的，它往往是有问题的，以开发一个风险算法，既可以准确地预测风险，并能够将患者分为高风险和低风险组。这是健康研究中的一个常见问题，并且通常不会通过从许多中心或长时间收集患者数据来缓解。来自许多中心的数据还存在另一个统计问题，因为不同中心之间的结果可能存在差异。对于相对常见的事件，如冠心病、心脏手术后的住院死亡率和抑郁症，存在稳健的模型。然而，可靠的预后模型是稀缺的，或不可用，为罕见的健康结果，例如死亡或复发后诊断的罕见类型的癌症，和帕金森病的发作。当试图为相对较小的人群中的常见事件开发预后模型时，也存在类似的问题，例如，预测患有严重心理健康问题的人的冠心病的模型。一些方法学研究已经完成，以处理的问题，拟合统计模型的罕见结果在遗传学研究。然而，有限的工作已经做了开发方法，以产生可靠的预后模型，在临床环境中，如公共卫生和卫生服务研究罕见的结果。此外，由于缺乏软件和适当的评价，迄今为止开发的方法没有得到常规使用。目前没有关于统计人员和其他研究人员应如何在实践中使用这些方法的指导方针。拟议的研究将评估现有的统计方法，当感兴趣的健康结果罕见时，该方法可用于处理风险预测，并将在必要时开发新方法。拟议的研究将就这些方法在实践中的使用提出建议。此外，本研究项目中开发的方法将在广泛使用的统计软件中实施，以使其能够日常使用。使用这些方法开发的预后模型应该使临床医生和政策制定者能够在这些情况下为患者预测健康结果，即使结果是罕见的

Clinicians, health service researchers and epidemiologists often wish to predict a future health outcome for patients and the public. Examples of such outcomes include development of coronary heart disease, the occurrence of in-hospital mortality following surgery, and the onset of depression. These predictions are used by clinicians to determine the prognosis of patients to plan their treatment, to detect high risk patients, and to provide information to patients enabling them to make decisions about their treatment options. Policy makers often use these predictions to assess the performance of hospitals and general practices and identify under performing institutions.Statistical models using patients' clinical and demographic characteristics are typically used to make these predictions. These models are referred to as prognostic models. To develop such models, information is collected on patients or relevant subjects, regarding their risk factors and the health outcome they experienced. The relationship between the risk factors and the outcome is quantified using a statistical model, which can then be used to make predictions for new patients. Models are usually presented in the form of a risk algorithm. This algorithm is then tested on new patients to ensure that it makes reliable predictions. If its performance is found to be satisfactory, it is recommended for use by clinicians in practice. Examples of risk algorithms used in practice include the Framingham risk score to predict the 10 year risk of coronary heart disease, Euroscore to predict in-hospital mortality following cardiac surgery and the PREDICT score to predict the risk of developing depression. When the health outcome of interest is rare it is often problematic to develop a risk algorithm that will both predict risk accurately and be able to classify patients into high and low risk groups. This is a common problem in health research and is often not alleviated by collecting patient data from many centres, or over a long period of time. A further statistical problem occurs with data from many centres as there may be variability in the outcomes between the centres. Robust models exist for relatively common events such as coronary heart disease, in-hospital mortality following cardiac surgery, and depression. However reliable prognostic models are scarce, or not available, for rarer health outcomes, for example death or recurrence following diagnosis of rare types of cancer, and the onset of Parkinson's disease. There is a similar problem when trying to develop prognostic models for common events in relatively small subgroups of people, for example, a model to predict coronary heart disease in people who have severe mental health problems. Some methodological research has been done to handle the problem of fitting statistical models for rare outcomes in genetic studies. However, limited work has been done to develop methods to produce reliable prognostic models with rare outcomes in clinical settings such as public health and health services research. Moreover, the methods that have been developed to date are not used routinely because of lack of software and adequate evaluation. There are currently no guidelines regarding how statisticians and other researchers should be using these methods in practice. The proposed research will evaluate the existing statistical methodology that is available to handle risk predictions when the health outcome of interest is rare, and will develop new methods where necessary. The proposed research will make recommendations regarding the use of these methods in practice. Additionally, the methods developed in this research project will be implemented in widely available statistical software to enable their routine use. The prognostic models developed using these methods should enable clinicians and policy makers to make predictions for patients regarding health outcomes, in these settings even if the outcome is rare